bezier-js - npm Package Compare versions

Comparing version 2.5.1 to 2.6.0

bezier.js

@@ -1,1 +0,1 @@
-var Bezier=function(t){function r(i){if(n[i])return n[i].exports;var e=n[i]={exports:{},id:i,loaded:!1};return t[i].call(e.exports,e,e.exports,r),e.loaded=!0,e.exports}var n={};return r.m=t,r.c=n,r.p="",r(0)}([function(t,r,n){"use strict";t.exports=n(1)},function(t,r,n){"use strict";var i="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(t){return typeof t}:function(t){return t&&"function"==typeof Symbol&&t.constructor===Symbol&&t!==Symbol.prototype?"symbol":typeof t};!function(){function r(t,r,n,i,e){"undefined"==typeof e&&(e=.5);var o=y.projectionratio(e,t),s=1-o,u={x:o*r.x+s*i.x,y:o*r.y+s*i.y},a=y.abcratio(e,t),f={x:n.x+(n.x-u.x)/a,y:n.y+(n.y-u.y)/a};return{A:f,B:n,C:u}}var e=Math.abs,o=Math.min,s=Math.max,u=Math.cos,a=Math.sin,f=Math.acos,c=Math.sqrt,h=Math.PI,x={x:0,y:0,z:0},y=n(2),l=n(3),p=function(t){var r=t&&t.forEach?t:[].slice.call(arguments),n=!1;if("object"===i(r[0])){n=r.length;var o=[];r.forEach(function(t){["x","y","z"].forEach(function(r){"undefined"!=typeof t[r]&&o.push(t[r])})}),r=o}var s=!1,u=r.length;if(n){if(n>4){if(1!==arguments.length)throw new Error("Only new Bezier(point[]) is accepted for 4th and higher order curves");s=!0}}else if(6!==u&&8!==u&&9!==u&&12!==u&&1!==arguments.length)throw new Error("Only new Bezier(point[]) is accepted for 4th and higher order curves");var a=!s&&(9===u||12===u)||t&&t[0]&&"undefined"!=typeof t[0].z;this._3d=a;for(var f=[],c=0,h=a?3:2;c<u;c+=h){var x={x:r[c],y:r[c+1]};a&&(x.z=r[c+2]),f.push(x)}this.order=f.length-1,this.points=f;var l=["x","y"];a&&l.push("z"),this.dims=l,this.dimlen=l.length,function(t){for(var r=t.order,n=t.points,i=y.align(n,{p1:n[0],p2:n[r]}),o=0;o<i.length;o++)if(e(i[o].y)>1e-4)return void(t._linear=!1);t._linear=!0}(this),this._t1=0,this._t2=1,this.update()},v=n(4);p.SVGtoBeziers=function(t){return v(p,t)},p.quadraticFromPoints=function(t,n,i,e){if("undefined"==typeof e&&(e=.5),0===e)return new p(n,n,i);if(1===e)return new p(t,n,n);var o=r(2,t,n,i,e);return new p(t,o.A,i)},p.cubicFromPoints=function(t,n,i,e,o){"undefined"==typeof e&&(e=.5);var s=r(3,t,n,i,e);"undefined"==typeof o&&(o=y.dist(n,s.C));var u=o*(1-e)/e,a=y.dist(t,i),f=(i.x-t.x)/a,c=(i.y-t.y)/a,h=o*f,x=o*c,l=u*f,v=u*c,d={x:n.x-h,y:n.y-x},m={x:n.x+l,y:n.y+v},z=s.A,g={x:z.x+(d.x-z.x)/(1-e),y:z.y+(d.y-z.y)/(1-e)},b={x:z.x+(m.x-z.x)/e,y:z.y+(m.y-z.y)/e},_={x:t.x+(g.x-t.x)/e,y:t.y+(g.y-t.y)/e},w={x:i.x+(b.x-i.x)/(1-e),y:i.y+(b.y-i.y)/(1-e)};return new p(t,_,w,i)};var d=function(){return y};p.getUtils=d,p.PolyBezier=l,p.prototype={getUtils:d,valueOf:function(){return this.toString()},toString:function(){return y.pointsToString(this.points)},toSVG:function(t){if(this._3d)return!1;for(var r=this.points,n=r[0].x,i=r[0].y,e=["M",n,i,2===this.order?"Q":"C"],o=1,s=r.length;o<s;o++)e.push(r[o].x),e.push(r[o].y);return e.join(" ")},setRatios:function(t){if(t.length!