@thi.ng/math - npm Package Compare versions

Comparing version 1.4.2 to 1.5.0

CHANGELOG.md

@@ -6,2 +6,13 @@ # Change Log
 
+# [1.5.0](https://github.com/thi-ng/umbrella/compare/@thi.ng/math@[e-mail]/math@1.5.0) (2019-11-09)
+
+
+### Features
+
+* **math:** add mixCubicHermite & tangent fns ([d6b4b37](https://github.com/thi-ng/umbrella/commit/d6b4b3710b80fa1366cb40c193ad745bc63d4253))
+
+
+
+
+
 ## [1.4.2](https://github.com/thi-ng/umbrella/compare/@thi.ng/math@[e-mail]/math@1.4.2) (2019-07-31)
@@ -8,0 +19,0 @@

extrema.d.ts

@@ -46,3 +46,3 @@ /**
  */
-export declare const minimaIndices: (values: number[], from?: number, to?: number) => IterableIterator<number>;
+export declare const minimaIndices: (values: number[], from?: number, to?: number) => Generator<number, void, unknown>;
 /**
@@ -57,2 +57,2 @@ * Returns an iterator yielding all maxima indices in given `values`
  */
-export declare const maximaIndices: (values: number[], from?: number, to?: number) => IterableIterator<number>;
+export declare const maximaIndices: (values: number[], from?: number, to?: number) => Generator<number, void, unknown>;

lib/index.js

@@ -281,2 +281,19 @@ 'use strict';
 };
+const mixHermite = (a, b, c, d, t) => {
+    const y1 = 0.5 * (c - a);
+    const y2 = 1.5 * (b - c) + 0.5 * (d - a);
+    return ((y2 * t + a - b + y1 - y2) * t + y1) * t + b;
+};
+const mixCubicHermite = (a, ta, b, tb, t) => {
+    const s = t - 1;
+    const t2 = t * t;
+    const s2 = s * s;
+    const h00 = (1 + 2 * t) * s2;
+    const h10 = t * s2;
+    const h01 = t2 * (3 - 2 * t);
+    const h11 = t2 * s;
+    return h00 * a + h10 * ta + h01 * b + h11 * tb;
+};
+const tangentCardinal = (prev, next, scale = 0.5, ta = 0, tc = 2) => scale * ((next - prev) / (tc - ta));
+const tangentDiff3 = (prev, curr, next, ta = 0, tb = 1, tc = 2) => 0.5 * ((next - curr) / (tc - tb) + (curr - prev) / (tb - ta));
 const tween = (f, from, to) => (t) => mix(from, to, f(t));
@@ -497,2 +514,4 @@ const circular = (t) => {
 exports.mixCubic = mixCubic;
+exports.mixCubicHermite = mixCubicHermite;
+exports.mixHermite = mixHermite;
 exports.mixQuadratic = mixQuadratic;
@@ -554,2 +573,4 @@ exports.muli16 = muli16;
 exports.subu8 = subu8;
+exports.tangentCardinal = tangentCardinal;
+exports.tangentDiff3 = tangentDiff3;
 exports.trunc = trunc;
@@ -556,0 +577,0 @@ exports.tween = tween;

