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- /*!
- @fileoverview gl-matrix - High performance matrix and vector operations
- @author Brandon Jones
- @author Colin MacKenzie IV
- @version 3.4.3
- Copyright (c) 2015-2021, Brandon Jones, Colin MacKenzie IV.
- Permission is hereby granted, free of charge, to any person obtaining a copy
- of this software and associated documentation files (the "Software"), to deal
- in the Software without restriction, including without limitation the rights
- to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
- copies of the Software, and to permit persons to whom the Software is
- furnished to do so, subject to the following conditions:
- The above copyright notice and this permission notice shall be included in
- all copies or substantial portions of the Software.
- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
- AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
- OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
- THE SOFTWARE.
- */
- (function (global, factory) {
- typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
- typeof define === 'function' && define.amd ? define(['exports'], factory) :
- (global = global || self, factory(global.glMatrix = {}));
- }(this, (function (exports) { 'use strict';
- /**
- * Common utilities
- * @module glMatrix
- */
- // Configuration Constants
- var EPSILON = 0.000001;
- var ARRAY_TYPE = typeof Float32Array !== 'undefined' ? Float32Array : Array;
- var RANDOM = Math.random;
- /**
- * Sets the type of array used when creating new vectors and matrices
- *
- * @param {Float32ArrayConstructor | ArrayConstructor} type Array type, such as Float32Array or Array
- */
- function setMatrixArrayType(type) {
- ARRAY_TYPE = type;
- }
- var degree = Math.PI / 180;
- /**
- * Convert Degree To Radian
- *
- * @param {Number} a Angle in Degrees
- */
- function toRadian(a) {
- return a * degree;
- }
- /**
- * Tests whether or not the arguments have approximately the same value, within an absolute
- * or relative tolerance of glMatrix.EPSILON (an absolute tolerance is used for values less
- * than or equal to 1.0, and a relative tolerance is used for larger values)
- *
- * @param {Number} a The first number to test.
- * @param {Number} b The second number to test.
- * @returns {Boolean} True if the numbers are approximately equal, false otherwise.
- */
- function equals(a, b) {
- return Math.abs(a - b) <= EPSILON * Math.max(1.0, Math.abs(a), Math.abs(b));
- }
- if (!Math.hypot) Math.hypot = function () {
- var y = 0,
- i = arguments.length;
- while (i--) {
- y += arguments[i] * arguments[i];
- }
- return Math.sqrt(y);
- };
- var common = /*#__PURE__*/Object.freeze({
- __proto__: null,
- EPSILON: EPSILON,
- get ARRAY_TYPE () { return ARRAY_TYPE; },
- RANDOM: RANDOM,
- setMatrixArrayType: setMatrixArrayType,
- toRadian: toRadian,
- equals: equals
- });
- /**
- * 2x2 Matrix
- * @module mat2
- */
- /**
- * Creates a new identity mat2
- *
- * @returns {mat2} a new 2x2 matrix
- */
- function create() {
- var out = new ARRAY_TYPE(4);
- if (ARRAY_TYPE != Float32Array) {
- out[1] = 0;
- out[2] = 0;
- }
- out[0] = 1;
- out[3] = 1;
- return out;
- }
- /**
- * Creates a new mat2 initialized with values from an existing matrix
- *
- * @param {ReadonlyMat2} a matrix to clone
- * @returns {mat2} a new 2x2 matrix
- */
- function clone(a) {
- var out = new ARRAY_TYPE(4);
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- return out;
- }
- /**
- * Copy the values from one mat2 to another
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the source matrix
- * @returns {mat2} out
- */
- function copy(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- return out;
- }
- /**
- * Set a mat2 to the identity matrix
- *
- * @param {mat2} out the receiving matrix
- * @returns {mat2} out
- */
- function identity(out) {
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 1;
- return out;
- }
- /**
- * Create a new mat2 with the given values
- *
- * @param {Number} m00 Component in column 0, row 0 position (index 0)
- * @param {Number} m01 Component in column 0, row 1 position (index 1)
- * @param {Number} m10 Component in column 1, row 0 position (index 2)
- * @param {Number} m11 Component in column 1, row 1 position (index 3)
- * @returns {mat2} out A new 2x2 matrix
- */
- function fromValues(m00, m01, m10, m11) {
- var out = new ARRAY_TYPE(4);
- out[0] = m00;
- out[1] = m01;
- out[2] = m10;
- out[3] = m11;
- return out;
- }
- /**
- * Set the components of a mat2 to the given values
- *
- * @param {mat2} out the receiving matrix
- * @param {Number} m00 Component in column 0, row 0 position (index 0)
- * @param {Number} m01 Component in column 0, row 1 position (index 1)
- * @param {Number} m10 Component in column 1, row 0 position (index 2)
- * @param {Number} m11 Component in column 1, row 1 position (index 3)
- * @returns {mat2} out
- */
- function set(out, m00, m01, m10, m11) {
- out[0] = m00;
- out[1] = m01;
- out[2] = m10;
- out[3] = m11;
- return out;
- }
- /**
- * Transpose the values of a mat2
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the source matrix
- * @returns {mat2} out
- */
- function transpose(out, a) {
- // If we are transposing ourselves we can skip a few steps but have to cache
- // some values
- if (out === a) {
- var a1 = a[1];
- out[1] = a[2];
- out[2] = a1;
- } else {
- out[0] = a[0];
- out[1] = a[2];
- out[2] = a[1];
- out[3] = a[3];
- }
- return out;
- }
- /**
- * Inverts a mat2
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the source matrix
- * @returns {mat2} out
- */
- function invert(out, a) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3]; // Calculate the determinant
- var det = a0 * a3 - a2 * a1;
- if (!det) {
- return null;
- }
- det = 1.0 / det;
- out[0] = a3 * det;
- out[1] = -a1 * det;
- out[2] = -a2 * det;
- out[3] = a0 * det;
- return out;
- }
- /**
- * Calculates the adjugate of a mat2
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the source matrix
- * @returns {mat2} out
- */
- function adjoint(out, a) {
- // Caching this value is nessecary if out == a
- var a0 = a[0];
- out[0] = a[3];
- out[1] = -a[1];
- out[2] = -a[2];
- out[3] = a0;
- return out;
- }
- /**
- * Calculates the determinant of a mat2
- *
- * @param {ReadonlyMat2} a the source matrix
- * @returns {Number} determinant of a
- */
- function determinant(a) {
- return a[0] * a[3] - a[2] * a[1];
- }
- /**
- * Multiplies two mat2's
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the first operand
- * @param {ReadonlyMat2} b the second operand
- * @returns {mat2} out
- */
- function multiply(out, a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3];
- out[0] = a0 * b0 + a2 * b1;
- out[1] = a1 * b0 + a3 * b1;
- out[2] = a0 * b2 + a2 * b3;
- out[3] = a1 * b2 + a3 * b3;
- return out;
- }
- /**
- * Rotates a mat2 by the given angle
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the matrix to rotate
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat2} out
- */
- function rotate(out, a, rad) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3];
- var s = Math.sin(rad);
- var c = Math.cos(rad);
- out[0] = a0 * c + a2 * s;
- out[1] = a1 * c + a3 * s;
- out[2] = a0 * -s + a2 * c;
- out[3] = a1 * -s + a3 * c;
- return out;
- }
- /**
- * Scales the mat2 by the dimensions in the given vec2
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the matrix to rotate
- * @param {ReadonlyVec2} v the vec2 to scale the matrix by
