Approximating Geometric Slerp / Volodymyr Agafonkin

Engineer at Mapbox, creator of Leaflet, algorithms geek, open source enthusiast, musician, father of twin girls, Ukrainian. 🇺🇦

Published

Edited

May 22, 2019

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Approximating Geometric Slerp

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slerp = (a, b, t) => {

const k = Math.acos(dot(a, b));

const q = Math.sin(k * (1 - t));

const p = Math.sin(k * t);

return unitLerp(a, b, q, p);

}

fslerp = function fslerp(a, b, t) {

if (t === 0.5) return unitLerp(a, b, t, t);

const d = dot(a, b);

if (d < 0) { // angle > 90; recurse into one of the halves

const m = unitLerp(a, b, 0.5, 0.5);

return t < 0.5 ? fslerp(a, m, t * 2) : fslerp(m, b, t * 2 - 1);

}

const A = 1.0904 + d * (-3.2452 + d * (3.55645 - d * 1.43519));

const B = 0.848013 + d * (-1.06021 + d * 0.215638);

const K = A * (t - 0.5) * (t - 0.5) + B;

const p = t + t * (t - 0.5) * (t - 1) * K;

return unitLerp(a, b, 1 - p, p);

}

unitLerp = ([ax, ay], [bx, by], t0, t1) => {

const x = ax * t0 + bx * t1;

const y = ay * t0 + by * t1;

const d = Math.sqrt(x * x + y * y);

return [x / d, y / d];

}

dot = ([ax, ay], [bx, by]) => ax * bx + ay * by

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