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curve-interpolator

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curve-interpolator - npm Package Compare versions

Comparing version

3.1.0
to
3.1.1

2

dist/index.cjs.js

@@ -15,2 +15,2 @@ "use strict";

and limitations under the License.
***************************************************************************** */var extendStatics=function(d,b){return extendStatics=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(d,b){d.__proto__=b}||function(d,b){for(var p in b)b.hasOwnProperty(p)&&(d[p]=b[p])},extendStatics(d,b)};function __extends(d,b){function __(){this.constructor=d}extendStatics(d,b),d.prototype=null===b?Object.create(b):(__.prototype=b.prototype,new __)}var __assign=function(){return __assign=Object.assign||function(t){for(var s,i=1,n=arguments.length;i<n;i++)for(var p in s=arguments[i])Object.prototype.hasOwnProperty.call(s,p)&&(t[p]=s[p]);return t},__assign.apply(this,arguments)};function extrapolateControlPoint(u,v){for(var e=new Array(u.length),i=0;i<u.length;i++)e[i]=2*u[i]-v[i];return e}function getControlPoints(idx,points,closed){var p0,p1,p2,p3,maxIndex=points.length-1;if(closed)p0=points[idx-1<0?maxIndex:idx-1],p1=points[idx%points.length],p2=points[(idx+1)%points.length],p3=points[(idx+2)%points.length];else{if(idx===maxIndex)throw Error("There is no spline segment at this index for a closed curve!");p1=points[idx],p2=points[idx+1],p0=idx>0?points[idx-1]:extrapolateControlPoint(p1,p2),p3=idx<maxIndex-1?points[idx+2]:extrapolateControlPoint(p2,p1)}return[p0,p1,p2,p3]}function getSegmentIndexAndT(ct,points,closed){void 0===closed&&(closed=!1);var nPoints=closed?points.length:points.length-1;if(1===ct)return{index:nPoints-1,weight:1};var p=nPoints*ct,index=Math.floor(p);return{index:index,weight:p-index}}function fill(v,val){for(var i=0;i<v.length;i++)v[i]=val;return v}function map(v,func){for(var i=0;i<v.length;i++)v[i]=func(v[i],i);return v}function reduce(v,func,r){void 0===r&&(r=0);for(var i=0;i<v.length;i++)r=func(r,v[i],i);return r}function copyValues(source,target){target=target||new Array(source.length);for(var i=0;i<source.length;i++)target[i]=source[i];return target}function clamp(value,min,max){return void 0===min&&(min=0),void 0===max&&(max=1),value<min?min:value>max?max:value}function binarySearch(targetValue,accumulatedValues){var min=accumulatedValues[0];if(targetValue>=accumulatedValues[accumulatedValues.length-1])return accumulatedValues.length-1;if(targetValue<=min)return 0;for(var left=0,right=accumulatedValues.length-1;left<=right;){var mid=Math.floor((left+right)/2),lMid=accumulatedValues[mid];if(lMid<targetValue)left=mid+1;else{if(!(lMid>targetValue))return mid;right=mid-1}}return Math.max(0,right)}var EPS=Math.pow(2,-42);function cuberoot(x){var y=Math.pow(Math.abs(x),1/3);return x<0?-y:y}function getQuadRoots(a,b,c){if(Math.abs(a)<EPS)return Math.abs(b)<EPS?[]:[-c/b];var D=b*b-4*a*c;return Math.abs(D)<EPS?[-b/(2*a)]:D>0?[(-b+Math.sqrt(D))/(2*a),(-b-Math.sqrt(D))/(2*a)]:[]}function getCubicRoots(a,b,c,d){if(Math.abs(a)<EPS)return getQuadRoots(b,c,d);var roots,p=(3*a*c-b*b)/(3*a*a),q=(2*b*b*b-9*a*b*c+27*a*a*d)/(27*a*a*a);if(Math.abs(p)<EPS)roots=[cuberoot(-q)];else if(Math.abs(q)<EPS)roots=[0].concat(p<0?[Math.sqrt(-p),-Math.sqrt(-p)]:[]);else{var D=q*q/4+p*p*p/27;if(Math.abs(D)<EPS)roots=[-1.5*q/p,3*q/p];else if(D>0){roots=[(u=cuberoot(-q/2-Math.sqrt(D)))-p/(3*u)]}else{var u=2*Math.sqrt(-p/3),t=Math.acos(3*q/p/u)/3,k=2*Math.PI/3;roots=[u*Math.cos(t),u*Math.cos(t-k),u*Math.cos(t-2*k)]}}for(var i=0;i<roots.length;i++)roots[i]-=b/(3*a);return roots}function dot(v1,v2){if(v1.length!==v2.length)throw Error("Vectors must be of equal length!");for(var p=0,k=0;k<v1.length;k++)p+=v1[k]*v2[k];return p}function cross(v1,v2,target){if(!(v1.length>3)){target=target||new Array(3);var ax=v1[0],ay=v1[1],az=v1[2]||0,bx=v2[0],by=v2[1],bz=v2[2]||0;return target[0]=ay*bz-az*by,target[1]=az*bx-ax*bz,target[2]=ax*by-ay*bx,target}}function sumOfSquares(v1,v2){for(var sumOfSquares=0,i=0;i<v1.length;i++)sumOfSquares+=(v1[i]-v2[i])*(v1[i]-v2[i]);return sumOfSquares}function magnitude(v){for(var sumOfSquares=0,i=0;i<v.length;i++)sumOfSquares+=v[i]*v[i];return Math.sqrt(sumOfSquares)}function distance(p1,p2){var sqrs=sumOfSquares(p1,p2);return 0===sqrs?0:Math.sqrt(sqrs)}function normalize(v,target){var u=target?copyValues(v,target):v,squared=reduce(u,(function(s,c){return s+Math.pow(c,2)})),l=Math.sqrt(squared);return 0===l?fill(u,0):map(u,(function(c){return c/l}))}function orthogonal(v,target){if(v.length>2)throw Error("Only supported for 2d vectors");var u=target?copyValues(v,target):v,x=-u[1];return u[1]=u[0],u[0]=x,u}function calcKnotSequence(p0,p1,p2,p3,alpha){if(void 0===alpha&&(alpha=0),0===alpha)return[0,1,2,3];var deltaT=function(u,v){return Math.pow(sumOfSquares(u,v),.5*alpha)},t1=deltaT(p1,p0),t2=deltaT(p2,p1)+t1;return[0,t1,t2,deltaT(p3,p2)+t2]}function calculateCoefficients(p0,p1,p2,p3,options){for(var tension=Number.isFinite(options.tension)?options.tension:.5,alpha=Number.isFinite(options.alpha)?options.alpha:null,knotSequence=alpha>0?calcKnotSequence(p0,p1,p2,p3,alpha):null,coefficientsList=new Array(p0.length),k=0;k<p0.length;k++){var u=0,v=0,v0=p0[k],v1=p1[k],v2=p2[k],v3=p3[k];if(knotSequence){var t0=knotSequence[0],t1=knotSequence[1],t2=knotSequence[2],t3=knotSequence[3];t1-t2!=0&&(t0-t1!=0&&t0-t2!=0&&(u=(1-tension)*(t2-t1)*((v0-v1)/(t0-t1)-(v0-v2)/(t0-t2)+(v1-v2)/(t1-t2))),t1-t3!=0&&t2-t3!=0&&(v=(1-tension)*(t2-t1)*((v1-v2)/(t1-t2)-(v1-v3)/(t1-t3)+(v2-v3)/(t2-t3))))}else u=(1-tension)*(v2-v0)*.5,v=(1-tension)*(v3-v1)*.5;var a=2*v1-2*v2+u+v,b=-3*v1+3*v2-2*u-v,d=v1;coefficientsList[k]=[a,b,u,d]}return coefficientsList}function valueAtT(t,coefficients){var t2=t*t,t3=t*t2;return coefficients[0]*t3+coefficients[1]*t2+coefficients[2]*t+coefficients[3]}function derivativeAtT(t,coefficients){var t2=t*t;return 3*coefficients[0]*t2+2*coefficients[1]*t+coefficients[2]}function secondDerivativeAtT(t,coefficients){return 6*coefficients[0]*t+2*coefficients[1]}function findRootsOfT(lookup,coefficients){var a=coefficients[0],b=coefficients[1],c=coefficients[2],x=coefficients[3]-lookup;return 0===a&&0===b&&0===c&&0===x?[0]:getCubicRoots(a,b,c,x).filter((function(t){return t>-EPS&&t<=1+EPS})).map((function(t){return clamp(t,0,1)}))}function evaluateForT(func,t,coefficients,target){void 0===target&&(target=null),target=target||new Array(coefficients.length);for(var k=0;k<coefficients.length;k++)target[k]=func(t,coefficients[k]);return target}var AbstractCurveMapper=function(){function AbstractCurveMapper(onInvalidateCache){void 0===onInvalidateCache&&(onInvalidateCache=null),this._alpha=0,this._tension=.5,this._closed=!1,this._onInvalidateCache=null,this._onInvalidateCache=onInvalidateCache,this._cache={arcLengths:null,coefficients:null}}return AbstractCurveMapper.prototype._invalidateCache=function(){this.points&&(this._cache={arcLengths:null,coefficients:null},this._onInvalidateCache&&this._onInvalidateCache())},Object.defineProperty(AbstractCurveMapper.prototype,"alpha",{get:function(){return this._alpha},set:function(alpha){Number.isFinite(alpha)&&alpha!==this._alpha&&(this._invalidateCache(),this._alpha=alpha)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"tension",{get:function(){return this._tension},set:function(tension){Number.isFinite(tension)&&tension!==this._tension&&(this._invalidateCache(),this._tension=tension)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"points",{get:function(){return this._points},set:function(points){if(!points||points.length<2)throw Error("At least 2 control points are required!");this._points=points,this._invalidateCache()},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"closed",{get:function(){return this._closed},set:function(closed){closed=!!closed,this._closed!==closed&&(this._invalidateCache(),this._closed=closed)},enumerable:!1,configurable:!0}),AbstractCurveMapper.prototype.reset=function(){this._invalidateCache()},AbstractCurveMapper.prototype.evaluateForT=function(func,t,target){var _a=getSegmentIndexAndT(t,this.points,this.closed),index=_a.index;return evaluateForT(func,_a.weight,this.getCoefficients(index),target)},AbstractCurveMapper.prototype.getCoefficients=function(idx){if(this.points){if(this._cache.coefficients||(this._cache.coefficients=new Map),!this._cache.coefficients.has(idx)){var _a=getControlPoints(idx,this.points,this.closed),coefficients=calculateCoefficients(_a[0],_a[1],_a[2],_a[3],{tension:this.tension,alpha:this.alpha});this._cache.coefficients.set(idx,coefficients)}return this._cache.coefficients.get(idx)}},AbstractCurveMapper}(),SegmentedCurveMapper=function(_super){function SegmentedCurveMapper(subDivisions,onInvalidateCache){void 0===subDivisions&&(subDivisions=300),void 0===onInvalidateCache&&(onInvalidateCache=null);var _this=_super.call(this,onInvalidateCache)||this;return _this._subDivisions=subDivisions,_this}return __extends(SegmentedCurveMapper,_super),Object.defineProperty(SegmentedCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),SegmentedCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null},SegmentedCurveMapper.prototype.computeArcLengths=function(){var current,lengths=[],last=this.evaluateForT(valueAtT,0),sum=0;lengths.push(0);for(var p=1;p<=this._subDivisions;p++)sum+=distance(current=this.evaluateForT(valueAtT,p/this._subDivisions),last),lengths.push(sum),last=current;return lengths},SegmentedCurveMapper.prototype.lengthAt=function(u){var arcLengths=this.arcLengths;return u*arcLengths[arcLengths.length-1]},SegmentedCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths);if(arcLengths[i]===targetArcLength)return i/(il-1);var lengthBefore=arcLengths[i];return(i+(targetArcLength-lengthBefore)/(arcLengths[i+1]-lengthBefore))/(il-1)},SegmentedCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=subIdx/al;return(l1+distance(this.evaluateForT(valueAtT,t0),this.evaluateForT(valueAtT,t)))/totalLength},SegmentedCurveMapper}(AbstractCurveMapper),lut=[[[-.906179845938664,.23692688505618908],[-.5384693101056831,.47862867049936647],[0,.5688888888888889],[.5384693101056831,.47862867049936647],[.906179845938664,.23692688505618908]],[[-.932469514203152,.17132449237917036],[-.6612093864662645,.3607615730481386],[-.2386191860831969,.46791393457269104],[.2386191860831969,.46791393457269104],[.6612093864662645,.3607615730481386],[.932469514203152,.17132449237917036]],[[-.9491079123427585,.1294849661688697],[-.7415311855993945,.27970539148927664],[-.4058451513773972,.3818300505051189],[0,.4179591836734694],[.4058451513773972,.3818300505051189],[.7415311855993945,.27970539148927664],[.9491079123427585,.1294849661688697]],[[-.9602898564975363,.10122853629037626],[-.7966664774136267,.22238103445337448],[-.525532409916329,.31370664587788727],[-.1834346424956498,.362683783378362],[.1834346424956498,.362683783378362],[.525532409916329,.31370664587788727],[.7966664774136267,.22238103445337448],[.9602898564975363,.10122853629037626]],[[-.9681602395076261,.08127438836157441],[-.8360311073266358,.1806481606948574],[-.6133714327005904,.26061069640293544],[-.3242534234038089,.31234707704000286],[0,.3302393550012598],[.3242534234038089,.31234707704000286],[.6133714327005904,.26061069640293544],[.8360311073266358,.1806481606948574],[.9681602395076261,.08127438836157441]],[[-.9739065285171717,.06667134430868814],[-.8650633666889845,.1494513491505806],[-.6794095682990244,.21908636251598204],[-.4333953941292472,.26926671930999635],[-.14887433898163122,.29552422471475287],[.14887433898163122,.29552422471475287],[.4333953941292472,.26926671930999635],[.6794095682990244,.21908636251598204],[.8650633666889845,.1494513491505806],[.9739065285171717,.06667134430868814]],[[-.978228658146056,.0556685671161736],[-.887062599768095,.125580369464904],[-.730152005574049,.186290210927734],[-.519096129206811,.23319376459199],[-.269543155952344,.262804544510246],[0,.2729250867779],[.269543155952344,.262804544510246],[.519096129206811,.23319376459199],[.730152005574049,.186290210927734],[.887062599768095,.125580369464904],[.978228658146056,.0556685671161736]],[[-.981560634246719,.0471753363865118],[-.904117256370474,.106939325995318],[-.769902674194304,.160078328543346],[-.587317954286617,.203167426723065],[-.36783149899818,.233492536538354],[-.125233408511468,.249147045813402],[.125233408511468,.249147045813402],[.36783149899818,.233492536538354],[.587317954286617,.203167426723065],[.769902674194304,.160078328543346],[.904117256370474,.106939325995318],[.981560634246719,.0471753363865118]],[[-.984183054718588,.0404840047653158],[-.917598399222977,.0921214998377284],[-.801578090733309,.138873510219787],[-.64234933944034,.178145980761945],[-.448492751036446,.207816047536888],[-.230458315955134,.226283180262897],[0,.232551553230873],[.230458315955134,.226283180262897],[.448492751036446,.207816047536888],[.64234933944034,.178145980761945],[.801578090733309,.138873510219787],[.917598399222977,.0921214998377284],[.984183054718588,.0404840047653158]],[[-.986283808696812,.0351194603317518],[-.928434883663573,.0801580871597602],[-.827201315069764,.121518570687903],[-.687292904811685,.157203167158193],[-.515248636358154,.185538397477937],[-.319112368927889,.205198463721295],[-.108054948707343,.215263853463157],[.108054948707343,.215263853463157],[.319112368927889,.205198463721295],[.515248636358154,.185538397477937],[.687292904811685,.157203167158193],[.827201315069764,.121518570687903],[.928434883663573,.0801580871597602],[.986283808696812,.0351194603317518]],[[-.987992518020485,.0307532419961172],[-.937273392400705,.0703660474881081],[-.848206583410427,.107159220467171],[-.72441773136017,.139570677926154],[-.570972172608538,.166269205816993],[-.394151347077563,.186161000015562],[-.201194093997434,.198431485327111],[0,.202578241925561],[.201194093997434,.198431485327111],[.394151347077563,.186161000015562],[.570972172608538,.166269205816993],[.72441773136017,.139570677926154],[.848206583410427,.107159220467171],[.937273392400705,.0703660474881081],[.987992518020485,.0307532419961172]],[[-.989400934991649,.027152459411754],[-.944575023073232,.0622535239386478],[-.865631202387831,.0951585116824927],[-.755404408355003,.124628971255533],[-.617876244402643,.149595988816576],[-.458016777657227,.169156519395002],[-.281603550779258,.182603415044923],[-.0950125098376374,.189450610455068],[.0950125098376374,.189450610455068],[.281603550779258,.182603415044923],[.458016777657227,.169156519395002],[.617876244402643,.149595988816576],[.755404408355003,.124628971255533],[.865631202387831,.0951585116824927],[.944575023073232,.0622535239386478],[.989400934991649,.027152459411754]],[[-.990575475314417,.0241483028685479],[-.950675521768767,.0554595293739872],[-.880239153726985,.0850361483171791],[-.781514003896801,.111883847193403],[-.65767115921669,.135136368468525],[-.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NumericalCurveMapper=function(_super){function NumericalCurveMapper(nQuadraturePoints,nInverseSamples,onInvalidateCache){void 0===nQuadraturePoints&&(nQuadraturePoints=24),void 0===nInverseSamples&&(nInverseSamples=21);var _this=_super.call(this,onInvalidateCache)||this;return _this._nSamples=21,_this._gauss=function(order){if(order<5||order>maxOrder)throw Error("Order for Gaussian Quadrature must be in the range of ".concat(5," and ").concat(maxOrder,"."));return lut[order-5]}(nQuadraturePoints),_this._nSamples=nInverseSamples,_this}return __extends(NumericalCurveMapper,_super),NumericalCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null,this._cache.samples=null},Object.defineProperty(NumericalCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),NumericalCurveMapper.prototype.getSamples=function(idx){if(this.points){if(this._cache.samples||(this._cache.samples=new Map),!this._cache.samples.has(idx)){for(var samples=this._nSamples,lengths=[],slopes=[],coefficients=this.getCoefficients(idx),i=0;i<samples;++i){var ti=i/(samples-1);lengths.push(this.computeArcLength(idx,0,ti));var dtln=magnitude(evaluateForT(derivativeAtT,ti,coefficients)),slope=0===dtln?0:1/dtln;this.tension>.95&&(slope=clamp(slope,-1,1)),slopes.push(slope)}var nCoeff=samples-1,dis=[],cis=[],li_prev=lengths[0],tdi_prev=slopes[0],step=1/nCoeff;for(i=0;i<nCoeff;++i){var li=li_prev,lDiff=(li_prev=lengths[i+1])-li,tdi=tdi_prev,tdi_next=slopes[i+1];tdi_prev=tdi_next;var si=step/lDiff,di=(tdi+tdi_next-2*si)/(lDiff*lDiff),ci=(3*si-2*tdi-tdi_next)/lDiff;dis.push(di),cis.push(ci)}this._cache.samples.set(idx,[lengths,slopes,cis,dis])}return this._cache.samples.get(idx)}},NumericalCurveMapper.prototype.computeArcLength=function(index,t0,t1){if(void 0===t0&&(t0=0),void 0===t1&&(t1=1),t0===t1)return 0;for(var coefficients=this.getCoefficients(index),z=.5*(t1-t0),sum=0,i=0;i<this._gauss.length;i++){var _a=this._gauss[i],T=_a[0];sum+=_a[1]*magnitude(evaluateForT(derivativeAtT,z*T+z+t0,coefficients))}return z*sum},NumericalCurveMapper.prototype.computeArcLengths=function(){if(this.points){var lengths=[];lengths.push(0);for(var nPoints=this.closed?this.points.length:this.points.length-1,tl=0,i=0;i<nPoints;i++){tl+=this.computeArcLength(i),lengths.push(tl)}return lengths}},NumericalCurveMapper.prototype.inverse=function(idx,len){var step=1/(this._nSamples-1),_a=this.getSamples(idx),lengths=_a[0],slopes=_a[1],cis=_a[2],dis=_a[3];if(len>=lengths[lengths.length-1])return 1;if(len<=0)return 0;var i=Math.max(0,binarySearch(len,lengths)),ti=i*step;if(lengths[i]===len)return ti;var tdi=slopes[i],di=dis[i],ci=cis[i],ld=len-lengths[i];return((di*ld+ci)*ld+tdi)*ld+ti},NumericalCurveMapper.prototype.lengthAt=function(u){return u*this.arcLengths[this.arcLengths.length-1]},NumericalCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths),ti=i/(il-1);if(arcLengths[i]===targetArcLength)return ti;var len=targetArcLength-arcLengths[i];return(i+this.inverse(i,len))/(il-1)},NumericalCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=tIdx-subIdx;return(l1+this.computeArcLength(subIdx,0,t0))/totalLength},NumericalCurveMapper}(AbstractCurveMapper),CurveInterpolator=function(){function CurveInterpolator(points,options){void 0===options&&(options={});var _this=this;this._cache=new Map;var curveMapper=(options=__assign({tension:.5,alpha:0,closed:!1},options)).arcDivisions?new SegmentedCurveMapper(options.arcDivisions,(function(){return _this._invalidateCache()})):new NumericalCurveMapper(options.numericalApproximationOrder,options.numericalInverseSamples,(function(){return _this._invalidateCache()}));curveMapper.alpha=options.alpha,curveMapper.tension=options.tension,curveMapper.closed=options.closed,curveMapper.points=points,this._lmargin=options.lmargin||1-curveMapper.tension,this._curveMapper=curveMapper}return CurveInterpolator.prototype.getTimeFromPosition=function(position,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getT(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getPositionFromTime=function(t,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getU(clampInput?clamp(t,0,1):t)},CurveInterpolator.prototype.getPositionFromLength=function(length,clampInput){void 0===clampInput&&(clampInput=!1);var l=clampInput?clamp(length,0,this.length):length;return this._curveMapper.getU(l/this.length)},CurveInterpolator.prototype.getLengthAt=function(position,clampInput){return void 0===position&&(position=1),void 0===clampInput&&(clampInput=!1),this._curveMapper.lengthAt(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getTimeAtKnot=function(index){if(index<0||index>this.points.length-1)throw Error("Invalid index!");return 0===index?0:this.closed||index!==this.points.length-1?index/(this.closed?this.points.length:this.points.length-1):1},CurveInterpolator.prototype.getPositionAtKnot=function(index){return this.getPositionFromTime(this.getTimeAtKnot(index))},CurveInterpolator.prototype.getPointAtTime=function(t,target){return 0===(t=clamp(t,0,1))?copyValues(this.points[0],target):1===t?copyValues(this.closed?this.points[0]:this.points[this.points.length-1],target):this._curveMapper.evaluateForT(valueAtT,t,target)},CurveInterpolator.prototype.getPointAt=function(position,target){return this.getPointAtTime(this.getTimeFromPosition(position),target)},CurveInterpolator.prototype.getTangentAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getTangentAtTime(t,target)},CurveInterpolator.prototype.getTangentAtTime=function(t,target){return normalize(this._curveMapper.evaluateForT(derivativeAtT,t,target))},CurveInterpolator.prototype.getNormalAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getNormalAtTime(t,target)},CurveInterpolator.prototype.getNormalAtTime=function(t,target){var dt=normalize(this._curveMapper.evaluateForT(derivativeAtT,t));if(!(dt.length<2||dt.length>3)){var normal=target||new Array(dt.length);if(2===dt.length)return normal[0]=-dt[1],normal[1]=dt[0],normal;var ddt=normalize(this._curveMapper.evaluateForT(secondDerivativeAtT,t));return normalize(cross(cross(dt,ddt),dt),normal)}},CurveInterpolator.prototype.getCurvatureAt=function(position){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getCurvatureAtTime(t)},CurveInterpolator.prototype.getCurvatureAtTime=function(t){var dt=this._curveMapper.evaluateForT(derivativeAtT,t),ddt=this._curveMapper.evaluateForT(secondDerivativeAtT,t),tangent=normalize(dt,[]),curvature=0,direction=void 0;if(2===dt.length){if(0!==(denominator=Math.pow(dt[0]*dt[0]+dt[1]*dt[1],1.5))){var signedCurvature=(dt[0]*ddt[1]-dt[1]*ddt[0])/denominator;direction=signedCurvature<0?