typescript-cubic-spline/dist/Spline.js

Spline interpolation

"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
var Spline = /** @class */ (function () {
    function Spline(xs, ys) {
        this.xs = xs;
        this.ys = ys;
        this.ks = this.getNaturalKs(new Float64Array(this.xs.length));
    }
    Spline.prototype.getNaturalKs = function (ks) {
        var n = this.xs.length - 1;
        var A = zerosMat(n + 1, n + 2);
        for (var i = 1; i < n; i++ // rows
        ) {
            A[i][i - 1] = 1 / (this.xs[i] - this.xs[i - 1]);
            A[i][i] =
                2 *
                    (1 / (this.xs[i] - this.xs[i - 1]) + 1 / (this.xs[i + 1] - this.xs[i]));
            A[i][i + 1] = 1 / (this.xs[i + 1] - this.xs[i]);
            A[i][n + 1] =
                3 *
                    ((this.ys[i] - this.ys[i - 1]) /
                        ((this.xs[i] - this.xs[i - 1]) * (this.xs[i] - this.xs[i - 1])) +
                        (this.ys[i + 1] - this.ys[i]) /
                            ((this.xs[i + 1] - this.xs[i]) * (this.xs[i + 1] - this.xs[i])));
        }
        A[0][0] = 2 / (this.xs[1] - this.xs[0]);
        A[0][1] = 1 / (this.xs[1] - this.xs[0]);
        A[0][n + 1] =
            (3 * (this.ys[1] - this.ys[0])) /
                ((this.xs[1] - this.xs[0]) * (this.xs[1] - this.xs[0]));
        A[n][n - 1] = 1 / (this.xs[n] - this.xs[n - 1]);
        A[n][n] = 2 / (this.xs[n] - this.xs[n - 1]);
        A[n][n + 1] =
            (3 * (this.ys[n] - this.ys[n - 1])) /
                ((this.xs[n] - this.xs[n - 1]) * (this.xs[n] - this.xs[n - 1]));
        return solve(A, ks);
    };
    /**
     * inspired by https://stackoverflow.com/a/40850313/4417327
     */
    Spline.prototype.getIndexBefore = function (target) {
        var low = 0;
        var high = this.xs.length;
        var mid = 0;
        while (low < high) {
            mid = Math.floor((low + high) / 2);
            if (this.xs[mid] < target && mid !== low) {
                low = mid;
            }
            else if (this.xs[mid] >= target && mid !== high) {
                high = mid;
            }
            else {
                high = low;
            }
        }
        return low + 1;
    };
    Spline.prototype.at = function (x) {
        var i = this.getIndexBefore(x);
        var t = (x - this.xs[i - 1]) / (this.xs[i] - this.xs[i - 1]);
        var a = this.ks[i - 1] * (this.xs[i] - this.xs[i - 1]) -
            (this.ys[i] - this.ys[i - 1]);
        var b = -this.ks[i] * (this.xs[i] - this.xs[i - 1]) +
            (this.ys[i] - this.ys[i - 1]);
        var q = (1 - t) * this.ys[i - 1] +
            t * this.ys[i] +
            t * (1 - t) * (a * (1 - t) + b * t);
        return q;
    };
    return Spline;
}());
function solve(A, ks) {
    var m = A.length;
    var h = 0;
    var k = 0;
    while (h < m && k <= m) {
        var i_max = 0;
        var max = -Infinity;
        for (var i = h; i < m; i++) {
            var v_1 = Math.abs(A[i][k]);
            if (v_1 > max) {
                i_max = i;
                max = v_1;
            }
        }
        if (A[i_max][k] === 0) {
            k++;
        }
        else {
            swapRows(A, h, i_max);
            for (var i = h + 1; i < m; i++) {
                var f = A[i][k] / A[h][k];
                A[i][k] = 0;
                for (var j = k + 1; j <= m; j++)
                    A[i][j] -= A[h][j] * f;
            }
            h++;
            k++;
        }
    }
    for (var i = m - 1; i >= 0; i-- // rows = columns
    ) {
        var v = 0;
        if (A[i][i]) {
            v = A[i][m] / A[i][i];
        }
        ks[i] = v;
        for (var j = i - 1; j >= 0; j-- // rows
        ) {
            A[j][m] -= A[j][i] * v;
            A[j][i] = 0;
        }
    }
    return ks;
}
function zerosMat(r, c) {
    var A = [];
    for (var i = 0; i < r; i++)
        A.push(new Float64Array(c));
    return A;
}
function swapRows(m, k, l) {
    var p = m[k];
    m[k] = m[l];
    m[l] = p;
}
exports.default = Spline;