==this.points.length)throw new Error("incorrect number of ratio values");this.ratios=t,this._lut=[]},update:function(){this._lut=[],this.dpoints=y.derive(this.points,this._3d),this.computedirection()},computedirection:function(){var t=this.points,r=y.angle(t[0],t[this.order],t[1]);this.clockwise=r>0},length:function(){return y.length(this.derivative.bind(this))},_lut:[],getLUT:function(t){if(t=t||100,this._lut.length===t)return this._lut;this._lut=[],t--;for(var r=0;r<=t;r++)this._lut.push(this.compute(r/t));return this._lut},on:function(t,r){r=r||5;for(var n,i=this.getLUT(),e=[],o=0,s=0;s<i.length;s++)n=i[s],y.dist(n,t)<r&&(e.push(n),o+=s/i.length);return!!e.length&&(o/=e.length)},project:function(t){var r,n,i,e,o=this.getLUT(),s=o.length-1,u=y.closest(o,t),a=u.mdist,f=u.mpos,c=(f-1)/s,h=(f+1)/s,x=.1/s;for(a+=1,n=c,r=n;n<h+x;n+=x)i=this.compute(n),e=y.dist(t,i),e<a&&(a=e,r=n);return i=this.compute(r),i.t=r,i.d=a,i},get:function(t){return this.compute(t)},point:function(t){return this.points[t]},compute:function(t){return this.ratios?y.computeWithRatios(t,this.points,this.ratios,this._3d):y.compute(t,this.points,this._3d,this.ratios)},raise:function(){for(var t,r,n,i=this.points,e=[i[0]],o=i.length,t=1;t<o;t++)r=i[t],n=i[t-1],e[t]={x:(o-t)/o*r.x+t/o*n.x,y:(o-t)/o*r.y+t/o*n.y};return e[o]=i[o-1],new p(e)},derivative:function(t){var r,n,i=1-t,e=0,o=this.dpoints[0];2===this.order&&(o=[o[0],o[1],x],r=i,n=t),3===this.order&&(r=i*i,n=i*t*2,e=t*t);var s={x:r*o[0].x+n*o[1].x+e*o[2].x,y:r*o[0].y+n*o[1].y+e*o[2].y};return this._3d&&(s.z=r*o[0].z+n*o[1].z+e*o[2].z),s},curvature:function(t){return y.curvature(t,this.points,this._3d)},inflections:function(){return y.inflections(this.points)},normal:function(t){return this._3d?this.__normal3(t):this.__normal2(t)},__normal2:function(t){var r=this.derivative(t),n=c(r.x*r.x+r.y*r.y);return{x:-r.y/n,y:r.x/n}},__normal3:function(t){var r=this.derivative(t),n=this.derivative(t+.01),i=c(r.x*r.x+r.y*r.y+r.z*r.z),e=c(n.x*n.x+n.y*n.y+n.z*n.z);r.x/=i,r.y/=i,r.z/=i,n.x/=e,n.y/=e,n.z/=e;var o={x:n.y*r.z-n.z*r.y,y:n.z*r.x-n.x*r.z,z:n.x*r.y-n.y*r.x},s=c(o.x*o.x+o.y*o.y+o.z*o.z);o.x/=s,o.y/=s,o.z/=s;var u=[o.x*o.x,o.x*o.y-o.z,o.x*o.z+o.y,o.x*o.y+o.z,o.y*o.y,o.y*o.z-o.x,o.x*o.z-o.y,o.y*o.z+o.x,o.z*o.z],a={x:u[0]*r.x+u[1]*r.y+u[2]*r.z,y:u[3]*r.x+u[4]*r.y+u[5]*r.z,z:u[6]*r.x+u[7]*r.y+u[8]*r.z};return a},hull:function(t){var r,n=this.points,i=[],e=[],o=0,s=0,u=0;for(e[o++]=n[0],e[o++]=n[1],e[o++]=n[2],3===this.order&&(e[o++]=n[3]);n.length>1;){for(i=[],s=0,u=n.length-1;s<u;s++)r=y.lerp(t,n[s],n[s+1]),e[o++]=r,i.push(r);n=i}return e},split:function(t,r){if(0===t&&r)return this.split(r).left;if(1===r)return this.split(t).right;var n=this.hull(t),i={left:new p(2===this.order?[n[0],n[3],n[5]]:[n[0],n[4],n[7],n[9]]),right:new 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r,n,i,e,o=this.reduce(),s=o.length-2,u=[];for(r=0;r<s;r++)i=o.slice(r,r+1),e=o.slice(r+2),n=this.curveintersects(i,e,t),u=u.concat(n);return u},curveintersects:function(t,r,n){var i=[];t.forEach(function(t){r.forEach(function(r){t.overlaps(r)&&i.push({left:t,right:r})})});var e=[];return i.forEach(function(t){var r=y.pairiteration(t.left,t.right,n);r.length>0&&(e=e.concat(r))}),e},arcs:function(t){t=t||.5;var r=[];return this._iterate(t,r)},_error:function(t,r,n,i){var o=(i-n)/4,s=this.get(n+o),u=this.get(i-o),a=y.dist(t,r),f=y.dist(t,s),c=y.dist(t,u);return e(f-a)+e(c-a)},_iterate:function(t,r){var