@adaskothebeast/splines/NaturalSpline.cjs.js

Spline interpolation for TypeScript

'use strict';

var splineBase = require('./spline-base.cjs.js');

/**
 * Copyright (C) 2022 Adam Pluciński
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU Affero General Public License as published
 *  by the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Affero General Public License for more details.
 *
 *  You should have received a copy of the GNU Affero General Public License
 *  along with this program.  If not, see <https://www.gnu.org/licenses/>.
 */
class NaturalSpline extends splineBase.SplineBase {
  constructor(values) {
    super(values);
    this.a = [];
    this.h = [];
    this.a[0] = 0.0;
    this.h[0] = 0.0;
    const length = values.length;
    for (let i = 1; i < length; i++) {
      this.h[i] = this.xs[i] - this.xs[i - 1];
    }
    if (length <= 2) {
      return;
    }
    const sub = [];
    const diag = [];
    const sup = [];
    sub[0] = 0.0;
    diag[0] = 0.0;
    sup[0] = 0.0;
    for (let i = 1; i < length - 1; i++) {
      diag[i] = (this.h[i] + this.h[i + 1]) / 3.0;
      sup[i] = this.h[i + 1] / 6.0;
      sub[i] = this.h[i] / 6.0;
      ///this.a[i] = (this.xs[i + 1] - this.xs[i]) / this.h[i + 1] - (this.xs[i] - this.xs[i - 1]) / this.h[i];
      this.a[i] = (this.ys[i + 1] - this.ys[i]) / this.h[i + 1] - (this.ys[i] - this.ys[i - 1]) / this.h[i];
    }
    this.solve(sub, diag, sup, length - 2);
    this.a[length - 1] = 0.0;
  }
  solve(sub, diag, sup, n) {
    for (let i = 2; i < n; i++) {
      sub[i] = sub[i] / diag[i - 1];
      diag[i] = diag[i] - sub[i] * sup[i - 1];
      this.a[i] = this.a[i] - sub[i] * this.a[i - 1];
    }
    this.a[n] = this.a[n] / diag[n];
    for (let i = n - 1; i >= 1; i--) {
      this.a[i] = (this.a[i] - sup[i] * this.a[i + 1]) / diag[i];
    }
  }
  interpolate(x) {
    if (this.xs.length === 0) {
      return 0;
    }
    if (this.xs.length === 1) {
      return this.ys[0];
    }
    // Handle x below or at the left boundary
    if (x <= this.xs[0]) {
      return this.ys[0];
    }
    // Handle x at or above the right boundary
    if (x >= this.xs[this.xs.length - 1]) {
      return this.ys[this.xs.length - 1];
    }
    // Find the segment containing x using binary search
    let low = 0;
    let high = this.xs.length - 1;
    while (high - low > 1) {
      const mid = Math.floor((low + high) / 2);
      if (this.xs[mid] <= x) {
        low = mid;
      } else {
        high = mid;
      }
    }
    // gap is the index of the right endpoint of the segment (1-based in original algorithm)
    const gap = high;
    const x1 = x - this.xs[gap - 1];
    const x2 = this.h[gap] - x1;
    return ((-this.a[gap - 1] / 6.0 * (x2 + this.h[gap]) * x1 + this.ys[gap - 1]) * x2 + (-this.a[gap] / 6.0 * (x1 + this.h[gap]) * x2 + this.ys[gap]) * x1) / this.h[gap];
  }
}

exports.NumberPair = splineBase.NumberPair;
exports.SplineBase = splineBase.SplineBase;
exports.isNumberPairArray = splineBase.isNumberPairArray;
exports.isNumberTupleArray = splineBase.isNumberTupleArray;
exports.sortNumberPairIndexes = splineBase.sortNumberPairIndexes;
exports.sortNumberTupleIndexes = splineBase.sortNumberTupleIndexes;
exports.NaturalSpline = NaturalSpline;