[tangent[1],-tangent[0]]:[-tangent[1],tangent[0]],curvature=Math.abs(signedCurvature)}}else if(3===dt.length){var a=magnitude(dt),cp=cross(dt,ddt);direction=normalize(cross(cp,dt)),0!==a&&(curvature=magnitude(cp)/Math.pow(a,3))}else{a=magnitude(dt);var b=magnitude(ddt),denominator=Math.pow(a,3),dotProduct=dot(dt,ddt);0!==denominator&&(curvature=Math.sqrt(Math.pow(a,2)*Math.pow(b,2)-Math.pow(dotProduct,2))/denominator)}return{curvature:curvature,radius:0!==curvature?1/curvature:0,tangent:tangent,direction:direction}},CurveInterpolator.prototype.getDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(derivativeAtT,t,target)},CurveInterpolator.prototype.getSecondDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(secondDerivativeAtT,t,target)},CurveInterpolator.prototype.getBoundingBox=function(from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),0===from&&1===to&&this._cache.has("bbox"))return this._cache.get("bbox");for(var min=[],max=[],t0=this.getTimeFromPosition(from),t1=this.getTimeFromPosition(to),start=this.getPointAtTime(t0),end=this.getPointAtTime(t1),nPoints=this.closed?this.points.length:this.points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var p2=getControlPoints(i-1,this_1.points,this_1.closed)[2];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(this_1.tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=this_1._curveMapper.getCoefficients(i-1),_loop_2=function(c){var _b=coefficients_1[c];getQuadRoots(3*_b[0],2*_b[1],_b[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},this_1=this,i=i0+1;i<=i1;i++)_loop_1(i);var bbox={min:min,max:max};return 0===from&&1===to&&this._cache.set("bbox",bbox),bbox},CurveInterpolator.prototype.getPoints=function(segments,returnType,from,to){if(void 0===segments&&(segments=100),void 0===from&&(from=0),void 0===to&&(to=1),!segments||segments<=0)throw Error("Invalid arguments passed to getPoints(). You must specify at least 1 sample/segment.");if(!(from<0||to>1||to<from)){for(var pts=[],d=0;d<=segments;d++){var u=0===from&&1===to?d/segments:from+d/segments*(to-from);pts.push(this.getPointAt(u,returnType&&new returnType))}return pts}},CurveInterpolator.prototype.getNearestPosition=function(point,threshold){var _this=this;if(void 0===threshold&&(threshold=1e-5),threshold<=0||!Number.isFinite(threshold))throw Error("Invalid threshold. Must be a number greater than zero!");var samples=10*this.points.length-1,pu=new Array(point.length),minDist=1/0,minU=0,lut=this.createLookupTable(samples);Array.from(lut.keys()).forEach((function(key){var c=lut.get(key),dist=distance(point,c);if(dist<minDist)return minDist=dist,minU=key,!0}));for(var minT=this.getTimeFromPosition(minU),bisect=function(t){if(t>=0&&t<=1){_this.getPointAtTime(t,pu);var dist=distance(point,pu);if(dist<minDist)return minDist=dist,minT=t,!0}},step=.005;step>threshold;)bisect(minT-step)||bisect(minT+step)||(step/=2);return{u:minU=this._curveMapper.getU(minT),distance:minDist,point:pu}},CurveInterpolator.prototype.getIntersects=function(v,axis,max,margin){var _this=this;void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var solutions=this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPointAtTime(t)}));return 1===Math.abs(max)?1===solutions.length?solutions[0]:null:solutions},CurveInterpolator.prototype.getIntersectsAsPositions=function(v,axis,max,margin){var _this=this;return void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin),this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPositionFromTime(t)}))},CurveInterpolator.prototype.getIntersectsAsTime=function(v,axis,max,margin){void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);for(var k=axis,solutions=new Set,nPoints=this.closed?this.points.length:this.points.length-1,i=0;i<nPoints&&(0===max||solutions.size<Math.abs(max));i+=1){var idx=max<0?nPoints-(i+1):i,_a=getControlPoints(idx,this.points,this.closed),p1=_a[1],p2=_a[2],coefficients=this._curveMapper.getCoefficients(idx),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),v-margin<=vmax&&v+margin>=vmin){var ts=findRootsOfT(v,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),0!==max&&solutions.size===Math.abs(max))break}}}return Array.from(solutions)},CurveInterpolator.prototype.createLookupTable=function(samples,from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),!samples||samples<=1)throw Error("Invalid arguments passed to createLookupTable(). You must specify at least 2 samples.");if(!(from<0||to>1||to<from)){var cacheKey="lut_".concat(samples,"_").concat(from,"_").concat(to);if(!this._cache.has(cacheKey)){for(var lut=new Map,d=0;d<samples;d++){var u=0===from&&1===to?d/(samples-1):from+d/(samples-1)*(to-from),point=this.getPointAt(u);lut.set(u,point)}this._cache.set(cacheKey,lut)}return this._cache.get(cacheKey)}},CurveInterpolator.prototype.forEach=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to forEach(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;positions.forEach((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in forEach!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});prev={u:u,t:t,i:i,value:current}}))},CurveInterpolator.prototype.map=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;return positions.map((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});return prev={u:u,t:t,i:i,value:current},current}))},CurveInterpolator.prototype.reduce=function(func,initialValue,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);return positions.reduce((function(acc,u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u);return func({acc:acc,u:u,t:t,i:i})}),initialValue)},CurveInterpolator.prototype._invalidateCache=function(){return this._cache=new Map,this},CurveInterpolator.prototype.reset=function(){this._curveMapper.reset()},Object.defineProperty(CurveInterpolator.prototype,"points",{get:function(){return this._curveMapper.points},set:function(pts){this._curveMapper.points=pts},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"tension",{get:function(){return this._curveMapper.tension},set:function(t){this._curveMapper.tension=t},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"alpha",{get:function(){return this._curveMapper.alpha},set:function(a){this._curveMapper.alpha=a},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"closed",{get:function(){return this._curveMapper.closed},set:function(isClosed){this._curveMapper.closed=isClosed},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"length",{get:function(){return this._curveMapper.lengthAt(1)},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minX",{get:function(){return this.getBoundingBox().min[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxX",{get:function(){return this.getBoundingBox().max[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minY",{get:function(){return this.getBoundingBox().min[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxY",{get:function(){return this.getBoundingBox().max[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minZ",{get:function(){return this.getBoundingBox().min[2]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxZ",{get:function(){return this.getBoundingBox().max[2]},enumerable:!1,configurable:!0}),CurveInterpolator}(),Point=function(){function Point(x,y,z,w){void 0===x&&(x=0),void 0===y&&(y=0),void 0===z&&(z=null),void 0===w&&(w=null),this.x=x,this.y=y,this.z=z,this.w=w}return Object.defineProperty(Point.prototype,0,{get:function(){return this.x},set:function(x){this.x=x},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,1,{get:function(){return this.y},set:function(y){this.y=y},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,2,{get:function(){return this.z},set:function(z){this.z=z},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,3,{get:function(){return this.w},set:function(w){this.w=w},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,"length",{get:function(){return Number.isFinite(this.w)?4:Number.isFinite(this.z)?3:2},enumerable:!1,configurable:!0}),Point}(),CurveInterpolator2D=function(_super){function CurveInterpolator2D(points,tension,arcDivisions,closed,alpha){return void 0===tension&&(tension=.5),void 0===arcDivisions&&(arcDivisions=300),void 0===closed&&(closed=!1),void 0===alpha&&(alpha=0),_super.call(this,points.map((function(p){return[p[0],p[1]]})),{tension:tension,alpha:alpha,arcDivisions:arcDivisions,closed:closed})||this}return __extends(CurveInterpolator2D,_super),CurveInterpolator2D.prototype.x=function(y,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(y,1,max,margin);return 1===Math.abs(max)?res[0]:res.map((function(d){return d[0]}))},CurveInterpolator2D.prototype.y=function(x,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(x,0,max,margin);return 1===Math.abs(max)?res[1]:res.map((function(d){return d[1]}))},CurveInterpolator2D.prototype.getNormalAt=function(position,target){return normalize(orthogonal(this.getTangentAt(position,target)))},CurveInterpolator2D.prototype.getAngleAt=function(position){var tan=this.getTangentAt(position);return Math.atan2(tan[1],tan[0])},CurveInterpolator2D.prototype.getBoundingBox=function(from,to){void 0===from&&(from=0),void 0===to&&(to=1);var bbox=_super.prototype.getBoundingBox.call(this,from,to);return{x1:bbox.min[0],x2:bbox.max[0],y1:bbox.min[1],y2:bbox.max[1],min:bbox.min,max:bbox.max}},CurveInterpolator2D}(CurveInterpolator);function getPointAtT(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(valueAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))}exports.CurveInterpolator=CurveInterpolator,exports.CurveInterpolator2D=CurveInterpolator2D,exports.EPS=EPS,exports.LinearCurveMapper=SegmentedCurveMapper,exports.NumericalCurveMapper=NumericalCurveMapper,exports.Point=Point,exports.binarySearch=binarySearch,exports.calcKnotSequence=calcKnotSequence,exports.calculateCoefficients=calculateCoefficients,exports.clamp=clamp,exports.copyValues=copyValues,exports.cross=cross,exports.derivativeAtT=derivativeAtT,exports.distance=distance,exports.dot=dot,exports.evaluateForT=evaluateForT,exports.extrapolateControlPoint=extrapolateControlPoint,exports.fill=fill,exports.findRootsOfT=findRootsOfT,exports.getBoundingBox=function(points,options){void 0===options&&(options={});for(var _a=__assign({tension:.5,alpha:0,closed:!1,from:0,to:1},options),tension=_a.tension,alpha=_a.alpha,closed=_a.closed,t0=_a.from,t1=_a.to,nPoints=closed?points.length:points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),start=getPointAtT(t0,points,{tension:tension,alpha:alpha,closed:closed}),end=getPointAtT(t1,points,{tension:tension,alpha:alpha,closed:closed}),min=[],max=[],c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var _b=getControlPoints(i-1,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],p3=_b[3];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=calculateCoefficients(p0,p1,p2,p3,{tension:tension,alpha:alpha}),_loop_2=function(c){var _c=coefficients_1[c];getQuadRoots(3*_c[0],2*_c[1],_c[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},i=i0+1;i<=i1;i++)_loop_1(i);return{min:min,max:max}},exports.getControlPoints=getControlPoints,exports.getCubicRoots=getCubicRoots,exports.getPointAtT=getPointAtT,exports.getQuadRoots=getQuadRoots,exports.getSegmentIndexAndT=getSegmentIndexAndT,exports.getTangentAtT=function(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(derivativeAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))},exports.magnitude=magnitude,exports.map=map,exports.normalize=normalize,exports.orthogonal=orthogonal,exports.positionsLookup=function(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,k=axis,solutions=new Set,nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var idx=max<0?points.length-i:i,_b=getControlPoints(i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),solutions.size===Math.abs(max))return Array.from(solutions)}}}return Array.from(solutions)},exports.reduce=reduce,exports.secondDerivativeAtT=secondDerivativeAtT,exports.simplify2d=function(inputArr,maxOffset,maxDistance){var _a;if(void 0===maxOffset&&(maxOffset=.001),void 0===maxDistance&&(maxDistance=10),inputArr.length<=4)return inputArr;for(var _b=inputArr[0],o0=_b[0],o1=_b[1],arr=inputArr.map((function(d){return[d[0]-o0,d[1]-o1]})),_c=arr[0],a0=_c[0],a1=_c[1],sim=[inputArr[0]],i=1;i+1<arr.length;i++){var _d=arr[i],t0=_d[0],t1=_d[1],_e=arr[i+1],b0=_e[0],b1=_e[1];if(b0-t0!=0||b1-t1!=0){var proximity=Math.abs(a0*b1-a1*b0+b0*t1-b1*t0+a1*t0-a0*t1)/Math.sqrt(Math.pow(b0-a0,2)+Math.pow(b1-a1,2)),dir=[a0-t0,a1-t1],len=Math.sqrt(Math.pow(dir[0],2)+Math.pow(dir[1],2));(proximity>maxOffset||len>=maxDistance)&&(sim.push([t0+o0,t1+o1]),a0=(_a=[t0,t1])[0],a1=_a[1])}}var last=arr[arr.length-1];return sim.push([last[0]+o0,last[1]+o1]),sim},exports.sumOfSquares=sumOfSquares,exports.valueAtT=valueAtT,exports.valuesLookup=function(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0,processRefAxis:!1},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,processRefAxis=_a.processRefAxis,k=axis,solutions=[],nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var _b=getControlPoints(max<0?nPoints-(i+1):i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){for(var coord=[],c=0;c<p0.length;c++){var v=void 0;v=c!==k||processRefAxis?valueAtT(ts[j],coefficients[c]):lookup,coord[c]=v}if(solutions.push(coord),solutions.length===Math.abs(max))return solutions}}}return solutions};
***************************************************************************** */var extendStatics=function(d,b){return extendStatics=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(d,b){d.__proto__=b}||function(d,b){for(var p in b)b.hasOwnProperty(p)&&(d[p]=b[p])},extendStatics(d,b)};function __extends(d,b){function __(){this.constructor=d}extendStatics(d,b),d.prototype=null===b?Object.create(b):(__.prototype=b.prototype,new __)}var __assign=function(){return __assign=Object.assign||function(t){for(var s,i=1,n=arguments.length;i<n;i++)for(var p in s=arguments[i])Object.prototype.hasOwnProperty.call(s,p)&&(t[p]=s[p]);return t},__assign.apply(this,arguments)};function extrapolateControlPoint(u,v){for(var e=new Array(u.length),i=0;i<u.length;i++)e[i]=2*u[i]-v[i];return e}function getControlPoints(idx,points,closed){var p0,p1,p2,p3,maxIndex=points.length-1;if(closed)p0=points[idx-1<0?maxIndex:idx-1],p1=points[idx%points.length],p2=points[(idx+1)%points.length],p3=points[(idx+2)%points.length];else{if(idx===maxIndex)throw Error("There is no spline segment at this index for a closed curve!");p1=points[idx],p2=points[idx+1],p0=idx>0?points[idx-1]:extrapolateControlPoint(p1,p2),p3=idx<maxIndex-1?points[idx+2]:extrapolateControlPoint(p2,p1)}return[p0,p1,p2,p3]}function getSegmentIndexAndT(ct,points,closed){void 0===closed&&(closed=!1);var nPoints=closed?points.length:points.length-1;if(1===ct)return{index:nPoints-1,weight:1};var p=nPoints*ct,index=Math.floor(p);return{index:index,weight:p-index}}function fill(v,val){for(var i=0;i<v.length;i++)v[i]=val;return v}function map(v,func){for(var i=0;i<v.length;i++)v[i]=func(v[i],i);return v}function reduce(v,func,r){void 0===r&&(r=0);for(var i=0;i<v.length;i++)r=func(r,v[i],i);return r}function copyValues(source,target){target=target||new Array(source.length);for(var i=0;i<source.length;i++)target[i]=source[i];return target}function clamp(value,min,max){return void 0===min&&(min=0),void 0===max&&(max=1),value<min?min:value>max?max:value}function binarySearch(targetValue,accumulatedValues){var min=accumulatedValues[0];if(targetValue>=accumulatedValues[accumulatedValues.length-1])return accumulatedValues.length-1;if(targetValue<=min)return 0;for(var left=0,right=accumulatedValues.length-1;left<=right;){var mid=Math.floor((left+right)/2),lMid=accumulatedValues[mid];if(lMid<targetValue)left=mid+1;else{if(!(lMid>targetValue))return mid;right=mid-1}}return Math.max(0,right)}var EPS=Math.pow(2,-42);function cuberoot(x){var y=Math.pow(Math.abs(x),1/3);return x<0?-y:y}function getQuadRoots(a,b,c){if(Math.abs(a)<EPS)return Math.abs(b)<EPS?[]:[-c/b];var D=b*b-4*a*c;return Math.abs(D)<EPS?[-b/(2*a)]:D>0?[(-b+Math.sqrt(D))/(2*a),(-b-Math.sqrt(D))/(2*a)]:[]}function getCubicRoots(a,b,c,d){if(Math.abs(a)<EPS)return getQuadRoots(b,c,d);var roots,p=(3*a*c-b*b)/(3*a*a),q=(2*b*b*b-9*a*b*c+27*a*a*d)/(27*a*a*a);if(Math.abs(p)<EPS)roots=[cuberoot(-q)];else if(Math.abs(q)<EPS)roots=[0].concat(p<0?[Math.sqrt(-p),-Math.sqrt(-p)]:[]);else{var D=q*q/4+p*p*p/27;if(Math.abs(D)<EPS)roots=[-1.5*q/p,3*q/p];else if(D>0){roots=[(u=cuberoot(-q/2-Math.sqrt(D)))-p/(3*u)]}else{var u=2*Math.sqrt(-p/3),t=Math.acos(3*q/p/u)/3,k=2*Math.PI/3;roots=[u*Math.cos(t),u*Math.cos(t-k),u*Math.cos(t-2*k)]}}for(var i=0;i<roots.length;i++)roots[i]-=b/(3*a);return roots}function dot(v1,v2){if(v1.length!==v2.length)throw Error("Vectors must be of equal length!");for(var p=0,k=0;k<v1.length;k++)p+=v1[k]*v2[k];return p}function cross(v1,v2,target){if(!(v1.length>3)){target=target||new Array(3);var ax=v1[0],ay=v1[1],az=v1[2]||0,bx=v2[0],by=v2[1],bz=v2[2]||0;return target[0]=ay*bz-az*by,target[1]=az*bx-ax*bz,target[2]=ax*by-ay*bx,target}}function sumOfSquares(v1,v2){for(var sumOfSquares=0,i=0;i<v1.length;i++)sumOfSquares+=(v1[i]-v2[i])*(v1[i]-v2[i]);return sumOfSquares}function magnitude(v){for(var sumOfSquares=0,i=0;i<v.length;i++)sumOfSquares+=v[i]*v[i];return Math.sqrt(sumOfSquares)}function distance(p1,p2){var sqrs=sumOfSquares(p1,p2);return 0===sqrs?0:Math.sqrt(sqrs)}function normalize(v,target){var u=target?copyValues(v,target):v,squared=reduce(u,(function(s,c){return s+Math.pow(c,2)})),l=Math.sqrt(squared);return 0===l?fill(u,0):map(u,(function(c){return c/l}))}function orthogonal(v,target){if(v.length>2)throw Error("Only supported for 2d vectors");var u=target?copyValues(v,target):v,x=-u[1];return u[1]=u[0],u[0]=x,u}function calcKnotSequence(p0,p1,p2,p3,alpha){if(void 0===alpha&&(alpha=0),0===alpha)return[0,1,2,3];var deltaT=function(u,v){return Math.pow(sumOfSquares(u,v),.5*alpha)},t1=deltaT(p1,p0),t2=deltaT(p2,p1)+t1;return[0,t1,t2,deltaT(p3,p2)+t2]}function calculateCoefficients(p0,p1,p2,p3,options){for(var tension=Number.isFinite(options.tension)?options.tension:.5,alpha=Number.isFinite(options.alpha)?options.alpha:null,knotSequence=alpha>0?calcKnotSequence(p0,p1,p2,p3,alpha):null,coefficientsList=new Array(p0.length),k=0;k<p0.length;k++){var u=0,v=0,v0=p0[k],v1=p1[k],v2=p2[k],v3=p3[k];if(knotSequence){var t0=knotSequence[0],t1=knotSequence[1],t2=knotSequence[2],t3=knotSequence[3];t1-t2!=0&&(t0-t1!=0&&t0-t2!=0&&(u=(1-tension)*(t2-t1)*((v0-v1)/(t0-t1)-(v0-v2)/(t0-t2)+(v1-v2)/(t1-t2))),t1-t3!=0&&t2-t3!=0&&(v=(1-tension)*(t2-t1)*((v1-v2)/(t1-t2)-(v1-v3)/(t1-t3)+(v2-v3)/(t2-t3))))}else u=(1-tension)*(v2-v0)*.5,v=(1-tension)*(v3-v1)*.5;var a=2*v1-2*v2+u+v,b=-3*v1+3*v2-2*u-v,c=u,d=v1;coefficientsList[k]=[a,b,c,d]}return coefficientsList}function valueAtT(t,coefficients){var t2=t*t,t3=t*t2;return coefficients[0]*t3+coefficients[1]*t2+coefficients[2]*t+coefficients[3]}function derivativeAtT(t,coefficients){var t2=t*t;return 3*coefficients[0]*t2+2*coefficients[1]*t+coefficients[2]}function secondDerivativeAtT(t,coefficients){return 6*coefficients[0]*t+2*coefficients[1]}function findRootsOfT(lookup,coefficients){var a=coefficients[0],b=coefficients[1],c=coefficients[2],x=coefficients[3]-lookup;return 0===a&&0===b&&0===c&&0===x?[0]:getCubicRoots(a,b,c,x).filter((function(t){return t>-EPS&&t<=1+EPS})).map((function(t){return clamp(t,0,1)}))}function evaluateForT(func,t,coefficients,target){void 0===target&&(target=null),target=target||new Array(coefficients.length);for(var k=0;k<coefficients.length;k++)target[k]=func(t,coefficients[k]);return target}var AbstractCurveMapper=function(){function AbstractCurveMapper(onInvalidateCache){void 0===onInvalidateCache&&(onInvalidateCache=null),this._alpha=0,this._tension=.5,this._closed=!1,this._onInvalidateCache=null,this._onInvalidateCache=onInvalidateCache,this._cache={arcLengths:null,coefficients:null}}return AbstractCurveMapper.prototype._invalidateCache=function(){this.points&&(this._cache={arcLengths:null,coefficients:null},this._onInvalidateCache&&this._onInvalidateCache())},Object.defineProperty(AbstractCurveMapper.prototype,"alpha",{get:function(){return this._alpha},set:function(alpha){Number.isFinite(alpha)&&alpha!==this._alpha&&(this._invalidateCache(),this._alpha=alpha)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"tension",{get:function(){return this._tension},set:function(tension){Number.isFinite(tension)&&tension!==this._tension&&(this._invalidateCache(),this._tension=tension)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"points",{get:function(){return this._points},set:function(points){if(!points||points.length<2)throw Error("At least 2 control points are required!");this._points=points,this._invalidateCache()},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"closed",{get:function(){return this._closed},set:function(closed){closed=!!closed,this._closed!