- * @returns {mat2} out
- **/
- function scale(out, a, v) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3];
- var v0 = v[0],
- v1 = v[1];
- out[0] = a0 * v0;
- out[1] = a1 * v0;
- out[2] = a2 * v1;
- out[3] = a3 * v1;
- return out;
- }
- /**
- * Creates a matrix from a given angle
- * This is equivalent to (but much faster than):
- *
- * mat2.identity(dest);
- * mat2.rotate(dest, dest, rad);
- *
- * @param {mat2} out mat2 receiving operation result
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat2} out
- */
- function fromRotation(out, rad) {
- var s = Math.sin(rad);
- var c = Math.cos(rad);
- out[0] = c;
- out[1] = s;
- out[2] = -s;
- out[3] = c;
- return out;
- }
- /**
- * Creates a matrix from a vector scaling
- * This is equivalent to (but much faster than):
- *
- * mat2.identity(dest);
- * mat2.scale(dest, dest, vec);
- *
- * @param {mat2} out mat2 receiving operation result
- * @param {ReadonlyVec2} v Scaling vector
- * @returns {mat2} out
- */
- function fromScaling(out, v) {
- out[0] = v[0];
- out[1] = 0;
- out[2] = 0;
- out[3] = v[1];
- return out;
- }
- /**
- * Returns a string representation of a mat2
- *
- * @param {ReadonlyMat2} a matrix to represent as a string
- * @returns {String} string representation of the matrix
- */
- function str(a) {
- return "mat2(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ")";
- }
- /**
- * Returns Frobenius norm of a mat2
- *
- * @param {ReadonlyMat2} a the matrix to calculate Frobenius norm of
- * @returns {Number} Frobenius norm
- */
- function frob(a) {
- return Math.hypot(a[0], a[1], a[2], a[3]);
- }
- /**
- * Returns L, D and U matrices (Lower triangular, Diagonal and Upper triangular) by factorizing the input matrix
- * @param {ReadonlyMat2} L the lower triangular matrix
- * @param {ReadonlyMat2} D the diagonal matrix
- * @param {ReadonlyMat2} U the upper triangular matrix
- * @param {ReadonlyMat2} a the input matrix to factorize
- */
- function LDU(L, D, U, a) {
- L[2] = a[2] / a[0];
- U[0] = a[0];
- U[1] = a[1];
- U[3] = a[3] - L[2] * U[1];
- return [L, D, U];
- }
- /**
- * Adds two mat2's
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the first operand
- * @param {ReadonlyMat2} b the second operand
- * @returns {mat2} out
- */
- function add(out, a, b) {
- out[0] = a[0] + b[0];
- out[1] = a[1] + b[1];
- out[2] = a[2] + b[2];
- out[3] = a[3] + b[3];
- return out;
- }
- /**
- * Subtracts matrix b from matrix a
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the first operand
- * @param {ReadonlyMat2} b the second operand
- * @returns {mat2} out
- */
- function subtract(out, a, b) {
- out[0] = a[0] - b[0];
- out[1] = a[1] - b[1];
- out[2] = a[2] - b[2];
- out[3] = a[3] - b[3];
- return out;
- }
- /**
- * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyMat2} a The first matrix.
- * @param {ReadonlyMat2} b The second matrix.
- * @returns {Boolean} True if the matrices are equal, false otherwise.
- */
- function exactEquals(a, b) {
- return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];
- }
- /**
- * Returns whether or not the matrices have approximately the same elements in the same position.
- *
- * @param {ReadonlyMat2} a The first matrix.
- * @param {ReadonlyMat2} b The second matrix.
- * @returns {Boolean} True if the matrices are equal, false otherwise.
- */
- function equals$1(a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3];
- return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3));
- }
- /**
- * Multiply each element of the matrix by a scalar.
- *
- * @param {mat2} out the receiving matrix
- * @param {ReadonlyMat2} a the matrix to scale
- * @param {Number} b amount to scale the matrix's elements by
- * @returns {mat2} out
- */
- function multiplyScalar(out, a, b) {
- out[0] = a[0] * b;
- out[1] = a[1] * b;
- out[2] = a[2] * b;
- out[3] = a[3] * b;
- return out;
- }
- /**
- * Adds two mat2's after multiplying each element of the second operand by a scalar value.
- *
- * @param {mat2} out the receiving vector
- * @param {ReadonlyMat2} a the first operand
- * @param {ReadonlyMat2} b the second operand
- * @param {Number} scale the amount to scale b's elements by before adding
- * @returns {mat2} out
- */
- function multiplyScalarAndAdd(out, a, b, scale) {
- out[0] = a[0] + b[0] * scale;
- out[1] = a[1] + b[1] * scale;
- out[2] = a[2] + b[2] * scale;
- out[3] = a[3] + b[3] * scale;
- return out;
- }
- /**
- * Alias for {@link mat2.multiply}
- * @function
- */
- var mul = multiply;
- /**
- * Alias for {@link mat2.subtract}
- * @function
- */
- var sub = subtract;
- var mat2 = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create,
- clone: clone,
- copy: copy,
- identity: identity,
- fromValues: fromValues,
- set: set,
- transpose: transpose,
- invert: invert,
- adjoint: adjoint,
- determinant: determinant,
- multiply: multiply,
- rotate: rotate,
- scale: scale,
- fromRotation: fromRotation,
- fromScaling: fromScaling,
- str: str,
- frob: frob,
- LDU: LDU,
- add: add,
- subtract: subtract,
- exactEquals: exactEquals,
- equals: equals$1,
- multiplyScalar: multiplyScalar,
- multiplyScalarAndAdd: multiplyScalarAndAdd,
- mul: mul,
- sub: sub
- });
- /**
- * 2x3 Matrix
- * @module mat2d
- * @description
- * A mat2d contains six elements defined as:
- * <pre>
- * [a, b,
- * c, d,
- * tx, ty]
- * </pre>
- * This is a short form for the 3x3 matrix:
- * <pre>
- * [a, b, 0,
- * c, d, 0,
- * tx, ty, 1]
- * </pre>
- * The last column is ignored so the array is shorter and operations are faster.
- */
- /**
- * Creates a new identity mat2d
- *
- * @returns {mat2d} a new 2x3 matrix
- */
- function create$1() {
- var out = new ARRAY_TYPE(6);
- if (ARRAY_TYPE != Float32Array) {
- out[1] = 0;
- out[2] = 0;
- out[4] = 0;
- out[5] = 0;
- }
- out[0] = 1;
- out[3] = 1;
- return out;
- }
- /**
- * Creates a new mat2d initialized with values from an existing matrix
- *
- * @param {ReadonlyMat2d} a matrix to clone
- * @returns {mat2d} a new 2x3 matrix
- */
- function clone$1(a) {
- var out = new ARRAY_TYPE(6);
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- out[4] = a[4];
- out[5] = a[5];
- return out;
- }
- /**
- * Copy the values from one mat2d to another
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the source matrix
- * @returns {mat2d} out
- */
- function copy$1(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- out[4] = a[4];
- out[5] = a[5];
- return out;
- }
- /**
- * Set a mat2d to the identity matrix
- *
- * @param {mat2d} out the receiving matrix
- * @returns {mat2d} out
- */
- function identity$1(out) {
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 1;
- out[4] = 0;
- out[5] = 0;
- return out;
- }
- /**
- * Create a new mat2d with the given values
- *
- * @param {Number} a Component A (index 0)
- * @param {Number} b Component B (index 1)
- * @param {Number} c Component C (index 2)
- * @param {Number} d Component D (index 3)
- * @param {Number} tx Component TX (index 4)
- * @param {Number} ty Component TY (index 5)
- * @returns {mat2d} A new mat2d
- */
- function fromValues$1(a, b, c, d, tx, ty) {
- var out = new ARRAY_TYPE(6);
- out[0] = a;
- out[1] = b;
- out[2] = c;
- out[3] = d;
- out[4] = tx;
- out[5] = ty;
- return out;
- }
- /**
- * Set the components of a mat2d to the given values
- *
- * @param {mat2d} out the receiving matrix
- * @param {Number} a Component A (index 0)
- * @param {Number} b Component B (index 1)
- * @param {Number} c Component C (index 2)
- * @param {Number} d Component D (index 3)
