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102 lines
2.6 KiB
JavaScript
102 lines
2.6 KiB
JavaScript
// Adapted from https://github.com/morganherlocker/cubic-spline
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export default function spline(xs, ys) {
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const ks = getNaturalKs(xs, ys);
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const maxX = xs[xs.length - 1];
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const allYs = [];
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let i = 1;
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for (let x = 0; x <= maxX; x++) {
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while (xs[i] < x) i++;
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const t = (x - xs[i - 1]) / (xs[i] - xs[i - 1]);
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const a = ks[i - 1] * (xs[i] - xs[i - 1]) - (ys[i] - ys[i - 1]);
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const b = -ks[i] * (xs[i] - xs[i - 1]) + (ys[i] - ys[i - 1]);
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const q =
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(1 - t) * ys[i - 1] + t * ys[i] + t * (1 - t) * (a * (1 - t) + b * t);
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allYs.push(q);
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}
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return allYs;
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}
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function getNaturalKs(xs, ys) {
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const ks = xs.map(() => 0);
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const n = xs.length - 1;
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const matrix = zerosMatrix(n + 1, n + 2);
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for (
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let i = 1;
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i < n;
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i++ // rows
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) {
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matrix[i][i - 1] = 1 / (xs[i] - xs[i - 1]);
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matrix[i][i] = 2 * (1 / (xs[i] - xs[i - 1]) + 1 / (xs[i + 1] - xs[i]));
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matrix[i][i + 1] = 1 / (xs[i + 1] - xs[i]);
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matrix[i][n + 1] =
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3 *
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((ys[i] - ys[i - 1]) / ((xs[i] - xs[i - 1]) * (xs[i] - xs[i - 1])) +
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(ys[i + 1] - ys[i]) / ((xs[i + 1] - xs[i]) * (xs[i + 1] - xs[i])));
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}
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matrix[0][0] = 2 / (xs[1] - xs[0]);
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matrix[0][1] = 1 / (xs[1] - xs[0]);
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matrix[0][n + 1] =
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(3 * (ys[1] - ys[0])) / ((xs[1] - xs[0]) * (xs[1] - xs[0]));
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matrix[n][n - 1] = 1 / (xs[n] - xs[n - 1]);
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matrix[n][n] = 2 / (xs[n] - xs[n - 1]);
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matrix[n][n + 1] =
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(3 * (ys[n] - ys[n - 1])) / ((xs[n] - xs[n - 1]) * (xs[n] - xs[n - 1]));
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return solve(matrix, ks);
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}
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function solve(matrix, ks) {
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const m = matrix.length;
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// column
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for (let k = 0; k < m; k++) {
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// pivot for column
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let iMax = 0;
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let vali = Number.NEGATIVE_INFINITY;
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for (let i = k; i < m; i++)
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if (matrix[i][k] > vali) {
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iMax = i;
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vali = matrix[i][k];
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}
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swapRows(matrix, k, iMax);
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// for all rows below pivot
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for (let i = k + 1; i < m; i++) {
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for (let j = k + 1; j < m + 1; j++)
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matrix[i][j] =
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matrix[i][j] - matrix[k][j] * (matrix[i][k] / matrix[k][k]);
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matrix[i][k] = 0;
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}
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}
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// rows = columns
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for (let i = m - 1; i >= 0; i--) {
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const v = matrix[i][m] / matrix[i][i];
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ks[i] = v;
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// rows
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for (let j = i - 1; j >= 0; j--) {
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matrix[j][m] -= matrix[j][i] * v;
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matrix[j][i] = 0;
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}
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}
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return ks;
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}
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function zerosMatrix(rows, columns) {
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const matrix = [];
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for (let i = 0; i < rows; i++) {
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matrix.push([]);
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for (let j = 0; j < columns; j++) {
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matrix[i].push(0);
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}
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}
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return matrix;
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}
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function swapRows(m, k, l) {
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const p = m[k];
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m[k] = m[l];
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m[l] = p;
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}
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