==closed&&(this._invalidateCache(),this._closed=closed)},enumerable:!1,configurable:!0}),AbstractCurveMapper.prototype.reset=function(){this._invalidateCache()},AbstractCurveMapper.prototype.evaluateForT=function(func,t,target){var _a=getSegmentIndexAndT(t,this.points,this.closed),index=_a.index;return evaluateForT(func,_a.weight,this.getCoefficients(index),target)},AbstractCurveMapper.prototype.getCoefficients=function(idx){if(this.points){if(this._cache.coefficients||(this._cache.coefficients=new Map),!this._cache.coefficients.has(idx)){var _a=getControlPoints(idx,this.points,this.closed),coefficients=calculateCoefficients(_a[0],_a[1],_a[2],_a[3],{tension:this.tension,alpha:this.alpha});this._cache.coefficients.set(idx,coefficients)}return this._cache.coefficients.get(idx)}},AbstractCurveMapper}(),SegmentedCurveMapper=function(_super){function SegmentedCurveMapper(subDivisions,onInvalidateCache){void 0===subDivisions&&(subDivisions=300),void 0===onInvalidateCache&&(onInvalidateCache=null);var _this=_super.call(this,onInvalidateCache)||this;return _this._subDivisions=subDivisions,_this}return __extends(SegmentedCurveMapper,_super),Object.defineProperty(SegmentedCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),SegmentedCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null},SegmentedCurveMapper.prototype.computeArcLengths=function(){var current,lengths=[],last=this.evaluateForT(valueAtT,0),sum=0;lengths.push(0);for(var p=1;p<=this._subDivisions;p++)sum+=distance(current=this.evaluateForT(valueAtT,p/this._subDivisions),last),lengths.push(sum),last=current;return lengths},SegmentedCurveMapper.prototype.lengthAt=function(u){var arcLengths=this.arcLengths;return u*arcLengths[arcLengths.length-1]},SegmentedCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths);if(arcLengths[i]===targetArcLength)return i/(il-1);var lengthBefore=arcLengths[i];return(i+(targetArcLength-lengthBefore)/(arcLengths[i+1]-lengthBefore))/(il-1)},SegmentedCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var 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NumericalCurveMapper=function(_super){function NumericalCurveMapper(nQuadraturePoints,nInverseSamples,onInvalidateCache){void 0===nQuadraturePoints&&(nQuadraturePoints=24),void 0===nInverseSamples&&(nInverseSamples=21);var _this=_super.call(this,onInvalidateCache)||this;return _this._nSamples=21,_this._gauss=function(order){if(order<5||order>maxOrder)throw Error("Order for Gaussian Quadrature must be in the range of ".concat(5," and ").concat(maxOrder,"."));return lut[order-5]}(nQuadraturePoints),_this._nSamples=nInverseSamples,_this}return __extends(NumericalCurveMapper,_super),NumericalCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null,this._cache.samples=null},Object.defineProperty(NumericalCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),NumericalCurveMapper.prototype.getSamples=function(idx){if(this.points){if(this._cache.samples||(this._cache.samples=new Map),!this._cache.samples.has(idx)){for(var samples=this._nSamples,lengths=[],slopes=[],coefficients=this.getCoefficients(idx),i=0;i<samples;++i){var ti=i/(samples-1);lengths.push(this.computeArcLength(idx,0,ti));var dtln=magnitude(evaluateForT(derivativeAtT,ti,coefficients)),slope=0===dtln?0:1/dtln;this.tension>.95&&(slope=clamp(slope,-1,1)),slopes.push(slope)}var nCoeff=samples-1,dis=[],cis=[],li_prev=lengths[0],tdi_prev=slopes[0],step=1/nCoeff;for(i=0;i<nCoeff;++i){var li=li_prev,lDiff=(li_prev=lengths[i+1])-li,tdi=tdi_prev,tdi_next=slopes[i+1];tdi_prev=tdi_next;var si=step/lDiff,di=(tdi+tdi_next-2*si)/(lDiff*lDiff),ci=(3*si-2*tdi-tdi_next)/lDiff;dis.push(di),cis.push(ci)}this._cache.samples.set(idx,[lengths,slopes,cis,dis])}return this._cache.samples.get(idx)}},NumericalCurveMapper.prototype.computeArcLength=function(index,t0,t1){if(void 0===t0&&(t0=0),void 0===t1&&(t1=1),t0===t1)return 0;for(var coefficients=this.getCoefficients(index),z=.5*(t1-t0),sum=0,i=0;i<this._gauss.length;i++){var _a=this._gauss[i],T=_a[0];sum+=_a[1]*magnitude(evaluateForT(derivativeAtT,z*T+z+t0,coefficients))}return z*sum},NumericalCurveMapper.prototype.computeArcLengths=function(){if(this.points){var lengths=[];lengths.push(0);for(var nPoints=this.closed?this.points.length:this.points.length-1,tl=0,i=0;i<nPoints;i++){tl+=this.computeArcLength(i),lengths.push(tl)}return lengths}},NumericalCurveMapper.prototype.inverse=function(idx,len){var step=1/(this._nSamples-1),_a=this.getSamples(idx),lengths=_a[0],slopes=_a[1],cis=_a[2],dis=_a[3];if(len>=lengths[lengths.length-1])return 1;if(len<=0)return 0;var i=Math.max(0,binarySearch(len,lengths)),ti=i*step;if(lengths[i]===len)return ti;var tdi=slopes[i],di=dis[i],ci=cis[i],ld=len-lengths[i];return((di*ld+ci)*ld+tdi)*ld+ti},NumericalCurveMapper.prototype.lengthAt=function(u){return u*this.arcLengths[this.arcLengths.length-1]},NumericalCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths),ti=i/(il-1);if(arcLengths[i]===targetArcLength)return ti;var len=targetArcLength-arcLengths[i];return(i+this.inverse(i,len))/(il-1)},NumericalCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=tIdx-subIdx;return(l1+this.computeArcLength(subIdx,0,t0))/totalLength},NumericalCurveMapper}(AbstractCurveMapper),CurveInterpolator=function(){function CurveInterpolator(points,options){void 0===options&&(options={});var _this=this;this._cache=new Map;var curveMapper=(options=__assign({tension:.5,alpha:0,closed:!1},options)).arcDivisions?new SegmentedCurveMapper(options.arcDivisions,(function(){return _this._invalidateCache()})):new NumericalCurveMapper(options.numericalApproximationOrder,options.numericalInverseSamples,(function(){return _this._invalidateCache()}));curveMapper.alpha=options.alpha,curveMapper.tension=options.tension,curveMapper.closed=options.closed,curveMapper.points=points,this._lmargin=options.lmargin||1-curveMapper.tension,this._curveMapper=curveMapper}return CurveInterpolator.prototype.getTimeFromPosition=function(position,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getT(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getPositionFromTime=function(t,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getU(clampInput?clamp(t,0,1):t)},CurveInterpolator.prototype.getPositionFromLength=function(length,clampInput){void 0===clampInput&&(clampInput=!1);var l=clampInput?clamp(length,0,this.length):length;return this._curveMapper.getU(l/this.length)},CurveInterpolator.prototype.getLengthAt=function(position,clampInput){return void 0===position&&(position=1),void 0===clampInput&&(clampInput=!1),this._curveMapper.lengthAt(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getTimeAtKnot=function(index){if(index<0||index>this.points.length-1)throw Error("Invalid index!");return 0===index?0:this.closed||index!==this.points.length-1?index/(this.closed?this.points.length:this.points.length-1):1},CurveInterpolator.prototype.getPositionAtKnot=function(index){return this.getPositionFromTime(this.getTimeAtKnot(index))},CurveInterpolator.prototype.getPointAtTime=function(t,target){return 0===(t=clamp(t,0,1))?copyValues(this.points[0],target):1===t?copyValues(this.closed?this.points[0]:this.points[this.points.length-1],target):this._curveMapper.evaluateForT(valueAtT,t,target)},CurveInterpolator.prototype.getPointAt=function(position,target){return this.getPointAtTime(this.getTimeFromPosition(position),target)},CurveInterpolator.prototype.getTangentAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getTangentAtTime(t,target)},CurveInterpolator.prototype.getTangentAtTime=function(t,target){return normalize(this._curveMapper.evaluateForT(derivativeAtT,t,target))},CurveInterpolator.prototype.getNormalAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getNormalAtTime(t,target)},CurveInterpolator.prototype.getNormalAtTime=function(t,target){var dt=normalize(this._curveMapper.evaluateForT(derivativeAtT,t));if(!(dt.length<2||dt.length>3)){var normal=target||new Array(dt.length);if(2===dt.length)return normal[0]=-dt[1],normal[1]=dt[0],normal;var ddt=normalize(this._curveMapper.evaluateForT(secondDerivativeAtT,t));return normalize(cross(cross(dt,ddt),dt),normal)}},CurveInterpolator.prototype.getCurvatureAt=function(position){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getCurvatureAtTime(t)},CurveInterpolator.prototype.getCurvatureAtTime=function(t){var dt=this._curveMapper.evaluateForT(derivativeAtT,t),ddt=this._curveMapper.evaluateForT(secondDerivativeAtT,t),tangent=normalize(dt,[]),curvature=0,direction=void 0;if(2===dt.length){if(0!==(denominator=Math.pow(dt[0]*dt[0]+dt[1]*dt[1],1.5))){var signedCurvature=(dt[0]*ddt[1]-dt[1]*ddt[0])/denominator;direction=signedCurvature<0?[tangent[1],-tangent[0]]:[-tangent[1],tangent[0]],curvature=Math.abs(signedCurvature)}}else if(3===dt.length){var a=magnitude(dt),cp=cross(dt,ddt);direction=normalize(cross(cp,dt)),0!==a&&(curvature=magnitude(cp)/Math.pow(a,3))}else{a=magnitude(dt);var b=magnitude(ddt),denominator=Math.pow(a,3),dotProduct=dot(dt,ddt);0!==denominator&&(curvature=Math.sqrt(Math.pow(a,2)*Math.pow(b,2)-Math.pow(dotProduct,2))/denominator)}return{curvature:curvature,radius:0!==curvature?1/curvature:0,tangent:tangent,direction:direction}},CurveInterpolator.prototype.getDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(derivativeAtT,t,target)},CurveInterpolator.prototype.getSecondDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(secondDerivativeAtT,t,target)},CurveInterpolator.prototype.getBoundingBox=function(from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),0===from&&1===to&&this._cache.has("bbox"))return this._cache.get("bbox");for(var min=[],max=[],t0=this.getTimeFromPosition(from),t1=this.getTimeFromPosition(to),start=this.getPointAtTime(t0),end=this.getPointAtTime(t1),nPoints=this.closed?this.points.length:this.points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var p2=getControlPoints(i-1,this_1.points,this_1.closed)[2];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(this_1.tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=this_1._curveMapper.getCoefficients(i-1),_loop_2=function(c){var _b=coefficients_1[c];getQuadRoots(3*_b[0],2*_b[1],_b[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},this_1=this,i=i0+1;i<=i1;i++)_loop_1(i);var bbox={min:min,max:max};return 0===from&&1===to&&this._cache.set("bbox",bbox),bbox},CurveInterpolator.prototype.getPoints=function(segments,returnType,from,to){if(void 0===segments&&(segments=100),void 0===from&&(from=0),void 0===to&&(to=1),!segments||segments<=0)throw Error("Invalid arguments passed to getPoints(). You must specify at least 1 sample/segment.");if(!(from<0||to>1||to<from)){for(var pts=[],d=0;d<=segments;d++){var u=0===from&&1===to?d/segments:from+d/segments*(to-from);pts.push(this.getPointAt(u,returnType&&new returnType))}return pts}},CurveInterpolator.prototype.getNearestPosition=function(point,threshold){var _this=this;if(void 0===threshold&&(threshold=1e-5),threshold<=0||!Number.isFinite(threshold))throw Error("Invalid threshold. Must be a number greater than zero!");var samples=10*this.points.length-1,pu=new Array(point.length),minDist=1/0,minU=0,lut=this.createLookupTable(samples);Array.from(lut.keys()).forEach((function(key){var c=lut.get(key),dist=distance(point,c);if(dist<minDist)return minDist=dist,minU=key,!0}));for(var minT=this.getTimeFromPosition(minU),bisect=function(t){if(t>=0&&t<=1){_this.getPointAtTime(t,pu);var dist=distance(point,pu);if(dist<minDist)return minDist=dist,minT=t,!0}},step=.005;step>threshold;)bisect(minT-step)||bisect(minT+step)||(step/=2);return{u:minU=this._curveMapper.getU(minT),distance:minDist,point:pu}},CurveInterpolator.prototype.getIntersects=function(v,axis,max,margin){var _this=this;void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var solutions=this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPointAtTime(t)}));return 1===Math.abs(max)?1===solutions.length?solutions[0]:null:solutions},CurveInterpolator.prototype.getIntersectsAsPositions=function(v,axis,max,margin){var _this=this;return void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin),this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPositionFromTime(t)}))},CurveInterpolator.prototype.getIntersectsAsTime=function(v,axis,max,margin){void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);for(var k=axis,solutions=new Set,nPoints=this.closed?this.points.length:this.points.length-1,i=0;i<nPoints&&(0===max||solutions.size<Math.abs(max));i+=1){var idx=max<0?nPoints-(i+1):i,_a=getControlPoints(idx,this.points,this.closed),p1=_a[1],p2=_a[2],coefficients=this._curveMapper.getCoefficients(idx),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),v-margin<=vmax&&v+margin>=vmin){var ts=findRootsOfT(v,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),0!==max&&solutions.size===Math.abs(max))break}}}return Array.from(solutions)},CurveInterpolator.prototype.createLookupTable=function(samples,from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),!samples||samples<=1)throw Error("Invalid arguments passed to createLookupTable(). You must specify at least 2 samples.");if(!(from<0||to>1||to<from)){var cacheKey="lut_".concat(samples,"_").concat(from,"_").concat(to);if(!this._cache.has(cacheKey)){for(var lut=new Map,d=0;d<samples;d++){var u=0===from&&1===to?d/(samples-1):from+d/(samples-1)*(to-from),point=this.getPointAt(u);lut.set(u,point)}this._cache.set(cacheKey,lut)}return this._cache.get(cacheKey)}},CurveInterpolator.prototype.forEach=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to forEach(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;positions.forEach((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in forEach!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});prev={u:u,t:t,i:i,value:current}}))},CurveInterpolator.prototype.map=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;return positions.map((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});return prev={u:u,t:t,i:i,value:current},current}))},CurveInterpolator.prototype.reduce=function(func,initialValue,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);return positions.reduce((function(acc,u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u);return func({acc:acc,u:u,t:t,i:i})}),initialValue)},CurveInterpolator.prototype._invalidateCache=function(){return this._cache=new Map,this},CurveInterpolator.prototype.reset=function(){this._curveMapper.reset()},Object.defineProperty(CurveInterpolator.prototype,"points",{get:function(){return this._curveMapper.points},set:function(pts){this._curveMapper.points=pts},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"tension",{get:function(){return this._curveMapper.tension},set:function(t){this._curveMapper.tension=t},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"alpha",{get:function(){return this._curveMapper.alpha},set:function(a){this._curveMapper.alpha=a},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"closed",{get:function(){return this._curveMapper.closed},set:function(isClosed){this._curveMapper.closed=isClosed},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"length",{get:function(){return this._curveMapper.lengthAt(1)},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minX",{get:function(){return this.getBoundingBox().min[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxX",{get:function(){return this.getBoundingBox().max[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minY",{get:function(){return this.getBoundingBox().min[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxY",{get:function(){return this.getBoundingBox().max[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minZ",{get:function(){return this.getBoundingBox().min[2]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxZ",{get:function(){return this.getBoundingBox().max[2]},enumerable:!1,configurable:!0}),CurveInterpolator}(),Point=function(){function Point(x,y,z,w){void 0===x&&(x=0),void 0===y&&(y=0),void 0===z&&(z=null),void 0===w&&(w=null),this.x=x,this.y=y,this.z=z,this.w=w}return Object.defineProperty(Point.prototype,0,{get:function(){return this.x},set:function(x){this.x=x},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,1,{get:function(){return this.y},set:function(y){this.y=y},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,2,{get:function(){return this.z},set:function(z){this.z=z},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,3,{get:function(){return this.w},set:function(w){this.w=w},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,"length",{get:function(){return Number.isFinite(this.w)?4:Number.isFinite(this.z)?3:2},enumerable:!1,configurable:!0}),Point}(),CurveInterpolator2D=function(_super){function CurveInterpolator2D(points,tension,arcDivisions,closed,alpha){return void 0===tension&&(tension=.5),void 0===arcDivisions&&(arcDivisions=300),void 0===closed&&(closed=!1),void 0===alpha&&(alpha=0),_super.call(this,points.map((function(p){return[p[0],p[1]]})),{tension:tension,alpha:alpha,arcDivisions:arcDivisions,closed:closed})||this}return __extends(CurveInterpolator2D,_super),CurveInterpolator2D.prototype.x=function(y,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(y,1,max,margin);return 1===Math.abs(max)?res[0]:res.map((function(d){return d[0]}))},CurveInterpolator2D.prototype.y=function(x,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(x,0,max,margin);return 1===Math.abs(max)?res[1]:res.map((function(d){return d[1]}))},CurveInterpolator2D.prototype.getNormalAt=function(position,target){return normalize(orthogonal(this.getTangentAt(position,target)))},CurveInterpolator2D.prototype.getAngleAt=function(position){var tan=this.getTangentAt(position);return Math.atan2(tan[1],tan[0])},CurveInterpolator2D.prototype.getBoundingBox=function(from,to){void 0===from&&(from=0),void 0===to&&(to=1);var bbox=_super.prototype.getBoundingBox.call(this,from,to);return{x1:bbox.min[0],x2:bbox.max[0],y1:bbox.min[1],y2:bbox.max[1],min:bbox.min,max:bbox.max}},CurveInterpolator2D}(CurveInterpolator);function getPointAtT(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(valueAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))}exports.CurveInterpolator=CurveInterpolator,exports.CurveInterpolator2D=CurveInterpolator2D,exports.EPS=EPS,exports.LinearCurveMapper=SegmentedCurveMapper,exports.NumericalCurveMapper=NumericalCurveMapper,exports.Point=Point,exports.binarySearch=binarySearch,exports.calcKnotSequence=calcKnotSequence,exports.calculateCoefficients=calculateCoefficients,exports.clamp=clamp,exports.copyValues=copyValues,exports.cross=cross,exports.derivativeAtT=derivativeAtT,exports.distance=distance,exports.dot=dot,exports.evaluateForT=evaluateForT,exports.extrapolateControlPoint=extrapolateControlPoint,exports.fill=fill,exports.findRootsOfT=findRootsOfT,exports.getBoundingBox=function(points,options){void 0===options&&(options={});for(var _a=__assign({tension:.5,alpha:0,closed:!1,from:0,to:1},options),tension=_a.tension,alpha=_a.alpha,closed=_a.closed,t0=_a.from,t1=_a.to,nPoints=closed?points.length:points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),start=getPointAtT(t0,points,{tension:tension,alpha:alpha,closed:closed}),end=getPointAtT(t1,points,{tension:tension,alpha:alpha,closed:closed}),min=[],max=[],c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var _b=getControlPoints(i-1,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],p3=_b[3];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=calculateCoefficients(p0,p1,p2,p3,{tension:tension,alpha:alpha}),_loop_2=function(c){var _c=coefficients_1[c];getQuadRoots(3*_c[0],2*_c[1],_c[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},i=i0+1;i<=i1;i++)_loop_1(i);return{min:min,max:max}},exports.getControlPoints=getControlPoints,exports.getCubicRoots=getCubicRoots,exports.getPointAtT=getPointAtT,exports.getQuadRoots=getQuadRoots,exports.getSegmentIndexAndT=getSegmentIndexAndT,exports.getTangentAtT=function(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(derivativeAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))},exports.magnitude=magnitude,exports.map=map,exports.normalize=normalize,exports.orthogonal=orthogonal,exports.positionsLookup=function(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,k=axis,solutions=new Set,nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var idx=max<0?points.length-i:i,_b=getControlPoints(i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),solutions.size===Math.abs(max))return Array.from(solutions)}}}return Array.from(solutions)},exports.reduce=reduce,exports.secondDerivativeAtT=secondDerivativeAtT,exports.simplify2d=function(inputArr,maxOffset,maxDistance){var _a;if(void 0===maxOffset&&(maxOffset=.001),void 0===maxDistance&&(maxDistance=10),inputArr.length<=4)return inputArr;for(var _b=inputArr[0],o0=_b[0],o1=_b[1],arr=inputArr.map((function(d){return[d[0]-o0,d[1]-o1]})),_c=arr[0],a0=_c[0],a1=_c[1],sim=[inputArr[0]],i=1;i+1<arr.length;i++){var _d=arr[i],t0=_d[0],t1=_d[1],_e=arr[i+1],b0=_e[0],b1=_e[1];if(b0-t0!=0||b1-t1!=0){var proximity=Math.abs(a0*b1-a1*b0+b0*t1-b1*t0+a1*t0-a0*t1)/Math.sqrt(Math.pow(b0-a0,2)+Math.pow(b1-a1,2)),dir=[a0-t0,a1-t1],len=Math.sqrt(Math.pow(dir[0],2)+Math.pow(dir[1],2));(proximity>maxOffset||len>=maxDistance)&&(sim.push([t0+o0,t1+o1]),a0=(_a=[t0,t1])[0],a1=_a[1])}}var last=arr[arr.length-1];return sim.push([last[0]+o0,last[1]+o1]),sim},exports.sumOfSquares=sumOfSquares,exports.valueAtT=valueAtT,exports.valuesLookup=function(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0,processRefAxis:!1},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,processRefAxis=_a.processRefAxis,k=axis,solutions=[],nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var _b=getControlPoints(max<0?nPoints-(i+1):i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){for(var coord=[],c=0;c<p0.length;c++){var v=void 0;v=c!==k||processRefAxis?valueAtT(ts[j],coefficients[c]):lookup,coord[c]=v}if(solutions.push(coord),solutions.length===Math.abs(max))return solutions}}}return solutions};