- * @param {Number} tx Component TX (index 4)
- * @param {Number} ty Component TY (index 5)
- * @returns {mat2d} out
- */
- function set$1(out, a, b, c, d, tx, ty) {
- out[0] = a;
- out[1] = b;
- out[2] = c;
- out[3] = d;
- out[4] = tx;
- out[5] = ty;
- return out;
- }
- /**
- * Inverts a mat2d
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the source matrix
- * @returns {mat2d} out
- */
- function invert$1(out, a) {
- var aa = a[0],
- ab = a[1],
- ac = a[2],
- ad = a[3];
- var atx = a[4],
- aty = a[5];
- var det = aa * ad - ab * ac;
- if (!det) {
- return null;
- }
- det = 1.0 / det;
- out[0] = ad * det;
- out[1] = -ab * det;
- out[2] = -ac * det;
- out[3] = aa * det;
- out[4] = (ac * aty - ad * atx) * det;
- out[5] = (ab * atx - aa * aty) * det;
- return out;
- }
- /**
- * Calculates the determinant of a mat2d
- *
- * @param {ReadonlyMat2d} a the source matrix
- * @returns {Number} determinant of a
- */
- function determinant$1(a) {
- return a[0] * a[3] - a[1] * a[2];
- }
- /**
- * Multiplies two mat2d's
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the first operand
- * @param {ReadonlyMat2d} b the second operand
- * @returns {mat2d} out
- */
- function multiply$1(out, a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3],
- a4 = a[4],
- a5 = a[5];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3],
- b4 = b[4],
- b5 = b[5];
- out[0] = a0 * b0 + a2 * b1;
- out[1] = a1 * b0 + a3 * b1;
- out[2] = a0 * b2 + a2 * b3;
- out[3] = a1 * b2 + a3 * b3;
- out[4] = a0 * b4 + a2 * b5 + a4;
- out[5] = a1 * b4 + a3 * b5 + a5;
- return out;
- }
- /**
- * Rotates a mat2d by the given angle
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the matrix to rotate
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat2d} out
- */
- function rotate$1(out, a, rad) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3],
- a4 = a[4],
- a5 = a[5];
- var s = Math.sin(rad);
- var c = Math.cos(rad);
- out[0] = a0 * c + a2 * s;
- out[1] = a1 * c + a3 * s;
- out[2] = a0 * -s + a2 * c;
- out[3] = a1 * -s + a3 * c;
- out[4] = a4;
- out[5] = a5;
- return out;
- }
- /**
- * Scales the mat2d by the dimensions in the given vec2
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the matrix to translate
- * @param {ReadonlyVec2} v the vec2 to scale the matrix by
- * @returns {mat2d} out
- **/
- function scale$1(out, a, v) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3],
- a4 = a[4],
- a5 = a[5];
- var v0 = v[0],
- v1 = v[1];
- out[0] = a0 * v0;
- out[1] = a1 * v0;
- out[2] = a2 * v1;
- out[3] = a3 * v1;
- out[4] = a4;
- out[5] = a5;
- return out;
- }
- /**
- * Translates the mat2d by the dimensions in the given vec2
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the matrix to translate
- * @param {ReadonlyVec2} v the vec2 to translate the matrix by
- * @returns {mat2d} out
- **/
- function translate(out, a, v) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3],
- a4 = a[4],
- a5 = a[5];
- var v0 = v[0],
- v1 = v[1];
- out[0] = a0;
- out[1] = a1;
- out[2] = a2;
- out[3] = a3;
- out[4] = a0 * v0 + a2 * v1 + a4;
- out[5] = a1 * v0 + a3 * v1 + a5;
- return out;
- }
- /**
- * Creates a matrix from a given angle
- * This is equivalent to (but much faster than):
- *
- * mat2d.identity(dest);
- * mat2d.rotate(dest, dest, rad);
- *
- * @param {mat2d} out mat2d receiving operation result
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat2d} out
- */
- function fromRotation$1(out, rad) {
- var s = Math.sin(rad),
- c = Math.cos(rad);
- out[0] = c;
- out[1] = s;
- out[2] = -s;
- out[3] = c;
- out[4] = 0;
- out[5] = 0;
- return out;
- }
- /**
- * Creates a matrix from a vector scaling
- * This is equivalent to (but much faster than):
- *
- * mat2d.identity(dest);
- * mat2d.scale(dest, dest, vec);
- *
- * @param {mat2d} out mat2d receiving operation result
- * @param {ReadonlyVec2} v Scaling vector
- * @returns {mat2d} out
- */
- function fromScaling$1(out, v) {
- out[0] = v[0];
- out[1] = 0;
- out[2] = 0;
- out[3] = v[1];
- out[4] = 0;
- out[5] = 0;
- return out;
- }
- /**
- * Creates a matrix from a vector translation
- * This is equivalent to (but much faster than):
- *
- * mat2d.identity(dest);
- * mat2d.translate(dest, dest, vec);
- *
- * @param {mat2d} out mat2d receiving operation result
- * @param {ReadonlyVec2} v Translation vector
- * @returns {mat2d} out
- */
- function fromTranslation(out, v) {
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 1;
- out[4] = v[0];
- out[5] = v[1];
- return out;
- }
- /**
- * Returns a string representation of a mat2d
- *
- * @param {ReadonlyMat2d} a matrix to represent as a string
- * @returns {String} string representation of the matrix
- */
- function str$1(a) {
- return "mat2d(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ", " + a[4] + ", " + a[5] + ")";
- }
- /**
- * Returns Frobenius norm of a mat2d
- *
- * @param {ReadonlyMat2d} a the matrix to calculate Frobenius norm of
- * @returns {Number} Frobenius norm
- */
- function frob$1(a) {
- return Math.hypot(a[0], a[1], a[2], a[3], a[4], a[5], 1);
- }
- /**
- * Adds two mat2d's
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the first operand
- * @param {ReadonlyMat2d} b the second operand
- * @returns {mat2d} out
- */
- function add$1(out, a, b) {
- out[0] = a[0] + b[0];
- out[1] = a[1] + b[1];
- out[2] = a[2] + b[2];
- out[3] = a[3] + b[3];
- out[4] = a[4] + b[4];
- out[5] = a[5] + b[5];
- return out;
- }
- /**
- * Subtracts matrix b from matrix a
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the first operand
- * @param {ReadonlyMat2d} b the second operand
- * @returns {mat2d} out
- */
- function subtract$1(out, a, b) {
- out[0] = a[0] - b[0];
- out[1] = a[1] - b[1];
- out[2] = a[2] - b[2];
- out[3] = a[3] - b[3];
- out[4] = a[4] - b[4];
- out[5] = a[5] - b[5];
- return out;
- }
- /**
- * Multiply each element of the matrix by a scalar.
- *
- * @param {mat2d} out the receiving matrix
- * @param {ReadonlyMat2d} a the matrix to scale
- * @param {Number} b amount to scale the matrix's elements by
- * @returns {mat2d} out
- */
- function multiplyScalar$1(out, a, b) {
- out[0] = a[0] * b;
- out[1] = a[1] * b;
- out[2] = a[2] * b;
- out[3] = a[3] * b;
- out[4] = a[4] * b;
- out[5] = a[5] * b;
- return out;
- }
- /**
- * Adds two mat2d's after multiplying each element of the second operand by a scalar value.
- *
- * @param {mat2d} out the receiving vector
- * @param {ReadonlyMat2d} a the first operand
- * @param {ReadonlyMat2d} b the second operand
- * @param {Number} scale the amount to scale b's elements by before adding
- * @returns {mat2d} out
- */
- function multiplyScalarAndAdd$1(out, a, b, scale) {
- out[0] = a[0] + b[0] * scale;
- out[1] = a[1] + b[1] * scale;
- out[2] = a[2] + b[2] * scale;
- out[3] = a[3] + b[3] * scale;
- out[4] = a[4] + b[4] * scale;
- out[5] = a[5] + b[5] * scale;
- return out;
- }
- /**
- * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyMat2d} a The first matrix.
- * @param {ReadonlyMat2d} b The second matrix.
- * @returns {Boolean} True if the matrices are equal, false otherwise.
- */
- function exactEquals$1(a, b) {
- 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];
- }
- /**
- * Returns whether or not the matrices have approximately the same elements in the same position.
- *
- * @param {ReadonlyMat2d} a The first matrix.
- * @param {ReadonlyMat2d} b The second matrix.
- * @returns {Boolean} True if the matrices are equal, false otherwise.
