feat(math): add easing functions

- add easing functions, ported from thi.ng/shader-ast-std pkg

Author: postspectacular

packages/math/package.json

@@ -51,6 +51,7 @@
 		"animation",
 		"bezier",
 		"cubic",
+		"easing",
 		"hermite",
 		"interpolation",
 		"interval",
@@ -89,6 +90,9 @@
 		"./crossing": {
 			"default": "./crossing.js"
 		},
+		"./easing": {
+			"default": "./easing.js"
+		},
 		"./eqdelta": {
 			"default": "./eqdelta.js"
 		},

packages/math/src/easing.ts

@@ -0,0 +1,103 @@
+import type { FnN } from "@thi.ng/api";
+import { HALF_PI, PI, TAU } from "./api.js";
+
+const { cos, sin, sqrt } = Math;
+
+export const defEaseInExp =
+	(k: number): FnN =>
+	(t) =>
+		t ** k;
+
+export const defEaseOutExp =
+	(k: number): FnN =>
+	(t) =>
+		1 - (1 - t) ** k;
+
+export const defEaseInOutExp = (k: number): FnN => {
+	const k2 = 2 ** (k - 1);
+	return (t) => (t < 0.5 ? k2 * t ** k : 1 - (-2 * t + 2) ** k / 2);
+};
+
+export const easeLinear: FnN = (t) => t;
+
+export const easeIn2 = defEaseInExp(2);
+export const easeOut2 = defEaseOutExp(2);
+export const easeInOut2 = defEaseInOutExp(2);
+
+export const easeIn3 = defEaseInExp(3);
+export const easeOut3 = defEaseOutExp(3);
+export const easeInOut3 = defEaseInOutExp(3);
+
+export const easeIn4 = defEaseInExp(4);
+export const easeOut4 = defEaseOutExp(4);
+export const easeInOut4 = defEaseInOutExp(4);
+
+export const easeIn5 = defEaseInExp(5);
+export const easeOut5 = defEaseOutExp(5);
+export const easeInOut5 = defEaseInOutExp(5);
+
+export const easeInBack: FnN = (t) => 2.70158 * t ** 3 - 1.70158 * t ** 2;
+export const easeOutBack: FnN = (t) =>
+	2.70158 * (t - 1) ** 3 + 1 + 1.70158 * (t - 1) ** 2;
+export const easeInOutBack: FnN = (t) =>
+	t < 0.5
+		? ((2 * t) ** 2 * ((2.5949095 + 1) * 2 * t - 2.5949095)) / 2
+		: ((2 * t - 2) ** 2 * ((2.5949095 + 1) * (t * 2 - 2) + 2.5949095) + 2) /
+		  2;
+
+export const easeInBounce: FnN = (t) => 1 - easeOutBounce(1 - t);
+export const easeOutBounce: FnN = (t) =>
+	t < 1 / 2.75
+		? 7.5625 * (t * t)
+		: t < 2 / 2.75
+		? 7.5625 * (t - 1.5 / 2.75) * (t - 1.5 / 2.75) + 0.75
+		: t < 2.5 / 2.75
+		? 7.5625 * (t - 2.25 / 2.75) * (t - 2.25 / 2.75) + 0.9375
+		: 7.5625 * (t - 2.625 / 2.75) * (t - 2.625 / 2.75) + 0.984375;
+export const easeInOutBounce: FnN = (t) =>
+	t < 0.5
+		? (1 - easeOutBounce(1 - 2 * t)) / 2
+		: (1 + easeOutBounce(2 * t - 1)) / 2;
+
+export const easeInCirc: FnN = (t) => 1 - sqrt(1 - t ** 2);
+export const easeOutCirc: FnN = (t) => sqrt(1 - (t - 1) ** 2);
+export const easeInOutCirc: FnN = (t) =>
+	t < 0.5
+		? (1 - sqrt(1 - (2 * t) ** 2)) / 2
+		: (sqrt(1 - (-2 * t + 2) ** 2) + 1) / 2;
+
+export const easeInElastic: FnN = (t) =>
+	t <= 0
+		? 0
+		: t >= 1
+		? 1
+		: -(2 ** (10 * t - 10)) * sin((t * 10 - 10.75) * (TAU / 3));
+export const easeOutElastic: FnN = (t) =>
+	t <= 0
+		? 0
+		: t >= 1
+		? 1
+		: 2 ** (-10 * t) * sin((t * 10 - 0.75) * (TAU / 3)) + 1;
+export const easeInOutElastic: FnN = (t) =>
+	t <= 0
+		? 0
+		: t >= 1
+		? 1
+		: t < 0.5
+		? -(2 ** (20 * t - 10) * sin((20 * t - 11.125) * (TAU / 4.5))) / 2
+		: (2 ** (-20 * t + 10) * sin((20 * t - 11.125) * (TAU / 4.5))) / 2 + 1;
+
+export const easeInExp2: FnN = (t) => (t <= 0 ? 0 : 2 ** (10 * t - 10));
+export const easeOutExp2: FnN = (t) => (t >= 1 ? 1 : 1 - 2 ** (-10 * t));
+export const easeInOutExp2: FnN = (t) =>
+	t < 0
+		? 0
+		: t >= 1
+		? 1
+		: t < 0.5
+		? 2 ** (20 * t - 10) / 2
+		: (2 - 2 ** (-20 * t + 10)) / 2;
+
+export const easeInSine: FnN = (t) => 1 - cos(t * HALF_PI);
+export const easeOutSine: FnN = (t) => sin(t * HALF_PI);
+export const easeInOutSine: FnN = (t) => -(cos(PI * t) - 1) / 2;

packages/math/src/index.ts

@@ -4,6 +4,7 @@ export * from "./angle.js";
 export * from "./crossing.js";
 export * from "./eqdelta.js";
 export * from "./extrema.js";
+export * from "./easing.js";
 export * from "./fit.js";
 export * from "./int.js";
 export * from "./interval.js";