2

dist/index.esm.js

@@ -15,2 +15,2 @@ /*! *****************************************************************************

***************************************************************************** */
var extendStatics=function(d,b){return extendStatics=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(d,b){d.__proto__=b}||function(d,b){for(var p in b)b.hasOwnProperty(p)&&(d[p]=b[p])},extendStatics(d,b)};function __extends(d,b){function __(){this.constructor=d}extendStatics(d,b),d.prototype=null===b?Object.create(b):(__.prototype=b.prototype,new __)}var __assign=function(){return __assign=Object.assign||function(t){for(var s,i=1,n=arguments.length;i<n;i++)for(var p in s=arguments[i])Object.prototype.hasOwnProperty.call(s,p)&&(t[p]=s[p]);return t},__assign.apply(this,arguments)};function extrapolateControlPoint(u,v){for(var e=new Array(u.length),i=0;i<u.length;i++)e[i]=2*u[i]-v[i];return e}function getControlPoints(idx,points,closed){var p0,p1,p2,p3,maxIndex=points.length-1;if(closed)p0=points[idx-1<0?maxIndex:idx-1],p1=points[idx%points.length],p2=points[(idx+1)%points.length],p3=points[(idx+2)%points.length];else{if(idx===maxIndex)throw Error("There is no spline segment at this index for a closed curve!");p1=points[idx],p2=points[idx+1],p0=idx>0?points[idx-1]:extrapolateControlPoint(p1,p2),p3=idx<maxIndex-1?points[idx+2]:extrapolateControlPoint(p2,p1)}return[p0,p1,p2,p3]}function getSegmentIndexAndT(ct,points,closed){void 0===closed&&(closed=!1);var nPoints=closed?points.length:points.length-1;if(1===ct)return{index:nPoints-1,weight:1};var p=nPoints*ct,index=Math.floor(p);return{index:index,weight:p-index}}function fill(v,val){for(var i=0;i<v.length;i++)v[i]=val;return v}function map(v,func){for(var i=0;i<v.length;i++)v[i]=func(v[i],i);return v}function reduce(v,func,r){void 0===r&&(r=0);for(var i=0;i<v.length;i++)r=func(r,v[i],i);return r}function copyValues(source,target){target=target||new Array(source.length);for(var i=0;i<source.length;i++)target[i]=source[i];return target}function simplify2d(inputArr,maxOffset,maxDistance){var _a;if(void 0===maxOffset&&(maxOffset=.001),void 0===maxDistance&&(maxDistance=10),inputArr.length<=4)return inputArr;for(var _b=inputArr[0],o0=_b[0],o1=_b[1],arr=inputArr.map((function(d){return[d[0]-o0,d[1]-o1]})),_c=arr[0],a0=_c[0],a1=_c[1],sim=[inputArr[0]],i=1;i+1<arr.length;i++){var _d=arr[i],t0=_d[0],t1=_d[1],_e=arr[i+1],b0=_e[0],b1=_e[1];if(b0-t0!=0||b1-t1!=0){var proximity=Math.abs(a0*b1-a1*b0+b0*t1-b1*t0+a1*t0-a0*t1)/Math.sqrt(Math.pow(b0-a0,2)+Math.pow(b1-a1,2)),dir=[a0-t0,a1-t1],len=Math.sqrt(Math.pow(dir[0],2)+Math.pow(dir[1],2));(proximity>maxOffset||len>=maxDistance)&&(sim.push([t0+o0,t1+o1]),a0=(_a=[t0,t1])[0],a1=_a[1])}}var last=arr[arr.length-1];return sim.push([last[0]+o0,last[1]+o1]),sim}function clamp(value,min,max){return void 0===min&&(min=0),void 0===max&&(max=1),value<min?min:value>max?max:value}function binarySearch(targetValue,accumulatedValues){var min=accumulatedValues[0];if(targetValue>=accumulatedValues[accumulatedValues.length-1])return accumulatedValues.length-1;if(targetValue<=min)return 0;for(var left=0,right=accumulatedValues.length-1;left<=right;){var mid=Math.floor((left+right)/2),lMid=accumulatedValues[mid];if(lMid<targetValue)left=mid+1;else{if(!(lMid>targetValue))return mid;right=mid-1}}return Math.max(0,right)}var EPS=Math.pow(2,-42);function cuberoot(x){var y=Math.pow(Math.abs(x),1/3);return x<0?-y:y}function getQuadRoots(a,b,c){if(Math.abs(a)<EPS)return Math.abs(b)<EPS?[]:[-c/b];var D=b*b-4*a*c;return Math.abs(D)<EPS?[-b/(2*a)]:D>0?[(-b+Math.sqrt(D))/(2*a),(-b-Math.sqrt(D))/(2*a)]:[]}function getCubicRoots(a,b,c,d){if(Math.abs(a)<EPS)return getQuadRoots(b,c,d);var roots,p=(3*a*c-b*b)/(3*a*a),q=(2*b*b*b-9*a*b*c+27*a*a*d)/(27*a*a*a);if(Math.abs(p)<EPS)roots=[cuberoot(-q)];else if(Math.abs(q)<EPS)roots=[0].concat(p<0?[Math.sqrt(-p),-Math.sqrt(-p)]:[]);else{var D=q*q/4+p*p*p/27;if(Math.abs(D)<EPS)roots=[-1.5*q/p,3*q/p];else if(D>0){roots=[(u=cuberoot(-q/2-Math.sqrt(D)))-p/(3*u)]}else{var u=2*Math.sqrt(-p/3),t=Math.acos(3*q/p/u)/3,k=2*Math.PI/3;roots=[u*Math.cos(t),u*Math.cos(t-k),u*Math.cos(t-2*k)]}}for(var i=0;i<roots.length;i++)roots[i]-=b/(3*a);return roots}function dot(v1,v2){if(v1.length!==v2.length)throw Error("Vectors must be of equal length!");for(var p=0,k=0;k<v1.length;k++)p+=v1[k]*v2[k];return p}function cross(v1,v2,target){if(!(v1.length>3)){target=target||new Array(3);var ax=v1[0],ay=v1[1],az=v1[2]||0,bx=v2[0],by=v2[1],bz=v2[2]||0;return target[0]=ay*bz-az*by,target[1]=az*bx-ax*bz,target[2]=ax*by-ay*bx,target}}function sumOfSquares(v1,v2){for(var sumOfSquares=0,i=0;i<v1.length;i++)sumOfSquares+=(v1[i]-v2[i])*(v1[i]-v2[i]);return sumOfSquares}function magnitude(v){for(var sumOfSquares=0,i=0;i<v.length;i++)sumOfSquares+=v[i]*v[i];return Math.sqrt(sumOfSquares)}function distance(p1,p2){var sqrs=sumOfSquares(p1,p2);return 0===sqrs?0:Math.sqrt(sqrs)}function normalize(v,target){var u=target?copyValues(v,target):v,squared=reduce(u,(function(s,c){return s+Math.pow(c,2)})),l=Math.sqrt(squared);return 0===l?fill(u,0):map(u,(function(c){return c/l}))}function orthogonal(v,target){if(v.length>2)throw Error("Only supported for 2d vectors");var u=target?copyValues(v,target):v,x=-u[1];return u[1]=u[0],u[0]=x,u}function calcKnotSequence(p0,p1,p2,p3,alpha){if(void 0===alpha&&(alpha=0),0===alpha)return[0,1,2,3];var deltaT=function(u,v){return Math.pow(sumOfSquares(u,v),.5*alpha)},t1=deltaT(p1,p0),t2=deltaT(p2,p1)+t1;return[0,t1,t2,deltaT(p3,p2)+t2]}function calculateCoefficients(p0,p1,p2,p3,options){for(var tension=Number.isFinite(options.tension)?options.tension:.5,alpha=Number.isFinite(options.alpha)?options.alpha:null,knotSequence=alpha>0?calcKnotSequence(p0,p1,p2,p3,alpha):null,coefficientsList=new Array(p0.length),k=0;k<p0.length;k++){var u=0,v=0,v0=p0[k],v1=p1[k],v2=p2[k],v3=p3[k];if(knotSequence){var t0=knotSequence[0],t1=knotSequence[1],t2=knotSequence[2],t3=knotSequence[3];t1-t2!=0&&(t0-t1!=0&&t0-t2!=0&&(u=(1-tension)*(t2-t1)*((v0-v1)/(t0-t1)-(v0-v2)/(t0-t2)+(v1-v2)/(t1-t2))),t1-t3!=0&&t2-t3!=0&&(v=(1-tension)*(t2-t1)*((v1-v2)/(t1-t2)-(v1-v3)/(t1-t3)+(v2-v3)/(t2-t3))))}else u=(1-tension)*(v2-v0)*.5,v=(1-tension)*(v3-v1)*.5;var a=2*v1-2*v2+u+v,b=-3*v1+3*v2-2*u-v,d=v1;coefficientsList[k]=[a,b,u,d]}return coefficientsList}function valueAtT(t,coefficients){var t2=t*t,t3=t*t2;return coefficients[0]*t3+coefficients[1]*t2+coefficients[2]*t+coefficients[3]}function derivativeAtT(t,coefficients){var t2=t*t;return 3*coefficients[0]*t2+2*coefficients[1]*t+coefficients[2]}function secondDerivativeAtT(t,coefficients){return 6*coefficients[0]*t+2*coefficients[1]}function findRootsOfT(lookup,coefficients){var a=coefficients[0],b=coefficients[1],c=coefficients[2],x=coefficients[3]-lookup;return 0===a&&0===b&&0===c&&0===x?[0]:getCubicRoots(a,b,c,x).filter((function(t){return t>-EPS&&t<=1+EPS})).map((function(t){return clamp(t,0,1)}))}function evaluateForT(func,t,coefficients,target){void 0===target&&(target=null),target=target||new Array(coefficients.length);for(var k=0;k<coefficients.length;k++)target[k]=func(t,coefficients[k]);return target}var AbstractCurveMapper=function(){function AbstractCurveMapper(onInvalidateCache){void 0===onInvalidateCache&&(onInvalidateCache=null),this._alpha=0,this._tension=.5,this._closed=!1,this._onInvalidateCache=null,this._onInvalidateCache=onInvalidateCache,this._cache={arcLengths:null,coefficients:null}}return AbstractCurveMapper.prototype._invalidateCache=function(){this.points&&(this._cache={arcLengths:null,coefficients:null},this._onInvalidateCache&&this._onInvalidateCache())},Object.defineProperty(AbstractCurveMapper.prototype,"alpha",{get:function(){return this._alpha},set:function(alpha){Number.isFinite(alpha)&&alpha!==this._alpha&&(this._invalidateCache(),this._alpha=alpha)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"tension",{get:function(){return this._tension},set:function(tension){Number.isFinite(tension)&&tension!==this._tension&&(this._invalidateCache(),this._tension=tension)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"points",{get:function(){return this._points},set:function(points){if(!points||points.length<2)throw Error("At least 2 control points are required!");this._points=points,this._invalidateCache()},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"closed",{get:function(){return this._closed},set:function(closed){closed=!!closed,this._closed!==closed&&(this._invalidateCache(),this._closed=closed)},enumerable:!1,configurable:!0}),AbstractCurveMapper.prototype.reset=function(){this._invalidateCache()},AbstractCurveMapper.prototype.evaluateForT=function(func,t,target){var _a=getSegmentIndexAndT(t,this.points,this.closed),index=_a.index;return evaluateForT(func,_a.weight,this.getCoefficients(index),target)},AbstractCurveMapper.prototype.getCoefficients=function(idx){if(this.points){if(this._cache.coefficients||(this._cache.coefficients=new Map),!this._cache.coefficients.has(idx)){var _a=getControlPoints(idx,this.points,this.closed),coefficients=calculateCoefficients(_a[0],_a[1],_a[2],_a[3],{tension:this.tension,alpha:this.alpha});this._cache.coefficients.set(idx,coefficients)}return this._cache.coefficients.get(idx)}},AbstractCurveMapper}(),SegmentedCurveMapper=function(_super){function SegmentedCurveMapper(subDivisions,onInvalidateCache){void 0===subDivisions&&(subDivisions=300),void 0===onInvalidateCache&&(onInvalidateCache=null);var _this=_super.call(this,onInvalidateCache)||this;return _this._subDivisions=subDivisions,_this}return __extends(SegmentedCurveMapper,_super),Object.defineProperty(SegmentedCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),SegmentedCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null},SegmentedCurveMapper.prototype.computeArcLengths=function(){var current,lengths=[],last=this.evaluateForT(valueAtT,0),sum=0;lengths.push(0);for(var p=1;p<=this._subDivisions;p++)sum+=distance(current=this.evaluateForT(valueAtT,p/this._subDivisions),last),lengths.push(sum),last=current;return lengths},SegmentedCurveMapper.prototype.lengthAt=function(u){var arcLengths=this.arcLengths;return u*arcLengths[arcLengths.length-1]},SegmentedCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths);if(arcLengths[i]===targetArcLength)return i/(il-1);var lengthBefore=arcLengths[i];return(i+(targetArcLength-lengthBefore)/(arcLengths[i+1]-lengthBefore))/(il-1)},SegmentedCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=subIdx/al;return(l1+distance(this.evaluateForT(valueAtT,t0),this.evaluateForT(valueAtT,t)))/totalLength},SegmentedCurveMapper}(AbstractCurveMapper),lut=[[[-.906179845938664,.23692688505618908],[-.5384693101056831,.47862867049936647],[0,.5688888888888889],[.5384693101056831,.47862867049936647],[.906179845938664,.23692688505618908]],[[-.932469514203152,.17132449237917036],[-.6612093864662645,.3607615730481386],[-.2386191860831969,.46791393457269104],[.2386191860831969,.46791393457269104],[.6612093864662645,.3607615730481386],[.932469514203152,.17132449237917036]],[[-.9491079123427585,.1294849661688697],[-.7415311855993945,.27970539148927664],[-.4058451513773972,.3818300505051189],[0,.4179591836734694],[.4058451513773972,.3818300505051189],[.7415311855993945,.27970539148927664],[.9491079123427585,.1294849661688697]],[[-.9602898564975363,.10122853629037626],[-.7966664774136267,.22238103445337448],[-.525532409916329,.31370664587788727],[-.1834346424956498,.362683783378362],[.1834346424956498,.362683783378362],[.525532409916329,.31370664587788727],[.7966664774136267,.22238103445337448],[.9602898564975363,.10122853629037626]],[[-.9681602395076261,.08127438836157441],[-.8360311073266358,.1806481606948574],[-.6133714327005904,.26061069640293544],[-.3242534234038089,.31234707704000286],[0,.3302393550012598],[.3242534234038089,.31234707704000286],[.6133714327005904,.26061069640293544],[.8360311073266358,.1806481606948574],[.9681602395076261,.08127438836157441]],[[-.9739065285171717,.06667134430868814],[-.8650633666889845,.1494513491505806],[-.6794095682990244,.21908636251598204],[-.4333953941292472,.26926671930999635],[-.14887433898163122,.29552422471475287],[.14887433898163122,.29552422471475287],[.4333953941292472,.26926671930999635],[.6794095682990244,.21908636251598204],[.8650633666889845,.1494513491505806],[.9739065285171717,.06667134430868814]],[[-.978228658146056,.0556685671161736],[-.887062599768095,.125580369464904],[-.730152005574049,.186290210927734],[-.519096129206811,.23319376459199],[-.269543155952344,.262804544510246],[0,.2729250867779],[.269543155952344,.262804544510246],[.519096129206811,.23319376459199],[.730152005574049,.186290210927734],[.887062599768095,.125580369464904],[.978228658146056,.0556685671161736]],[[-.981560634246719,.0471753363865118],[-.904117256370474,.106939325995318],[-.769902674194304,.160078328543346],[-.587317954286617,.203167426723065],[-.36783149899818,.233492536538354],[-.125233408511468,.249147045813402],[.125233408511468,.249147045813402],[.36783149899818,.233492536538354],[.587317954286617,.203167426723065],[.769902674194304,.160078328543346],[.904117256370474,.106939325995318],[.981560634246719,.0471753363865118]],[[-.984183054718588,.0404840047653158],[-.917598399222977,.0921214998377284],[-.801578090733309,.138873510219787],[-.64234933944034,.178145980761945],[-.448492751036446,.207816047536888],[-.230458315955134,.226283180262897],[0,.232551553230873],[.230458315955134,.226283180262897],[.448492751036446,.207816047536888],[.64234933944034,.178145980761945],[.801578090733309,.138873510219787],[.917598399222977,.0921214998377284],[.984183054718588,.0404840047653158]],[[-.986283808696812,.0351194603317518],[-.928434883663573,.0801580871597602],[-.827201315069764,.121518570687903],[-.687292904811685,.157203167158193],[-.515248636358154,.185538397477937],[-.319112368927889,.205198463721295],[-.108054948707343,.215263853463157],[.108054948707343,.215263853463157],[.319112368927889,.205198463721295],[.515248636358154,.185538397477937],[.687292904811685,.157203167158193],[.827201315069764,.121518570687903],[.928434883663573,.0801580871597602],[.986283808696812,.0351194603317518]],[[-.987992518020485,.0307532419961172],[-.937273392400705,.0703660474881081],[-.848206583410427,.107159220467171],[-.72441773136017,.139570677926154],[-.570972172608538,.166269205816993],[-.394151347077563,.186161000015562],[-.201194093997434,.198431485327111],[0,.202578241925561],[.201194093997434,.198431485327111],[.394151347077563,.186161000015562],[.570972172608538,.166269205816993],[.72441773136017,.139570677926154],[.848206583410427,.107159220467171],[.937273392400705,.0703660474881081],[.987992518020485,.0307532419961172]],[[-.989400934991649,.027152459411754],[-.944575023073232,.0622535239386478],[-.865631202387831,.0951585116824927],[-.755404408355003,.124628971255533],[-.617876244402643,.149595988816576],[-.458016777657227,.169156519395002],[-.281603550779258,.182603415044923],[-.0950125098376374,.189450610455068],[.0950125098376374,.189450610455068],[.281603550779258,.182603415044923],[.458016777657227,.169156519395002],[.617876244402643,.149595988816576],[.755404408355003,.124628971255533],[.865631202387831,.0951585116824927],[.944575023073232,.0622535239386478],[.989400934991649,.027152459411754]],[[-.990575475314417,.0241483028685479],[-.950675521768767,.0554595293739872],[-.880239153726985,.0850361483171791],[-.781514003896801,.111883847193403],[-.65767115921669,.135136368468525],[-.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NumericalCurveMapper=function(_super){function NumericalCurveMapper(nQuadraturePoints,nInverseSamples,onInvalidateCache){void 0===nQuadraturePoints&&(nQuadraturePoints=24),void 0===nInverseSamples&&(nInverseSamples=21);var _this=_super.call(this,onInvalidateCache)||this;return _this._nSamples=21,_this._gauss=function(order){if(order<5||order>maxOrder)throw Error("Order for Gaussian Quadrature must be in the range of ".concat(5," and ").concat(maxOrder,"."));return lut[order-5]}(nQuadraturePoints),_this._nSamples=nInverseSamples,_this}return __extends(NumericalCurveMapper,_super),NumericalCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null,this._cache.samples=null},Object.defineProperty(NumericalCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),NumericalCurveMapper.prototype.getSamples=function(idx){if(this.points){if(this._cache.samples||(this._cache.samples=new Map),!this._cache.samples.has(idx)){for(var samples=this._nSamples,lengths=[],slopes=[],coefficients=this.getCoefficients(idx),i=0;i<samples;++i){var ti=i/(samples-1);lengths.push(this.computeArcLength(idx,0,ti));var dtln=magnitude(evaluateForT(derivativeAtT,ti,coefficients)),slope=0===dtln?0:1/dtln;this.tension>.95&&(slope=clamp(slope,-1,1)),slopes.push(slope)}var nCoeff=samples-1,dis=[],cis=[],li_prev=lengths[0],tdi_prev=slopes[0],step=1/nCoeff;for(i=0;i<nCoeff;++i){var li=li_prev,lDiff=(li_prev=lengths[i+1])-li,tdi=tdi_prev,tdi_next=slopes[i+1];tdi_prev=tdi_next;var si=step/lDiff,di=(tdi+tdi_next-2*si)/(lDiff*lDiff),ci=(3*si-2*tdi-tdi_next)/lDiff;dis.push(di),cis.push(ci)}this._cache.samples.set(idx,[lengths,slopes,cis,dis])}return this._cache.samples.get(idx)}},NumericalCurveMapper.prototype.computeArcLength=function(index,t0,t1){if(void 0===t0&&(t0=0),void 0===t1&&(t1=1),t0===t1)return 0;for(var coefficients=this.getCoefficients(index),z=.5*(t1-t0),sum=0,i=0;i<this._gauss.length;i++){var _a=this._gauss[i],T=_a[0];sum+=_a[1]*magnitude(evaluateForT(derivativeAtT,z*T+z+t0,coefficients))}return z*sum},NumericalCurveMapper.prototype.computeArcLengths=function(){if(this.points){var lengths=[];lengths.push(0);for(var nPoints=this.closed?this.points.length:this.points.length-1,tl=0,i=0;i<nPoints;i++){tl+=this.computeArcLength(i),lengths.push(tl)}return lengths}},NumericalCurveMapper.prototype.inverse=function(idx,len){var step=1/(this._nSamples-1),_a=this.getSamples(idx),lengths=_a[0],slopes=_a[1],cis=_a[2],dis=_a[3];if(len>=lengths[lengths.length-1])return 1;if(len<=0)return 0;var i=Math.max(0,binarySearch(len,lengths)),ti=i*step;if(lengths[i]===len)return ti;var tdi=slopes[i],di=dis[i],ci=cis[i],ld=len-lengths[i];return((di*ld+ci)*ld+tdi)*ld+ti},NumericalCurveMapper.prototype.lengthAt=function(u){return u*this.arcLengths[this.arcLengths.length-1]},NumericalCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths),ti=i/(il-1);if(arcLengths[i]===targetArcLength)return ti;var len=targetArcLength-arcLengths[i];return(i+this.inverse(i,len))/(il-1)},NumericalCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=tIdx-subIdx;return(l1+this.computeArcLength(subIdx,0,t0))/totalLength},NumericalCurveMapper}(AbstractCurveMapper),CurveInterpolator=function(){function CurveInterpolator(points,options){void 0===options&&(options={});var _this=this;this._cache=new Map;var curveMapper=(options=__assign({tension:.5,alpha:0,closed:!1},options)).arcDivisions?new SegmentedCurveMapper(options.arcDivisions,(function(){return _this._invalidateCache()})):new NumericalCurveMapper(options.numericalApproximationOrder,options.numericalInverseSamples,(function(){return _this._invalidateCache()}));curveMapper.alpha=options.alpha,curveMapper.tension=options.tension,curveMapper.closed=options.closed,curveMapper.points=points,this._lmargin=options.lmargin||1-curveMapper.tension,this._curveMapper=curveMapper}return CurveInterpolator.prototype.getTimeFromPosition=function(position,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getT(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getPositionFromTime=function(t,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getU(clampInput?clamp(t,0,1):t)},CurveInterpolator.prototype.getPositionFromLength=function(length,clampInput){void 0===clampInput&&(clampInput=!1);var l=clampInput?clamp(length,0,this.length):length;return this._curveMapper.getU(l/this.length)},CurveInterpolator.prototype.getLengthAt=function(position,clampInput){return void 0===position&&(position=1),void 0===clampInput&&(clampInput=!1),this._curveMapper.lengthAt(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getTimeAtKnot=function(index){if(index<0||index>this.points.length-1)throw Error("Invalid index!");return 0===index?0:this.closed||index!==this.points.length-1?index/(this.closed?this.points.length:this.points.length-1):1},CurveInterpolator.prototype.getPositionAtKnot=function(index){return this.getPositionFromTime(this.getTimeAtKnot(index))},CurveInterpolator.prototype.getPointAtTime=function(t,target){return 0===(t=clamp(t,0,1))?copyValues(this.points[0],target):1===t?copyValues(this.closed?this.points[0]:this.points[this.points.length-1],target):this._curveMapper.evaluateForT(valueAtT,t,target)},CurveInterpolator.prototype.getPointAt=function(position,target){return this.getPointAtTime(this.getTimeFromPosition(position),target)},CurveInterpolator.prototype.getTangentAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getTangentAtTime(t,target)},CurveInterpolator.prototype.getTangentAtTime=function(t,target){return normalize(this._curveMapper.evaluateForT(derivativeAtT,t,target))},CurveInterpolator.prototype.getNormalAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getNormalAtTime(t,target)},CurveInterpolator.prototype.getNormalAtTime=function(t,target){var dt=normalize(this._curveMapper.evaluateForT(derivativeAtT,t));if(!(dt.length<2||dt.length>3)){var normal=target||new Array(dt.length);if(2===dt.length)return normal[0]=-dt[1],normal[1]=dt[0],normal;var ddt=normalize(this._curveMapper.evaluateForT(secondDerivativeAtT,t));return normalize(cross(cross(dt,ddt),dt),normal)}},CurveInterpolator.prototype.getCurvatureAt=function(position){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getCurvatureAtTime(t)},CurveInterpolator.prototype.getCurvatureAtTime=function(t){var dt=this._curveMapper.evaluateForT(derivativeAtT,t),ddt=this._curveMapper.evaluateForT(secondDerivativeAtT,t),tangent=normalize(dt,[]),curvature=0,direction=void 0;if(2===dt.length){if(0!==(denominator=Math.pow(dt[0]*dt[0]+dt[1]*dt[1],1.5))){var signedCurvature=(dt[0]*ddt[1]-dt[1]*ddt[0])/denominator;direction=signedCurvature<0?[tangent[1],-tangent[0]]:[-tangent[1],tangent[0]],curvature=Math.abs(signedCurvature)}}else if(3===dt.length){var a=magnitude(dt),cp=cross(dt,ddt);direction=normalize(cross(cp,dt)),0!==a&&(curvature=magnitude(cp)/Math.pow(a,3))}else{a=magnitude(dt);var b=magnitude(ddt),denominator=Math.pow(a,3),dotProduct=dot(dt,ddt);0!==denominator&&(curvature=Math.sqrt(Math.pow(a,2)*Math.pow(b,2)-Math.pow(dotProduct,2))/denominator)}return{curvature:curvature,radius:0!==curvature?1/curvature:0,tangent:tangent,direction:direction}},CurveInterpolator.prototype.getDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(derivativeAtT,t,target)},CurveInterpolator.prototype.getSecondDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(secondDerivativeAtT,t,target)},CurveInterpolator.prototype.getBoundingBox=function(from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),0===from&&1===to&&this._cache.has("bbox"))return this._cache.get("bbox");for(var min=[],max=[],t0=this.getTimeFromPosition(from),t1=this.getTimeFromPosition(to),start=this.getPointAtTime(t0),end=this.getPointAtTime(t1),nPoints=this.closed?this.points.length:this.points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var p2=getControlPoints(i-1,this_1.points,this_1.closed)[2];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(this_1.tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=this_1._curveMapper.getCoefficients(i-1),_loop_2=function(c){var _b=coefficients_1[c];getQuadRoots(3*_b[0],2*_b[1],_b[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},this_1=this,i=i0+1;i<=i1;i++)_loop_1(i);var bbox={min:min,max:max};return 0===from&&1===to&&this._cache.set("bbox",bbox),bbox},CurveInterpolator.prototype.getPoints=function(segments,returnType,from,to){if(void 0===segments&&(segments=100),void 0===from&&(from=0),void 0===to&&(to=1),!segments||segments<=0)throw Error("Invalid arguments passed to getPoints(). You must specify at least 1 sample/segment.");if(!(from<0||to>1||to<from)){for(var pts=[],d=0;d<=segments;d++){var u=0===from&&1===to?d/segments:from+d/segments*(to-from);pts.push(this.getPointAt(u,returnType&&new returnType))}return pts}},CurveInterpolator.prototype.getNearestPosition=function(point,threshold){var _this=this;if(void 0===threshold&&(threshold=1e-5),threshold<=0||!Number.isFinite(threshold))throw Error("Invalid threshold. Must be a number greater than zero!");var samples=10*this.points.length-1,pu=new Array(point.length),minDist=1/0,minU=0,lut=this.createLookupTable(samples);Array.from(lut.keys()).forEach((function(key){var c=lut.get(key),dist=distance(point,c);if(dist<minDist)return minDist=dist,minU=key,!0}));for(var minT=this.getTimeFromPosition(minU),bisect=function(t){if(t>=0&&t<=1){_this.getPointAtTime(t,pu);var dist=distance(point,pu);if(dist<minDist)return minDist=dist,minT=t,!0}},step=.005;step>threshold;)bisect(minT-step)||bisect(minT+step)||(step/=2);return{u:minU=this._curveMapper.getU(minT),distance:minDist,point:pu}},CurveInterpolator.prototype.getIntersects=function(v,axis,max,margin){var _this=this;void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var solutions=this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPointAtTime(t)}));return 1===Math.abs(max)?1===solutions.length?solutions[0]:null:solutions},CurveInterpolator.prototype.getIntersectsAsPositions=function(v,axis,max,margin){var _this=this;return void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin),this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPositionFromTime(t)}))},CurveInterpolator.prototype.getIntersectsAsTime=function(v,axis,max,margin){void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);for(var k=axis,solutions=new Set,nPoints=this.closed?this.points.length:this.points.length-1,i=0;i<nPoints&&(0===max||solutions.size<Math.abs(max));i+=1){var idx=max<0?nPoints-(i+1):i,_a=getControlPoints(idx,this.points,this.closed),p1=_a[1],p2=_a[2],coefficients=this._curveMapper.getCoefficients(idx),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),v-margin<=vmax&&v+margin>=vmin){var ts=findRootsOfT(v,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),0!==max&&solutions.size===Math.abs(max))break}}}return Array.from(solutions)},CurveInterpolator.prototype.createLookupTable=function(samples,from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),!samples||samples<=1)throw Error("Invalid arguments passed to createLookupTable(). You must specify at least 2 samples.");if(!(from<0||to>1||to<from)){var cacheKey="lut_".concat(samples,"_").concat(from,"_").concat(to);if(!this._cache.has(cacheKey)){for(var lut=new Map,d=0;d<samples;d++){var u=0===from&&1===to?d/(samples-1):from+d/(samples-1)*(to-from),point=this.getPointAt(u);lut.set(u,point)}this._cache.set(cacheKey,lut)}return this._cache.get(cacheKey)}},CurveInterpolator.prototype.forEach=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to forEach(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;positions.forEach((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in forEach!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});prev={u:u,t:t,i:i,value:current}}))},CurveInterpolator.prototype.map=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;return positions.map((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});return prev={u:u,t:t,i:i,value:current},current}))},CurveInterpolator.prototype.reduce=function(func,initialValue,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);return positions.reduce((function(acc,u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u);return func({acc:acc,u:u,t:t,i:i})}),initialValue)},CurveInterpolator.prototype._invalidateCache=function(){return this._cache=new Map,this},CurveInterpolator.prototype.reset=function(){this._curveMapper.reset()},Object.defineProperty(CurveInterpolator.prototype,"points",{get:function(){return this._curveMapper.points},set:function(pts){this._curveMapper.points=pts},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"tension",{get:function(){return this._curveMapper.tension},set:function(t){this._curveMapper.tension=t},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"alpha",{get:function(){return this._curveMapper.alpha},set:function(a){this._curveMapper.alpha=a},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"closed",{get:function(){return this._curveMapper.closed},set:function(isClosed){this._curveMapper.closed=isClosed},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"length",{get:function(){return this._curveMapper.lengthAt(1)},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minX",{get:function(){return this.getBoundingBox().min[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxX",{get:function(){return this.getBoundingBox().max[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minY",{get:function(){return this.getBoundingBox().min[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxY",{get:function(){return this.getBoundingBox().max[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minZ",{get:function(){return this.getBoundingBox().min[2]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxZ",{get:function(){return this.getBoundingBox().max[2]},enumerable:!1,configurable:!0}),CurveInterpolator}(),Point=function(){function Point(x,y,z,w){void 0===x&&(x=0),void 0===y&&(y=0),void 0===z&&(z=null),void 0===w&&(w=null),this.x=x,this.y=y,this.z=z,this.w=w}return Object.defineProperty(Point.prototype,0,{get:function(){return this.x},set:function(x){this.x=x},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,1,{get:function(){return this.y},set:function(y){this.y=y},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,2,{get:function(){return this.z},set:function(z){this.z=z},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,3,{get:function(){return this.w},set:function(w){this.w=w},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,"length",{get:function(){return Number.isFinite(this.w)?4:Number.isFinite(this.z)?3:2},enumerable:!1,configurable:!0}),Point}(),CurveInterpolator2D=function(_super){function CurveInterpolator2D(points,tension,arcDivisions,closed,alpha){return void 0===tension&&(tension=.5),void 0===arcDivisions&&(arcDivisions=300),void 0===closed&&(closed=!1),void 0===alpha&&(alpha=0),_super.call(this,points.map((function(p){return[p[0],p[1]]})),{tension:tension,alpha:alpha,arcDivisions:arcDivisions,closed:closed})||this}return __extends(CurveInterpolator2D,_super),CurveInterpolator2D.prototype.x=function(y,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(y,1,max,margin);return 1===Math.abs(max)?res[0]:res.map((function(d){return d[0]}))},CurveInterpolator2D.prototype.y=function(x,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(x,0,max,margin);return 1===Math.abs(max)?res[1]:res.map((function(d){return d[1]}))},CurveInterpolator2D.prototype.getNormalAt=function(position,target){return normalize(orthogonal(this.getTangentAt(position,target)))},CurveInterpolator2D.prototype.getAngleAt=function(position){var tan=this.getTangentAt(position);return Math.atan2(tan[1],tan[0])},CurveInterpolator2D.prototype.getBoundingBox=function(from,to){void 0===from&&(from=0),void 0===to&&(to=1);var bbox=_super.prototype.getBoundingBox.call(this,from,to);return{x1:bbox.min[0],x2:bbox.max[0],y1:bbox.min[1],y2:bbox.max[1],min:bbox.min,max:bbox.max}},CurveInterpolator2D}(CurveInterpolator);function getPointAtT(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(valueAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))}function getTangentAtT(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(derivativeAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))}function valuesLookup(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0,processRefAxis:!1},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,processRefAxis=_a.processRefAxis,k=axis,solutions=[],nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var _b=getControlPoints(max<0?nPoints-(i+1):i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){for(var coord=[],c=0;c<p0.length;c++){var v=void 0;v=c!==k||processRefAxis?valueAtT(ts[j],coefficients[c]):lookup,coord[c]=v}if(solutions.push(coord),solutions.length===Math.abs(max))return solutions}}}return solutions}function positionsLookup(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,k=axis,solutions=new Set,nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var idx=max<0?points.length-i:i,_b=getControlPoints(i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),solutions.size===Math.abs(max))return Array.from(solutions)}}}return Array.from(solutions)}function getBoundingBox(points,options){void 0===options&&(options={});for(var _a=__assign({tension:.5,alpha:0,closed:!1,from:0,to:1},options),tension=_a.tension,alpha=_a.alpha,closed=_a.closed,t0=_a.from,t1=_a.to,nPoints=closed?points.length:points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),start=getPointAtT(t0,points,{tension:tension,alpha:alpha,closed:closed}),end=getPointAtT(t1,points,{tension:tension,alpha:alpha,closed:closed}),min=[],max=[],c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var _b=getControlPoints(i-1,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],p3=_b[3];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=calculateCoefficients(p0,p1,p2,p3,{tension:tension,alpha:alpha}),_loop_2=function(c){var _c=coefficients_1[c];getQuadRoots(3*_c[0],2*_c[1],_c[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},i=i0+1;i<=i1;i++)_loop_1(i);return{min:min,max:max}}export{CurveInterpolator,CurveInterpolator2D,EPS,SegmentedCurveMapper as LinearCurveMapper,NumericalCurveMapper,Point,binarySearch,calcKnotSequence,calculateCoefficients,clamp,copyValues,cross,derivativeAtT,distance,dot,evaluateForT,extrapolateControlPoint,fill,findRootsOfT,getBoundingBox,getControlPoints,getCubicRoots,getPointAtT,getQuadRoots,getSegmentIndexAndT,getTangentAtT,magnitude,map,normalize,orthogonal,positionsLookup,reduce,secondDerivativeAtT,simplify2d,sumOfSquares,valueAtT,valuesLookup};
