Source: node_modules/gl-matrix/esm/mat2d.js

  1. import * as glMatrix from "./common.js";
  2. /**
  3.  * 2x3 Matrix
  4.  * @module mat2d
  5.  * @description
  6.  * A mat2d contains six elements defined as:
  7.  * <pre>
  8.  * [a, b,
  9.  *  c, d,
  10.  *  tx, ty]
  11.  * </pre>
  12.  * This is a short form for the 3x3 matrix:
  13.  * <pre>
  14.  * [a, b, 0,
  15.  *  c, d, 0,
  16.  *  tx, ty, 1]
  17.  * </pre>
  18.  * The last column is ignored so the array is shorter and operations are faster.
  19.  */
  21. /**
  22.  * Creates a new identity mat2d
  23.  *
  24.  * @returns {mat2d} a new 2x3 matrix
  25.  */
  27. export function create() {
  28.   var out = new glMatrix.ARRAY_TYPE(6);
  30.   if (glMatrix.ARRAY_TYPE != Float32Array) {
  31.     out[1] = 0;
  32.     out[2] = 0;
  33.     out[4] = 0;
  34.     out[5] = 0;
  35.   }
  37.   out[0] = 1;
  38.   out[3] = 1;
  39.   return out;
  40. }
  41. /**
  42.  * Creates a new mat2d initialized with values from an existing matrix
  43.  *
  44.  * @param {ReadonlyMat2d} a matrix to clone
  45.  * @returns {mat2d} a new 2x3 matrix
  46.  */
  48. export function clone(a) {
  49.   var out = new glMatrix.ARRAY_TYPE(6);
  50.   out[0] = a[0];
  51.   out[1] = a[1];
  52.   out[2] = a[2];
  53.   out[3] = a[3];
  54.   out[4] = a[4];
  55.   out[5] = a[5];
  56.   return out;
  57. }
  58. /**
  59.  * Copy the values from one mat2d to another
  60.  *
  61.  * @param {mat2d} out the receiving matrix
  62.  * @param {ReadonlyMat2d} a the source matrix
  63.  * @returns {mat2d} out
  64.  */
  66. export function copy(out, a) {
  67.   out[0] = a[0];
  68.   out[1] = a[1];
  69.   out[2] = a[2];
  70.   out[3] = a[3];
  71.   out[4] = a[4];
  72.   out[5] = a[5];
  73.   return out;
  74. }
  75. /**
  76.  * Set a mat2d to the identity matrix
  77.  *
  78.  * @param {mat2d} out the receiving matrix
  79.  * @returns {mat2d} out
  80.  */
  82. export function identity(out) {
  83.   out[0] = 1;
  84.   out[1] = 0;
  85.   out[2] = 0;
  86.   out[3] = 1;
  87.   out[4] = 0;
  88.   out[5] = 0;
  89.   return out;
  90. }
  91. /**
  92.  * Create a new mat2d with the given values
  93.  *
  94.  * @param {Number} a Component A (index 0)
  95.  * @param {Number} b Component B (index 1)
  96.  * @param {Number} c Component C (index 2)
  97.  * @param {Number} d Component D (index 3)
  98.  * @param {Number} tx Component TX (index 4)
  99.  * @param {Number} ty Component TY (index 5)
  100.  * @returns {mat2d} A new mat2d
  101.  */
  103. export function fromValues(a, b, c, d, tx, ty) {
  104.   var out = new glMatrix.ARRAY_TYPE(6);
  105.   out[0] = a;
  106.   out[1] = b;
  107.   out[2] = c;
  108.   out[3] = d;
  109.   out[4] = tx;
  110.   out[5] = ty;
  111.   return out;
  112. }
  113. /**
  114.  * Set the components of a mat2d to the given values
  115.  *
  116.  * @param {mat2d} out the receiving matrix
  117.  * @param {Number} a Component A (index 0)
  118.  * @param {Number} b Component B (index 1)
  119.  * @param {Number} c Component C (index 2)
  120.  * @param {Number} d Component D (index 3)
  121.  * @param {Number} tx Component TX (index 4)
  122.  * @param {Number} ty Component TY (index 5)
  123.  * @returns {mat2d} out
  124.  */
  126. export function set(out, a, b, c, d, tx, ty) {
  127.   out[0] = a;
  128.   out[1] = b;
  129.   out[2] = c;
  130.   out[3] = d;
  131.   out[4] = tx;