n,i=0,e=1;do{n=0,e=1;var o,s,f,c,h,x=this.get(i),l=!1,p=!1,v=e,d=1,m=0;do{p=l,c=f,v=(i+e)/2,m++,o=this.get(v),s=this.get(e),f=y.getccenter(x,o,s),f.interval={start:i,end:e};var z=this._error(f,x,i,e);if(l=z<=t,h=p&&!l,h||(d=e),l){if(e>=1){if(f.interval.end=d=1,c=f,e>1){var g={x:f.x+f.r*u(f.e),y:f.y+f.r*a(f.e)};f.e+=y.angle({x:f.x,y:f.y},g,this.get(1))}break}e+=(e-i)/2}else 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i+s*a},lerp:function(t,r,n){var i={x:r.x+t*(n.x-r.x),y:r.y+t*(n.y-r.y)};return r.z&&n.z&&(i.z=r.z+t*(n.z-r.z)),i},pointToString:function(t){var r=t.x+"/"+t.y;return"undefined"!=typeof t.z&&(r+="/"+t.z),r},pointsToString:function(t){return"["+t.map(d.pointToString).join(", ")+"]"},copy:function(t){return JSON.parse(JSON.stringify(t))},angle:function(t,r,n){var i=r.x-t.x,e=r.y-t.y,o=n.x-t.x,u=n.y-t.y,a=i*u-e*o,f=i*o+e*u;return s(a,f)},round:function(t,r){var n=""+t,i=n.indexOf(".");return parseFloat(n.substring(0,i+1+r))},dist:function(t,r){var n=t.x-r.x,i=t.y-r.y;return u(n*n+i*i)},closest:function(t,r){var n,i,e=a(2,63);return t.forEach(function(t,o){i=d.dist(r,t),i<e&&(e=i,n=o)}),{mdist:e,mpos:n}},abcratio:function(t,n){if(2!==n&&3!==n)return!1;if("undefined"==typeof t)t=.5;else if(0===t||1===t)return t;var i=a(t,n)+a(1-t,n),e=i-1;return r(e/i)},projectionratio:function(t,r){if(2!==r&&3!==r)return!1;if("undefined"==typeof t)t=.5;else if(0===t||1===t)return t;var n=a(1-t,r),i=a(t,r)+n;return n/i},lli8:function(t,r,n,i,e,o,s,u){var a=(t*i-r*n)*(e-s)-(t-n)*(e*u-o*s),f=(t*i-r*n)*(o-u)-(r-i)*(e*u-o*s),c=(t-n)*(o-u)-(r-i)*(e-s);return 0!=c&&{x:a/c,y:f/c}},lli4:function(t,r,n,i){var e=t.x,o=t.y,s=r.x,u=r.y,a=n.x,f=n.y,c=i.x,h=i.y;return d.lli8(e,o,s,u,a,f,c,h)},lli:function(t,r){return d.lli4(t,t.c,r,r.c)},makeline:function(t,r){var i=n(1),e=t.x,o=t.y,s=r.x,u=r.y,a=(s-e)/3,f=(u-o)/3;return new i(e,o,e+a,o+f,e+2*a,o+2*f,s,u)},findbbox:function(t){var r=l,n=l,i=p,e=p;return t.forEach(function(t){var o=t.bbox();r>o.x.min&&(r=o.x.min),n>o.y.min&&(n=o.y.min),i<o.x.max&&(i=o.x.max),e<o.y.max&&(e=o.y.max)}),{x:{min:r,mid:(r+i)/2,max:i,size:i-r},y:{min:n,mid:(n+e)/2,max:e,size:e-n}}},shapeintersections:function(t,r,n,i,e){if(!d.bboxoverlap(r,i))return[];var o=[],s=[t.startcap,t.forward,t.back,t.endcap],u=[n.startcap,n.forward,n.back,n.endcap];return s.forEach(function(r){r.virtual||u.forEach(function(i){if(!i.virtual){var s=r.intersects(i,e);s.length>0&&(s.c1=r,s.c2=i,s.s1=t,s.s2=n,o.push(s))}})}),o},makeshape:function(t,r,n){var i=r.points.length,e=t.points.length,o=d.makeline(r.points[i-1],t.points[0]),s=d.makeline(t.points[e-1],r.points[0]),u={startcap:o,forward:t,back:r,endcap:s,bbox:d.findbbox([o,t,r,s])},a=d;return u.intersections=function(t){return a.shapeintersections(u,u.bbox,t,t.bbox,n)},u},getminmax:function(t,r,n){if(!n)return{min:0,max:0};var i,e,o=l,s=p;n.indexOf(0)===-1&&(n=[0].concat(n)),n.indexOf(1)===-1&&n.push(1);for(var u=0,a=n.length;u<a;u++)i=n[u],e=t.get(i),e[r]<o&&(o=e[r]),e[r]>s&&(s=e[r]);return{min:o,mid:(o+s)/2,max:s,size:s-o}},align:function(t,r){var n=r.p1.x,o=r.p1.y,u=-s(r.p2.y-o,r.p2.x-n),a=function(t){return{x:(t.x-n)*i(u)-(t.y-o)*e(u),y:(t.x-n)*e(u)+(t.y-o)*i(u)}};return t.map(a)},roots:function(t,r){r=r||{p1:{x:0,y:0},p2:{x:1,y:0}};var n=t.length-1,e=d.align(t,r),s=function(t){return 0<=t&&t<=1};if(2===n){var a=e[0].y,c=e[1].y,x=e[2].y,y=a-2*c+x;if(0!