var extendStatics=function(d,b){return extendStatics=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(d,b){d.__proto__=b}||function(d,b){for(var p in b)b.hasOwnProperty(p)&&(d[p]=b[p])},extendStatics(d,b)};function __extends(d,b){function __(){this.constructor=d}extendStatics(d,b),d.prototype=null===b?Object.create(b):(__.prototype=b.prototype,new __)}var __assign=function(){return __assign=Object.assign||function(t){for(var s,i=1,n=arguments.length;i<n;i++)for(var p in s=arguments[i])Object.prototype.hasOwnProperty.call(s,p)&&(t[p]=s[p]);return t},__assign.apply(this,arguments)};function extrapolateControlPoint(u,v){for(var e=new Array(u.length),i=0;i<u.length;i++)e[i]=2*u[i]-v[i];return e}function getControlPoints(idx,points,closed){var p0,p1,p2,p3,maxIndex=points.length-1;if(closed)p0=points[idx-1<0?maxIndex:idx-1],p1=points[idx%points.length],p2=points[(idx+1)%points.length],p3=points[(idx+2)%points.length];else{if(idx===maxIndex)throw Error("There is no spline segment at this index for a closed curve!");p1=points[idx],p2=points[idx+1],p0=idx>0?points[idx-1]:extrapolateControlPoint(p1,p2),p3=idx<maxIndex-1?points[idx+2]:extrapolateControlPoint(p2,p1)}return[p0,p1,p2,p3]}function getSegmentIndexAndT(ct,points,closed){void 0===closed&&(closed=!1);var nPoints=closed?points.length:points.length-1;if(1===ct)return{index:nPoints-1,weight:1};var p=nPoints*ct,index=Math.floor(p);return{index:index,weight:p-index}}function fill(v,val){for(var i=0;i<v.length;i++)v[i]=val;return v}function map(v,func){for(var i=0;i<v.length;i++)v[i]=func(v[i],i);return v}function reduce(v,func,r){void 0===r&&(r=0);for(var i=0;i<v.length;i++)r=func(r,v[i],i);return r}function copyValues(source,target){target=target||new Array(source.length);for(var i=0;i<source.length;i++)target[i]=source[i];return target}function simplify2d(inputArr,maxOffset,maxDistance){var _a;if(void 0===maxOffset&&(maxOffset=.001),void 0===maxDistance&&(maxDistance=10),inputArr.length<=4)return inputArr;for(var _b=inputArr[0],o0=_b[0],o1=_b[1],arr=inputArr.map((function(d){return[d[0]-o0,d[1]-o1]})),_c=arr[0],a0=_c[0],a1=_c[1],sim=[inputArr[0]],i=1;i+1<arr.length;i++){var _d=arr[i],t0=_d[0],t1=_d[1],_e=arr[i+1],b0=_e[0],b1=_e[1];if(b0-t0!=0||b1-t1!=0){var proximity=Math.abs(a0*b1-a1*b0+b0*t1-b1*t0+a1*t0-a0*t1)/Math.sqrt(Math.pow(b0-a0,2)+Math.pow(b1-a1,2)),dir=[a0-t0,a1-t1],len=Math.sqrt(Math.pow(dir[0],2)+Math.pow(dir[1],2));(proximity>maxOffset||len>=maxDistance)&&(sim.push([t0+o0,t1+o1]),a0=(_a=[t0,t1])[0],a1=_a[1])}}var last=arr[arr.length-1];return sim.push([last[0]+o0,last[1]+o1]),sim}function clamp(value,min,max){return void 0===min&&(min=0),void 0===max&&(max=1),value<min?min:value>max?max:value}function binarySearch(targetValue,accumulatedValues){var min=accumulatedValues[0];if(targetValue>=accumulatedValues[accumulatedValues.length-1])return accumulatedValues.length-1;if(targetValue<=min)return 0;for(var left=0,right=accumulatedValues.length-1;left<=right;){var mid=Math.floor((left+right)/2),lMid=accumulatedValues[mid];if(lMid<targetValue)left=mid+1;else{if(!(lMid>targetValue))return mid;right=mid-1}}return Math.max(0,right)}var EPS=Math.pow(2,-42);function cuberoot(x){var y=Math.pow(Math.abs(x),1/3);return x<0?-y:y}function getQuadRoots(a,b,c){if(Math.abs(a)<EPS)return Math.abs(b)<EPS?[]:[-c/b];var D=b*b-4*a*c;return Math.abs(D)<EPS?[-b/(2*a)]:D>0?[(-b+Math.sqrt(D))/(2*a),(-b-Math.sqrt(D))/(2*a)]:[]}function getCubicRoots(a,b,c,d){if(Math.abs(a)<EPS)return getQuadRoots(b,c,d);var roots,p=(3*a*c-b*b)/(3*a*a),q=(2*b*b*b-9*a*b*c+27*a*a*d)/(27*a*a*a);if(Math.abs(p)<EPS)roots=[cuberoot(-q)];else if(Math.abs(q)<EPS)roots=[0].concat(p<0?[Math.sqrt(-p),-Math.sqrt(-p)]:[]);else{var D=q*q/4+p*p*p/27;if(Math.abs(D)<EPS)roots=[-1.5*q/p,3*q/p];else if(D>0){roots=[(u=cuberoot(-q/2-Math.sqrt(D)))-p/(3*u)]}else{var u=2*Math.sqrt(-p/3),t=Math.acos(3*q/p/u)/3,k=2*Math.PI/3;roots=[u*Math.cos(t),u*Math.cos(t-k),u*Math.cos(t-2*k)]}}for(var i=0;i<roots.length;i++)roots[i]-=b/(3*a);return roots}function dot(v1,v2){if(v1.length!==v2.length)throw Error("Vectors must be of equal length!");for(var p=0,k=0;k<v1.length;k++)p+=v1[k]*v2[k];return p}function cross(v1,v2,target){if(!(v1.length>3)){target=target||new Array(3);var ax=v1[0],ay=v1[1],az=v1[2]||0,bx=v2[0],by=v2[1],bz=v2[2]||0;return target[0]=ay*bz-az*by,target[1]=az*bx-ax*bz,target[2]=ax*by-ay*bx,target}}function sumOfSquares(v1,v2){for(var sumOfSquares=0,i=0;i<v1.length;i++)sumOfSquares+=(v1[i]-v2[i])*(v1[i]-v2[i]);return sumOfSquares}function magnitude(v){for(var sumOfSquares=0,i=0;i<v.length;i++)sumOfSquares+=v[i]*v[i];return Math.sqrt(sumOfSquares)}function distance(p1,p2){var sqrs=sumOfSquares(p1,p2);return 0===sqrs?0:Math.sqrt(sqrs)}function normalize(v,target){var u=target?copyValues(v,target):v,squared=reduce(u,(function(s,c){return s+Math.pow(c,2)})),l=Math.sqrt(squared);return 0===l?fill(u,0):map(u,(function(c){return c/l}))}function orthogonal(v,target){if(v.length>2)throw Error("Only supported for 2d vectors");var u=target?copyValues(v,target):v,x=-u[1];return u[1]=u[0],u[0]=x,u}function calcKnotSequence(p0,p1,p2,p3,alpha){if(void 0===alpha&&(alpha=0),0===alpha)return[0,1,2,3];var deltaT=function(u,v){return Math.pow(sumOfSquares(u,v),.5*alpha)},t1=deltaT(p1,p0),t2=deltaT(p2,p1)+t1;return[0,t1,t2,deltaT(p3,p2)+t2]}function calculateCoefficients(p0,p1,p2,p3,options){for(var tension=Number.isFinite(options.tension)?options.tension:.5,alpha=Number.isFinite(options.alpha)?options.alpha:null,knotSequence=alpha>0?calcKnotSequence(p0,p1,p2,p3,alpha):null,coefficientsList=new Array(p0.length),k=0;k<p0.length;k++){var u=0,v=0,v0=p0[k],v1=p1[k],v2=p2[k],v3=p3[k];if(knotSequence){var t0=knotSequence[0],t1=knotSequence[1],t2=knotSequence[2],t3=knotSequence[3];t1-t2!=0&&(t0-t1!=0&&t0-t2!=0&&(u=(1-tension)*(t2-t1)*((v0-v1)/(t0-t1)-(v0-v2)/(t0-t2)+(v1-v2)/(t1-t2))),t1-t3!=0&&t2-t3!=0&&(v=(1-tension)*(t2-t1)*((v1-v2)/(t1-t2)-(v1-v3)/(t1-t3)+(v2-v3)/(t2-t3))))}else u=(1-tension)*(v2-v0)*.5,v=(1-tension)*(v3-v1)*.5;var a=2*v1-2*v2+u+v,b=-3*v1+3*v2-2*u-v,c=u,d=v1;coefficientsList[k]=[a,b,c,d]}return coefficientsList}function valueAtT(t,coefficients){var t2=t*t,t3=t*t2;return coefficients[0]*t3+coefficients[1]*t2+coefficients[2]*t+coefficients[3]}function derivativeAtT(t,coefficients){var t2=t*t;return 3*coefficients[0]*t2+2*coefficients[1]*t+coefficients[2]}function secondDerivativeAtT(t,coefficients){return 6*coefficients[0]*t+2*coefficients[1]}function findRootsOfT(lookup,coefficients){var a=coefficients[0],b=coefficients[1],c=coefficients[2],x=coefficients[3]-lookup;return 0===a&&0===b&&0===c&&0===x?[0]:getCubicRoots(a,b,c,x).filter((function(t){return t>-EPS&&t<=1+EPS})).map((function(t){return clamp(t,0,1)}))}function evaluateForT(func,t,coefficients,target){void 0===target&&(target=null),target=target||new Array(coefficients.length);for(var k=0;k<coefficients.length;k++)target[k]=func(t,coefficients[k]);return target}var AbstractCurveMapper=function(){function AbstractCurveMapper(onInvalidateCache){void 0===onInvalidateCache&&(onInvalidateCache=null),this._alpha=0,this._tension=.5,this._closed=!1,this._onInvalidateCache=null,this._onInvalidateCache=onInvalidateCache,this._cache={arcLengths:null,coefficients:null}}return AbstractCurveMapper.prototype._invalidateCache=function(){this.points&&(this._cache={arcLengths:null,coefficients:null},this._onInvalidateCache&&this._onInvalidateCache())},Object.defineProperty(AbstractCurveMapper.prototype,"alpha",{get:function(){return this._alpha},set:function(alpha){Number.isFinite(alpha)&&alpha!==this._alpha&&(this._invalidateCache(),this._alpha=alpha)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"tension",{get:function(){return this._tension},set:function(tension){Number.isFinite(tension)&&tension!==this._tension&&(this._invalidateCache(),this._tension=tension)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"points",{get:function(){return this._points},set:function(points){if(!points||points.length<2)throw Error("At least 2 control points are required!");this._points=points,this._invalidateCache()},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"closed",{get:function(){return this._closed},set:function(closed){closed=!!closed,this._closed!==closed&&(this._invalidateCache(),this._closed=closed)},enumerable:!1,configurable:!0}),AbstractCurveMapper.prototype.reset=function(){this._invalidateCache()},AbstractCurveMapper.prototype.evaluateForT=function(func,t,target){var _a=getSegmentIndexAndT(t,this.points,this.closed),index=_a.index;return evaluateForT(func,_a.weight,this.getCoefficients(index),target)},AbstractCurveMapper.prototype.getCoefficients=function(idx){if(this.points){if(this._cache.coefficients||(this._cache.coefficients=new Map),!this._cache.coefficients.has(idx)){var _a=getControlPoints(idx,this.points,this.closed),coefficients=calculateCoefficients(_a[0],_a[1],_a[2],_a[3],{tension:this.tension,alpha:this.alpha});this._cache.coefficients.set(idx,coefficients)}return this._cache.coefficients.get(idx)}},AbstractCurveMapper}(),SegmentedCurveMapper=function(_super){function SegmentedCurveMapper(subDivisions,onInvalidateCache){void 0===subDivisions&&(subDivisions=300),void 0===onInvalidateCache&&(onInvalidateCache=null);var _this=_super.call(this,onInvalidateCache)||this;return _this._subDivisions=subDivisions,_this}return __extends(SegmentedCurveMapper,_super),Object.defineProperty(SegmentedCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),SegmentedCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null},SegmentedCurveMapper.prototype.computeArcLengths=function(){var current,lengths=[],last=this.evaluateForT(valueAtT,0),sum=0;lengths.push(0);for(var p=1;p<=this._subDivisions;p++)sum+=distance(current=this.evaluateForT(valueAtT,p/this._subDivisions),last),lengths.push(sum),last=current;return lengths},SegmentedCurveMapper.prototype.lengthAt=function(u){var arcLengths=this.arcLengths;return u*arcLengths[arcLengths.length-1]},SegmentedCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths);if(arcLengths[i]===targetArcLength)return i/(il-1);var lengthBefore=arcLengths[i];return(i+(targetArcLength-lengthBefore)/(arcLengths[i+1]-lengthBefore))/(il-1)},SegmentedCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var 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NumericalCurveMapper=function(_super){function NumericalCurveMapper(nQuadraturePoints,nInverseSamples,onInvalidateCache){void 0===nQuadraturePoints&&(nQuadraturePoints=24),void 0===nInverseSamples&&(nInverseSamples=21);var _this=_super.call(this,onInvalidateCache)||this;return _this._nSamples=21,_this._gauss=function(order){if(order<5||order>maxOrder)throw Error("Order for Gaussian Quadrature must be in the range of ".concat(5," and ").concat(maxOrder,"."));return lut[order-5]}(nQuadraturePoints),_this._nSamples=nInverseSamples,_this}return __extends(NumericalCurveMapper,_super),NumericalCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null,this._cache.samples=null},Object.defineProperty(NumericalCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),NumericalCurveMapper.prototype.getSamples=function(idx){if(this.points){if(this._cache.samples||(this._cache.samples=new Map),!this._cache.samples.has(idx)){for(var samples=this._nSamples,lengths=[],slopes=[],coefficients=this.getCoefficients(idx),i=0;i<samples;++i){var ti=i/(samples-1);lengths.push(this.computeArcLength(idx,0,ti));var dtln=magnitude(evaluateForT(derivativeAtT,ti,coefficients)),slope=0===dtln?0:1/dtln;this.tension>.95&&(slope=clamp(slope,-1,1)),slopes.push(slope)}var nCoeff=samples-1,dis=[],cis=[],li_prev=lengths[0],tdi_prev=slopes[0],step=1/nCoeff;for(i=0;i<nCoeff;++i){var li=li_prev,lDiff=(li_prev=lengths[i+1])-li,tdi=tdi_prev,tdi_next=slopes[i+1];tdi_prev=tdi_next;var si=step/lDiff,di=(tdi+tdi_next-2*si)/(lDiff*lDiff),ci=(3*si-2*tdi-tdi_next)/lDiff;dis.push(di),cis.push(ci)}this._cache.samples.set(idx,[lengths,slopes,cis,dis])}return this._cache.samples.get(idx)}},NumericalCurveMapper.prototype.computeArcLength=function(index,t0,t1){if(void 0===t0&&(t0=0),void 0===t1&&(t1=1),t0===t1)return 0;for(var coefficients=this.getCoefficients(index),z=.5*(t1-t0),sum=0,i=0;i<this._gauss.length;i++){var _a=this._gauss[i],T=_a[0];sum+=_a[1]*magnitude(evaluateForT(derivativeAtT,z*T+z+t0,coefficients))}return z*sum},NumericalCurveMapper.prototype.computeArcLengths=function(){if(this.points){var lengths=[];lengths.push(0);for(var nPoints=this.closed?this.points.length:this.points.length-1,tl=0,i=0;i<nPoints;i++){tl+=this.computeArcLength(i),lengths.push(tl)}return lengths}},NumericalCurveMapper.prototype.inverse=function(idx,len){var step=1/(this._nSamples-1),_a=this.getSamples(idx),lengths=_a[0],slopes=_a[1],cis=_a[2],dis=_a[3];if(len>=lengths[lengths.length-1])return 1;if(len<=0)return 0;var i=Math.max(0,binarySearch(len,lengths)),ti=i*step;if(lengths[i]===len)return ti;var tdi=slopes[i],di=dis[i],ci=cis[i],ld=len-lengths[i];return((di*ld+ci)*ld+tdi)*ld+ti},NumericalCurveMapper.prototype.lengthAt=function(u){return u*this.arcLengths[this.arcLengths.length-1]},NumericalCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths),ti=i/(il-1);if(arcLengths[i]===targetArcLength)return ti;var len=targetArcLength-arcLengths[i];return(i+this.inverse(i,len))/(il-1)},NumericalCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=tIdx-subIdx;return(l1+this.computeArcLength(subIdx,0,t0))/totalLength},NumericalCurveMapper}(AbstractCurveMapper),CurveInterpolator=function(){function CurveInterpolator(points,options){void 0===options&&(options={});var _this=this;this._cache=new Map;var curveMapper=(options=__assign({tension:.5,alpha:0,closed:!1},options)).arcDivisions?new SegmentedCurveMapper(options.arcDivisions,(function(){return _this._invalidateCache()})):new NumericalCurveMapper(options.numericalApproximationOrder,options.numericalInverseSamples,(function(){return _this._invalidateCache()}));curveMapper.alpha=options.alpha,curveMapper.tension=options.tension,curveMapper.closed=options.closed,curveMapper.points=points,this._lmargin=options.lmargin||1-curveMapper.tension,this._curveMapper=curveMapper}return CurveInterpolator.prototype.getTimeFromPosition=function(position,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getT(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getPositionFromTime=function(t,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getU(clampInput?clamp(t,0,1):t)},CurveInterpolator.prototype.getPositionFromLength=function(length,clampInput){void 0===clampInput&&(clampInput=!1);var l=clampInput?clamp(length,0,this.length):length;return this._curveMapper.getU(l/this.length)},CurveInterpolator.prototype.getLengthAt=function(position,clampInput){return void 0===position&&(position=1),void 0===clampInput&&(clampInput=!1),this._curveMapper.lengthAt(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getTimeAtKnot=function(index){if(index<0||index>this.points.length-1)throw Error("Invalid index!");return 0===index?0:this.closed||index!==this.points.length-1?index/(this.closed?this.points.length:this.points.length-1):1},CurveInterpolator.prototype.getPositionAtKnot=function(index){return this.getPositionFromTime(this.getTimeAtKnot(index))},CurveInterpolator.prototype.getPointAtTime=function(t,target){return 0===(t=clamp(t,0,1))?copyValues(this.points[0],target):1===t?copyValues(this.closed?this.points[0]:this.points[this.points.length-1],target):this._curveMapper.evaluateForT(valueAtT,t,target)},CurveInterpolator.prototype.getPointAt=function(position,target){return this.getPointAtTime(this.getTimeFromPosition(position),target)},CurveInterpolator.prototype.getTangentAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getTangentAtTime(t,target)},CurveInterpolator.prototype.getTangentAtTime=function(t,target){return normalize(this._curveMapper.evaluateForT(derivativeAtT,t,target))},CurveInterpolator.prototype.getNormalAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getNormalAtTime(t,target)},CurveInterpolator.prototype.getNormalAtTime=function(t,target){var dt=normalize(this._curveMapper.evaluateForT(derivativeAtT,t));if(!(dt.length<2||dt.length>3)){var normal=target||new Array(dt.length);if(2===dt.length)return normal[0]=-dt[1],normal[1]=dt[0],normal;var ddt=normalize(this._curveMapper.evaluateForT(secondDerivativeAtT,t));return normalize(cross(cross(dt,ddt),dt),normal)}},CurveInterpolator.prototype.getCurvatureAt=function(position){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getCurvatureAtTime(t)},CurveInterpolator.prototype.getCurvatureAtTime=function(t){var dt=this._curveMapper.evaluateForT(derivativeAtT,t),ddt=this._curveMapper.evaluateForT(secondDerivativeAtT,t),tangent=normalize(dt,[]),curvature=0,direction=void 0;if(2===dt.length){if(0!==(denominator=Math.pow(dt[0]*dt[0]+dt[1]*dt[1],1.5))){var signedCurvature=(dt[0]*ddt[1]-dt[1]*ddt[0])/denominator;direction=signedCurvature<0?[tangent[1],-tangent[0]]:[-tangent[1],tangent[0]],curvature=Math.abs(signedCurvature)}}else if(3===dt.length){var a=magnitude(dt),cp=cross(dt,ddt);direction=normalize(cross(cp,dt)),0!==a&&(curvature=magnitude(cp)/Math.pow(a,3))}else{a=magnitude(dt);var b=magnitude(ddt),denominator=Math.pow(a,3),dotProduct=dot(dt,ddt);0!==denominator&&(curvature=Math.sqrt(Math.pow(a,2)*Math.pow(b,2)-Math.pow(dotProduct,2))/denominator)}return{curvature:curvature,radius:0!==curvature?1/curvature:0,tangent:tangent,direction:direction}},CurveInterpolator.prototype.getDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(derivativeAtT,t,target)},CurveInterpolator.prototype.getSecondDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(secondDerivativeAtT,t,target)},CurveInterpolator.prototype.getBoundingBox=function(from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),0===from&&1===to&&this._cache.has("bbox"))return this._cache.get("bbox");for(var min=[],max=[],t0=this.getTimeFromPosition(from),t1=this.getTimeFromPosition(to),start=this.getPointAtTime(t0),end=this.getPointAtTime(t1),nPoints=this.closed?this.points.length:this.points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var p2=getControlPoints(i-1,this_1.points,this_1.closed)[2];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(this_1.tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=this_1._curveMapper.getCoefficients(i-1),_loop_2=function(c){var _b=coefficients_1[c];getQuadRoots(3*_b[0],2*_b[1],_b[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},this_1=this,i=i0+1;i<=i1;i++)_loop_1(i);var bbox={min:min,max:max};return 0===from&&1===to&&this._cache.set("bbox",bbox),bbox},CurveInterpolator.prototype.getPoints=function(segments,returnType,from,to){if(void 0===segments&&(segments=100),void 0===from&&(from=0),void 0===to&&(to=1),!segments||segments<=0)throw Error("Invalid arguments passed to getPoints(). You must specify at least 1 sample/segment.");if(!(from<0||to>1||to<from)){for(var pts=[],d=0;d<=segments;d++){var u=0===from&&1===to?d/segments:from+d/segments*(to-from);pts.push(this.getPointAt(u,returnType&&new returnType))}return pts}},CurveInterpolator.prototype.getNearestPosition=function(point,threshold){var _this=this;if(void 0===threshold&&(threshold=1e-5),threshold<=0||!Number.isFinite(threshold))throw Error("Invalid threshold. Must be a number greater than zero!");var samples=10*this.points.length-1,pu=new Array(point.length),minDist=1/0,minU=0,lut=this.createLookupTable(samples);Array.from(lut.keys()).forEach((function(key){var c=lut.get(key),dist=distance(point,c);if(dist<minDist)return minDist=dist,minU=key,!0}));for(var minT=this.getTimeFromPosition(minU),bisect=function(t){if(t>=0&&t<=1){_this.getPointAtTime(t,pu);var dist=distance(point,pu);if(dist<minDist)return minDist=dist,minT=t,!0}},step=.005;step>threshold;)bisect(minT-step)||bisect(minT+step)||(step/=2);return{u:minU=this._curveMapper.getU(minT),distance:minDist,point:pu}},CurveInterpolator.prototype.getIntersects=function(v,axis,max,margin){var _this=this;void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var solutions=this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPointAtTime(t)}));return 1===Math.abs(max)?1===solutions.length?solutions[0]:null:solutions},CurveInterpolator.prototype.getIntersectsAsPositions=function(v,axis,max,margin){var _this=this;return void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin),this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPositionFromTime(t)}))},CurveInterpolator.prototype.getIntersectsAsTime=function(v,axis,max,margin){void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);for(var k=axis,solutions=new Set,nPoints=this.closed?this.points.length:this.points.length-1,i=0;i<nPoints&&(0===max||solutions.size<Math.abs(max));i+=1){var idx=max<0?nPoints-(i+1):i,_a=getControlPoints(idx,this.points,this.closed),p1=_a[1],p2=_a[2],coefficients=this._curveMapper.getCoefficients(idx),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),v-margin<=vmax&&v+margin>=vmin){var ts=findRootsOfT(v,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),0!==max&&solutions.size===Math.abs(max))break}}}return Array.from(solutions)},CurveInterpolator.prototype.createLookupTable=function(samples,from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),!samples||samples<=1)throw Error("Invalid arguments passed to createLookupTable(). You must specify at least 2 samples.");if(!(from<0||to>1||to<from)){var cacheKey="lut_".concat(samples,"_").concat(from,"_").concat(to);if(!this._cache.has(cacheKey)){for(var lut=new Map,d=0;d<samples;d++){var u=0===from&&1===to?d/(samples-1):from+d/(samples-1)*(to-from),point=this.getPointAt(u);lut.set(u,point)}this._cache.set(cacheKey,lut)}return this._cache.get(cacheKey)}},CurveInterpolator.prototype.forEach=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to forEach(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;positions.forEach((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in forEach!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});prev={u:u,t:t,i:i,value:current}}))},CurveInterpolator.prototype.map=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;return positions.map((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});return prev={u:u,t:t,i:i,value:current},current}))},CurveInterpolator.prototype.reduce=function(func,initialValue,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);return positions.reduce((function(acc,u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u);return func({acc:acc,u:u,t:t,i:i})}),initialValue)},CurveInterpolator.prototype._invalidateCache=function(){return this._cache=new Map,this},CurveInterpolator.prototype.reset=function(){this._curveMapper.reset()},Object.defineProperty(CurveInterpolator.prototype,"points",{get:function(){return this._curveMapper.points},set:function(pts){this._curveMapper.points=pts},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"tension",{get:function(){return this._curveMapper.tension},set:function(t){this._curveMapper.tension=t},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"alpha",{get:function(){return this._curveMapper.alpha},set:function(a){this._curveMapper.alpha=a},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"closed",{get:function(){return this._curveMapper.closed},set:function(isClosed){this._curveMapper.closed=isClosed},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"length",{get:function(){return this._curveMapper.lengthAt(1)},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minX",{get:function(){return this.getBoundingBox().min[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxX",{get:function(){return this.getBoundingBox().max[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minY",{get:function(){return this.getBoundingBox().min[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxY",{get:function(){return this.getBoundingBox().max[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minZ",{get:function(){return this.getBoundingBox().min[2]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxZ",{get:function(){return this.getBoundingBox().max[2]},enumerable:!1,configurable:!0}),CurveInterpolator}(),Point=function(){function Point(x,y,z,w){void 0===x&&(x=0),void 0===y&&(y=0),void 0===z&&(z=null),void 0===w&&(w=null),this.x=x,this.y=y,this.z=z,this.w=w}return Object.defineProperty(Point.prototype,0,{get:function(){return this.x},set:function(x){this.x=x},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,1,{get:function(){return this.y},set:function(y){this.y=y},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,2,{get:function(){return this.z},set:function(z){this.z=z},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,3,{get:function(){return this.w},set:function(w){this.w=w},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,"length",{get:function(){return Number.isFinite(this.w)?4:Number.isFinite(this.z)?3:2},enumerable:!1,configurable:!0}),Point}(),CurveInterpolator2D=function(_super){function CurveInterpolator2D(points,tension,arcDivisions,closed,alpha){return void 0===tension&&(tension=.5),void 0===arcDivisions&&(arcDivisions=300),void 0===closed&&(closed=!1),void 0===alpha&&(alpha=0),_super.call(this,points.map((function(p){return[p[0],p[1]]})),{tension:tension,alpha:alpha,arcDivisions:arcDivisions,closed:closed})||this}return __extends(CurveInterpolator2D,_super),CurveInterpolator2D.prototype.x=function(y,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(y,1,max,margin);return 1===Math.abs(max)?res[0]:res.map((function(d){return d[0]}))},CurveInterpolator2D.prototype.y=function(x,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(x,0,max,margin);return 1===Math.abs(max)?res[1]:res.map((function(d){return d[1]}))},CurveInterpolator2D.prototype.getNormalAt=function(position,target){return normalize(orthogonal(this.getTangentAt(position,target)))},CurveInterpolator2D.prototype.getAngleAt=function(position){var tan=this.getTangentAt(position);return Math.atan2(tan[1],tan[0])},CurveInterpolator2D.prototype.getBoundingBox=function(from,to){void 0===from&&(from=0),void 0===to&&(to=1);var bbox=_super.prototype.getBoundingBox.call(this,from,to);return{x1:bbox.min[0],x2:bbox.max[0],y1:bbox.min[1],y2:bbox.max[1],min:bbox.min,max:bbox.max}},CurveInterpolator2D}(CurveInterpolator);function getPointAtT(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(valueAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))}function getTangentAtT(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(derivativeAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))}function valuesLookup(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0,processRefAxis:!1},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,processRefAxis=_a.processRefAxis,k=axis,solutions=[],nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var _b=getControlPoints(max<0?nPoints-(i+1):i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){for(var coord=[],c=0;c<p0.length;c++){var v=void 0;v=c!==k||processRefAxis?valueAtT(ts[j],coefficients[c]):lookup,coord[c]=v}if(solutions.push(coord),solutions.length===Math.abs(max))return solutions}}}return solutions}function positionsLookup(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,k=axis,solutions=new Set,nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var idx=max<0?points.length-i:i,_b=getControlPoints(i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),solutions.size===Math.abs(max))return Array.from(solutions)}}}return Array.from(solutions)}function getBoundingBox(points,options){void 0===options&&(options={});for(var _a=__assign({tension:.5,alpha:0,closed:!1,from:0,to:1},options),tension=_a.tension,alpha=_a.alpha,closed=_a.closed,t0=_a.from,t1=_a.to,nPoints=closed?points.length:points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),start=getPointAtT(t0,points,{tension:tension,alpha:alpha,closed:closed}),end=getPointAtT(t1,points,{tension:tension,alpha:alpha,closed:closed}),min=[],max=[],c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var _b=getControlPoints(i-1,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],p3=_b[3];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=calculateCoefficients(p0,p1,p2,p3,{tension:tension,alpha:alpha}),_loop_2=function(c){var _c=coefficients_1[c];getQuadRoots(3*_c[0],2*_c[1],_c[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},i=i0+1;i<=i1;i++)_loop_1(i);return{min:min,max:max}}export{CurveInterpolator,CurveInterpolator2D,EPS,SegmentedCurveMapper as LinearCurveMapper,NumericalCurveMapper,Point,binarySearch,calcKnotSequence,calculateCoefficients,clamp,copyValues,cross,derivativeAtT,distance,dot,evaluateForT,extrapolateControlPoint,fill,findRootsOfT,getBoundingBox,getControlPoints,getCubicRoots,getPointAtT,getQuadRoots,getSegmentIndexAndT,getTangentAtT,magnitude,map,normalize,orthogonal,positionsLookup,reduce,secondDerivativeAtT,simplify2d,sumOfSquares,valueAtT,valuesLookup};