lib/index.umd.js

@@ -1,1 +0,1 @@
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1-a*Math.sin(s)/s*Math.cos(i*n)},t.circular=t=>(t=1-t,Math.sqrt(1-t*t)),t.clamp=(t,a,i)=>t<a?a:t>i?i:t,t.clamp01=S,t.clamp11=w,t.classifyCrossing=(t,a,i,n,s=1e-6)=>D(t,a,i,n)?3:A(t,a,i,n)?2:v(t,i,s)&&v(a,n,s)?v(t,n,s)?1:0:4,t.cosine=t=>1-(.5*Math.cos(t*a)+.5),t.cossin=(t,a=1)=>[Math.cos(t)*a,Math.sin(t)*a],t.cot=t=>1/Math.tan(t),t.csc=t=>1/Math.sin(t),t.cubicPulse=(t,a,i)=>(i=Math.abs(i-a))>t?0:1-(i/=t)*i*(3-2*i),t.decimated=(t,a)=>Math.floor(a*t)/t,t.deg=t=>t*M,t.derivative=(t,a=1e-6)=>i=>(t(i+a)-t(i))/a,t.divi16=(t,a)=>N((0|t)/(0|a)),t.divi32=(t,a)=>(0|t)/(0|a)|0,t.divi8=(t,a)=>F((0|t)/(0|a)),t.divu16=(t,a)=>(t&L)/(a&L)&L,t.divu32=(t,a)=>(t>>>0)/(a>>>0)>>>0,t.divu8=(t,a)=>(t&y)/(a&y)&y,t.ease=(t,a)=>Math.pow(a,t),t.eqDelta=v,t.eqDeltaFixed=(t,a,i=1e-6)=>T(t-a)<=i,t.expStep=(t,a,i)=>1-Math.exp(-t*Math.pow(i,a)),t.fastCos=R,t.fastSin=t=>R(n-t),t.fit=(t,a,i,n,s)=>n+(s-n)*U(t,a,i),t.fit01=(t,a,i)=>a+(i-a)*S(t),t.fit10=(t,a,i)=>i+(a-i)*S(t),t.fit11=(t,a,i)=>a+(i-a)*(.5+.5*w(t)),t.fitClamped=(t,a,i,n,s)=>n+(s-n)*S(U(t,a,i)),t.fmod=(t,a)=>t-a*Math.floor(t/a),t.foldback=(t,a)=>a<-t||a>t?Math.abs(Math.abs((a-t)%(4*t))-2*t)-t:a,t.fract=G,t.gain=(t,a)=>a<.5?.5*Math.pow(2*a,t):1-.5*Math.pow(2-2*a,t),t.impulse=(t,a)=>{const i=t*a;return i*Math.exp(1-i)},t.inOpenRange=(t,a,i)=>t>a&&t<i,t.inRange=(t,a,i)=>t>=a&&t<=i,t.isCrossOver=D,t.isCrossUnder=A,t.isMaxima=_,t.isMinima=P,t.loc=(t,a,i)=>Math.sqrt(t*t+a*a-2*t*a*Math.cos(i)),t.lshifti16=(t,a)=>N((0|t)<<(0|a)),t.lshifti32=(t,a)=>(0|t)<<(0|a),t.lshifti8=(t,a)=>F((0|t)<<(0|a)),t.lshiftu16=(t,a)=>(t&L)<<(a&L)&L,t.lshiftu32=(t,a)=>t>>>0<<(a>>>0)>>>0,t.lshiftu8=(t,a)=>(t&y)<<(a&y)&y,t.max2id=(t,a)=>t>=a?0:1,t.max3id=(t,a,i)=>t>=a?t>=i?0:2:a>=i?1:2,t.max4id=(t,a,i,n)=>t>=a?t>=i?t>=n?0:3:i>=n?2:3:a>=i?a>=n?1:3:i>=n?2:3,t.maximaIndex=(t,a=0,i=t.length)=>q(_,t,a,i),t.maximaIndices=(t,a=0,i=t.length)=>H(C,t,a,i),t.min2id=(t,a)=>t<=a?0:1,t.min3id=(t,a,i)=>t<=a?t<=i?0:2:a<=i?1:2,t.min4id=(t,a,i,n)=>t<=a?t<=i?t<=n?0:3:i<=n?2:3:a<=i?a<=n?1:3:i<=n?2:3,t.minError=V,t.minimaIndex=C,t.minimaIndices=(t,a=0,i=t.length)=>H(C,t,a,i),t.mix=j,t.mixBilinear=(t,a,i,n,s,e)=>j(j(t,a,s),j(i,n,s),e),t.mixCubic=(t,a,i,n,s)=>{const