==y){var l=-u(c*c-a*x),p=-a+c,v=-(l+p)/y,m=-(-l+p)/y;return[v,m].filter(s)}return c!==x&&0===y?[(2*c-x)/(2*c-2*x)].filter(s):[]}var z=e[0].y,g=e[1].y,b=e[2].y,_=e[3].y,y=-z+3*g-3*b+_,a=3*z-6*g+3*b,c=-3*z+3*g,x=z;if(d.approximately(y,0)){if(d.approximately(a,0))return d.approximately(c,0)?[]:[-x/c].filter(s);var w=u(c*c-4*a*x),E=2*a;return[(w-c)/E,(-c-w)/E].filter(s)}a/=y,c/=y,x/=y;var S,v,M,k,j,e=(3*c-a*a)/3,O=e/3,w=(2*a*a*a-9*a*c+27*x)/27,T=w/2,C=T*T+O*O*O;if(C<0){var L=-e/3,N=L*L*L,A=u(N),B=-w/(2*A),F=B<-1?-1:B>1?1:B,I=o(F),q=f(A),P=2*q;return M=P*i(I/3)-a/3,k=P*i((I+h)/3)-a/3,j=P*i((I+2*h)/3)-a/3,[M,k,j].filter(s)}if(0===C)return S=T<0?f(-T):-f(T),M=2*S-a/3,k=-S-a/3,[M,k].filter(s);var R=u(C);return S=f(-T+R),v=f(T+R),[S-v-a/3].filter(s)},droots:function(t){if(3===t.length){var r=t[0],n=t[1],i=t[2],e=r-2*n+i;if(0!==e){var o=-u(n*n-r*i),s=-r+n,a=-(o+s)/e,f=-(-o+s)/e;return[a,f]}return n!==i&&0===e?[(2*n-i)/(2*(n-i))]:[]}if(2===t.length){var r=t[0],n=t[1];return r!==n?[r/(r-n)]:[]}},curvature:function(t,n,i,e){var o,s,f,c,h=d.derive(n),x=h[0],y=h[1],l=0,p=0,v=d.compute(t,x),m=d.compute(t,y),z=v.x*v.x+v.y*v.y;if(i?(o=u(a(v.y*m.z-m.y*v.z,2)+a(v.z*m.x-m.z*v.x,2)+a(v.x*m.y-m.x*v.y,2)),s=a(z+v.z*v.z,1.5)):(o=v.x*m.y-v.y*m.x,s=a(z,1.5)),0===o||0===s)return{k:0,r:0};if(l=o/s,p=s/o,!e){var g=d.curvature(t-.001,n,i,!0).k,b=d.curvature(t+.001,n,i,!0).k;c=(b-l+(l-g))/2,f=(r(b-l)+r(l-g))/2}return{k:l,r:p,dk:c,adk:f}},inflections:function(t){if(t.length<4)return[];var r=d.align(t,{p1:t[0],p2:t.slice(-1)[0]}),n=r[2].x*r[1].y,i=r[3].x*r[1].y,e=r[1].x*r[2].y,o=r[3].x*r[2].y,s=18*(-3*n+2*i+3*e-o),u=18*(3*n-i-3*e),a=18*(e-n);if(d.approximately(s,0)){if(!d.approximately(u,0)){var f=-a/u;if(0<=f&&f<=1)return[f]}return[]}var c=u*u-4*s*a,h=Math.sqrt(c),o=2*s;return d.approximately(o,0)?[]:[(h-u)/o,-(u+h)/o].filter(function(t){return 0<=t&&t<=1})},bboxoverlap:function(t,n){var i,e,o,s,u,a=["x","y"],f=a.length;for(i=0;i<f;i++)if(e=a[i],o=t[e].mid,s=n[e].mid,u=(t[e].size+n[e].size)/2,r(o-s)>=u)return!1;return!0},expandbox:function(t,r){r.x.min<t.x.min&&(t.x.min=r.x.min),r.y.min<t.y.min&&(t.y.min=r.y.min),r.z&&r.z.min<t.z.min&&(t.z.min=r.z.min),r.x.max>t.x.max&&(t.x.max=r.x.max),r.y.max>t.y.max&&(t.y.max=r.y.max),r.z&&r.z.max>t.z.max&&(t.z.max=r.z.max),t.x.mid=(t.x.min+t.x.max)/2,t.y.mid=(t.y.min+t.y.max)/2,t.z&&(t.z.mid=(t.z.min+t.z.max)/2),t.x.size=t.x.max-t.x.min,t.y.size=t.y.max-t.y.min,t.z&&(t.z.size=t.z.max-t.z.min)},pairiteration:function(t,r,n){var i=t.bbox(),e=r.bbox(),o=1e5,s=n||.5;if(i.x.size+i.y.size<s&&e.x.size+e.y.size<s)return[(o*(t._t1+t._t2)/2|0)/o+"/"+(o*(r._t1+r._t2)/2|0)/o];var u=t.split(.5),a=r.split(.5),f=[{left:u.left,right:a.left},{left:u.left,right:a.right},{left:u.right,right:a.right},{left:u.right,right:a.left}];f=f.filter(function(t){return d.bboxoverlap(t.left.bbox(),t.right.bbox())});var c=[];return 0===f.length?c:(f.forEach(function(t){c=c.concat(d.pairiteration(t.left,t.right,s))}),c=c.filter(function(t,r){return c.indexOf(t)===r}))},getccenter:function(t,r,n){var o,u=r.x-t.x,a=r.y-t.y,f=n.x-r.x,c=n.y-r.y,y=u*i(x)-a*e(x),l=u*e(x)+a*i(x),p=f*i(x)-c*e(x),v=f*e(x)+c*i(x),m=(t.x+r.x)/2,z=(t.y+r.y)/2,g=(r.x+n.x)/2,b=(r.y+n.y)/2,_=m+y,w=z+l,E=g+p,S=b+v,M=d.lli8(m,z,_,w,g,b,E,S),k=d.dist(M,t),j=s(t.y-M.y,t.x-M.x),O=s(r.y-M.y,r.x-M.x),T=s(n.y-M.y,n.x-M.x);return j<T?