2

dist/index.js

@@ -15,2 +15,2 @@ !function(global,factory){"object"==typeof exports&&"undefined"!=typeof module?factory(exports):"function"==typeof define&&define.amd?define(["exports"],factory):factory((global="undefined"!=typeof globalThis?globalThis:global||self)["curve-interpolator"]={})}(this,(function(exports){"use strict";

and limitations under the License.
***************************************************************************** */var extendStatics=function(d,b){return extendStatics=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(d,b){d.__proto__=b}||function(d,b){for(var p in b)b.hasOwnProperty(p)&&(d[p]=b[p])},extendStatics(d,b)};function __extends(d,b){function __(){this.constructor=d}extendStatics(d,b),d.prototype=null===b?Object.create(b):(__.prototype=b.prototype,new __)}var __assign=function(){return __assign=Object.assign||function(t){for(var s,i=1,n=arguments.length;i<n;i++)for(var p in s=arguments[i])Object.prototype.hasOwnProperty.call(s,p)&&(t[p]=s[p]);return t},__assign.apply(this,arguments)};function extrapolateControlPoint(u,v){for(var e=new Array(u.length),i=0;i<u.length;i++)e[i]=2*u[i]-v[i];return e}function getControlPoints(idx,points,closed){var p0,p1,p2,p3,maxIndex=points.length-1;if(closed)p0=points[idx-1<0?maxIndex:idx-1],p1=points[idx%points.length],p2=points[(idx+1)%points.length],p3=points[(idx+2)%points.length];else{if(idx===maxIndex)throw Error("There is no spline segment at this index for a closed curve!");p1=points[idx],p2=points[idx+1],p0=idx>0?points[idx-1]:extrapolateControlPoint(p1,p2),p3=idx<maxIndex-1?points[idx+2]:extrapolateControlPoint(p2,p1)}return[p0,p1,p2,p3]}function getSegmentIndexAndT(ct,points,closed){void 0===closed&&(closed=!1);var nPoints=closed?points.length:points.length-1;if(1===ct)return{index:nPoints-1,weight:1};var p=nPoints*ct,index=Math.floor(p);return{index:index,weight:p-index}}function fill(v,val){for(var i=0;i<v.length;i++)v[i]=val;return v}function map(v,func){for(var i=0;i<v.length;i++)v[i]=func(v[i],i);return v}function reduce(v,func,r){void 0===r&&(r=0);for(var i=0;i<v.length;i++)r=func(r,v[i],i);return r}function copyValues(source,target){target=target||new Array(source.length);for(var i=0;i<source.length;i++)target[i]=source[i];return target}function clamp(value,min,max){return void 0===min&&(min=0),void 0===max&&(max=1),value<min?min:value>max?max:value}function binarySearch(targetValue,accumulatedValues){var min=accumulatedValues[0];if(targetValue>=accumulatedValues[accumulatedValues.length-1])return accumulatedValues.length-1;if(targetValue<=min)return 0;for(var left=0,right=accumulatedValues.length-1;left<=right;){var mid=Math.floor((left+right)/2),lMid=accumulatedValues[mid];if(lMid<targetValue)left=mid+1;else{if(!(lMid>targetValue))return mid;right=mid-1}}return Math.max(0,right)}var EPS=Math.pow(2,-42);function cuberoot(x){var y=Math.pow(Math.abs(x),1/3);return x<0?-y:y}function getQuadRoots(a,b,c){if(Math.abs(a)<EPS)return Math.abs(b)<EPS?[]:[-c/b];var D=b*b-4*a*c;return Math.abs(D)<EPS?[-b/(2*a)]:D>0?[(-b+Math.sqrt(D))/(2*a),(-b-Math.sqrt(D))/(2*a)]:[]}function getCubicRoots(a,b,c,d){if(Math.abs(a)<EPS)return getQuadRoots(b,c,d);var roots,p=(3*a*c-b*b)/(3*a*a),q=(2*b*b*b-9*a*b*c+27*a*a*d)/(27*a*a*a);if(Math.abs(p)<EPS)roots=[cuberoot(-q)];else if(Math.abs(q)<EPS)roots=[0].concat(p<0?[Math.sqrt(-p),-Math.sqrt(-p)]:[]);else{var D=q*q/4+p*p*p/27;if(Math.abs(D)<EPS)roots=[-1.5*q/p,3*q/p];else if(D>0){roots=[(u=cuberoot(-q/2-Math.sqrt(D)))-p/(3*u)]}else{var u=2*Math.sqrt(-p/3),t=Math.acos(3*q/p/u)/3,k=2*Math.PI/3;roots=[u*Math.cos(t),u*Math.cos(t-k),u*Math.cos(t-2*k)]}}for(var i=0;i<roots.length;i++)roots[i]-=b/(3*a);return roots}function dot(v1,v2){if(v1.length!==v2.length)throw Error("Vectors must be of equal length!");for(var p=0,k=0;k<v1.length;k++)p+=v1[k]*v2[k];return p}function cross(v1,v2,target){if(!(v1.length>3)){target=target||new Array(3);var ax=v1[0],ay=v1[1],az=v1[2]||0,bx=v2[0],by=v2[1],bz=v2[2]||0;return target[0]=ay*bz-az*by,target[1]=az*bx-ax*bz,target[2]=ax*by-ay*bx,target}}function sumOfSquares(v1,v2){for(var sumOfSquares=0,i=0;i<v1.length;i++)sumOfSquares+=(v1[i]-v2[i])*(v1[i]-v2[i]);return sumOfSquares}function magnitude(v){for(var sumOfSquares=0,i=0;i<v.length;i++)sumOfSquares+=v[i]*v[i];return Math.sqrt(sumOfSquares)}function distance(p1,p2){var sqrs=sumOfSquares(p1,p2);return 0===sqrs?0:Math.sqrt(sqrs)}function normalize(v,target){var u=target?copyValues(v,target):v,squared=reduce(u,(function(s,c){return s+Math.pow(c,2)})),l=Math.sqrt(squared);return 0===l?fill(u,0):map(u,(function(c){return c/l}))}function orthogonal(v,target){if(v.length>2)throw Error("Only supported for 2d vectors");var u=target?copyValues(v,target):v,x=-u[1];return u[1]=u[0],u[0]=x,u}function calcKnotSequence(p0,p1,p2,p3,alpha){if(void 0===alpha&&(alpha=0),0===alpha)return[0,1,2,3];var deltaT=function(u,v){return Math.pow(sumOfSquares(u,v),.5*alpha)},t1=deltaT(p1,p0),t2=deltaT(p2,p1)+t1;return[0,t1,t2,deltaT(p3,p2)+t2]}function calculateCoefficients(p0,p1,p2,p3,options){for(var tension=Number.isFinite(options.tension)?options.tension:.5,alpha=Number.isFinite(options.alpha)?options.alpha:null,knotSequence=alpha>0?calcKnotSequence(p0,p1,p2,p3,alpha):null,coefficientsList=new Array(p0.length),k=0;k<p0.length;k++){var u=0,v=0,v0=p0[k],v1=p1[k],v2=p2[k],v3=p3[k];if(knotSequence){var t0=knotSequence[0],t1=knotSequence[1],t2=knotSequence[2],t3=knotSequence[3];t1-t2!=0&&(t0-t1!=0&&t0-t2!=0&&(u=(1-tension)*(t2-t1)*((v0-v1)/(t0-t1)-(v0-v2)/(t0-t2)+(v1-v2)/(t1-t2))),t1-t3!=0&&t2-t3!=0&&(v=(1-tension)*(t2-t1)*((v1-v2)/(t1-t2)-(v1-v3)/(t1-t3)+(v2-v3)/(t2-t3))))}else u=(1-tension)*(v2-v0)*.5,v=(1-tension)*(v3-v1)*.5;var a=2*v1-2*v2+u+v,b=-3*v1+3*v2-2*u-v,d=v1;coefficientsList[k]=[a,b,u,d]}return coefficientsList}function valueAtT(t,coefficients){var t2=t*t,t3=t*t2;return coefficients[0]*t3+coefficients[1]*t2+coefficients[2]*t+coefficients[3]}function derivativeAtT(t,coefficients){var t2=t*t;return 3*coefficients[0]*t2+2*coefficients[1]*t+coefficients[2]}function secondDerivativeAtT(t,coefficients){return 6*coefficients[0]*t+2*coefficients[1]}function findRootsOfT(lookup,coefficients){var a=coefficients[0],b=coefficients[1],c=coefficients[2],x=coefficients[3]-lookup;return 0===a&&0===b&&0===c&&0===x?[0]:getCubicRoots(a,b,c,x).filter((function(t){return t>-EPS&&t<=1+EPS})).map((function(t){return clamp(t,0,1)}))}function evaluateForT(func,t,coefficients,target){void 0===target&&(target=null),target=target||new Array(coefficients.length);for(var k=0;k<coefficients.length;k++)target[k]=func(t,coefficients[k]);return target}var AbstractCurveMapper=function(){function AbstractCurveMapper(onInvalidateCache){void 0===onInvalidateCache&&(onInvalidateCache=null),this._alpha=0,this._tension=.5,this._closed=!1,this._onInvalidateCache=null,this._onInvalidateCache=onInvalidateCache,this._cache={arcLengths:null,coefficients:null}}return AbstractCurveMapper.prototype._invalidateCache=function(){this.points&&(this._cache={arcLengths:null,coefficients:null},this._onInvalidateCache&&this._onInvalidateCache())},Object.defineProperty(AbstractCurveMapper.prototype,"alpha",{get:function(){return this._alpha},set:function(alpha){Number.isFinite(alpha)&&alpha!==this._alpha&&(this._invalidateCache(),this._alpha=alpha)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"tension",{get:function(){return this._tension},set:function(tension){Number.isFinite(tension)&&tension!==this._tension&&(this._invalidateCache(),this._tension=tension)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"points",{get:function(){return this._points},set:function(points){if(!points||points.length<2)throw Error("At least 2 control points are required!");this._points=points,this._invalidateCache()},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"closed",{get:function(){return this._closed},set:function(closed){closed=!!closed,this._closed!==closed&&(this._invalidateCache(),this._closed=closed)},enumerable:!1,configurable:!0}),AbstractCurveMapper.prototype.reset=function(){this._invalidateCache()},AbstractCurveMapper.prototype.evaluateForT=function(func,t,target){var _a=getSegmentIndexAndT(t,this.points,this.closed),index=_a.index;return evaluateForT(func,_a.weight,this.getCoefficients(index),target)},AbstractCurveMapper.prototype.getCoefficients=function(idx){if(this.points){if(this._cache.coefficients||(this._cache.coefficients=new Map),!this._cache.coefficients.has(idx)){var _a=getControlPoints(idx,this.points,this.closed),coefficients=calculateCoefficients(_a[0],_a[1],_a[2],_a[3],{tension:this.tension,alpha:this.alpha});this._cache.coefficients.set(idx,coefficients)}return this._cache.coefficients.get(idx)}},AbstractCurveMapper}(),SegmentedCurveMapper=function(_super){function SegmentedCurveMapper(subDivisions,onInvalidateCache){void 0===subDivisions&&(subDivisions=300),void 0===onInvalidateCache&&(onInvalidateCache=null);var _this=_super.call(this,onInvalidateCache)||this;return _this._subDivisions=subDivisions,_this}return __extends(SegmentedCurveMapper,_super),Object.defineProperty(SegmentedCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),SegmentedCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null},SegmentedCurveMapper.prototype.computeArcLengths=function(){var current,lengths=[],last=this.evaluateForT(valueAtT,0),sum=0;lengths.push(0);for(var p=1;p<=this._subDivisions;p++)sum+=distance(current=this.evaluateForT(valueAtT,p/this._subDivisions),last),lengths.push(sum),last=current;return lengths},SegmentedCurveMapper.prototype.lengthAt=function(u){var arcLengths=this.arcLengths;return u*arcLengths[arcLengths.length-1]},SegmentedCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths);if(arcLengths[i]===targetArcLength)return i/(il-1);var lengthBefore=arcLengths[i];return(i+(targetArcLength-lengthBefore)/(arcLengths[i+1]-lengthBefore))/(il-1)},SegmentedCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=subIdx/al;return(l1+distance(this.evaluateForT(valueAtT,t0),this.evaluateForT(valueAtT,t)))/totalLength},SegmentedCurveMapper}(AbstractCurveMapper),lut=[[[-.906179845938664,.23692688505618908],[-.5384693101056831,.47862867049936647],[0,.5688888888888889],[.5384693101056831,.47862867049936647],[.906179845938664,.23692688505618908]],[[-.932469514203152,.17132449237917036],[-.6612093864662645,.3607615730481386],[-.2386191860831969,.46791393457269104],[.2386191860831969,.46791393457269104],[.6612093864662645,.3607615730481386],[.932469514203152,.17132449237917036]],[[-.9491079123427585,.1294849661688697],[-.7415311855993945,.27970539148927664],[-.4058451513773972,.3818300505051189],[0,.4179591836734694],[.4058451513773972,.3818300505051189],[.7415311855993945,.27970539148927664],[.9491079123427585,.1294849661688697]],[[-.9602898564975363,.10122853629037626],[-.7966664774136267,.22238103445337448],[-.525532409916329,.31370664587788727],[-.1834346424956498,.362683783378362],[.1834346424956498,.362683783378362],[.525532409916329,.31370664587788727],[.7966664774136267,.22238103445337448],[.9602898564975363,.10122853629037626]],[[-.9681602395076261,.08127438836157441],[-.8360311073266358,.1806481606948574],[-.6133714327005904,.26061069640293544],[-.3242534234038089,.31234707704000286],[0,.3302393550012598],[.3242534234038089,.31234707704000286],[.6133714327005904,.26061069640293544],[.8360311073266358,.1806481606948574],[.9681602395076261,.08127438836157441]],[[-.9739065285171717,.06667134430868814],[-.8650633666889845,.1494513491505806],[-.6794095682990244,.21908636251598204],[-.4333953941292472,.26926671930999635],[-.14887433898163122,.29552422471475287],[.14887433898163122,.29552422471475287],[.4333953941292472,.26926671930999635],[.6794095682990244,.21908636251598204],[.8650633666889845,.1494513491505806],[.9739065285171717,.06667134430868814]],[[-.978228658146056,.0556685671161736],[-.887062599768095,.125580369464904],[-.730152005574049,.186290210927734],[-.519096129206811,.23319376459199],[-.269543155952344,.262804544510246],[0,.2729250867779],[.269543155952344,.262804544510246],[.519096129206811,.23319376459199],[.730152005574049,.186290210927734],[.887062599768095,.125580369464904],[.978228658146056,.0556685671161736]],[[-.981560634246719,.0471753363865118],[-.904117256370474,.106939325995318],[-.769902674194304,.160078328543346],[-.587317954286617,.203167426723065],[-.36783149899818,.233492536538354],[-.125233408511468,.249147045813402],[.125233408511468,.249147045813402],[.36783149899818,.233492536538354],[.587317954286617,.203167426723065],[.769902674194304,.160078328543346],[.904117256370474,.106939325995318],[.981560634246719,.0471753363865118]],[[-.984183054718588,.0404840047653158],[-.917598399222977,.0921214998377284],[-.801578090733309,.138873510219787],[-.64234933944034,.178145980761945],[-.448492751036446,.207816047536888],[-.230458315955134,.226283180262897],[0,.232551553230873],[.230458315955134,.226283180262897],[.448492751036446,.207816047536888],[.64234933944034,.178145980761945],[.801578090733309,.138873510219787],[.917598399222977,.0921214998377284],[.984183054718588,.0404840047653158]],[[-.986283808696812,.0351194603317518],[-.928434883663573,.0801580871597602],[-.827201315069764,.121518570687903],[-.687292904811685,.157203167158193],[-.515248636358154,.185538397477937],[-.319112368927889,.205198463721295],[-.108054948707343,.215263853463157],[.108054948707343,.215263853463157],[.319112368927889,.205198463721295],[.515248636358154,.185538397477937],[.687292904811685,.157203167158193],[.827201315069764,.121518570687903],[.928434883663573,.0801580871597602],[.986283808696812,.0351194603317518]],[[-.987992518020485,.0307532419961172],[-.937273392400705,.0703660474881081],[-.848206583410427,.107159220467171],[-.72441773136017,.139570677926154],[-.570972172608538,.166269205816993],[-.394151347077563,.186161000015562],[-.201194093997434,.198431485327111],[0,.202578241925561],[.201194093997434,.198431485327111],[.394151347077563,.186161000015562],[.570972172608538,.166269205816993],[.72441773136017,.139570677926154],[.848206583410427,.107159220467171],[.937273392400705,.0703660474881081],[.987992518020485,.0307532419961172]],[[-.989400934991649,.027152459411754],[-.944575023073232,.0622535239386478],[-.865631202387831,.0951585116824927],[-.755404408355003,.124628971255533],[-.617876244402643,.149595988816576],[-.458016777657227,.169156519395002],[-.281603550779258,.182603415044923],[-.0950125098376374,.189450610455068],[.0950125098376374,.189450610455068],[.281603550779258,.182603415044923],[.458016777657227,.169156519395002],[.617876244402643,.149595988816576],[.755404408355003,.124628971255533],[.865631202387831,.0951585116824927],[.944575023073232,.0622535239386478],[.989400934991649,.027152459411754]],[[-.990575475314417,.0241483028685479],[-.950675521768767,.0554595293739872],[-.880239153726985,.0850361483171791],[-.781514003896801,.111883847193403],[-.65767115921669,.135136368468525],[-.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NumericalCurveMapper=function(_super){function NumericalCurveMapper(nQuadraturePoints,nInverseSamples,onInvalidateCache){void 0===nQuadraturePoints&&(nQuadraturePoints=24),void 0===nInverseSamples&&(nInverseSamples=21);var _this=_super.call(this,onInvalidateCache)||this;return _this._nSamples=21,_this._gauss=function(order){if(order<5||order>maxOrder)throw Error("Order for Gaussian Quadrature must be in the range of ".concat(5," and ").concat(maxOrder,"."));return lut[order-5]}(nQuadraturePoints),_this._nSamples=nInverseSamples,_this}return __extends(NumericalCurveMapper,_super),NumericalCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null,this._cache.samples=null},Object.defineProperty(NumericalCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),NumericalCurveMapper.prototype.getSamples=function(idx){if(this.points){if(this._cache.samples||(this._cache.samples=new Map),!this._cache.samples.has(idx)){for(var samples=this._nSamples,lengths=[],slopes=[],coefficients=this.getCoefficients(idx),i=0;i<samples;++i){var ti=i/(samples-1);lengths.push(this.computeArcLength(idx,0,ti));var dtln=magnitude(evaluateForT(derivativeAtT,ti,coefficients)),slope=0===dtln?0:1/dtln;this.tension>.95&&(slope=clamp(slope,-1,1)),slopes.push(slope)}var nCoeff=samples-1,dis=[],cis=[],li_prev=lengths[0],tdi_prev=slopes[0],step=1/nCoeff;for(i=0;i<nCoeff;++i){var li=li_prev,lDiff=(li_prev=lengths[i+1])-li,tdi=tdi_prev,tdi_next=slopes[i+1];tdi_prev=tdi_next;var si=step/lDiff,di=(tdi+tdi_next-2*si)/(lDiff*lDiff),ci=(3*si-2*tdi-tdi_next)/lDiff;dis.push(di),cis.push(ci)}this._cache.samples.set(idx,[lengths,slopes,cis,dis])}return this._cache.samples.get(idx)}},NumericalCurveMapper.prototype.computeArcLength=function(index,t0,t1){if(void 0===t0&&(t0=0),void 0===t1&&(t1=1),t0===t1)return 0;for(var coefficients=this.getCoefficients(index),z=.5*(t1-t0),sum=0,i=0;i<this._gauss.length;i++){var _a=this._gauss[i],T=_a[0];sum+=_a[1]*magnitude(evaluateForT(derivativeAtT,z*T+z+t0,coefficients))}return z*sum},NumericalCurveMapper.prototype.computeArcLengths=function(){if(this.points){var lengths=[];lengths.push(0);for(var nPoints=this.closed?this.points.length:this.points.length-1,tl=0,i=0;i<nPoints;i++){tl+=this.computeArcLength(i),lengths.push(tl)}return lengths}},NumericalCurveMapper.prototype.inverse=function(idx,len){var step=1/(this._nSamples-1),_a=this.getSamples(idx),lengths=_a[0],slopes=_a[1],cis=_a[2],dis=_a[3];if(len>=lengths[lengths.length-1])return 1;if(len<=0)return 0;var i=Math.max(0,binarySearch(len,lengths)),ti=i*step;if(lengths[i]===len)return ti;var tdi=slopes[i],di=dis[i],ci=cis[i],ld=len-lengths[i];return((di*ld+ci)*ld+tdi)*ld+ti},NumericalCurveMapper.prototype.lengthAt=function(u){return u*this.arcLengths[this.arcLengths.length-1]},NumericalCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths),ti=i/(il-1);if(arcLengths[i]===targetArcLength)return ti;var len=targetArcLength-arcLengths[i];return(i+this.inverse(i,len))/(il-1)},NumericalCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=tIdx-subIdx;return(l1+this.computeArcLength(subIdx,0,t0))/totalLength},NumericalCurveMapper}(AbstractCurveMapper),CurveInterpolator=function(){function CurveInterpolator(points,options){void 0===options&&(options={});var _this=this;this._cache=new Map;var curveMapper=(options=__assign({tension:.5,alpha:0,closed:!1},options)).arcDivisions?new SegmentedCurveMapper(options.arcDivisions,(function(){return _this._invalidateCache()})):new NumericalCurveMapper(options.numericalApproximationOrder,options.numericalInverseSamples,(function(){return _this._invalidateCache()}));curveMapper.alpha=options.alpha,curveMapper.tension=options.tension,curveMapper.closed=options.closed,curveMapper.points=points,this._lmargin=options.lmargin||1-curveMapper.tension,this._curveMapper=curveMapper}return CurveInterpolator.prototype.getTimeFromPosition=function(position,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getT(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getPositionFromTime=function(t,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getU(clampInput?clamp(t,0,1):t)},CurveInterpolator.prototype.getPositionFromLength=function(length,clampInput){void 0===clampInput&&(clampInput=!1);var l=clampInput?clamp(length,0,this.length):length;return this._curveMapper.getU(l/this.length)},CurveInterpolator.prototype.getLengthAt=function(position,clampInput){return void 0===position&&(position=1),void 0===clampInput&&(clampInput=!1),this._curveMapper.lengthAt(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getTimeAtKnot=function(index){if(index<0||index>this.points.length-1)throw Error("Invalid index!");return 0===index?0:this.closed||index!==this.points.length-1?index/(this.closed?this.points.length:this.points.length-1):1},CurveInterpolator.prototype.getPositionAtKnot=function(index){return this.getPositionFromTime(this.getTimeAtKnot(index))},CurveInterpolator.prototype.getPointAtTime=function(t,target){return 0===(t=clamp(t,0,1))?copyValues(this.points[0],target):1===t?copyValues(this.closed?this.points[0]:this.points[this.points.length-1],target):this._curveMapper.evaluateForT(valueAtT,t,target)},CurveInterpolator.prototype.getPointAt=function(position,target){return this.getPointAtTime(this.getTimeFromPosition(position),target)},CurveInterpolator.prototype.getTangentAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getTangentAtTime(t,target)},CurveInterpolator.prototype.getTangentAtTime=function(t,target){return normalize(this._curveMapper.evaluateForT(derivativeAtT,t,target))},CurveInterpolator.prototype.getNormalAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getNormalAtTime(t,target)},CurveInterpolator.prototype.getNormalAtTime=function(t,target){var dt=normalize(this._curveMapper.evaluateForT(derivativeAtT,t));if(!(dt.length<2||dt.length>3)){var normal=target||new Array(dt.length);if(2===dt.length)return normal[0]=-dt[1],normal[1]=dt[0],normal;var ddt=normalize(this._curveMapper.evaluateForT(secondDerivativeAtT,t));return normalize(cross(cross(dt,ddt),dt),normal)}},CurveInterpolator.prototype.getCurvatureAt=function(position){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getCurvatureAtTime(t)},CurveInterpolator.prototype.getCurvatureAtTime=function(t){var dt=this._curveMapper.evaluateForT(derivativeAtT,t),ddt=this._curveMapper.evaluateForT(secondDerivativeAtT,t),tangent=normalize(dt,[]),curvature=0,direction=void 0;if(2===dt.length){if(0!==(denominator=Math.pow(dt[0]*dt[0]+dt[1]*dt[1],1.5))){var signedCurvature=(dt[0]*ddt[1]-dt[1]*ddt[0])/denominator;direction=signedCurvature<0?[tangent[1],-tangent[0]]:[-tangent[1],tangent[0]],curvature=Math.abs(signedCurvature)}}else if(3===dt.length){var a=magnitude(dt),cp=cross(dt,ddt);direction=normalize(cross(cp,dt)),0!==a&&(curvature=magnitude(cp)/Math.pow(a,3))}else{a=magnitude(dt);var b=magnitude(ddt),denominator=Math.pow(a,3),dotProduct=dot(dt,ddt);0!==denominator&&(curvature=Math.sqrt(Math.pow(a,2)*Math.pow(b,2)-Math.pow(dotProduct,2))/denominator)}return{curvature:curvature,radius:0!