  132.   out[5] = ty;
  133.   return out;
  134. }
  135. /**
  136.  * Inverts a mat2d
  137.  *
  138.  * @param {mat2d} out the receiving matrix
  139.  * @param {ReadonlyMat2d} a the source matrix
  140.  * @returns {mat2d} out
  141.  */
  143. export function invert(out, a) {
  144.   var aa = a[0],
  145.       ab = a[1],
  146.       ac = a[2],
  147.       ad = a[3];
  148.   var atx = a[4],
  149.       aty = a[5];
  150.   var det = aa * ad - ab * ac;
  152.   if (!det) {
  153.     return null;
  154.   }
  156.   det = 1.0 / det;
  157.   out[0] = ad * det;
  158.   out[1] = -ab * det;
  159.   out[2] = -ac * det;
  160.   out[3] = aa * det;
  161.   out[4] = (ac * aty - ad * atx) * det;
  162.   out[5] = (ab * atx - aa * aty) * det;
  163.   return out;
  164. }
  165. /**
  166.  * Calculates the determinant of a mat2d
  167.  *
  168.  * @param {ReadonlyMat2d} a the source matrix
  169.  * @returns {Number} determinant of a
  170.  */
  172. export function determinant(a) {
  173.   return a[0] * a[3] - a[1] * a[2];
  174. }
  175. /**
  176.  * Multiplies two mat2d's
  177.  *
  178.  * @param {mat2d} out the receiving matrix
  179.  * @param {ReadonlyMat2d} a the first operand
  180.  * @param {ReadonlyMat2d} b the second operand
  181.  * @returns {mat2d} out
  182.  */
  184. export function multiply(out, a, b) {
  185.   var a0 = a[0],
  186.       a1 = a[1],
  187.       a2 = a[2],
  188.       a3 = a[3],
  189.       a4 = a[4],
  190.       a5 = a[5];
  191.   var b0 = b[0],
  192.       b1 = b[1],
  193.       b2 = b[2],
  194.       b3 = b[3],
  195.       b4 = b[4],
  196.       b5 = b[5];
  197.   out[0] = a0 * b0 + a2 * b1;
  198.   out[1] = a1 * b0 + a3 * b1;
  199.   out[2] = a0 * b2 + a2 * b3;
  200.   out[3] = a1 * b2 + a3 * b3;
  201.   out[4] = a0 * b4 + a2 * b5 + a4;
  202.   out[5] = a1 * b4 + a3 * b5 + a5;
  203.   return out;
  204. }
  205. /**
  206.  * Rotates a mat2d by the given angle
  207.  *
  208.  * @param {mat2d} out the receiving matrix
  209.  * @param {ReadonlyMat2d} a the matrix to rotate
  210.  * @param {Number} rad the angle to rotate the matrix by
  211.  * @returns {mat2d} out
  212.  */
  214. export function rotate(out, a, rad) {
  215.   var a0 = a[0],
  216.       a1 = a[1],
  217.       a2 = a[2],
  218.       a3 = a[3],
  219.       a4 = a[4],
  220.       a5 = a[5];
  221.   var s = Math.sin(rad);
  222.   var c = Math.cos(rad);
  223.   out[0] = a0 * c + a2 * s;
  224.   out[1] = a1 * c + a3 * s;
  225.   out[2] = a0 * -s + a2 * c;
  226.   out[3] = a1 * -s + a3 * c;
  227.   out[4] = a4;
  228.   out[5] = a5;
  229.   return out;
  230. }
  231. /**
  232.  * Scales the mat2d by the dimensions in the given vec2
  233.  *
  234.  * @param {mat2d} out the receiving matrix
  235.  * @param {ReadonlyMat2d} a the matrix to translate
  236.  * @param {ReadonlyVec2} v the vec2 to scale the matrix by
  237.  * @returns {mat2d} out
  238.  **/
  240. export function scale(out, a, v) {
  241.   var a0 = a[0],
  242.       a1 = a[1],
  243.       a2 = a[2],
  244.       a3 = a[3],
  245.       a4 = a[4],
  246.       a5 = a[5];
  247.   var v0 = v[0],
  248.       v1 = v[1];
  249.   out[0] = a0 * v0;
  250.   out[1] = a1 * v0;
  251.   out[2] = a2 * v1;
  252.   out[3] = a3 * v1;
  253.   out[4] = a4;
  254.   out[5] = a5;
  255.   return out;
  256. }
  257. /**
  258.  * Translates the mat2d by the dimensions in the given vec2
