heli-agri/lib/math.js

HeliAgri is a high-performance, feature-packed library for creating interactive maps on the web. It can display map tiles, vector data and markers loaded from any source on any web page. OpenLayers has been developed to further the use of geographic infor

/**
 * @module ol/math
 */

/**
 * Takes a number and clamps it to within the provided bounds.
 * @param {number} value The input number.
 * @param {number} min The minimum value to return.
 * @param {number} max The maximum value to return.
 * @return {number} The input number if it is within bounds, or the nearest
 *     number within the bounds.
 */
export function clamp(value, min, max) {
  return Math.min(Math.max(value, min), max);
}

/**
 * Returns the square of the closest distance between the point (x, y) and the
 * line segment (x1, y1) to (x2, y2).
 * @param {number} x X.
 * @param {number} y Y.
 * @param {number} x1 X1.
 * @param {number} y1 Y1.
 * @param {number} x2 X2.
 * @param {number} y2 Y2.
 * @return {number} Squared distance.
 */
export function squaredSegmentDistance(x, y, x1, y1, x2, y2) {
  const dx = x2 - x1;
  const dy = y2 - y1;
  if (dx !== 0 || dy !== 0) {
    const t = ((x - x1) * dx + (y - y1) * dy) / (dx * dx + dy * dy);
    if (t > 1) {
      x1 = x2;
      y1 = y2;
    } else if (t > 0) {
      x1 += dx * t;
      y1 += dy * t;
    }
  }
  return squaredDistance(x, y, x1, y1);
}

/**
 * Returns the square of the distance between the points (x1, y1) and (x2, y2).
 * @param {number} x1 X1.
 * @param {number} y1 Y1.
 * @param {number} x2 X2.
 * @param {number} y2 Y2.
 * @return {number} Squared distance.
 */
export function squaredDistance(x1, y1, x2, y2) {
  const dx = x2 - x1;
  const dy = y2 - y1;
  return dx * dx + dy * dy;
}

/**
 * Solves system of linear equations using Gaussian elimination method.
 *
 * @param {Array<Array<number>>} mat Augmented matrix (n x n + 1 column)
 *                                     in row-major order.
 * @return {Array<number>} The resulting vector.
 */
export function solveLinearSystem(mat) {
  const n = mat.length;

  for (let i = 0; i < n; i++) {
    // Find max in the i-th column (ignoring i - 1 first rows)
    let maxRow = i;
    let maxEl = Math.abs(mat[i][i]);
    for (let r = i + 1; r < n; r++) {
      const absValue = Math.abs(mat[r][i]);
      if (absValue > maxEl) {
        maxEl = absValue;
        maxRow = r;
      }
    }

    if (maxEl === 0) {
      return null; // matrix is singular
    }

    // Swap max row with i-th (current) row
    const tmp = mat[maxRow];
    mat[maxRow] = mat[i];
    mat[i] = tmp;

    // Subtract the i-th row to make all the remaining rows 0 in the i-th column
    for (let j = i + 1; j < n; j++) {
      const coef = -mat[j][i] / mat[i][i];
      for (let k = i; k < n + 1; k++) {
        if (i == k) {
          mat[j][k] = 0;
        } else {
          mat[j][k] += coef * mat[i][k];
        }
      }
    }
  }

  // Solve Ax=b for upper triangular matrix A (mat)
  const x = new Array(n);
  for (let l = n - 1; l >= 0; l--) {
    x[l] = mat[l][n] / mat[l][l];
    for (let m = l - 1; m >= 0; m--) {
      mat[m][n] -= mat[m][l] * x[l];
    }
  }
  return x;
}

/**
 * Converts radians to to degrees.
 *
 * @param {number} angleInRadians Angle in radians.
 * @return {number} Angle in degrees.
 */
export function toDegrees(angleInRadians) {
  return (angleInRadians * 180) / Math.PI;
}

/**
 * Converts degrees to radians.
 *
 * @param {number} angleInDegrees Angle in degrees.
 * @return {number} Angle in radians.
 */
export function toRadians(angleInDegrees) {
  return (angleInDegrees * Math.PI) / 180;
}

/**
 * Returns the modulo of a / b, depending on the sign of b.
 *
 * @param {number} a Dividend.
 * @param {number} b Divisor.
 * @return {number} Modulo.
 */
export function modulo(a, b) {
  const r = a % b;
  return r * b < 0 ? r + b : r;
}

/**
 * Calculates the linearly interpolated value of x between a and b.
 *
 * @param {number} a Number
 * @param {number} b Number
 * @param {number} x Value to be interpolated.
 * @return {number} Interpolated value.
 */
export function lerp(a, b, x) {
  return a + x * (b - a);
}

/**
 * Returns a number with a limited number of decimal digits.
 * @param {number} n The input number.
 * @param {number} decimals The maximum number of decimal digits.
 * @return {number} The input number with a limited number of decimal digits.
 */
export function toFixed(n, decimals) {
  const factor = Math.pow(10, decimals);
  return Math.round(n * factor) / factor;
}

/**
 * Rounds a number to the nearest integer value considering only the given number
 * of decimal digits (with rounding on the final digit).
 * @param {number} n The input number.
 * @param {number} decimals The maximum number of decimal digits.
 * @return {number} The nearest integer.
 */
export function round(n, decimals) {
  return Math.round(toFixed(n, decimals));
}

/**
 * Rounds a number to the next smaller integer considering only the given number
 * of decimal digits (with rounding on the final digit).
 * @param {number} n The input number.
 * @param {number} decimals The maximum number of decimal digits.
 * @return {number} The next smaller integer.
 */
export function floor(n, decimals) {
  return Math.floor(toFixed(n, decimals));
}

/**
 * Rounds a number to the next bigger integer considering only the given number
 * of decimal digits (with rounding on the final digit).
 * @param {number} n The input number.
 * @param {number} decimals The maximum number of decimal digits.
 * @return {number} The next bigger integer.
 */
export function ceil(n, decimals) {
  return Math.ceil(toFixed(n, decimals));
}