==curvature?1/curvature:0,tangent:tangent,direction:direction}},CurveInterpolator.prototype.getDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(derivativeAtT,t,target)},CurveInterpolator.prototype.getSecondDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(secondDerivativeAtT,t,target)},CurveInterpolator.prototype.getBoundingBox=function(from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),0===from&&1===to&&this._cache.has("bbox"))return this._cache.get("bbox");for(var min=[],max=[],t0=this.getTimeFromPosition(from),t1=this.getTimeFromPosition(to),start=this.getPointAtTime(t0),end=this.getPointAtTime(t1),nPoints=this.closed?this.points.length:this.points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var p2=getControlPoints(i-1,this_1.points,this_1.closed)[2];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(this_1.tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=this_1._curveMapper.getCoefficients(i-1),_loop_2=function(c){var _b=coefficients_1[c];getQuadRoots(3*_b[0],2*_b[1],_b[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},this_1=this,i=i0+1;i<=i1;i++)_loop_1(i);var bbox={min:min,max:max};return 0===from&&1===to&&this._cache.set("bbox",bbox),bbox},CurveInterpolator.prototype.getPoints=function(segments,returnType,from,to){if(void 0===segments&&(segments=100),void 0===from&&(from=0),void 0===to&&(to=1),!segments||segments<=0)throw Error("Invalid arguments passed to getPoints(). You must specify at least 1 sample/segment.");if(!(from<0||to>1||to<from)){for(var pts=[],d=0;d<=segments;d++){var u=0===from&&1===to?d/segments:from+d/segments*(to-from);pts.push(this.getPointAt(u,returnType&&new returnType))}return pts}},CurveInterpolator.prototype.getNearestPosition=function(point,threshold){var _this=this;if(void 0===threshold&&(threshold=1e-5),threshold<=0||!Number.isFinite(threshold))throw Error("Invalid threshold. Must be a number greater than zero!");var samples=10*this.points.length-1,pu=new Array(point.length),minDist=1/0,minU=0,lut=this.createLookupTable(samples);Array.from(lut.keys()).forEach((function(key){var c=lut.get(key),dist=distance(point,c);if(dist<minDist)return minDist=dist,minU=key,!0}));for(var minT=this.getTimeFromPosition(minU),bisect=function(t){if(t>=0&&t<=1){_this.getPointAtTime(t,pu);var dist=distance(point,pu);if(dist<minDist)return minDist=dist,minT=t,!0}},step=.005;step>threshold;)bisect(minT-step)||bisect(minT+step)||(step/=2);return{u:minU=this._curveMapper.getU(minT),distance:minDist,point:pu}},CurveInterpolator.prototype.getIntersects=function(v,axis,max,margin){var _this=this;void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var solutions=this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPointAtTime(t)}));return 1===Math.abs(max)?1===solutions.length?solutions[0]:null:solutions},CurveInterpolator.prototype.getIntersectsAsPositions=function(v,axis,max,margin){var _this=this;return void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin),this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPositionFromTime(t)}))},CurveInterpolator.prototype.getIntersectsAsTime=function(v,axis,max,margin){void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);for(var k=axis,solutions=new Set,nPoints=this.closed?this.points.length:this.points.length-1,i=0;i<nPoints&&(0===max||solutions.size<Math.abs(max));i+=1){var idx=max<0?nPoints-(i+1):i,_a=getControlPoints(idx,this.points,this.closed),p1=_a[1],p2=_a[2],coefficients=this._curveMapper.getCoefficients(idx),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),v-margin<=vmax&&v+margin>=vmin){var ts=findRootsOfT(v,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),0!==max&&solutions.size===Math.abs(max))break}}}return Array.from(solutions)},CurveInterpolator.prototype.createLookupTable=function(samples,from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),!samples||samples<=1)throw Error("Invalid arguments passed to createLookupTable(). You must specify at least 2 samples.");if(!(from<0||to>1||to<from)){var cacheKey="lut_".concat(samples,"_").concat(from,"_").concat(to);if(!this._cache.has(cacheKey)){for(var lut=new Map,d=0;d<samples;d++){var u=0===from&&1===to?d/(samples-1):from+d/(samples-1)*(to-from),point=this.getPointAt(u);lut.set(u,point)}this._cache.set(cacheKey,lut)}return this._cache.get(cacheKey)}},CurveInterpolator.prototype.forEach=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to forEach(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;positions.forEach((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in forEach!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});prev={u:u,t:t,i:i,value:current}}))},CurveInterpolator.prototype.map=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;return positions.map((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});return prev={u:u,t:t,i:i,value:current},current}))},CurveInterpolator.prototype.reduce=function(func,initialValue,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);return positions.reduce((function(acc,u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u);return func({acc:acc,u:u,t:t,i:i})}),initialValue)},CurveInterpolator.prototype._invalidateCache=function(){return this._cache=new Map,this},CurveInterpolator.prototype.reset=function(){this._curveMapper.reset()},Object.defineProperty(CurveInterpolator.prototype,"points",{get:function(){return this._curveMapper.points},set:function(pts){this._curveMapper.points=pts},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"tension",{get:function(){return this._curveMapper.tension},set:function(t){this._curveMapper.tension=t},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"alpha",{get:function(){return this._curveMapper.alpha},set:function(a){this._curveMapper.alpha=a},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"closed",{get:function(){return this._curveMapper.closed},set:function(isClosed){this._curveMapper.closed=isClosed},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"length",{get:function(){return this._curveMapper.lengthAt(1)},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minX",{get:function(){return this.getBoundingBox().min[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxX",{get:function(){return this.getBoundingBox().max[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minY",{get:function(){return this.getBoundingBox().min[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxY",{get:function(){return this.getBoundingBox().max[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minZ",{get:function(){return this.getBoundingBox().min[2]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxZ",{get:function(){return this.getBoundingBox().max[2]},enumerable:!1,configurable:!0}),CurveInterpolator}(),Point=function(){function Point(x,y,z,w){void 0===x&&(x=0),void 0===y&&(y=0),void 0===z&&(z=null),void 0===w&&(w=null),this.x=x,this.y=y,this.z=z,this.w=w}return Object.defineProperty(Point.prototype,0,{get:function(){return this.x},set:function(x){this.x=x},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,1,{get:function(){return this.y},set:function(y){this.y=y},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,2,{get:function(){return this.z},set:function(z){this.z=z},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,3,{get:function(){return this.w},set:function(w){this.w=w},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,"length",{get:function(){return Number.isFinite(this.w)?4:Number.isFinite(this.z)?3:2},enumerable:!1,configurable:!0}),Point}(),CurveInterpolator2D=function(_super){function CurveInterpolator2D(points,tension,arcDivisions,closed,alpha){return void 0===tension&&(tension=.5),void 0===arcDivisions&&(arcDivisions=300),void 0===closed&&(closed=!1),void 0===alpha&&(alpha=0),_super.call(this,points.map((function(p){return[p[0],p[1]]})),{tension:tension,alpha:alpha,arcDivisions:arcDivisions,closed:closed})||this}return __extends(CurveInterpolator2D,_super),CurveInterpolator2D.prototype.x=function(y,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(y,1,max,margin);return 1===Math.abs(max)?res[0]:res.map((function(d){return d[0]}))},CurveInterpolator2D.prototype.y=function(x,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(x,0,max,margin);return 1===Math.abs(max)?res[1]:res.map((function(d){return d[1]}))},CurveInterpolator2D.prototype.getNormalAt=function(position,target){return normalize(orthogonal(this.getTangentAt(position,target)))},CurveInterpolator2D.prototype.getAngleAt=function(position){var tan=this.getTangentAt(position);return Math.atan2(tan[1],tan[0])},CurveInterpolator2D.prototype.getBoundingBox=function(from,to){void 0===from&&(from=0),void 0===to&&(to=1);var bbox=_super.prototype.getBoundingBox.call(this,from,to);return{x1:bbox.min[0],x2:bbox.max[0],y1:bbox.min[1],y2:bbox.max[1],min:bbox.min,max:bbox.max}},CurveInterpolator2D}(CurveInterpolator);function getPointAtT(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(valueAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))}exports.CurveInterpolator=CurveInterpolator,exports.CurveInterpolator2D=CurveInterpolator2D,exports.EPS=EPS,exports.LinearCurveMapper=SegmentedCurveMapper,exports.NumericalCurveMapper=NumericalCurveMapper,exports.Point=Point,exports.binarySearch=binarySearch,exports.calcKnotSequence=calcKnotSequence,exports.calculateCoefficients=calculateCoefficients,exports.clamp=clamp,exports.copyValues=copyValues,exports.cross=cross,exports.derivativeAtT=derivativeAtT,exports.distance=distance,exports.dot=dot,exports.evaluateForT=evaluateForT,exports.extrapolateControlPoint=extrapolateControlPoint,exports.fill=fill,exports.findRootsOfT=findRootsOfT,exports.getBoundingBox=function(points,options){void 0===options&&(options={});for(var _a=__assign({tension:.5,alpha:0,closed:!1,from:0,to:1},options),tension=_a.tension,alpha=_a.alpha,closed=_a.closed,t0=_a.from,t1=_a.to,nPoints=closed?points.length:points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),start=getPointAtT(t0,points,{tension:tension,alpha:alpha,closed:closed}),end=getPointAtT(t1,points,{tension:tension,alpha:alpha,closed:closed}),min=[],max=[],c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var _b=getControlPoints(i-1,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],p3=_b[3];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=calculateCoefficients(p0,p1,p2,p3,{tension:tension,alpha:alpha}),_loop_2=function(c){var _c=coefficients_1[c];getQuadRoots(3*_c[0],2*_c[1],_c[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},i=i0+1;i<=i1;i++)_loop_1(i);return{min:min,max:max}},exports.getControlPoints=getControlPoints,exports.getCubicRoots=getCubicRoots,exports.getPointAtT=getPointAtT,exports.getQuadRoots=getQuadRoots,exports.getSegmentIndexAndT=getSegmentIndexAndT,exports.getTangentAtT=function(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(derivativeAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))},exports.magnitude=magnitude,exports.map=map,exports.normalize=normalize,exports.orthogonal=orthogonal,exports.positionsLookup=function(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,k=axis,solutions=new Set,nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var idx=max<0?points.length-i:i,_b=getControlPoints(i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),solutions.size===Math.abs(max))return Array.from(solutions)}}}return Array.from(solutions)},exports.reduce=reduce,exports.secondDerivativeAtT=secondDerivativeAtT,exports.simplify2d=function(inputArr,maxOffset,maxDistance){var _a;if(void 0===maxOffset&&(maxOffset=.001),void 0===maxDistance&&(maxDistance=10),inputArr.length<=4)return inputArr;for(var _b=inputArr[0],o0=_b[0],o1=_b[1],arr=inputArr.map((function(d){return[d[0]-o0,d[1]-o1]})),_c=arr[0],a0=_c[0],a1=_c[1],sim=[inputArr[0]],i=1;i+1<arr.length;i++){var _d=arr[i],t0=_d[0],t1=_d[1],_e=arr[i+1],b0=_e[0],b1=_e[1];if(b0-t0!=0||b1-t1!=0){var proximity=Math.abs(a0*b1-a1*b0+b0*t1-b1*t0+a1*t0-a0*t1)/Math.sqrt(Math.pow(b0-a0,2)+Math.pow(b1-a1,2)),dir=[a0-t0,a1-t1],len=Math.sqrt(Math.pow(dir[0],2)+Math.pow(dir[1],2));(proximity>maxOffset||len>=maxDistance)&&(sim.push([t0+o0,t1+o1]),a0=(_a=[t0,t1])[0],a1=_a[1])}}var last=arr[arr.length-1];return sim.push([last[0]+o0,last[1]+o1]),sim},exports.sumOfSquares=sumOfSquares,exports.valueAtT=valueAtT,exports.valuesLookup=function(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0,processRefAxis:!1},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,processRefAxis=_a.processRefAxis,k=axis,solutions=[],nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var _b=getControlPoints(max<0?nPoints-(i+1):i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){for(var coord=[],c=0;c<p0.length;c++){var v=void 0;v=c!==k||processRefAxis?valueAtT(ts[j],coefficients[c]):lookup,coord[c]=v}if(solutions.push(coord),solutions.length===Math.abs(max))return solutions}}}return solutions}}));
***************************************************************************** */var extendStatics=function(d,b){return extendStatics=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(d,b){d.__proto__=b}||function(d,b){for(var p in b)b.hasOwnProperty(p)&&(d[p]=b[p])},extendStatics(d,b)};function __extends(d,b){function __(){this.constructor=d}extendStatics(d,b),d.prototype=null===b?Object.create(b):(__.prototype=b.prototype,new __)}var __assign=function(){return __assign=Object.assign||function(t){for(var s,i=1,n=arguments.length;i<n;i++)for(var p in s=arguments[i])Object.prototype.hasOwnProperty.call(s,p)&&(t[p]=s[p]);return t},__assign.apply(this,arguments)};function extrapolateControlPoint(u,v){for(var e=new Array(u.length),i=0;i<u.length;i++)e[i]=2*u[i]-v[i];return e}function getControlPoints(idx,points,closed){var p0,p1,p2,p3,maxIndex=points.length-1;if(closed)p0=points[idx-1<0?maxIndex:idx-1],p1=points[idx%points.length],p2=points[(idx+1)%points.length],p3=points[(idx+2)%points.length];else{if(idx===maxIndex)throw Error("There is no spline segment at this index for a closed curve!");p1=points[idx],p2=points[idx+1],p0=idx>0?points[idx-1]:extrapolateControlPoint(p1,p2),p3=idx<maxIndex-1?points[idx+2]:extrapolateControlPoint(p2,p1)}return[p0,p1,p2,p3]}function getSegmentIndexAndT(ct,points,closed){void 0===closed&&(closed=!1);var nPoints=closed?points.length:points.length-1;if(1===ct)return{index:nPoints-1,weight:1};var p=nPoints*ct,index=Math.floor(p);return{index:index,weight:p-index}}function fill(v,val){for(var i=0;i<v.length;i++)v[i]=val;return v}function map(v,func){for(var i=0;i<v.length;i++)v[i]=func(v[i],i);return v}function reduce(v,func,r){void 0===r&&(r=0);for(var i=0;i<v.length;i++)r=func(r,v[i],i);return r}function copyValues(source,target){target=target||new Array(source.length);for(var i=0;i<source.length;i++)target[i]=source[i];return target}function clamp(value,min,max){return void 0===min&&(min=0),void 0===max&&(max=1),value<min?min:value>max?max:value}function binarySearch(targetValue,accumulatedValues){var min=accumulatedValues[0];if(targetValue>=accumulatedValues[accumulatedValues.length-1])return accumulatedValues.length-1;if(targetValue<=min)return 0;for(var left=0,right=accumulatedValues.length-1;left<=right;){var mid=Math.floor((left+right)/2),lMid=accumulatedValues[mid];if(lMid<targetValue)left=mid+1;else{if(!(lMid>targetValue))return mid;right=mid-1}}return Math.max(0,right)}var EPS=Math.pow(2,-42);function cuberoot(x){var y=Math.pow(Math.abs(x),1/3);return x<0?-y:y}function getQuadRoots(a,b,c){if(Math.abs(a)<EPS)return Math.abs(b)<EPS?[]:[-c/b];var D=b*b-4*a*c;return Math.abs(D)<EPS?[-b/(2*a)]:D>0?[(-b+Math.sqrt(D))/(2*a),(-b-Math.sqrt(D))/(2*a)]:[]}function getCubicRoots(a,b,c,d){if(Math.abs(a)<EPS)return getQuadRoots(b,c,d);var roots,p=(3*a*c-b*b)/(3*a*a),q=(2*b*b*b-9*a*b*c+27*a*a*d)/(27*a*a*a);if(Math.abs(p)<EPS)roots=[cuberoot(-q)];else if(Math.abs(q)<EPS)roots=[0].concat(p<0?[Math.sqrt(-p),-Math.sqrt(-p)]:[]);else{var D=q*q/4+p*p*p/27;if(Math.abs(D)<EPS)roots=[-1.5*q/p,3*q/p];else if(D>0){roots=[(u=cuberoot(-q/2-Math.sqrt(D)))-p/(3*u)]}else{var u=2*Math.sqrt(-p/3),t=Math.acos(3*q/p/u)/3,k=2*Math.PI/3;roots=[u*Math.cos(t),u*Math.cos(t-k),u*Math.cos(t-2*k)]}}for(var i=0;i<roots.length;i++)roots[i]-=b/(3*a);return roots}function dot(v1,v2){if(v1.length!==v2.length)throw Error("Vectors must be of equal length!");for(var p=0,k=0;k<v1.length;k++)p+=v1[k]*v2[k];return p}function cross(v1,v2,target){if(!(v1.length>3)){target=target||new Array(3);var ax=v1[0],ay=v1[1],az=v1[2]||0,bx=v2[0],by=v2[1],bz=v2[2]||0;return target[0]=ay*bz-az*by,target[1]=az*bx-ax*bz,target[2]=ax*by-ay*bx,target}}function sumOfSquares(v1,v2){for(var sumOfSquares=0,i=0;i<v1.length;i++)sumOfSquares+=(v1[i]-v2[i])*(v1[i]-v2[i]);return sumOfSquares}function magnitude(v){for(var sumOfSquares=0,i=0;i<v.length;i++)sumOfSquares+=v[i]*v[i];return Math.sqrt(sumOfSquares)}function distance(p1,p2){var sqrs=sumOfSquares(p1,p2);return 0===sqrs?0:Math.sqrt(sqrs)}function normalize(v,target){var u=target?copyValues(v,target):v,squared=reduce(u,(function(s,c){return s+Math.pow(c,2)})),l=Math.sqrt(squared);return 0===l?fill(u,0):map(u,(function(c){return c/l}))}function orthogonal(v,target){if(v.length>2)throw Error("Only supported for 2d vectors");var u=target?copyValues(v,target):v,x=-u[1];return u[1]=u[0],u[0]=x,u}function calcKnotSequence(p0,p1,p2,p3,alpha){if(void 0===alpha&&(alpha=0),0===alpha)return[0,1,2,3];var deltaT=function(u,v){return Math.pow(sumOfSquares(u,v),.5*alpha)},t1=deltaT(p1,p0),t2=deltaT(p2,p1)+t1;return[0,t1,t2,deltaT(p3,p2)+t2]}function calculateCoefficients(p0,p1,p2,p3,options){for(var tension=Number.isFinite(options.tension)?options.tension:.5,alpha=Number.isFinite(options.alpha)?options.alpha:null,knotSequence=alpha>0?calcKnotSequence(p0,p1,p2,p3,alpha):null,coefficientsList=new Array(p0.length),k=0;k<p0.length;k++){var u=0,v=0,v0=p0[k],v1=p1[k],v2=p2[k],v3=p3[k];if(knotSequence){var t0=knotSequence[0],t1=knotSequence[1],t2=knotSequence[2],t3=knotSequence[3];t1-t2!=0&&(t0-t1!=0&&t0-t2!=0&&(u=(1-tension)*(t2-t1)*((v0-v1)/(t0-t1)-(v0-v2)/(t0-t2)+(v1-v2)/(t1-t2))),t1-t3!=0&&t2-t3!=0&&(v=(1-tension)*(t2-t1)*((v1-v2)/(t1-t2)-(v1-v3)/(t1-t3)+(v2-v3)/(t2-t3))))}else u=(1-tension)*(v2-v0)*.5,v=(1-tension)*(v3-v1)*.5;var a=2*v1-2*v2+u+v,b=-3*v1+3*v2-2*u-v,c=u,d=v1;coefficientsList[k]=[a,b,c,d]}return coefficientsList}function valueAtT(t,coefficients){var t2=t*t,t3=t*t2;return coefficients[0]*t3+coefficients[1]*t2+coefficients[2]*t+coefficients[3]}function derivativeAtT(t,coefficients){var t2=t*t;return 3*coefficients[0]*t2+2*coefficients[1]*t+coefficients[2]}function secondDerivativeAtT(t,coefficients){return 6*coefficients[0]*t+2*coefficients[1]}function findRootsOfT(lookup,coefficients){var a=coefficients[0],b=coefficients[1],c=coefficients[2],x=coefficients[3]-lookup;return 0===a&&0===b&&0===c&&0===x?[0]:getCubicRoots(a,b,c,x).filter((function(t){return t>-EPS&&t<=1+EPS})).map((function(t){return clamp(t,0,1)}))}function evaluateForT(func,t,coefficients,target){void 0===target&&(target=null),target=target||new Array(coefficients.length);for(var k=0;k<coefficients.length;k++)target[k]=func(t,coefficients[k]);return target}var AbstractCurveMapper=function(){function AbstractCurveMapper(onInvalidateCache){void 0===onInvalidateCache&&(onInvalidateCache=null),this._alpha=0,this._tension=.5,this._closed=!1,this._onInvalidateCache=null,this._onInvalidateCache=onInvalidateCache,this._cache={arcLengths:null,coefficients:null}}return AbstractCurveMapper.prototype._invalidateCache=function(){this.points&&(this._cache={arcLengths:null,coefficients:null},this._onInvalidateCache&&this._onInvalidateCache())},Object.defineProperty(AbstractCurveMapper.prototype,"alpha",{get:function(){return this._alpha},set:function(alpha){Number.isFinite(alpha)&&alpha!==this._alpha&&(this._invalidateCache(),this._alpha=alpha)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"tension",{get:function(){return this._tension},set:function(tension){Number.isFinite(tension)&&tension!==this._tension&&(this._invalidateCache(),this._tension=tension)},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"points",{get:function(){return this._points},set:function(points){if(!points||points.length<2)throw Error("At least 2 control points are required!");this._points=points,this._invalidateCache()},enumerable:!1,configurable:!0}),Object.defineProperty(AbstractCurveMapper.prototype,"closed",{get:function(){return this._closed},set:function(closed){closed=!!closed,this._closed!