e=s*s,r=1-s,o=r*r;return t*o*r+3*a*o*s+3*i*e*r+n*e*s},t.mixCubicHermite=(t,a,i,n,s)=>{const e=s-1,r=s*s,o=e*e;return(1+2*s)*o*t+s*o*a+r*(3-2*s)*i+r*e*n},t.mixHermite=(t,a,i,n,s)=>{const e=.5*(i-t),r=1.5*(a-i)+.5*(n-t);return((r*s+t-a+e-r)*s+e)*s+a},t.mixQuadratic=(t,a,i,n)=>{const s=1-n;return t*s*s+2*a*s*n+i*n*n},t.muli16=(t,a)=>N((0|t)*(0|a)),t.muli32=(t,a)=>(0|t)*(0|a)|0,t.muli8=(t,a)=>F((0|t)*(0|a)),t.mulu16=(t,a)=>(t&L)*(a&L)&L,t.mulu32=(t,a)=>(t>>>0)*(a>>>0)>>>0,t.mulu8=(t,a)=>(t&y)*(a&y)&y,t.norm=U,t.normCos=t=>{const a=t*t;return 1+a*(2*a-4)},t.noti16=t=>N(~t),t.noti32=t=>~t,t.noti8=t=>F(~t),t.notu16=t=>~t&L,t.notu32=t=>~t>>>0,t.notu8=t=>~t&y,t.ori16=(t,a)=>N(0|t|a),t.ori32=(t,a)=>0|t|a,t.ori8=(t,a)=>F(0|t|a),t.oru16=(t,a)=>(t&L|a&L)&L,t.oru32=(t,a)=>(t>>>0|a>>>0)>>>0,t.oru8=(t,a)=>(t&y|a&y)&y,t.parabola=(t,a)=>Math.pow(4*a*(1-a),t),t.quadrant=t=>p(t)*u|0,t.rad=t=>t*c,t.roundEps=(t,a=1e-6)=>{const i=G(t);return i<=a||i>=1-a?Math.round(t):t},t.roundTo=(t,a=1)=>Math.round(t/a)*a,t.rshifti16=(t,a)=>N((0|t)>>(0|a)),t.rshifti32=(t,a)=>(0|t)>>(0|a),t.rshifti8=(t,a)=>F((0|t)>>(0|a)),t.rshiftu16=(t,a)=>(t&L)>>>(a&L)&L,t.rshiftu32=(t,a)=>t>>>0>>>(a>>>0)>>>0,t.rshiftu8=(t,a)=>(t&y)>>>(a&y)&y,t.sclamp=(t,a,i,n)=>Q(O(t,a,n),i,n),t.sec=t=>1/Math.cos(t),t.sigmoid=(t,a)=>1/(1+Math.exp(-t*(2*a-1))),t.sigmoid11=(t,a)=>1/(1+Math.exp(-t*a)),t.sign=(t,a=1e-6)=>t>a?1:t<-a?-1:0,t.signExtend16=N,t.signExtend8=F,t.simplifyRatio=(t,a)=>{let i=Math.abs(t),n=Math.abs(a);for(;;){if(i<n){const t=i;i=n,n=t}const s=i%n;if(!s)return[t/n,a/n];i=s}},t.sinc=(t,i)=>(i=a*(t*i-1),Math.sin(i)/i),t.sincos=(t,a=1)=>[Math.sin(t)*a,Math.cos(t)*a],t.smax=O,t.smin=Q,t.smoothStep=(t,a,i)=>(3-2*(i=S((i-t)/(a-t))))*i*i,t.smootherStep=(t,a,i)=>(i=S((i-t)/(a-t)))*i*i*(i*(6*i-15)+10),t.solveCubic=(t,a,i,n,s=1e-9)=>{const 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mix.d.ts

