splineBasis.js•1.3 kB
/*
Basis spline
------------
Given control points V0...Vn (our values)
S0 = V0
...
Si = 1/6 * Vi-1 + 2/3 * Vi + 1/6 * Vi+1
...
Sn = Vn
The Bézier curve has control points:
Bi = Si-1, 2/3 * Vi-1 + 1/3 * Vi, 1/3 * Vi-1 + 2/3 * Vi, Si
Which we can then factor into the Bezier's explicit form:
B(t) = (1-t)^3 * P0 + 3 * (1-t)^2 * t * P1 + (1-t) * t^2 * P2 + t^3 * P3
*/
const mod = (v, l) => (v + l) % l;
const bspline = (Vim2, Vim1, Vi, Vip1, t) => {
let t2 = t * t;
let t3 = t2 * t;
return (
((1 - 3 * t + 3 * t2 - t3) * Vim2 +
(4 - 6 * t2 + 3 * t3) * Vim1 +
(1 + 3 * t + 3 * t2 - 3 * t3) * Vi +
t3 * Vip1) /
6
);
};
export const interpolatorSplineBasis = arr => t => {
let classes = arr.length - 1;
let i = t >= 1 ? classes - 1 : Math.max(0, Math.floor(t * classes));
return bspline(
i > 0 ? arr[i - 1] : 2 * arr[i] - arr[i + 1],
arr[i],
arr[i + 1],
i < classes - 1 ? arr[i + 2] : 2 * arr[i + 1] - arr[i],
(t - i / classes) * classes
);
};
export const interpolatorSplineBasisClosed = arr => t => {
const classes = arr.length - 1;
const i = Math.floor(t * classes);
return bspline(
arr[mod(i - 1, arr.length)],
arr[mod(i, arr.length)],
arr[mod(i + 1, arr.length)],
arr[mod(i + 2, arr.length)],
(t - i / classes) * classes
);
};