==closed&&(this._invalidateCache(),this._closed=closed)},enumerable:!1,configurable:!0}),AbstractCurveMapper.prototype.reset=function(){this._invalidateCache()},AbstractCurveMapper.prototype.evaluateForT=function(func,t,target){var _a=getSegmentIndexAndT(t,this.points,this.closed),index=_a.index;return evaluateForT(func,_a.weight,this.getCoefficients(index),target)},AbstractCurveMapper.prototype.getCoefficients=function(idx){if(this.points){if(this._cache.coefficients||(this._cache.coefficients=new Map),!this._cache.coefficients.has(idx)){var _a=getControlPoints(idx,this.points,this.closed),coefficients=calculateCoefficients(_a[0],_a[1],_a[2],_a[3],{tension:this.tension,alpha:this.alpha});this._cache.coefficients.set(idx,coefficients)}return this._cache.coefficients.get(idx)}},AbstractCurveMapper}(),SegmentedCurveMapper=function(_super){function SegmentedCurveMapper(subDivisions,onInvalidateCache){void 0===subDivisions&&(subDivisions=300),void 0===onInvalidateCache&&(onInvalidateCache=null);var _this=_super.call(this,onInvalidateCache)||this;return _this._subDivisions=subDivisions,_this}return __extends(SegmentedCurveMapper,_super),Object.defineProperty(SegmentedCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),SegmentedCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null},SegmentedCurveMapper.prototype.computeArcLengths=function(){var current,lengths=[],last=this.evaluateForT(valueAtT,0),sum=0;lengths.push(0);for(var p=1;p<=this._subDivisions;p++)sum+=distance(current=this.evaluateForT(valueAtT,p/this._subDivisions),last),lengths.push(sum),last=current;return lengths},SegmentedCurveMapper.prototype.lengthAt=function(u){var arcLengths=this.arcLengths;return u*arcLengths[arcLengths.length-1]},SegmentedCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths);if(arcLengths[i]===targetArcLength)return i/(il-1);var lengthBefore=arcLengths[i];return(i+(targetArcLength-lengthBefore)/(arcLengths[i+1]-lengthBefore))/(il-1)},SegmentedCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var 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NumericalCurveMapper=function(_super){function NumericalCurveMapper(nQuadraturePoints,nInverseSamples,onInvalidateCache){void 0===nQuadraturePoints&&(nQuadraturePoints=24),void 0===nInverseSamples&&(nInverseSamples=21);var _this=_super.call(this,onInvalidateCache)||this;return _this._nSamples=21,_this._gauss=function(order){if(order<5||order>maxOrder)throw Error("Order for Gaussian Quadrature must be in the range of ".concat(5," and ").concat(maxOrder,"."));return lut[order-5]}(nQuadraturePoints),_this._nSamples=nInverseSamples,_this}return __extends(NumericalCurveMapper,_super),NumericalCurveMapper.prototype._invalidateCache=function(){_super.prototype._invalidateCache.call(this),this._cache.arcLengths=null,this._cache.samples=null},Object.defineProperty(NumericalCurveMapper.prototype,"arcLengths",{get:function(){return this._cache.arcLengths||(this._cache.arcLengths=this.computeArcLengths()),this._cache.arcLengths},enumerable:!1,configurable:!0}),NumericalCurveMapper.prototype.getSamples=function(idx){if(this.points){if(this._cache.samples||(this._cache.samples=new Map),!this._cache.samples.has(idx)){for(var samples=this._nSamples,lengths=[],slopes=[],coefficients=this.getCoefficients(idx),i=0;i<samples;++i){var ti=i/(samples-1);lengths.push(this.computeArcLength(idx,0,ti));var dtln=magnitude(evaluateForT(derivativeAtT,ti,coefficients)),slope=0===dtln?0:1/dtln;this.tension>.95&&(slope=clamp(slope,-1,1)),slopes.push(slope)}var nCoeff=samples-1,dis=[],cis=[],li_prev=lengths[0],tdi_prev=slopes[0],step=1/nCoeff;for(i=0;i<nCoeff;++i){var li=li_prev,lDiff=(li_prev=lengths[i+1])-li,tdi=tdi_prev,tdi_next=slopes[i+1];tdi_prev=tdi_next;var si=step/lDiff,di=(tdi+tdi_next-2*si)/(lDiff*lDiff),ci=(3*si-2*tdi-tdi_next)/lDiff;dis.push(di),cis.push(ci)}this._cache.samples.set(idx,[lengths,slopes,cis,dis])}return this._cache.samples.get(idx)}},NumericalCurveMapper.prototype.computeArcLength=function(index,t0,t1){if(void 0===t0&&(t0=0),void 0===t1&&(t1=1),t0===t1)return 0;for(var coefficients=this.getCoefficients(index),z=.5*(t1-t0),sum=0,i=0;i<this._gauss.length;i++){var _a=this._gauss[i],T=_a[0];sum+=_a[1]*magnitude(evaluateForT(derivativeAtT,z*T+z+t0,coefficients))}return z*sum},NumericalCurveMapper.prototype.computeArcLengths=function(){if(this.points){var lengths=[];lengths.push(0);for(var nPoints=this.closed?this.points.length:this.points.length-1,tl=0,i=0;i<nPoints;i++){tl+=this.computeArcLength(i),lengths.push(tl)}return lengths}},NumericalCurveMapper.prototype.inverse=function(idx,len){var step=1/(this._nSamples-1),_a=this.getSamples(idx),lengths=_a[0],slopes=_a[1],cis=_a[2],dis=_a[3];if(len>=lengths[lengths.length-1])return 1;if(len<=0)return 0;var i=Math.max(0,binarySearch(len,lengths)),ti=i*step;if(lengths[i]===len)return ti;var tdi=slopes[i],di=dis[i],ci=cis[i],ld=len-lengths[i];return((di*ld+ci)*ld+tdi)*ld+ti},NumericalCurveMapper.prototype.lengthAt=function(u){return u*this.arcLengths[this.arcLengths.length-1]},NumericalCurveMapper.prototype.getT=function(u){var arcLengths=this.arcLengths,il=arcLengths.length,targetArcLength=u*arcLengths[il-1],i=binarySearch(targetArcLength,arcLengths),ti=i/(il-1);if(arcLengths[i]===targetArcLength)return ti;var len=targetArcLength-arcLengths[i];return(i+this.inverse(i,len))/(il-1)},NumericalCurveMapper.prototype.getU=function(t){if(0===t)return 0;if(1===t)return 1;var arcLengths=this.arcLengths,al=arcLengths.length-1,totalLength=arcLengths[al],tIdx=t*al,subIdx=Math.floor(tIdx),l1=arcLengths[subIdx];if(tIdx===subIdx)return l1/totalLength;var t0=tIdx-subIdx;return(l1+this.computeArcLength(subIdx,0,t0))/totalLength},NumericalCurveMapper}(AbstractCurveMapper),CurveInterpolator=function(){function CurveInterpolator(points,options){void 0===options&&(options={});var _this=this;this._cache=new Map;var curveMapper=(options=__assign({tension:.5,alpha:0,closed:!1},options)).arcDivisions?new SegmentedCurveMapper(options.arcDivisions,(function(){return _this._invalidateCache()})):new NumericalCurveMapper(options.numericalApproximationOrder,options.numericalInverseSamples,(function(){return _this._invalidateCache()}));curveMapper.alpha=options.alpha,curveMapper.tension=options.tension,curveMapper.closed=options.closed,curveMapper.points=points,this._lmargin=options.lmargin||1-curveMapper.tension,this._curveMapper=curveMapper}return CurveInterpolator.prototype.getTimeFromPosition=function(position,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getT(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getPositionFromTime=function(t,clampInput){return void 0===clampInput&&(clampInput=!1),this._curveMapper.getU(clampInput?clamp(t,0,1):t)},CurveInterpolator.prototype.getPositionFromLength=function(length,clampInput){void 0===clampInput&&(clampInput=!1);var l=clampInput?clamp(length,0,this.length):length;return this._curveMapper.getU(l/this.length)},CurveInterpolator.prototype.getLengthAt=function(position,clampInput){return void 0===position&&(position=1),void 0===clampInput&&(clampInput=!1),this._curveMapper.lengthAt(clampInput?clamp(position,0,1):position)},CurveInterpolator.prototype.getTimeAtKnot=function(index){if(index<0||index>this.points.length-1)throw Error("Invalid index!");return 0===index?0:this.closed||index!==this.points.length-1?index/(this.closed?this.points.length:this.points.length-1):1},CurveInterpolator.prototype.getPositionAtKnot=function(index){return this.getPositionFromTime(this.getTimeAtKnot(index))},CurveInterpolator.prototype.getPointAtTime=function(t,target){return 0===(t=clamp(t,0,1))?copyValues(this.points[0],target):1===t?copyValues(this.closed?this.points[0]:this.points[this.points.length-1],target):this._curveMapper.evaluateForT(valueAtT,t,target)},CurveInterpolator.prototype.getPointAt=function(position,target){return this.getPointAtTime(this.getTimeFromPosition(position),target)},CurveInterpolator.prototype.getTangentAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getTangentAtTime(t,target)},CurveInterpolator.prototype.getTangentAtTime=function(t,target){return normalize(this._curveMapper.evaluateForT(derivativeAtT,t,target))},CurveInterpolator.prototype.getNormalAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getNormalAtTime(t,target)},CurveInterpolator.prototype.getNormalAtTime=function(t,target){var dt=normalize(this._curveMapper.evaluateForT(derivativeAtT,t));if(!(dt.length<2||dt.length>3)){var normal=target||new Array(dt.length);if(2===dt.length)return normal[0]=-dt[1],normal[1]=dt[0],normal;var ddt=normalize(this._curveMapper.evaluateForT(secondDerivativeAtT,t));return normalize(cross(cross(dt,ddt),dt),normal)}},CurveInterpolator.prototype.getCurvatureAt=function(position){var t=clamp(this.getTimeFromPosition(position),0,1);return this.getCurvatureAtTime(t)},CurveInterpolator.prototype.getCurvatureAtTime=function(t){var dt=this._curveMapper.evaluateForT(derivativeAtT,t),ddt=this._curveMapper.evaluateForT(secondDerivativeAtT,t),tangent=normalize(dt,[]),curvature=0,direction=void 0;if(2===dt.length){if(0!==(denominator=Math.pow(dt[0]*dt[0]+dt[1]*dt[1],1.5))){var signedCurvature=(dt[0]*ddt[1]-dt[1]*ddt[0])/denominator;direction=signedCurvature<0?[tangent[1],-tangent[0]]:[-tangent[1],tangent[0]],curvature=Math.abs(signedCurvature)}}else if(3===dt.length){var a=magnitude(dt),cp=cross(dt,ddt);direction=normalize(cross(cp,dt)),0!==a&&(curvature=magnitude(cp)/Math.pow(a,3))}else{a=magnitude(dt);var b=magnitude(ddt),denominator=Math.pow(a,3),dotProduct=dot(dt,ddt);0!==denominator&&(curvature=Math.sqrt(Math.pow(a,2)*Math.pow(b,2)-Math.pow(dotProduct,2))/denominator)}return{curvature:curvature,radius:0!==curvature?1/curvature:0,tangent:tangent,direction:direction}},CurveInterpolator.prototype.getDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(derivativeAtT,t,target)},CurveInterpolator.prototype.getSecondDerivativeAt=function(position,target){var t=clamp(this.getTimeFromPosition(position),0,1);return this._curveMapper.evaluateForT(secondDerivativeAtT,t,target)},CurveInterpolator.prototype.getBoundingBox=function(from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),0===from&&1===to&&this._cache.has("bbox"))return this._cache.get("bbox");for(var min=[],max=[],t0=this.getTimeFromPosition(from),t1=this.getTimeFromPosition(to),start=this.getPointAtTime(t0),end=this.getPointAtTime(t1),nPoints=this.closed?this.points.length:this.points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var p2=getControlPoints(i-1,this_1.points,this_1.closed)[2];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(this_1.tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=this_1._curveMapper.getCoefficients(i-1),_loop_2=function(c){var _b=coefficients_1[c];getQuadRoots(3*_b[0],2*_b[1],_b[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},this_1=this,i=i0+1;i<=i1;i++)_loop_1(i);var bbox={min:min,max:max};return 0===from&&1===to&&this._cache.set("bbox",bbox),bbox},CurveInterpolator.prototype.getPoints=function(segments,returnType,from,to){if(void 0===segments&&(segments=100),void 0===from&&(from=0),void 0===to&&(to=1),!segments||segments<=0)throw Error("Invalid arguments passed to getPoints(). You must specify at least 1 sample/segment.");if(!(from<0||to>1||to<from)){for(var pts=[],d=0;d<=segments;d++){var u=0===from&&1===to?d/segments:from+d/segments*(to-from);pts.push(this.getPointAt(u,returnType&&new returnType))}return pts}},CurveInterpolator.prototype.getNearestPosition=function(point,threshold){var _this=this;if(void 0===threshold&&(threshold=1e-5),threshold<=0||!Number.isFinite(threshold))throw Error("Invalid threshold. Must be a number greater than zero!");var samples=10*this.points.length-1,pu=new Array(point.length),minDist=1/0,minU=0,lut=this.createLookupTable(samples);Array.from(lut.keys()).forEach((function(key){var c=lut.get(key),dist=distance(point,c);if(dist<minDist)return minDist=dist,minU=key,!0}));for(var minT=this.getTimeFromPosition(minU),bisect=function(t){if(t>=0&&t<=1){_this.getPointAtTime(t,pu);var dist=distance(point,pu);if(dist<minDist)return minDist=dist,minT=t,!0}},step=.005;step>threshold;)bisect(minT-step)||bisect(minT+step)||(step/=2);return{u:minU=this._curveMapper.getU(minT),distance:minDist,point:pu}},CurveInterpolator.prototype.getIntersects=function(v,axis,max,margin){var _this=this;void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var solutions=this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPointAtTime(t)}));return 1===Math.abs(max)?1===solutions.length?solutions[0]:null:solutions},CurveInterpolator.prototype.getIntersectsAsPositions=function(v,axis,max,margin){var _this=this;return void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin),this.getIntersectsAsTime(v,axis,max,margin).map((function(t){return _this.getPositionFromTime(t)}))},CurveInterpolator.prototype.getIntersectsAsTime=function(v,axis,max,margin){void 0===axis&&(axis=0),void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);for(var k=axis,solutions=new Set,nPoints=this.closed?this.points.length:this.points.length-1,i=0;i<nPoints&&(0===max||solutions.size<Math.abs(max));i+=1){var idx=max<0?nPoints-(i+1):i,_a=getControlPoints(idx,this.points,this.closed),p1=_a[1],p2=_a[2],coefficients=this._curveMapper.getCoefficients(idx),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),v-margin<=vmax&&v+margin>=vmin){var ts=findRootsOfT(v,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),0!==max&&solutions.size===Math.abs(max))break}}}return Array.from(solutions)},CurveInterpolator.prototype.createLookupTable=function(samples,from,to){if(void 0===from&&(from=0),void 0===to&&(to=1),!samples||samples<=1)throw Error("Invalid arguments passed to createLookupTable(). You must specify at least 2 samples.");if(!(from<0||to>1||to<from)){var cacheKey="lut_".concat(samples,"_").concat(from,"_").concat(to);if(!this._cache.has(cacheKey)){for(var lut=new Map,d=0;d<samples;d++){var u=0===from&&1===to?d/(samples-1):from+d/(samples-1)*(to-from),point=this.getPointAt(u);lut.set(u,point)}this._cache.set(cacheKey,lut)}return this._cache.get(cacheKey)}},CurveInterpolator.prototype.forEach=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to forEach(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;positions.forEach((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in forEach!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});prev={u:u,t:t,i:i,value:current}}))},CurveInterpolator.prototype.map=function(func,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);var prev=null;return positions.map((function(u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u),current=func({u:u,t:t,i:i,prev:prev});return prev={u:u,t:t,i:i,value:current},current}))},CurveInterpolator.prototype.reduce=function(func,initialValue,samples,from,to){var _this=this;void 0===from&&(from=0),void 0===to&&(to=1);var positions=[];if(Number.isFinite(samples)){if(samples<=1)throw Error("Invalid arguments passed to map(). You must specify at least 2 samples.");for(var nSamples=samples,i=0;i<samples;i++){var u=0===from&&1===to?i/(nSamples-1):from+i/(nSamples-1)*(to-from);positions.push(u)}}else Array.isArray(samples)&&(positions=samples);return positions.reduce((function(acc,u,i){if(!Number.isFinite(u)||u<0||u>1)throw Error("Invalid position (u) for sample in map()!");var t=_this.getTimeFromPosition(u);return func({acc:acc,u:u,t:t,i:i})}),initialValue)},CurveInterpolator.prototype._invalidateCache=function(){return this._cache=new Map,this},CurveInterpolator.prototype.reset=function(){this._curveMapper.reset()},Object.defineProperty(CurveInterpolator.prototype,"points",{get:function(){return this._curveMapper.points},set:function(pts){this._curveMapper.points=pts},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"tension",{get:function(){return this._curveMapper.tension},set:function(t){this._curveMapper.tension=t},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"alpha",{get:function(){return this._curveMapper.alpha},set:function(a){this._curveMapper.alpha=a},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"closed",{get:function(){return this._curveMapper.closed},set:function(isClosed){this._curveMapper.closed=isClosed},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"length",{get:function(){return this._curveMapper.lengthAt(1)},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minX",{get:function(){return this.getBoundingBox().min[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxX",{get:function(){return this.getBoundingBox().max[0]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minY",{get:function(){return this.getBoundingBox().min[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxY",{get:function(){return this.getBoundingBox().max[1]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"minZ",{get:function(){return this.getBoundingBox().min[2]},enumerable:!1,configurable:!0}),Object.defineProperty(CurveInterpolator.prototype,"maxZ",{get:function(){return this.getBoundingBox().max[2]},enumerable:!1,configurable:!0}),CurveInterpolator}(),Point=function(){function Point(x,y,z,w){void 0===x&&(x=0),void 0===y&&(y=0),void 0===z&&(z=null),void 0===w&&(w=null),this.x=x,this.y=y,this.z=z,this.w=w}return Object.defineProperty(Point.prototype,0,{get:function(){return this.x},set:function(x){this.x=x},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,1,{get:function(){return this.y},set:function(y){this.y=y},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,2,{get:function(){return this.z},set:function(z){this.z=z},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,3,{get:function(){return this.w},set:function(w){this.w=w},enumerable:!1,configurable:!0}),Object.defineProperty(Point.prototype,"length",{get:function(){return Number.isFinite(this.w)?4:Number.isFinite(this.z)?3:2},enumerable:!1,configurable:!0}),Point}(),CurveInterpolator2D=function(_super){function CurveInterpolator2D(points,tension,arcDivisions,closed,alpha){return void 0===tension&&(tension=.5),void 0===arcDivisions&&(arcDivisions=300),void 0===closed&&(closed=!1),void 0===alpha&&(alpha=0),_super.call(this,points.map((function(p){return[p[0],p[1]]})),{tension:tension,alpha:alpha,arcDivisions:arcDivisions,closed:closed})||this}return __extends(CurveInterpolator2D,_super),CurveInterpolator2D.prototype.x=function(y,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(y,1,max,margin);return 1===Math.abs(max)?res[0]:res.map((function(d){return d[0]}))},CurveInterpolator2D.prototype.y=function(x,max,margin){void 0===max&&(max=0),void 0===margin&&(margin=this._lmargin);var res=this.getIntersects(x,0,max,margin);return 1===Math.abs(max)?res[1]:res.map((function(d){return d[1]}))},CurveInterpolator2D.prototype.getNormalAt=function(position,target){return normalize(orthogonal(this.getTangentAt(position,target)))},CurveInterpolator2D.prototype.getAngleAt=function(position){var tan=this.getTangentAt(position);return Math.atan2(tan[1],tan[0])},CurveInterpolator2D.prototype.getBoundingBox=function(from,to){void 0===from&&(from=0),void 0===to&&(to=1);var bbox=_super.prototype.getBoundingBox.call(this,from,to);return{x1:bbox.min[0],x2:bbox.max[0],y1:bbox.min[1],y2:bbox.max[1],min:bbox.min,max:bbox.max}},CurveInterpolator2D}(CurveInterpolator);function getPointAtT(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(valueAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))}exports.CurveInterpolator=CurveInterpolator,exports.CurveInterpolator2D=CurveInterpolator2D,exports.EPS=EPS,exports.LinearCurveMapper=SegmentedCurveMapper,exports.NumericalCurveMapper=NumericalCurveMapper,exports.Point=Point,exports.binarySearch=binarySearch,exports.calcKnotSequence=calcKnotSequence,exports.calculateCoefficients=calculateCoefficients,exports.clamp=clamp,exports.copyValues=copyValues,exports.cross=cross,exports.derivativeAtT=derivativeAtT,exports.distance=distance,exports.dot=dot,exports.evaluateForT=evaluateForT,exports.extrapolateControlPoint=extrapolateControlPoint,exports.fill=fill,exports.findRootsOfT=findRootsOfT,exports.getBoundingBox=function(points,options){void 0===options&&(options={});for(var _a=__assign({tension:.5,alpha:0,closed:!1,from:0,to:1},options),tension=_a.tension,alpha=_a.alpha,closed=_a.closed,t0=_a.from,t1=_a.to,nPoints=closed?points.length:points.length-1,i0=Math.floor(nPoints*t0),i1=Math.ceil(nPoints*t1),start=getPointAtT(t0,points,{tension:tension,alpha:alpha,closed:closed}),end=getPointAtT(t1,points,{tension:tension,alpha:alpha,closed:closed}),min=[],max=[],c=0;c<start.length;c++)min[c]=Math.min(start[c],end[c]),max[c]=Math.max(start[c],end[c]);for(var _loop_1=function(i){var _b=getControlPoints(i-1,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],p3=_b[3];if(i<i1)for(var c=0;c<p2.length;c++)p2[c]<min[c]&&(min[c]=p2[c]),p2[c]>max[c]&&(max[c]=p2[c]);if(tension<1){var w0_1=nPoints*t0-(i-1),w1_1=nPoints*t1-(i-1),valid=function(t){return t>-EPS&&t<=1+EPS&&(i-1!==i0||t>w0_1)&&(i!==i1||t<w1_1)},coefficients_1=calculateCoefficients(p0,p1,p2,p3,{tension:tension,alpha:alpha}),_loop_2=function(c){var _c=coefficients_1[c];getQuadRoots(3*_c[0],2*_c[1],_c[2]).filter(valid).forEach((function(t){var v=valueAtT(t,coefficients_1[c]);v<min[c]&&(min[c]=v),v>max[c]&&(max[c]=v)}))};for(c=0;c<coefficients_1.length;c++)_loop_2(c)}},i=i0+1;i<=i1;i++)_loop_1(i);return{min:min,max:max}},exports.getControlPoints=getControlPoints,exports.getCubicRoots=getCubicRoots,exports.getPointAtT=getPointAtT,exports.getQuadRoots=getQuadRoots,exports.getSegmentIndexAndT=getSegmentIndexAndT,exports.getTangentAtT=function(t,points,options,target){void 0===options&&(options={});var _a=getSegmentIndexAndT(t,points,!!options.closed),index=_a.index,weight=_a.weight,_b=getControlPoints(index,points,!!options.closed),p0=_b[0];return evaluateForT(derivativeAtT,weight,calculateCoefficients(p0,_b[1],_b[2],_b[3],options),target=target||new Array(p0.length))},exports.magnitude=magnitude,exports.map=map,exports.normalize=normalize,exports.orthogonal=orthogonal,exports.positionsLookup=function(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,k=axis,solutions=new Set,nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var idx=max<0?points.length-i:i,_b=getControlPoints(i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){var nt=(ts[j]+idx)/nPoints;if(solutions.add(nt),solutions.size===Math.abs(max))return Array.from(solutions)}}}return Array.from(solutions)},exports.reduce=reduce,exports.secondDerivativeAtT=secondDerivativeAtT,exports.simplify2d=function(inputArr,maxOffset,maxDistance){var _a;if(void 0===maxOffset&&(maxOffset=.001),void 0===maxDistance&&(maxDistance=10),inputArr.length<=4)return inputArr;for(var _b=inputArr[0],o0=_b[0],o1=_b[1],arr=inputArr.map((function(d){return[d[0]-o0,d[1]-o1]})),_c=arr[0],a0=_c[0],a1=_c[1],sim=[inputArr[0]],i=1;i+1<arr.length;i++){var _d=arr[i],t0=_d[0],t1=_d[1],_e=arr[i+1],b0=_e[0],b1=_e[1];if(b0-t0!=0||b1-t1!=0){var proximity=Math.abs(a0*b1-a1*b0+b0*t1-b1*t0+a1*t0-a0*t1)/Math.sqrt(Math.pow(b0-a0,2)+Math.pow(b1-a1,2)),dir=[a0-t0,a1-t1],len=Math.sqrt(Math.pow(dir[0],2)+Math.pow(dir[1],2));(proximity>maxOffset||len>=maxDistance)&&(sim.push([t0+o0,t1+o1]),a0=(_a=[t0,t1])[0],a1=_a[1])}}var last=arr[arr.length-1];return sim.push([last[0]+o0,last[1]+o1]),sim},exports.sumOfSquares=sumOfSquares,exports.valueAtT=valueAtT,exports.valuesLookup=function(lookup,points,options){for(var _a=__assign({axis:0,closed:!1,margin:.5,max:0,processRefAxis:!1},options),axis=_a.axis,closed=_a.closed,margin=_a.margin,max=_a.max,processRefAxis=_a.processRefAxis,k=axis,solutions=[],nPoints=closed?points.length:points.length-1,i=0;i<nPoints;i+=1){var _b=getControlPoints(max<0?nPoints-(i+1):i,points,closed),p0=_b[0],p1=_b[1],p2=_b[2],coefficients=calculateCoefficients(p0,p1,p2,_b[3],options),vmin=void 0,vmax=void 0;if(p1[k]<p2[k]?(vmin=p1[k],vmax=p2[k]):(vmin=p2[k],vmax=p1[k]),lookup-margin<=vmax&&lookup+margin>=vmin){var ts=findRootsOfT(lookup,coefficients[k]);max<0?ts.sort((function(a,b){return b-a})):max>=0&&ts.sort((function(a,b){return a-b}));for(var j=0;j<ts.length;j++)if(!(0===ts[j]&&i>0)){for(var coord=[],c=0;c<p0.length;c++){var v=void 0;v=c!==k||processRefAxis?valueAtT(ts[j],coefficients[c]):lookup,coord[c]=v}if(solutions.push(coord),solutions.length===Math.abs(max))return solutions}}}return solutions}}));

2

package.json
{
"private": false,
"name": "curve-interpolator",
"version": "3.1.0",
"version": "3.1.1",
"description": "Interpolate values on a Cardinal/Catmull-Rom spline curve",

@@ -6,0 +6,0 @@ "repository": "https://github.com/kjerandp/curve-interpolator",

LICENSE

Sorry, the diff of this file is not supported yet