- */
- function equals$2(a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3],
- a4 = a[4],
- a5 = a[5];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3],
- b4 = b[4],
- b5 = b[5];
- return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5));
- }
- /**
- * Alias for {@link mat2d.multiply}
- * @function
- */
- var mul$1 = multiply$1;
- /**
- * Alias for {@link mat2d.subtract}
- * @function
- */
- var sub$1 = subtract$1;
- var mat2d = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create$1,
- clone: clone$1,
- copy: copy$1,
- identity: identity$1,
- fromValues: fromValues$1,
- set: set$1,
- invert: invert$1,
- determinant: determinant$1,
- multiply: multiply$1,
- rotate: rotate$1,
- scale: scale$1,
- translate: translate,
- fromRotation: fromRotation$1,
- fromScaling: fromScaling$1,
- fromTranslation: fromTranslation,
- str: str$1,
- frob: frob$1,
- add: add$1,
- subtract: subtract$1,
- multiplyScalar: multiplyScalar$1,
- multiplyScalarAndAdd: multiplyScalarAndAdd$1,
- exactEquals: exactEquals$1,
- equals: equals$2,
- mul: mul$1,
- sub: sub$1
- });
- /**
- * 3x3 Matrix
- * @module mat3
- */
- /**
- * Creates a new identity mat3
- *
- * @returns {mat3} a new 3x3 matrix
- */
- function create$2() {
- var out = new ARRAY_TYPE(9);
- if (ARRAY_TYPE != Float32Array) {
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[5] = 0;
- out[6] = 0;
- out[7] = 0;
- }
- out[0] = 1;
- out[4] = 1;
- out[8] = 1;
- return out;
- }
- /**
- * Copies the upper-left 3x3 values into the given mat3.
- *
- * @param {mat3} out the receiving 3x3 matrix
- * @param {ReadonlyMat4} a the source 4x4 matrix
- * @returns {mat3} out
- */
- function fromMat4(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[4];
- out[4] = a[5];
- out[5] = a[6];
- out[6] = a[8];
- out[7] = a[9];
- out[8] = a[10];
- return out;
- }
- /**
- * Creates a new mat3 initialized with values from an existing matrix
- *
- * @param {ReadonlyMat3} a matrix to clone
- * @returns {mat3} a new 3x3 matrix
- */
- function clone$2(a) {
- var out = new ARRAY_TYPE(9);
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- out[4] = a[4];
- out[5] = a[5];
- out[6] = a[6];
- out[7] = a[7];
- out[8] = a[8];
- return out;
- }
- /**
- * Copy the values from one mat3 to another
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the source matrix
- * @returns {mat3} out
- */
- function copy$2(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- out[4] = a[4];
- out[5] = a[5];
- out[6] = a[6];
- out[7] = a[7];
- out[8] = a[8];
- return out;
- }
- /**
- * Create a new mat3 with the given values
- *
- * @param {Number} m00 Component in column 0, row 0 position (index 0)
- * @param {Number} m01 Component in column 0, row 1 position (index 1)
- * @param {Number} m02 Component in column 0, row 2 position (index 2)
- * @param {Number} m10 Component in column 1, row 0 position (index 3)
- * @param {Number} m11 Component in column 1, row 1 position (index 4)
- * @param {Number} m12 Component in column 1, row 2 position (index 5)
- * @param {Number} m20 Component in column 2, row 0 position (index 6)
- * @param {Number} m21 Component in column 2, row 1 position (index 7)
- * @param {Number} m22 Component in column 2, row 2 position (index 8)
- * @returns {mat3} A new mat3
- */
- function fromValues$2(m00, m01, m02, m10, m11, m12, m20, m21, m22) {
- var out = new ARRAY_TYPE(9);
- out[0] = m00;
- out[1] = m01;
- out[2] = m02;
- out[3] = m10;
- out[4] = m11;
- out[5] = m12;
- out[6] = m20;
- out[7] = m21;
- out[8] = m22;
- return out;
- }
- /**
- * Set the components of a mat3 to the given values
- *
- * @param {mat3} out the receiving matrix
- * @param {Number} m00 Component in column 0, row 0 position (index 0)
- * @param {Number} m01 Component in column 0, row 1 position (index 1)
- * @param {Number} m02 Component in column 0, row 2 position (index 2)
- * @param {Number} m10 Component in column 1, row 0 position (index 3)
- * @param {Number} m11 Component in column 1, row 1 position (index 4)
- * @param {Number} m12 Component in column 1, row 2 position (index 5)
- * @param {Number} m20 Component in column 2, row 0 position (index 6)
- * @param {Number} m21 Component in column 2, row 1 position (index 7)
- * @param {Number} m22 Component in column 2, row 2 position (index 8)
- * @returns {mat3} out
- */
- function set$2(out, m00, m01, m02, m10, m11, m12, m20, m21, m22) {
- out[0] = m00;
- out[1] = m01;
- out[2] = m02;
- out[3] = m10;
- out[4] = m11;
- out[5] = m12;
- out[6] = m20;
- out[7] = m21;
- out[8] = m22;
- return out;
- }
- /**
- * Set a mat3 to the identity matrix
- *
- * @param {mat3} out the receiving matrix
- * @returns {mat3} out
- */
- function identity$2(out) {
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 1;
- out[5] = 0;
- out[6] = 0;
- out[7] = 0;
- out[8] = 1;
- return out;
- }
- /**
- * Transpose the values of a mat3
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the source matrix
- * @returns {mat3} out
- */
- function transpose$1(out, a) {
- // If we are transposing ourselves we can skip a few steps but have to cache some values
- if (out === a) {
- var a01 = a[1],
- a02 = a[2],
- a12 = a[5];
- out[1] = a[3];
- out[2] = a[6];
- out[3] = a01;
- out[5] = a[7];
- out[6] = a02;
- out[7] = a12;
- } else {
- out[0] = a[0];
- out[1] = a[3];
- out[2] = a[6];
- out[3] = a[1];
- out[4] = a[4];
- out[5] = a[7];
- out[6] = a[2];
- out[7] = a[5];
- out[8] = a[8];
- }
- return out;
- }
- /**
- * Inverts a mat3
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the source matrix
- * @returns {mat3} out
- */
- function invert$2(out, a) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2];
- var a10 = a[3],
- a11 = a[4],
- a12 = a[5];
- var a20 = a[6],
- a21 = a[7],
- a22 = a[8];
- var b01 = a22 * a11 - a12 * a21;
- var b11 = -a22 * a10 + a12 * a20;
- var b21 = a21 * a10 - a11 * a20; // Calculate the determinant
- var det = a00 * b01 + a01 * b11 + a02 * b21;
- if (!det) {
- return null;
- }
- det = 1.0 / det;
- out[0] = b01 * det;
- out[1] = (-a22 * a01 + a02 * a21) * det;
- out[2] = (a12 * a01 - a02 * a11) * det;
- out[3] = b11 * det;
- out[4] = (a22 * a00 - a02 * a20) * det;
- out[5] = (-a12 * a00 + a02 * a10) * det;
- out[6] = b21 * det;
- out[7] = (-a21 * a00 + a01 * a20) * det;
- out[8] = (a11 * a00 - a01 * a10) * det;
- return out;
- }
- /**
- * Calculates the adjugate of a mat3
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the source matrix
- * @returns {mat3} out
- */
- function adjoint$1(out, a) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2];
- var a10 = a[3],
- a11 = a[4],
- a12 = a[5];
- var a20 = a[6],
- a21 = a[7],
- a22 = a[8];
- out[0] = a11 * a22 - a12 * a21;
- out[1] = a02 * a21 - a01 * a22;
- out[2] = a01 * a12 - a02 * a11;
- out[3] = a12 * a20 - a10 * a22;
- out[4] = a00 * a22 - a02 * a20;
- out[5] = a02 * a10 - a00 * a12;
- out[6] = a10 * a21 - a11 * a20;
- out[7] = a01 * a20 - a00 * a21;
- out[8] = a00 * a11 - a01 * a10;
- return out;
- }
- /**
- * Calculates the determinant of a mat3
- *
- * @param {ReadonlyMat3} a the source matrix
- * @returns {Number} determinant of a
- */
- function determinant$2(a) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2];
- var a10 = a[3],
- a11 = a[4],
- a12 = a[5];
- var a20 = a[6],
- a21 = a[7],
- a22 = a[8];
- return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
- }
- /**
- * Multiplies two mat3's
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the first operand
- * @param {ReadonlyMat3} b the second operand
- * @returns {mat3} out
- */
- function multiply$2(out, a, b) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2];
- var a10 = a[3],
- a11 = a[4],
- a12 = a[5];
- var a20 = a[6],
- a21 = a[7],
- a22 = a[8];
- var b00 = b[0],
- b01 = b[1],
- b02 = b[2];
- var b10 = b[3],
- b11 = b[4],
- b12 = b[5];
- var b20 = b[6],
- b21 = b[7],
- b22 = b[8];
- out[0] = b00 * a00 + b01 * a10 + b02 * a20;
- out[1] = b00 * a01 + b01 * a11 + b02 * a21;
- out[2] = b00 * a02 + b01 * a12 + b02 * a22;
- out[3] = b10 * a00 + b11 * a10 + b12 * a20;
- out[4] = b10 * a01 + b11 * a11 + b12 * a21;
- out[5] = b10 * a02 + b11 * a12 + b12 * a22;
