backend/libs/three/extras/core/Interpolations.js

/**
 * Bezier Curves formulas obtained from
 * https://en.wikipedia.org/wiki/B%C3%A9zier_curve
 */

function CatmullRom(t, p0, p1, p2, p3) {
	const v0 = (p2 - p0) * 0.5;
	const v1 = (p3 - p1) * 0.5;
	const t2 = t * t;
	const t3 = t * t2;
	return (2 * p1 - 2 * p2 + v0 + v1) * t3 + (-3 * p1 + 3 * p2 - 2 * v0 - v1) * t2 + v0 * t + p1;
}

//

function QuadraticBezierP0(t, p) {
	const k = 1 - t;
	return k * k * p;
}

function QuadraticBezierP1(t, p) {
	return 2 * (1 - t) * t * p;
}

function QuadraticBezierP2(t, p) {
	return t * t * p;
}

function QuadraticBezier(t, p0, p1, p2) {
	return QuadraticBezierP0(t, p0) + QuadraticBezierP1(t, p1) + QuadraticBezierP2(t, p2);
}

//

function CubicBezierP0(t, p) {
	const k = 1 - t;
	return k * k * k * p;
}

function CubicBezierP1(t, p) {
	const k = 1 - t;
	return 3 * k * k * t * p;
}

function CubicBezierP2(t, p) {
	return 3 * (1 - t) * t * t * p;
}

function CubicBezierP3(t, p) {
	return t * t * t * p;
}

function CubicBezier(t, p0, p1, p2, p3) {
	return CubicBezierP0(t, p0) + CubicBezierP1(t, p1) + CubicBezierP2(t, p2) + CubicBezierP3(t, p3);
}

export { CatmullRom, QuadraticBezier, CubicBezier };