bezier.ts

export function cubicBezier(p1x : number, p1y : number, p2x : number, p2y : number):(x: number)=> number {
	const ZERO_LIMIT = 1e-6;
	// Calculate the polynomial coefficients,
	// implicit first and last control points are (0,0) and (1,1).
	const ax = 3 * p1x - 3 * p2x + 1;
	const bx = 3 * p2x - 6 * p1x;
	const cx = 3 * p1x;

	const ay = 3 * p1y - 3 * p2y + 1;
	const by = 3 * p2y - 6 * p1y;
	const cy = 3 * p1y;

	function sampleCurveDerivativeX(t : number) : number {
		// `ax t^3 + bx t^2 + cx t` expanded using Horner's rule
		return (3 * ax * t + 2 * bx) * t + cx;
	}

	function sampleCurveX(t : number) : number {
		return ((ax * t + bx) * t + cx) * t;
	}

	function sampleCurveY(t : number) : number {
		return ((ay * t + by) * t + cy) * t;
	}

	// Given an x value, find a parametric value it came from.
	function solveCurveX(x : number) : number {
		let t2 = x;
		let derivative : number;
		let x2 : number;

		// https://trac.webkit.org/browser/trunk/Source/WebCore/platform/animation
		// first try a few iterations of Newton's method -- normally very fast.
		// http://en.wikipedia.org/wikiNewton's_method
		for (let i = 0; i < 8; i++) {
			// f(t) - x = 0
			x2 = sampleCurveX(t2) - x;
			if (Math.abs(x2) < ZERO_LIMIT) {
				return t2;
			}
			derivative = sampleCurveDerivativeX(t2);
			// == 0, failure
			/* istanbul ignore if */
			if (Math.abs(derivative) < ZERO_LIMIT) {
				break;
			}
			t2 -= x2 / derivative;
		}

		// Fall back to the bisection method for reliability.
		// bisection
		// http://en.wikipedia.org/wiki/Bisection_method
		let t1 = 1;
		/* istanbul ignore next */
		let t0 = 0;

		/* istanbul ignore next */
		t2 = x;
		/* istanbul ignore next */
		while (t1 > t0) {
			x2 = sampleCurveX(t2) - x;
			if (Math.abs(x2) < ZERO_LIMIT) {
				return t2;
			}
			if (x2 > 0) {
				t1 = t2;
			} else {
				t0 = t2;
			}
			t2 = (t1 + t0) / 2;
		}

		// Failure
		return t2;
	}

	return function (x : number) : number {
		return sampleCurveY(solveCurveX(x));
	}

	// return solve;
}