  259.  *
  260.  * @param {mat2d} out the receiving matrix
  261.  * @param {ReadonlyMat2d} a the matrix to translate
  262.  * @param {ReadonlyVec2} v the vec2 to translate the matrix by
  263.  * @returns {mat2d} out
  264.  **/
  266. export function translate(out, a, v) {
  267.   var a0 = a[0],
  268.       a1 = a[1],
  269.       a2 = a[2],
  270.       a3 = a[3],
  271.       a4 = a[4],
  272.       a5 = a[5];
  273.   var v0 = v[0],
  274.       v1 = v[1];
  275.   out[0] = a0;
  276.   out[1] = a1;
  277.   out[2] = a2;
  278.   out[3] = a3;
  279.   out[4] = a0 * v0 + a2 * v1 + a4;
  280.   out[5] = a1 * v0 + a3 * v1 + a5;
  281.   return out;
  282. }
  283. /**
  284.  * Creates a matrix from a given angle
  285.  * This is equivalent to (but much faster than):
  286.  *
  287.  *     mat2d.identity(dest);
  288.  *     mat2d.rotate(dest, dest, rad);
  289.  *
  290.  * @param {mat2d} out mat2d receiving operation result
  291.  * @param {Number} rad the angle to rotate the matrix by
  292.  * @returns {mat2d} out
  293.  */
  295. export function fromRotation(out, rad) {
  296.   var s = Math.sin(rad),
  297.       c = Math.cos(rad);
  298.   out[0] = c;
  299.   out[1] = s;
  300.   out[2] = -s;
  301.   out[3] = c;
  302.   out[4] = 0;
  303.   out[5] = 0;
  304.   return out;
  305. }
  306. /**
  307.  * Creates a matrix from a vector scaling
  308.  * This is equivalent to (but much faster than):
  309.  *
  310.  *     mat2d.identity(dest);
  311.  *     mat2d.scale(dest, dest, vec);
  312.  *
  313.  * @param {mat2d} out mat2d receiving operation result
  314.  * @param {ReadonlyVec2} v Scaling vector
  315.  * @returns {mat2d} out
  316.  */
  318. export function fromScaling(out, v) {
  319.   out[0] = v[0];
  320.   out[1] = 0;
  321.   out[2] = 0;
  322.   out[3] = v[1];
  323.   out[4] = 0;
  324.   out[5] = 0;
  325.   return out;
  326. }
  327. /**
  328.  * Creates a matrix from a vector translation
  329.  * This is equivalent to (but much faster than):
  330.  *
  331.  *     mat2d.identity(dest);
  332.  *     mat2d.translate(dest, dest, vec);
  333.  *
  334.  * @param {mat2d} out mat2d receiving operation result
  335.  * @param {ReadonlyVec2} v Translation vector
  336.  * @returns {mat2d} out
  337.  */
  339. export function fromTranslation(out, v) {
  340.   out[0] = 1;
  341.   out[1] = 0;
  342.   out[2] = 0;
  343.   out[3] = 1;
  344.   out[4] = v[0];
  345.   out[5] = v[1];
  346.   return out;
  347. }
  348. /**
  349.  * Returns a string representation of a mat2d
  350.  *
  351.  * @param {ReadonlyMat2d} a matrix to represent as a string
  352.  * @returns {String} string representation of the matrix
  353.  */
  355. export function str(a) {
  356.   return "mat2d(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ", " + a[4] + ", " + a[5] + ")";
  357. }
  358. /**
  359.  * Returns Frobenius norm of a mat2d
  360.  *
  361.  * @param {ReadonlyMat2d} a the matrix to calculate Frobenius norm of
  362.  * @returns {Number} Frobenius norm
  363.  */
  365. export function frob(a) {
  366.   return Math.hypot(a[0], a[1], a[2], a[3], a[4], a[5], 1);
  367. }
  368. /**
  369.  * Adds two mat2d's
  370.  *
  371.  * @param {mat2d} out the receiving matrix
  372.  * @param {ReadonlyMat2d} a the first operand
  373.  * @param {ReadonlyMat2d} b the second operand
  374.  * @returns {mat2d} out
  375.  */