- out[6] = b20 * a00 + b21 * a10 + b22 * a20;
- out[7] = b20 * a01 + b21 * a11 + b22 * a21;
- out[8] = b20 * a02 + b21 * a12 + b22 * a22;
- return out;
- }
- /**
- * Translate a mat3 by the given vector
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the matrix to translate
- * @param {ReadonlyVec2} v vector to translate by
- * @returns {mat3} out
- */
- function translate$1(out, a, v) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2],
- a10 = a[3],
- a11 = a[4],
- a12 = a[5],
- a20 = a[6],
- a21 = a[7],
- a22 = a[8],
- x = v[0],
- y = v[1];
- out[0] = a00;
- out[1] = a01;
- out[2] = a02;
- out[3] = a10;
- out[4] = a11;
- out[5] = a12;
- out[6] = x * a00 + y * a10 + a20;
- out[7] = x * a01 + y * a11 + a21;
- out[8] = x * a02 + y * a12 + a22;
- return out;
- }
- /**
- * Rotates a mat3 by the given angle
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the matrix to rotate
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat3} out
- */
- function rotate$2(out, a, rad) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2],
- a10 = a[3],
- a11 = a[4],
- a12 = a[5],
- a20 = a[6],
- a21 = a[7],
- a22 = a[8],
- s = Math.sin(rad),
- c = Math.cos(rad);
- out[0] = c * a00 + s * a10;
- out[1] = c * a01 + s * a11;
- out[2] = c * a02 + s * a12;
- out[3] = c * a10 - s * a00;
- out[4] = c * a11 - s * a01;
- out[5] = c * a12 - s * a02;
- out[6] = a20;
- out[7] = a21;
- out[8] = a22;
- return out;
- }
- /**
- * Scales the mat3 by the dimensions in the given vec2
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the matrix to rotate
- * @param {ReadonlyVec2} v the vec2 to scale the matrix by
- * @returns {mat3} out
- **/
- function scale$2(out, a, v) {
- var x = v[0],
- y = v[1];
- out[0] = x * a[0];
- out[1] = x * a[1];
- out[2] = x * a[2];
- out[3] = y * a[3];
- out[4] = y * a[4];
- out[5] = y * a[5];
- out[6] = a[6];
- out[7] = a[7];
- out[8] = a[8];
- return out;
- }
- /**
- * Creates a matrix from a vector translation
- * This is equivalent to (but much faster than):
- *
- * mat3.identity(dest);
- * mat3.translate(dest, dest, vec);
- *
- * @param {mat3} out mat3 receiving operation result
- * @param {ReadonlyVec2} v Translation vector
- * @returns {mat3} out
- */
- function fromTranslation$1(out, v) {
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 1;
- out[5] = 0;
- out[6] = v[0];
- out[7] = v[1];
- out[8] = 1;
- return out;
- }
- /**
- * Creates a matrix from a given angle
- * This is equivalent to (but much faster than):
- *
- * mat3.identity(dest);
- * mat3.rotate(dest, dest, rad);
- *
- * @param {mat3} out mat3 receiving operation result
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat3} out
- */
- function fromRotation$2(out, rad) {
- var s = Math.sin(rad),
- c = Math.cos(rad);
- out[0] = c;
- out[1] = s;
- out[2] = 0;
- out[3] = -s;
- out[4] = c;
- out[5] = 0;
- out[6] = 0;
- out[7] = 0;
- out[8] = 1;
- return out;
- }
- /**
- * Creates a matrix from a vector scaling
- * This is equivalent to (but much faster than):
- *
- * mat3.identity(dest);
- * mat3.scale(dest, dest, vec);
- *
- * @param {mat3} out mat3 receiving operation result
- * @param {ReadonlyVec2} v Scaling vector
- * @returns {mat3} out
- */
- function fromScaling$2(out, v) {
- out[0] = v[0];
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = v[1];
- out[5] = 0;
- out[6] = 0;
- out[7] = 0;
- out[8] = 1;
- return out;
- }
- /**
- * Copies the values from a mat2d into a mat3
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat2d} a the matrix to copy
- * @returns {mat3} out
- **/
- function fromMat2d(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = 0;
- out[3] = a[2];
- out[4] = a[3];
- out[5] = 0;
- out[6] = a[4];
- out[7] = a[5];
- out[8] = 1;
- return out;
- }
- /**
- * Calculates a 3x3 matrix from the given quaternion
- *
- * @param {mat3} out mat3 receiving operation result
- * @param {ReadonlyQuat} q Quaternion to create matrix from
- *
- * @returns {mat3} out
- */
- function fromQuat(out, q) {
- var x = q[0],
- y = q[1],
- z = q[2],
- w = q[3];
- var x2 = x + x;
- var y2 = y + y;
- var z2 = z + z;
- var xx = x * x2;
- var yx = y * x2;
- var yy = y * y2;
- var zx = z * x2;
- var zy = z * y2;
- var zz = z * z2;
- var wx = w * x2;
- var wy = w * y2;
- var wz = w * z2;
- out[0] = 1 - yy - zz;
- out[3] = yx - wz;
- out[6] = zx + wy;
- out[1] = yx + wz;
- out[4] = 1 - xx - zz;
- out[7] = zy - wx;
- out[2] = zx - wy;
- out[5] = zy + wx;
- out[8] = 1 - xx - yy;
- return out;
- }
- /**
- * Calculates a 3x3 normal matrix (transpose inverse) from the 4x4 matrix
- *
- * @param {mat3} out mat3 receiving operation result
- * @param {ReadonlyMat4} a Mat4 to derive the normal matrix from
- *
- * @returns {mat3} out
- */
- function normalFromMat4(out, a) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2],
- a03 = a[3];
- var a10 = a[4],
- a11 = a[5],
- a12 = a[6],
- a13 = a[7];
- var a20 = a[8],
- a21 = a[9],
- a22 = a[10],
- a23 = a[11];
- var a30 = a[12],
- a31 = a[13],
- a32 = a[14],
- a33 = a[15];
- var b00 = a00 * a11 - a01 * a10;
- var b01 = a00 * a12 - a02 * a10;
- var b02 = a00 * a13 - a03 * a10;
- var b03 = a01 * a12 - a02 * a11;
- var b04 = a01 * a13 - a03 * a11;
- var b05 = a02 * a13 - a03 * a12;
- var b06 = a20 * a31 - a21 * a30;
- var b07 = a20 * a32 - a22 * a30;
- var b08 = a20 * a33 - a23 * a30;
- var b09 = a21 * a32 - a22 * a31;
- var b10 = a21 * a33 - a23 * a31;
- var b11 = a22 * a33 - a23 * a32; // Calculate the determinant
- var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
- if (!det) {
- return null;
- }
- det = 1.0 / det;
- out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
- out[1] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
- out[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
- out[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
- out[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
- out[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
- out[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
- out[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
- out[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
- return out;
- }
- /**
- * Generates a 2D projection matrix with the given bounds
- *
- * @param {mat3} out mat3 frustum matrix will be written into
- * @param {number} width Width of your gl context
- * @param {number} height Height of gl context
- * @returns {mat3} out
- */
- function projection(out, width, height) {
- out[0] = 2 / width;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = -2 / height;
- out[5] = 0;
- out[6] = -1;
- out[7] = 1;
- out[8] = 1;
- return out;
- }
- /**
- * Returns a string representation of a mat3
- *
- * @param {ReadonlyMat3} a matrix to represent as a string
- * @returns {String} string representation of the matrix
- */
- function str$2(a) {
- return "mat3(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ", " + a[4] + ", " + a[5] + ", " + a[6] + ", " + a[7] + ", " + a[8] + ")";
- }
- /**
- * Returns Frobenius norm of a mat3
- *
- * @param {ReadonlyMat3} a the matrix to calculate Frobenius norm of
- * @returns {Number} Frobenius norm
- */
- function frob$2(a) {
- return Math.hypot(a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]);
- }
- /**
- * Adds two mat3's
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the first operand
- * @param {ReadonlyMat3} b the second operand
- * @returns {mat3} out
- */
- function add$2(out, a, b) {
- out[0] = a[0] + b[0];
- out[1] = a[1] + b[1];
- out[2] = a[2] + b[2];
- out[3] = a[3] + b[3];
- out[4] = a[4] + b[4];
- out[5] = a[5] + b[5];
- out[6] = a[6] + b[6];
- out[7] = a[7] + b[7];
- out[8] = a[8] + b[8];
- return out;
- }
- /**
- * Subtracts matrix b from matrix a
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the first operand
- * @param {ReadonlyMat3} b the second operand
- * @returns {mat3} out
- */
- function subtract$2(out, a, b) {
- out[0] = a[0] - b[0];
- out[1] = a[1] - b[1];
- out[2] = a[2] - b[2];
- out[3] = a[3] - b[3];
- out[4] = a[4] - b[4];
- out[5] = a[5] - b[5];
- out[6] = a[6] - b[6];
- out[7] = a[7] - b[7];
- out[8] = a[8] - b[8];
- return out;
- }
- /**
- * Multiply each element of the matrix by a scalar.