((j>O||O>T)&&(j+=h),j>T&&(o=T,T=j,j=o)):T<O&&O<j?(o=T,T=j,j=o):T+=h,M.s=j,M.e=T,M.r=k,M},numberSort:function(t,r){return t-r}};t.exports=d}()},function(t,r,n){"use strict";!function(){var r=n(2),i=function(t){this.curves=[],this._3d=!1,t&&(this.curves=t,this._3d=this.curves[0]._3d)};i.prototype={valueOf:function(){return this.toString()},toString:function(){return"["+this.curves.map(function(t){return r.pointsToString(t.points)}).join(", ")+"]"},addCurve:function(t){this.curves.push(t),this._3d=this._3d||t._3d},length:function(){return this.curves.map(function(t){return t.length()}).reduce(function(t,r){return t+r})},curve:function(t){return this.curves[t]},bbox:function t(){for(var n=this.curves,t=n[0].bbox(),i=1;i<n.length;i++)r.expandbox(t,n[i].bbox());return t},offset:function t(r){var t=[];return this.curves.forEach(function(n){t=t.concat(n.offset(r))}),new i(t)}},t.exports=i}()},function(t,r,n){"use strict";function i(t,r,n){if("Z"!==r){if("M"===r)return void(s={x:n[0],y:n[1]});var i=[!1,s.x,s.y].concat(n),e=t.bind.apply(t,i),o=new e,u=n.slice(-2);return s={x:u[0],y:u[1]},o}}function e(t,r){for(var n,e,s,u=o(r).split(" "),a=new RegExp("[MLCQZ]",""),f=[],c={C:6,Q:4,L:2,M:2};u.length;)n=u.splice(0,1)[0],a.test(n)&&(s=u.splice(0,c[n]).map(parseFloat),e=i(t,n,s),e&&f.push(e));return new t.PolyBezier(f)}var o=n(5),s={x:!1,y:!1};t.exports=e},function(t,r){"use strict";function n(t){t=t.replace(/,/g," ").replace(/-/g," - ").replace(/-\s+/g,"-").replace(/([a-zA-Z])/g," $1 ");var r,n,i,e,o,s,u=t.replace(/([a-zA-Z])\s?/g,"|$1").split("|"),a=u.length,f=[],c=0,h=0,x=0,y=0,l=0,p=0,v=0,d=0,m="";for(r=1;r<a;r++)if(n=u[r],i=n.substring(0,1),e=i.toLowerCase(),f=n.replace(i,"").trim().split(" "),f=f.filter(function(t){return""!==t}).map(parseFloat),o=f.length,"m"===e){if(m+="M ","m"===i?(x+=f[0],y+=f[1]):(x=f[0],y=f[1]),c=x,h=y,m+=x+" "+y+" ",o>2)for(s=0;s<o;s+=2)"m"===i?(x+=f[s],y+=f[s+1]):(x=f[s],y=f[s+1]),m+=["L",x,y,""].join(" ")}else if("l"===e)for(s=0;s<o;s+=2)"l"===i?(x+=f[s],y+=f[s+1]):(x=f[s],y=f[s+1]),m+=["L",x,y,""].join(" ");else if("h"===e)for(s=0;s<o;s++)"h"===i?x+=f[s]:x=f[s],m+=["L",x,y,""].join(" ");else if("v"===e)for(s=0;s<o;s++)"v"===i?y+=f[s]:y=f[s],m+=["L",x,y,""].join(" ");else if("q"===e)for(s=0;s<o;s+=4)"q"===i?(l=x+f[s],p=y+f[s+1],x+=f[s+2],y+=f[s+3]):(l=f[s],p=f[s+1],x=f[s+2],y=f[s+3]),m+=["Q",l,p,x,y,""].join(" ");else if("t"===e)for(s=0;s<o;s+=2)l=x+(x-l),p=y+(y-p),"t"===i?(x+=f[s],y+=f[s+1]):(x=f[s],y=f[s+1]),m+=["Q",l,p,x,y,""].join(" ");else if("c"===e)for(s=0;s<o;s+=6)"c"===i?(l=x+f[s],p=y+f[s+1],v=x+f[s+2],d=y+f[s+3],x+=f[s+4],y+=f[s+5]):(l=f[s],p=f[s+1],v=f[s+2],d=f[s+3],x=f[s+4],y=f[s+5]),m+=["C",l,p,v,d,x,y,""].join(" ");else if("s"===e)for(s=0;s<o;s+=4)l=x+(x-v),p=y+(y-d),"s"===i?(v=x+f[s],d=y+f[s+1],x+=f[s+2],y+=f[s+3]):(v=f[s],d=f[s+1],x=f[s+2],y=f[s+3]),m+=["C",l,p,v,d,x,y,""].join(" ");else"z"===e&&(m+="Z ",x=c,y=h);return m.trim()}t.exports=n}]);