  377. export function add(out, a, b) {
  378.   out[0] = a[0] + b[0];
  379.   out[1] = a[1] + b[1];
  380.   out[2] = a[2] + b[2];
  381.   out[3] = a[3] + b[3];
  382.   out[4] = a[4] + b[4];
  383.   out[5] = a[5] + b[5];
  384.   return out;
  385. }
  386. /**
  387.  * Subtracts matrix b from matrix a
  388.  *
  389.  * @param {mat2d} out the receiving matrix
  390.  * @param {ReadonlyMat2d} a the first operand
  391.  * @param {ReadonlyMat2d} b the second operand
  392.  * @returns {mat2d} out
  393.  */
  395. export function subtract(out, a, b) {
  396.   out[0] = a[0] - b[0];
  397.   out[1] = a[1] - b[1];
  398.   out[2] = a[2] - b[2];
  399.   out[3] = a[3] - b[3];
  400.   out[4] = a[4] - b[4];
  401.   out[5] = a[5] - b[5];
  402.   return out;
  403. }
  404. /**
  405.  * Multiply each element of the matrix by a scalar.
  406.  *
  407.  * @param {mat2d} out the receiving matrix
  408.  * @param {ReadonlyMat2d} a the matrix to scale
  409.  * @param {Number} b amount to scale the matrix's elements by
  410.  * @returns {mat2d} out
  411.  */
  413. export function multiplyScalar(out, a, b) {
  414.   out[0] = a[0] * b;
  415.   out[1] = a[1] * b;
  416.   out[2] = a[2] * b;
  417.   out[3] = a[3] * b;
  418.   out[4] = a[4] * b;
  419.   out[5] = a[5] * b;
  420.   return out;
  421. }
  422. /**
  423.  * Adds two mat2d's after multiplying each element of the second operand by a scalar value.
  424.  *
  425.  * @param {mat2d} out the receiving vector
  426.  * @param {ReadonlyMat2d} a the first operand
  427.  * @param {ReadonlyMat2d} b the second operand
  428.  * @param {Number} scale the amount to scale b's elements by before adding
  429.  * @returns {mat2d} out
  430.  */
  432. export function multiplyScalarAndAdd(out, a, b, scale) {
  433.   out[0] = a[0] + b[0] * scale;
  434.   out[1] = a[1] + b[1] * scale;
  435.   out[2] = a[2] + b[2] * scale;
  436.   out[3] = a[3] + b[3] * scale;
  437.   out[4] = a[4] + b[4] * scale;
  438.   out[5] = a[5] + b[5] * scale;
  439.   return out;
  440. }
  441. /**
  442.  * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
  443.  *
  444.  * @param {ReadonlyMat2d} a The first matrix.
  445.  * @param {ReadonlyMat2d} b The second matrix.
  446.  * @returns {Boolean} True if the matrices are equal, false otherwise.
  447.  */
  449. export function exactEquals(a, b) {
  450.   return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3] && a[4] === b[4] && a[5] === b[5];
  451. }
  452. /**
  453.  * Returns whether or not the matrices have approximately the same elements in the same position.
  454.  *
  455.  * @param {ReadonlyMat2d} a The first matrix.
  456.  * @param {ReadonlyMat2d} b The second matrix.
  457.  * @returns {Boolean} True if the matrices are equal, false otherwise.
  458.  */
  460. export function equals(a, b) {
  461.   var a0 = a[0],
  462.       a1 = a[1],
  463.       a2 = a[2],
  464.       a3 = a[3],
  465.       a4 = a[4],
  466.       a5 = a[5];
  467.   var b0 = b[0],
  468.       b1 = b[1],
  469.       b2 = b[2],
  470.       b3 = b[3],
  471.       b4 = b[4],
  472.       b5 = b[5];
  473.   return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5));
  474. }
  475. /**
  476.  * Alias for {@link mat2d.multiply}
  477.  * @function
  478.  */
  480. export var mul = multiply;
  481. /**
  482.  * Alias for {@link mat2d.subtract}
  483.  * @function
  484.  */
  486. export var sub = subtract;