- *
- * @param {mat3} out the receiving matrix
- * @param {ReadonlyMat3} a the matrix to scale
- * @param {Number} b amount to scale the matrix's elements by
- * @returns {mat3} out
- */
- function multiplyScalar$2(out, a, b) {
- out[0] = a[0] * b;
- out[1] = a[1] * b;
- out[2] = a[2] * b;
- out[3] = a[3] * b;
- out[4] = a[4] * b;
- out[5] = a[5] * b;
- out[6] = a[6] * b;
- out[7] = a[7] * b;
- out[8] = a[8] * b;
- return out;
- }
- /**
- * Adds two mat3's after multiplying each element of the second operand by a scalar value.
- *
- * @param {mat3} out the receiving vector
- * @param {ReadonlyMat3} a the first operand
- * @param {ReadonlyMat3} b the second operand
- * @param {Number} scale the amount to scale b's elements by before adding
- * @returns {mat3} out
- */
- function multiplyScalarAndAdd$2(out, a, b, scale) {
- out[0] = a[0] + b[0] * scale;
- out[1] = a[1] + b[1] * scale;
- out[2] = a[2] + b[2] * scale;
- out[3] = a[3] + b[3] * scale;
- out[4] = a[4] + b[4] * scale;
- out[5] = a[5] + b[5] * scale;
- out[6] = a[6] + b[6] * scale;
- out[7] = a[7] + b[7] * scale;
- out[8] = a[8] + b[8] * scale;
- return out;
- }
- /**
- * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyMat3} a The first matrix.
- * @param {ReadonlyMat3} b The second matrix.
- * @returns {Boolean} True if the matrices are equal, false otherwise.
- */
- function exactEquals$2(a, b) {
- 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] && a[6] === b[6] && a[7] === b[7] && a[8] === b[8];
- }
- /**
- * Returns whether or not the matrices have approximately the same elements in the same position.
- *
- * @param {ReadonlyMat3} a The first matrix.
- * @param {ReadonlyMat3} b The second matrix.
- * @returns {Boolean} True if the matrices are equal, false otherwise.
- */
- function equals$3(a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3],
- a4 = a[4],
- a5 = a[5],
- a6 = a[6],
- a7 = a[7],
- a8 = a[8];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3],
- b4 = b[4],
- b5 = b[5],
- b6 = b[6],
- b7 = b[7],
- b8 = b[8];
- return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) && Math.abs(a8 - b8) <= EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8));
- }
- /**
- * Alias for {@link mat3.multiply}
- * @function
- */
- var mul$2 = multiply$2;
- /**
- * Alias for {@link mat3.subtract}
- * @function
- */
- var sub$2 = subtract$2;
- var mat3 = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create$2,
- fromMat4: fromMat4,
- clone: clone$2,
- copy: copy$2,
- fromValues: fromValues$2,
- set: set$2,
- identity: identity$2,
- transpose: transpose$1,
- invert: invert$2,
- adjoint: adjoint$1,
- determinant: determinant$2,
- multiply: multiply$2,
- translate: translate$1,
- rotate: rotate$2,
- scale: scale$2,
- fromTranslation: fromTranslation$1,
- fromRotation: fromRotation$2,
- fromScaling: fromScaling$2,
- fromMat2d: fromMat2d,
- fromQuat: fromQuat,
- normalFromMat4: normalFromMat4,
- projection: projection,
- str: str$2,
- frob: frob$2,
- add: add$2,
- subtract: subtract$2,
- multiplyScalar: multiplyScalar$2,
- multiplyScalarAndAdd: multiplyScalarAndAdd$2,
- exactEquals: exactEquals$2,
- equals: equals$3,
- mul: mul$2,
- sub: sub$2
- });
- /**
- * 4x4 Matrix<br>Format: column-major, when typed out it looks like row-major<br>The matrices are being post multiplied.