lib/bezier.js

@@ -222,3 +222,15 @@ /**
     },
-    update: function() {
+    verify: function() {
+      var print = this.coordDigest();
+      if (print !== this._print) {
+        this._print = print;
+        this.update();
+      }
+    },
+    coordDigest: function() {
+      return this.points.map(function(c,pos) {
+        return '' + pos + c.x + c.y + c.z?c.z:0;
+      }).join('');
+    },
+    update: function(newprint) {
       // invalidate any precomputed LUT
@@ -239,2 +251,3 @@ this._lut = [];
     getLUT: function(steps) {
+      this.verify();
       steps = steps || 100;
@@ -241,0 +254,0 @@ if (this._lut.length === steps) {

package.json

 {
   "name": "bezier-js",
-  "version": "2.5.1",
+  "version": "2.6.0",
   "description": "A javascript library for working with Bezier curves",
@@ -5,0 +5,0 @@ "main": "./index.js",

test/autodraw/Abstractor.js

 // Bezier abstraction based on RDP reduced coordinates
-var Abstractor = function() {};
-Abstractor.prototype = {
+class Abstractor {
+  constructor(coords) {
+    this.coords = coords;
+  }
+
+  abstract() {
+    var list = abstractor.split(coords);
+    return list.map(list => this.convert(list));
+  }
+
   // create a virtual start and end point for CR-splining
-  prep: function(c,m,p5,p6,dx,dy) {
+  prep(c,m,p5,p6,dx,dy) {
     m = c.length - 1;
@@ -14,6 +22,6 @@ dx = c[1].x-c[0].x;
     return [p5].concat(c).concat([p6]);
-  },
+  }
 
   // form bezier segments using catmull-rom-to-bezier conversion
-  convert: function(c,p1,p2,p3,p4,dx,dy,cx1,cy1,cx2,cy2,p5,ci) {
+  convert(c,p1,p2,p3,p4,dx,dy,cx1,cy1,cx2,cy2,p5,ci) {
     var l = c.length, i, curves=[], f=1;
@@ -36,14 +44,6 @@ c = this.prep(c);
     return curves;
-  },
+  }
 
-  // angle between p1-p2 and p2-p3
-  getAngle: function(p1,p2,p3) {
-    var atan2 = Math.atan2,
-        v1 = { x: p2.x - p1.x, y: p2.y - p1.y },
-        v2 = { x: p3.x - p2.x, y: p3.y - p2.y };
-    return atan2(v2.y, v2.x) - atan2(v1.y, v1.x);
-  },
-
   // positive or negative winding triangle?
-  getTriangleWinding: function(p1,p2,p3) {
+  getTriangleWinding(p1,p2,p3) {
     if(p2 && p3) {
@@ -53,6 +53,6 @@ p1 = this.getAngle(p1,p2,p3);
     return p1 > 0 ? 1 : -1;
-  },
+  }
 
   // split the list of coordinates when we see a kink or discontinuity
-  split: function(c) {
+  split(c) {
     var threshold = Math.PI/3;
@@ -77,16 +77,1 @@ var list = [], i, s, p0, p1, p2, p3, a, b, t = Math.PI/2;
 };
-
-var abstractor = new Abstractor();
-
-function abstract(coords) {
-  var curves = [];
-  var list = abstractor.split(coords);
-  return list.map(function(list) {
-    return abstractor.convert(list);
-  });
-};
-
-
-if(typeof module !== "undefined") {
-  module.exports = abstract;
-}

test/autodraw/common.js

 var tau = Math.PI*2;
 
+function abs(x) {
+  return Math.abs(x);
+}
+
 function sqr(x) {
@@ -52,1 +56,39 @@ return x * x;
 };
+
+
+// angle between p1-p2 and p2-p3
+function getAngle(p1,p2,p3) {
+  var atan2 = Math.atan2,
+      v1 = { x: p1.x - p2.x, y: p1.y - p2.y },
+      v2 = { x: p3.x - p2.x, y: p3.y - p2.y };
+  return atan2(v2.y, v2.x) - atan2(v1.y, v1.x);
+}
+
+/*
+
+function dot2(a,b) {
+  return a.x*b.x + a.y*b.y;
+}
+
+
+// angle between p1-p2 and p2-p3
+function angle2(p1,p2,p3) {
+  let sqrt = Math.sqrt, acos = Math.acos;
+  let a = {
+    x: p1.x - p2.x,
+    y: p1.y - p2.y
+  };
+  let b = {
+    x: p3.x - p2.x,
+    y: p3.y - p2.y
+  };
+  let d = dot2(a,b);
+  let ma = sqrt(a.x*a.x + a.y*a.y);
+  let mb = sqrt(b.x*b.x + b.y*b.y);
+  let m = ma * mb;
+  let phi= acos(d/m);
+  //logNow(p1,p2,p3, a,b, d,m,phi);
+  return phi;
+}
+
+*/

test/autodraw/Handler.js

@@ -1,53 +0,258 @@
-var Handler = function(cvs) {
-  this.cvs = cvs;
-  this.ctx = cvs.getContext("2d");
-};
+class Handler {
+  constructor(cvs) {
+    this.cvs = cvs;
+    this.ctx = cvs.getContext("2d");
+    this.bg = false;
+  }
 
-Handler.prototype = {
-  recordPoint: function(evt) {
-    var x = evt.offsetX==undefined?evt.layerX:evt.offsetX;
-    var y = evt.offsetY==undefined?evt.layerY:evt.offsetY;
-    this.coords.push({ x:x, y:y });
+  /**
+   *
+   */
+  cacheBackground() {
+    var img = new Image();
+    img.src = this.cvs.toDataURL();
+    this.bg = img;
+  }
 
+  /**
+   *
+   * @param {*} evt
+   */
+  recordPoint(evt) {
+    var x = evt.clientX;
+    var y = evt.clientY - this.cvs.getBoundingClientRect().top;
+    this.coords.push({ x, y });
+
+    // draw point while we draw
     var ctx = this.ctx;
     ctx.beginPath();
-    ctx.arc(x,y,0.1,0,tau);
+    ctx.arc(x, y, 0.1, 0, tau);
     ctx.stroke();
-  },
+  }
 
