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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,95 @@ | ||
| /** | ||
| * I took this straight from Wikipedia, it must be good! | ||
| */ | ||
| export default function createMonotonicInterpolant(xs, ys) { | ||
| const length = xs.length; | ||
|
|
||
| // Rearrange xs and ys so that xs is sorted | ||
| const indexes = []; | ||
| for (let i = 0; i < length; i++) { | ||
| indexes.push(i); | ||
| } | ||
| indexes.sort((a, b) => xs[a] < xs[b] ? -1 : 1); | ||
|
|
||
| const oldXs = xs, oldYs = ys; | ||
| // Impl: Creating new arrays also prevents problems if the input arrays are mutated later | ||
| xs = []; | ||
| ys = []; | ||
| // Impl: Unary plus properly converts values to numbers | ||
| for (let i = 0; i < length; i++) { | ||
| xs.push(+oldXs[indexes[i]]); | ||
| ys.push(+oldYs[indexes[i]]); | ||
| } | ||
|
|
||
| // Get consecutive differences and slopes | ||
| const dys = []; | ||
| const dxs = []; | ||
| const ms = []; | ||
| let dx, dy; | ||
| for (let i = 0; i < length - 1; i++) { | ||
| dx = xs[i + 1] - xs[i]; | ||
| dy = ys[i + 1] - ys[i]; | ||
| dxs.push(dx); | ||
| dys.push(dy); | ||
| ms.push(dy / dx); | ||
| } | ||
|
|
||
| // Get degree-1 coefficients | ||
| const c1s = [ms[0]]; | ||
| for (let i = 0; i < dxs.length - 1; i++) { | ||
| const m = ms[i]; | ||
| const mNext = ms[i + 1]; | ||
| if (m * mNext <= 0) { | ||
| c1s.push(0); | ||
| } else { | ||
| dx = dxs[i]; | ||
| const dxNext = dxs[i + 1]; | ||
| const common = dx + dxNext; | ||
| c1s.push(3 * common / ((common + dxNext) / m + (common + dx) / mNext)); | ||
| } | ||
| } | ||
| c1s.push(ms[ms.length - 1]); | ||
|
|
||
| // Get degree-2 and degree-3 coefficients | ||
| const c2s = []; | ||
| const c3s = []; | ||
| let m; | ||
| for (let i = 0; i < c1s.length - 1; i++) { | ||
| m = ms[i]; | ||
| const c1 = c1s[i]; | ||
| const invDx = 1 / dxs[i]; | ||
| const common = c1 + c1s[i + 1] - m - m; | ||
| c2s.push((m - c1 - common) * invDx); | ||
| c3s.push(common * invDx * invDx); | ||
| } | ||
|
|
||
| // Return interpolant function | ||
| return function (x) { | ||
| // The rightmost point in the dataset should give an exact result | ||
| let i = xs.length - 1; | ||
| if (x === xs[i]) { | ||
| return ys[i]; | ||
| } | ||
|
|
||
| // Search for the interval x is in, returning the corresponding y if x is one of the original xs | ||
| let low = 0; | ||
| let high = c3s.length - 1; | ||
| let mid; | ||
| while (low <= high) { | ||
| mid = Math.floor(0.5 * (low + high)); | ||
| const xHere = xs[mid]; | ||
| if (xHere < x) { | ||
| low = mid + 1; | ||
| } else if (xHere > x) { | ||
| high = mid - 1; | ||
| } else { | ||
| return ys[mid]; | ||
| } | ||
| } | ||
| i = Math.max(0, high); | ||
|
|
||
| // Interpolate | ||
| const diff = x - xs[i], diffSq = diff * diff; | ||
| return ys[i] + c1s[i] * diff + c2s[i] * diffSq + c3s[i] * diff * diffSq; | ||
| }; | ||
| } |