@@ -21,2 +21,91 @@ export declare const mix: (a: number, b: number, t: number) => number;
 export declare const mixCubic: (a: number, b: number, c: number, d: number, t: number) => number;
+/**
+ * Returns hermite interpolation of `a, b, c, d` at normalized position
+ * `t`, where `a` and `d` are used as predecessor/successor of `b` / `c`
+ * and only inform the tangent of the interpolation curve. The
+ * interpolated result is that of `b` and `c`.
+ *
+ * Assumes all inputs are uniformly spaced. If that's not the case, use
+ * `mixCubicHermite()` with one of the tangent generators supporting
+ * non-uniform spacing of points.
+ *
+ * See: https://www.desmos.com/calculator/j4gf8g9vkr
+ *
+ * Source:
+ * https://www.musicdsp.org/en/latest/Other/93-hermite-interpollation.html
+ *
+ * @see mixCubicHermite
+ * @see tangentCardinal
+ * @see tangentDiff3
+ *
+ * @param a
+ * @param b
+ * @param c
+ * @param d
+ * @param t
+ */
+export declare const mixHermite: (a: number, b: number, c: number, d: number, t: number) => number;
+/**
+ * Computes cubic-hermite interpolation between `a` / `b` at normalized
+ * time `t` and using respective tangents `ta` / `tb`.
+ *
+ * https://en.wikipedia.org/wiki/Cubic_Hermite_spline
+ *
+ * @see mixHermite
+ * @see tangentCardinal
+ * @see tangentDiff3
+ *
+ * @param a
+ * @param ta
+ * @param b
+ * @param tb
+ * @param t
+ */
+export declare const mixCubicHermite: (a: number, ta: number, b: number, tb: number, t: number) => number;
+/**
+ * Helper function for `mixCubicHermite()`. Computes cardinal tangents
+ * based on point neighbors of a point B (not given), i.e. `a`
+ * (predecessor) and `c` (successor) and their times (defaults to
+ * uniformly spaced). The optional `tension` parameter can be used to
+ * scale the tangent where 0.0 produces a Cardinal spline tangent and
+ * 1.0 a Catmull-Rom (opposite to the Wikipedia ref).
+ *
+ * https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Cardinal_spline
+ *
+ * @param prev
+ * @param next
+ * @param scale
+ * @param ta
+ * @param tc
+ */
+export declare const tangentCardinal: (prev: number, next: number, scale?: number, ta?: number, tc?: number) => number;
+/**
+ * Helper function for `mixCubicHermite()`. Computes tangent for `curr`,
+ * based on 3-point finite difference, where `prev` & `next` are
+ * `curr`'s neighbors and the `tX` the three points' respective time
+ * values. The latter are equally spaced by default (each 1.0 apart).
+ *
+ * Using this function with equal spacing of 1.0 and together with
+ * `mixCubicHermite()` will produce same results as the somewhat
+ * optimized variant `mixHermite()`.
+ *
+ * https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Finite_difference
+ *
+ * @param prev
+ * @param curr
+ * @param next
+ * @param ta
+ * @param tb
+ * @param tc
+ */
+export declare const tangentDiff3: (prev: number, curr: number, next: number, ta?: number, tb?: number, tc?: number) => number;
+/**
+ * HOF interpolator. Takes a timing function `f` and interval `[from,
+ * to]`. Returns function which takes normalized time as single arg and
+ * returns interpolated value.
+ *
+ * @param f
+ * @param from
+ * @param to
+ */
 export declare const tween: (f: (t: number) => number, from: number, to: number) => (t: number) => number;
@@ -23,0 +112,0 @@ /**