-  md: function(evt) {
+  /**
+   *
+   * @param {*} evt
+   */
+  start(evt) {
     this.ctx.strokeStyle = "black";
+    if (this.bg)
+      this.ctx.drawImage(this.bg, 0, 0, this.cvs.width, this.cvs.height);
     this.recording = true;
     this.coords = [];
     this.recordPoint(evt);
-  },
+  }
 
-  mm: function(evt) {
-    if(this.recording) {
+  /**
+   *
+   * @param {*} evt
+   */
+  record(evt) {
+    if (this.recording) {
       this.recordPoint(evt);
     }
-  },
+  }
 
-  me: function(evt) {
+  /**
+   *
+   * @param {*} evt
+   */
+  end(evt) {
     this.recording = false;
     this.cvs.width = this.cvs.width;
-    var ctx = this.ctx;
+    if (this.bg)
+      this.ctx.drawImage(this.bg, 0, 0, this.cvs.width, this.cvs.height);
+    var rdpcoords = rdp.runRDP(this.coords);
 
-    // original poinds
-    ctx.strokeStyle="rgba(100,100,200,0.6)";
-    this.coords.forEach(function(p) {
+    this.drawCR(rdpcoords);
+    // this.drawBeziers(rdpcoords);
+    this.drawArcs(rdpcoords);
+    this.drawCoords();
+    this.drawRDP(rdpcoords);
+    this.cacheBackground();
+  }
+
+  /**
+   * Try to fit circular arcs to the original input data
+   * @param {*} coords
+   */
+  drawArcs(rdpcoords) {
+    const ctx = this.ctx;
+    const coords = this.coords;
+
+    function step(s, e) {
+      let m = (e - s) / 2,
+        start = rdpcoords[s],
+        spos = coords.indexOf(start),
+        midpoint,
+        end = rdpcoords[e],
+        epos = coords.indexOf(end);
+
+      if (m == (m | 0)) {
+        midpoint = rdpcoords[m];
+      } else {
+        let pos = m | 0,
+          c1 = rdpcoords[pos],
+          c2 = rdpcoords[pos + 1];
+        midpoint = {
+          x: (c1.x + c2.x) / 2,
+          y: (c1.y + c2.y) / 2
+        };
+      }
+
+      let arc = Bezier.getUtils().getccenter(start, midpoint, end),
+        center = { x: arc.x, y: arc.y },
+        subset = coords.slice(spos, epos),
+        n = subset.length,
+        MSE =
+          subset.reduce((t, v) => (t += Math.abs(dist(center, v) - arc.r)), 0) /
+          n;
+      return { arc, MSE, spos, epos };
+    }
+
+    for (let s = 0, e = 2, i = 0; i < rdpcoords.length - 2; i++) {
+      let ret = step(s, e + i);
+      let arc = ret.arc;
+      console.log(ret.MSE);
       ctx.beginPath();
-      ctx.arc(p.x,p.y,0.2,0,tau);
+      ctx.strokeStyle = ret.MSE < 1 ? "rgb(0,20,20)" : "rgba(0,200,200,0.4)";
+      ctx.arc(arc.x, arc.y, arc.r, arc.s, arc.e);
       ctx.stroke();
-    }.bind(this));
+    }
+  }
 
-    // reduced points
-    ctx.strokeStyle="red";
-    rdp.runRDP(this.coords).forEach(function(p) {
+  /**
+   *
+   */
+  drawCoords() {
+    const ctx = this.ctx;
+    ctx.strokeStyle = "rgba(100,100,200,0.6)";
+    this.coords.forEach(p => {
       ctx.beginPath();
-      ctx.arc(p.x,p.y,1,0,tau);
+      ctx.arc(p.x, p.y, 0.2, 0, tau);
       ctx.stroke();
-    }.bind(this));
+    });
+  }
 