- * @module mat4
- */
- /**
- * Creates a new identity mat4
- *
- * @returns {mat4} a new 4x4 matrix
- */
- function create$3() {
- var out = new ARRAY_TYPE(16);
- if (ARRAY_TYPE != Float32Array) {
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[11] = 0;
- out[12] = 0;
- out[13] = 0;
- out[14] = 0;
- }
- out[0] = 1;
- out[5] = 1;
- out[10] = 1;
- out[15] = 1;
- return out;
- }
- /**
- * Creates a new mat4 initialized with values from an existing matrix
- *
- * @param {ReadonlyMat4} a matrix to clone
- * @returns {mat4} a new 4x4 matrix
- */
- function clone$3(a) {
- var out = new ARRAY_TYPE(16);
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- out[4] = a[4];
- out[5] = a[5];
- out[6] = a[6];
- out[7] = a[7];
- out[8] = a[8];
- out[9] = a[9];
- out[10] = a[10];
- out[11] = a[11];
- out[12] = a[12];
- out[13] = a[13];
- out[14] = a[14];
- out[15] = a[15];
- return out;
- }
- /**
- * Copy the values from one mat4 to another
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the source matrix
- * @returns {mat4} out
- */
- function copy$3(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- out[4] = a[4];
- out[5] = a[5];
- out[6] = a[6];
- out[7] = a[7];
- out[8] = a[8];
- out[9] = a[9];
- out[10] = a[10];
- out[11] = a[11];
- out[12] = a[12];
- out[13] = a[13];
- out[14] = a[14];
- out[15] = a[15];
- return out;
- }
- /**
- * Create a new mat4 with the given values
- *
- * @param {Number} m00 Component in column 0, row 0 position (index 0)
- * @param {Number} m01 Component in column 0, row 1 position (index 1)
- * @param {Number} m02 Component in column 0, row 2 position (index 2)
- * @param {Number} m03 Component in column 0, row 3 position (index 3)
- * @param {Number} m10 Component in column 1, row 0 position (index 4)
- * @param {Number} m11 Component in column 1, row 1 position (index 5)
- * @param {Number} m12 Component in column 1, row 2 position (index 6)
- * @param {Number} m13 Component in column 1, row 3 position (index 7)
- * @param {Number} m20 Component in column 2, row 0 position (index 8)
- * @param {Number} m21 Component in column 2, row 1 position (index 9)
- * @param {Number} m22 Component in column 2, row 2 position (index 10)
- * @param {Number} m23 Component in column 2, row 3 position (index 11)
- * @param {Number} m30 Component in column 3, row 0 position (index 12)
- * @param {Number} m31 Component in column 3, row 1 position (index 13)
- * @param {Number} m32 Component in column 3, row 2 position (index 14)
- * @param {Number} m33 Component in column 3, row 3 position (index 15)
- * @returns {mat4} A new mat4
- */
- function fromValues$3(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
- var out = new ARRAY_TYPE(16);
- out[0] = m00;
- out[1] = m01;
- out[2] = m02;
- out[3] = m03;
- out[4] = m10;
- out[5] = m11;
- out[6] = m12;
- out[7] = m13;
- out[8] = m20;
- out[9] = m21;
- out[10] = m22;
- out[11] = m23;
- out[12] = m30;
- out[13] = m31;
- out[14] = m32;
- out[15] = m33;
- return out;
- }
- /**
- * Set the components of a mat4 to the given values
- *
- * @param {mat4} out the receiving matrix
- * @param {Number} m00 Component in column 0, row 0 position (index 0)
- * @param {Number} m01 Component in column 0, row 1 position (index 1)
- * @param {Number} m02 Component in column 0, row 2 position (index 2)
- * @param {Number} m03 Component in column 0, row 3 position (index 3)
- * @param {Number} m10 Component in column 1, row 0 position (index 4)
- * @param {Number} m11 Component in column 1, row 1 position (index 5)
- * @param {Number} m12 Component in column 1, row 2 position (index 6)
- * @param {Number} m13 Component in column 1, row 3 position (index 7)
- * @param {Number} m20 Component in column 2, row 0 position (index 8)
- * @param {Number} m21 Component in column 2, row 1 position (index 9)
- * @param {Number} m22 Component in column 2, row 2 position (index 10)
- * @param {Number} m23 Component in column 2, row 3 position (index 11)
- * @param {Number} m30 Component in column 3, row 0 position (index 12)
- * @param {Number} m31 Component in column 3, row 1 position (index 13)
- * @param {Number} m32 Component in column 3, row 2 position (index 14)
- * @param {Number} m33 Component in column 3, row 3 position (index 15)
- * @returns {mat4} out
- */
- function set$3(out, m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
- out[0] = m00;
- out[1] = m01;
- out[2] = m02;
- out[3] = m03;
- out[4] = m10;
- out[5] = m11;
- out[6] = m12;
- out[7] = m13;
- out[8] = m20;
- out[9] = m21;
- out[10] = m22;
- out[11] = m23;
- out[12] = m30;
- out[13] = m31;
- out[14] = m32;
- out[15] = m33;
- return out;
- }
- /**
- * Set a mat4 to the identity matrix
- *
- * @param {mat4} out the receiving matrix
- * @returns {mat4} out
- */
- function identity$3(out) {
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = 1;
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[10] = 1;
- out[11] = 0;
- out[12] = 0;
- out[13] = 0;
- out[14] = 0;
- out[15] = 1;
- return out;
- }
- /**
- * Transpose the values of a mat4
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the source matrix
- * @returns {mat4} out
- */
- function transpose$2(out, a) {
- // If we are transposing ourselves we can skip a few steps but have to cache some values
- if (out === a) {
- var a01 = a[1],
- a02 = a[2],
- a03 = a[3];
- var a12 = a[6],
- a13 = a[7];
- var a23 = a[11];
- out[1] = a[4];
- out[2] = a[8];
- out[3] = a[12];
- out[4] = a01;
- out[6] = a[9];
- out[7] = a[13];
- out[8] = a02;
- out[9] = a12;
- out[11] = a[14];
- out[12] = a03;
- out[13] = a13;
- out[14] = a23;
- } else {
- out[0] = a[0];
- out[1] = a[4];
- out[2] = a[8];
- out[3] = a[12];
- out[4] = a[1];
- out[5] = a[5];
- out[6] = a[9];
- out[7] = a[13];
- out[8] = a[2];
- out[9] = a[6];
- out[10] = a[10];
- out[11] = a[14];
- out[12] = a[3];
- out[13] = a[7];
- out[14] = a[11];
- out[15] = a[15];
- }
- return out;
- }
- /**
- * Inverts a mat4
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the source matrix
- * @returns {mat4} out
- */
- function invert$3(out, a) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2],
- a03 = a[3];
- var a10 = a[4],
- a11 = a[5],
- a12 = a[6],
- a13 = a[7];
- var a20 = a[8],
- a21 = a[9],
- a22 = a[10],
- a23 = a[11];
- var a30 = a[12],
- a31 = a[13],
- a32 = a[14],
- a33 = a[15];
- var b00 = a00 * a11 - a01 * a10;
- var b01 = a00 * a12 - a02 * a10;
- var b02 = a00 * a13 - a03 * a10;
- var b03 = a01 * a12 - a02 * a11;
- var b04 = a01 * a13 - a03 * a11;
- var b05 = a02 * a13 - a03 * a12;
- var b06 = a20 * a31 - a21 * a30;
- var b07 = a20 * a32 - a22 * a30;
- var b08 = a20 * a33 - a23 * a30;
- var b09 = a21 * a32 - a22 * a31;
- var b10 = a21 * a33 - a23 * a31;
- var b11 = a22 * a33 - a23 * a32; // Calculate the determinant
- var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
- if (!det) {
- return null;
- }
- det = 1.0 / det;
- out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
- out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
- out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
- out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
- out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
- out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
- out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
- out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
- out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
- out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
- out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
- out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
- out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
- out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
- out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
- out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
- return out;
- }
- /**
- * Calculates the adjugate of a mat4
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the source matrix
- * @returns {mat4} out
- */
- function adjoint$2(out, a) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2],
- a03 = a[3];
- var a10 = a[4],
- a11 = a[5],
- a12 = a[6],
- a13 = a[7];
- var a20 = a[8],
- a21 = a[9],
- a22 = a[10],
- a23 = a[11];
- var a30 = a[12],
- a31 = a[13],
- a32 = a[14],
- a33 = a[15];
- out[0] = a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22);
- out[1] = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22));
- out[2] = a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12);
- out[3] = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12));
- out[4] = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22));
- out[5] = a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22);
- out[6] = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12));
- out[7] = a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12);