mix.js

@@ -30,2 +30,104 @@ import { HALF_PI, PI } from "./api";
 };
+/**
+ * Returns hermite interpolation of `a, b, c, d` at normalized position
+ * `t`, where `a` and `d` are used as predecessor/successor of `b` / `c`
+ * and only inform the tangent of the interpolation curve. The
+ * interpolated result is that of `b` and `c`.
+ *
+ * Assumes all inputs are uniformly spaced. If that's not the case, use
+ * `mixCubicHermite()` with one of the tangent generators supporting
+ * non-uniform spacing of points.
+ *
+ * See: https://www.desmos.com/calculator/j4gf8g9vkr
+ *
+ * Source:
+ * https://www.musicdsp.org/en/latest/Other/93-hermite-interpollation.html
+ *
+ * @see mixCubicHermite
+ * @see tangentCardinal
+ * @see tangentDiff3
+ *
+ * @param a
+ * @param b
+ * @param c
+ * @param d
+ * @param t
+ */
+export const mixHermite = (a, b, c, d, t) => {
+    const y1 = 0.5 * (c - a);
+    const y2 = 1.5 * (b - c) + 0.5 * (d - a);
+    return ((y2 * t + a - b + y1 - y2) * t + y1) * t + b;
+};
+/**
+ * Computes cubic-hermite interpolation between `a` / `b` at normalized
+ * time `t` and using respective tangents `ta` / `tb`.
+ *
+ * https://en.wikipedia.org/wiki/Cubic_Hermite_spline
+ *
+ * @see mixHermite
+ * @see tangentCardinal
+ * @see tangentDiff3
+ *
+ * @param a
+ * @param ta
+ * @param b
+ * @param tb
+ * @param t
+ */
+export const mixCubicHermite = (a, ta, b, tb, t) => {
+    const s = t - 1;
+    const t2 = t * t;
+    const s2 = s * s;
+    const h00 = (1 + 2 * t) * s2;
+    const h10 = t * s2;
+    const h01 = t2 * (3 - 2 * t);
+    const h11 = t2 * s;
+    return h00 * a + h10 * ta + h01 * b + h11 * tb;
+};
+/**
+ * Helper function for `mixCubicHermite()`. Computes cardinal tangents
+ * based on point neighbors of a point B (not given), i.e. `a`
+ * (predecessor) and `c` (successor) and their times (defaults to
+ * uniformly spaced). The optional `tension` parameter can be used to
+ * scale the tangent where 0.0 produces a Cardinal spline tangent and
+ * 1.0 a Catmull-Rom (opposite to the Wikipedia ref).
+ *
+ * https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Cardinal_spline
+ *
+ * @param prev
+ * @param next
+ * @param scale
+ * @param ta
+ * @param tc
+ */
+export const tangentCardinal = (prev, next, scale = 0.5, ta = 0, tc = 2) => scale * ((next - prev) / (tc - ta));
+/**
+ * Helper function for `mixCubicHermite()`. Computes tangent for `curr`,
+ * based on 3-point finite difference, where `prev` & `next` are
+ * `curr`'s neighbors and the `tX` the three points' respective time
+ * values. The latter are equally spaced by default (each 1.0 apart).
+ *
+ * Using this function with equal spacing of 1.0 and together with
+ * `mixCubicHermite()` will produce same results as the somewhat
+ * optimized variant `mixHermite()`.
+ *
+ * https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Finite_difference
+ *
+ * @param prev
+ * @param curr
+ * @param next
+ * @param ta
+ * @param tb
+ * @param tc
+ */
+export const tangentDiff3 = (prev, curr, next, ta = 0, tb = 1, tc = 2) => 0.5 * ((next - curr) / (tc - tb) + (curr - prev) / (tb - ta));
+/**
+ * HOF interpolator. Takes a timing function `f` and interval `[from,
+ * to]`. Returns function which takes normalized time as single arg and
+ * returns interpolated value.
+ *
+ * @param f
+ * @param from
+ * @param to
+ */
 export const tween = (f, from, to) => (t) => mix(from, to, f(t));
@@ -32,0 +134,0 @@ /**

package.json

 {
     "name": "@thi.ng/math",
-    "version": "1.4.2",
+    "version": "1.5.0",
     "description": "Assorted common math functions & utilities",
@@ -32,4 +32,4 @@ "module": "./index.js",
         "nyc": "^14.0.0",
-        "typedoc": "^0.14.2",
-        "typescript": "^3.5.3"
+        "typedoc": "^0.15.0",
+        "typescript": "^3.6.4"
     },
@@ -49,3 +49,3 @@ "keywords": [
     "sideEffects": false,
-    "gitHead": "53eec7988c378fc37ae140e7174f36ef9b6208fe"
+    "gitHead": "97add769f24aa32a1a5e13c5c941605e1b9eb569"
 }

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