+  /**
+   *
+   * @param {*} rdcoords
+   */
+  drawRDP(rdpcoords) {
+    const ctx = this.ctx;
+    rdpcoords.forEach(p => {
+      ctx.strokeStyle = "red";
+      if (p.acute) {
+        ctx.strokeStyle = "purple";
+      }
+      ctx.beginPath();
+      ctx.arc(p.x, p.y, 1, 0, tau);
+      ctx.stroke();
+    });
   }
-};
+
+  /**
+   *
+   * @param {*} rdpcoords
+   */
+  drawCR(rdpcoords) {
+    // for CR curve fitting of all points, we need a virtual first and last coordinate
+    rdpcoords.unshift({
+      x: rdpcoords[0].x - (rdpcoords[0].x - rdpcoords[1].x),
+      y: rdpcoords[0].y - (rdpcoords[0].y - rdpcoords[1].y)
+    });
+
+    let last = rdpcoords.length - 1;
+    rdpcoords.push({
+      x: rdpcoords[last].x + (rdpcoords[last].x - rdpcoords[last - 1].x),
+      y: rdpcoords[last].y + (rdpcoords[last].y - rdpcoords[last - 1].y)
+    });
+
+    const ctx = this.ctx;
+    ctx.strokeStyle = "rgba(0,200,0,0.5)";
+    let c1 = rdpcoords[0],
+      c2 = rdpcoords[1],
+      c3 = rdpcoords[2],
+      c4 = rdpcoords[3],
+      p2,
+      p3,
+      p4;
+    ctx.moveTo(c2.x, c2.y);
+    for (let p = 4, e = rdpcoords.length; p <= e; p++) {
+      if (p % 2 === 0) {
+        ctx.strokeStyle = "rgba(200,100,0,0.5)";
+      } else {
+        ctx.strokeStyle = "rgba(0,200,0,0.5)";
+      }
+
+      if (c3.acute) {
+        c4 = {
+          x: c3.x + (c3.x - c2.x),
+          y: c3.y + (c3.y - c2.y),
+          original: c4
+        };
+      }
+
+      p2 = { x: c2.x + (c3.x - c1.x) / 6, y: c2.y + (c3.y - c1.y) / 6 };
+      p3 = { x: c3.x - (c4.x - c2.x) / 6, y: c3.y - (c4.y - c2.y) / 6 };
+      p4 = c3;
+
+      ctx.bezierCurveTo(p2.x, p2.y, p3.x, p3.y, p4.x, p4.y);
+      ctx.stroke();
+      ctx.beginPath();
+      ctx.moveTo(p4.x, p4.y);
+
+      c1 = !c3.acute
+        ? c2
+        : {
+            x: c3.x - (c4.original.x - c3.x),
+            y: c3.y - (c4.original.y - c3.y)
+          };
+      c2 = c3;
+      c3 = c3.acute ? c4.original : c4;
+      c4 = rdpcoords[p];
+    }
+
+    // and then we need to remove those virtual first/last coordinates again
+    rdpcoords.pop();
+    rdpcoords.shift();
+  }
+
+  /**
+   * Similar to POTrace, we try to fit a cubic Bezier by
+   * scaling and reorienting points so that they define
+   * a crude "bitmap", which we use as a lookup to find
+   * the "close enough without any curve fitting" curve.
+   * Then we see if we can massage that to a better fit.
+   * @param {*} rdpcoords
+   */
+  drawBeziers(rdpcoords) {
+    const ctx = this.ctx;
+
+    let endPos = rdpcoords.findIndex(v => v.actute);
+    endPos = endPos === -1 ? rdpcoords.length - 1 : endPos;
+    let start = rdpcoords[0],
+      end = rdpcoords[endPos],
+      points = rdpcoords.slice(1, endPos - 1);
+
+    // try to fit a single curve to this
+    let midpoint = points[(points.length / 2) | 0];
+
+    let b = Bezier.cubicFromPoints(start, midpoint, end, 0.5, 100);
+
+    // draw this curve
+    ctx.strokeStyle = "rgb(100,200,200)";
+    ctx.moveTo(b.points[0].x, b.points[0].y);
+    ctx.bezierCurveTo(
+      b.points[1].x,
+      b.points[1].y,
+      b.points[2].x,
+      b.points[2].y,
+      b.points[3].x,
+      b.points[3].y
+    );
+    ctx.stroke();
+  }
+}
+
+export { Handler };

test/autodraw/RDP.js

 // Ramer–Douglas–Peucker simplification
-var RDP = function(threshold) {
-  this.threshold = threshold || 2.5;
-};
+class RDP {
+  constructor(threshold) {
+    this.threshold = threshold || 2.5;
+  }
 
-RDP.prototype = {
-  runRDP: function(coords) {
+  runRDP(coords) {
     coords = coords.slice();
+    this.markAngles(coords);
     if(coords.length===2) {
@@ -14,6 +15,42 @@ coords[0].keep = true;
     }
-    return this.reducePoints(coords);
-  },
+    coords = this.reducePoints(coords)
+    // this.mergeClosePoints(coords);
+    this.markAngles(coords);
+    return coords;
+  }
 
-  reducePoints: function(coords) {
+  mergeClosePoints(coords) {
+    for(let i=0; i<coords.length-2; i++) {
+      let c = coords[i];
+      let n = coords[i+1];
+      if (c.acute) continue;
+      if (n.acute) continue;
+      if (dist(c,n) < 10) {
+        c.x = (c.x + n.x) / 2;
+        c.y = (c.y + n.y) / 2;
+        coords.splice(i+1, 1);
+      }
+    }
+  }
+
+  markAngles(coords) {
+    let a = coords[0],
+        b = coords[1],
+        c = coords[2],
+        angle;
+    for(let i=3, e=coords.length-1; i<e; i++) {
+      angle = abs(getAngle(a,b,c));
+      if (angle < 1.8) {
+        // TODO: this also depends on the fidelity of the curve. The closer
+        //       points are, the more neighbours play a role in determining
+        //       whether this is true acuteness or not.
+        b.acute = true;
+      }
+      a = b;
+      b = c;
+      c = coords[i];
+    }
+  }
+
+  reducePoints(coords) {
     var l = coords.length-1,
@@ -26,3 +63,2 @@ s = 0,
         mdi = 0,
-        t = this.threshold,
         p,i,d;
@@ -37,3 +73,3 @@
     // if a transition is detected, process each set separately
-    if(md > t) {
+    if(md > this.threshold) {
       this.runRDP(coords.slice(s,mdi+1))
@@ -47,10 +83,8 @@ this.runRDP(coords.slice(mdi));
     // filter out all unmarked coordinates
-    return coords.filter(function(c) { return c.keep; });
+    coords = coords.filter(function(c) { return c.keep; });
+
+    return coords;
   }
-};
+}
 
 var rdp = new RDP();
-
-if(typeof module !== "undefined") {
-  module.exports = rdp;
-}

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