- out[8] = a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21);
- out[9] = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21));
- out[10] = a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11);
- out[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11));
- out[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21));
- out[13] = a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21);
- out[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11));
- out[15] = a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11);
- return out;
- }
- /**
- * Calculates the determinant of a mat4
- *
- * @param {ReadonlyMat4} a the source matrix
- * @returns {Number} determinant of a
- */
- function determinant$3(a) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2],
- a03 = a[3];
- var a10 = a[4],
- a11 = a[5],
- a12 = a[6],
- a13 = a[7];
- var a20 = a[8],
- a21 = a[9],
- a22 = a[10],
- a23 = a[11];
- var a30 = a[12],
- a31 = a[13],
- a32 = a[14],
- a33 = a[15];
- var b00 = a00 * a11 - a01 * a10;
- var b01 = a00 * a12 - a02 * a10;
- var b02 = a00 * a13 - a03 * a10;
- var b03 = a01 * a12 - a02 * a11;
- var b04 = a01 * a13 - a03 * a11;
- var b05 = a02 * a13 - a03 * a12;
- var b06 = a20 * a31 - a21 * a30;
- var b07 = a20 * a32 - a22 * a30;
- var b08 = a20 * a33 - a23 * a30;
- var b09 = a21 * a32 - a22 * a31;
- var b10 = a21 * a33 - a23 * a31;
- var b11 = a22 * a33 - a23 * a32; // Calculate the determinant
- return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
- }
- /**
- * Multiplies two mat4s
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the first operand
- * @param {ReadonlyMat4} b the second operand
- * @returns {mat4} out
- */
- function multiply$3(out, a, b) {
- var a00 = a[0],
- a01 = a[1],
- a02 = a[2],
- a03 = a[3];
- var a10 = a[4],
- a11 = a[5],
- a12 = a[6],
- a13 = a[7];
- var a20 = a[8],
- a21 = a[9],
- a22 = a[10],
- a23 = a[11];
- var a30 = a[12],
- a31 = a[13],
- a32 = a[14],
- a33 = a[15]; // Cache only the current line of the second matrix
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3];
- out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
- out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
- out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
- out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
- b0 = b[4];
- b1 = b[5];
- b2 = b[6];
- b3 = b[7];
- out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
- out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
- out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
- out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
- b0 = b[8];
- b1 = b[9];
- b2 = b[10];
- b3 = b[11];
- out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
- out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
- out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
- out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
- b0 = b[12];
- b1 = b[13];
- b2 = b[14];
- b3 = b[15];
- out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
- out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
- out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
- out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
- return out;
- }
- /**
- * Translate a mat4 by the given vector
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the matrix to translate
- * @param {ReadonlyVec3} v vector to translate by
- * @returns {mat4} out
- */
- function translate$2(out, a, v) {
- var x = v[0],
- y = v[1],
- z = v[2];
- var a00, a01, a02, a03;
- var a10, a11, a12, a13;
- var a20, a21, a22, a23;
- if (a === out) {
- out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
- out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
- out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
- out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
- } else {
- a00 = a[0];
- a01 = a[1];
- a02 = a[2];
- a03 = a[3];
- a10 = a[4];
- a11 = a[5];
- a12 = a[6];
- a13 = a[7];
- a20 = a[8];
- a21 = a[9];
- a22 = a[10];
- a23 = a[11];
- out[0] = a00;
- out[1] = a01;
- out[2] = a02;
- out[3] = a03;
- out[4] = a10;
- out[5] = a11;
- out[6] = a12;
- out[7] = a13;
- out[8] = a20;
- out[9] = a21;
- out[10] = a22;
- out[11] = a23;
- out[12] = a00 * x + a10 * y + a20 * z + a[12];
- out[13] = a01 * x + a11 * y + a21 * z + a[13];
- out[14] = a02 * x + a12 * y + a22 * z + a[14];
- out[15] = a03 * x + a13 * y + a23 * z + a[15];
- }
- return out;
- }
- /**
- * Scales the mat4 by the dimensions in the given vec3 not using vectorization
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the matrix to scale
- * @param {ReadonlyVec3} v the vec3 to scale the matrix by
- * @returns {mat4} out
- **/
- function scale$3(out, a, v) {
- var x = v[0],
- y = v[1],
- z = v[2];
- out[0] = a[0] * x;
- out[1] = a[1] * x;
- out[2] = a[2] * x;
- out[3] = a[3] * x;
- out[4] = a[4] * y;
- out[5] = a[5] * y;
- out[6] = a[6] * y;
- out[7] = a[7] * y;
- out[8] = a[8] * z;
- out[9] = a[9] * z;
- out[10] = a[10] * z;
- out[11] = a[11] * z;
- out[12] = a[12];
- out[13] = a[13];
- out[14] = a[14];
- out[15] = a[15];
- return out;
- }
- /**
- * Rotates a mat4 by the given angle around the given axis
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the matrix to rotate
- * @param {Number} rad the angle to rotate the matrix by
- * @param {ReadonlyVec3} axis the axis to rotate around
- * @returns {mat4} out
- */
- function rotate$3(out, a, rad, axis) {
- var x = axis[0],
- y = axis[1],
- z = axis[2];
- var len = Math.hypot(x, y, z);
- var s, c, t;
- var a00, a01, a02, a03;
- var a10, a11, a12, a13;
- var a20, a21, a22, a23;
- var b00, b01, b02;
- var b10, b11, b12;
- var b20, b21, b22;
- if (len < EPSILON) {
- return null;
- }
- len = 1 / len;
- x *= len;
- y *= len;
- z *= len;
- s = Math.sin(rad);
- c = Math.cos(rad);
- t = 1 - c;
- a00 = a[0];
- a01 = a[1];
- a02 = a[2];
- a03 = a[3];
- a10 = a[4];
- a11 = a[5];
- a12 = a[6];
- a13 = a[7];
- a20 = a[8];
- a21 = a[9];
- a22 = a[10];
- a23 = a[11]; // Construct the elements of the rotation matrix
- b00 = x * x * t + c;
- b01 = y * x * t + z * s;
- b02 = z * x * t - y * s;
- b10 = x * y * t - z * s;
- b11 = y * y * t + c;
- b12 = z * y * t + x * s;
- b20 = x * z * t + y * s;
- b21 = y * z * t - x * s;
- b22 = z * z * t + c; // Perform rotation-specific matrix multiplication
- out[0] = a00 * b00 + a10 * b01 + a20 * b02;
- out[1] = a01 * b00 + a11 * b01 + a21 * b02;
- out[2] = a02 * b00 + a12 * b01 + a22 * b02;
- out[3] = a03 * b00 + a13 * b01 + a23 * b02;
- out[4] = a00 * b10 + a10 * b11 + a20 * b12;
- out[5] = a01 * b10 + a11 * b11 + a21 * b12;
- out[6] = a02 * b10 + a12 * b11 + a22 * b12;
- out[7] = a03 * b10 + a13 * b11 + a23 * b12;
- out[8] = a00 * b20 + a10 * b21 + a20 * b22;
- out[9] = a01 * b20 + a11 * b21 + a21 * b22;
- out[10] = a02 * b20 + a12 * b21 + a22 * b22;
- out[11] = a03 * b20 + a13 * b21 + a23 * b22;
- if (a !== out) {
- // If the source and destination differ, copy the unchanged last row
- out[12] = a[12];
- out[13] = a[13];
- out[14] = a[14];
- out[15] = a[15];
- }
- return out;
- }
- /**
- * Rotates a matrix by the given angle around the X axis
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the matrix to rotate
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat4} out
- */
- function rotateX(out, a, rad) {
- var s = Math.sin(rad);
- var c = Math.cos(rad);
- var a10 = a[4];
- var a11 = a[5];
- var a12 = a[6];
- var a13 = a[7];
- var a20 = a[8];
- var a21 = a[9];
- var a22 = a[10];
- var a23 = a[11];
- if (a !== out) {
- // If the source and destination differ, copy the unchanged rows
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- out[12] = a[12];
- out[13] = a[13];
- out[14] = a[14];
- out[15] = a[15];
- } // Perform axis-specific matrix multiplication
- out[4] = a10 * c + a20 * s;
- out[5] = a11 * c + a21 * s;
- out[6] = a12 * c + a22 * s;
- out[7] = a13 * c + a23 * s;
- out[8] = a20 * c - a10 * s;
- out[9] = a21 * c - a11 * s;
- out[10] = a22 * c - a12 * s;
- out[11] = a23 * c - a13 * s;
- return out;
- }
- /**
- * Rotates a matrix by the given angle around the Y axis
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the matrix to rotate
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat4} out
- */
- function rotateY(out, a, rad) {
- var s = Math.sin(rad);
- var c = Math.cos(rad);
- var a00 = a[0];
- var a01 = a[1];
- var a02 = a[2];
- var a03 = a[3];
- var a20 = a[8];
- var a21 = a[9];
- var a22 = a[10];
- var a23 = a[11];
- if (a !== out) {
- // If the source and destination differ, copy the unchanged rows
- out[4] = a[4];
- out[5] = a[5];
- out[6] = a[6];
- out[7] = a[7];
- out[12] = a[12];
- out[13] = a[13];
- out[14] = a[14];
- out[15] = a[15];
- } // Perform axis-specific matrix multiplication
- out[0] = a00 * c - a20 * s;
- out[1] = a01 * c - a21 * s;
- out[2] = a02 * c - a22 * s;
- out[3] = a03 * c - a23 * s;
- out[8] = a00 * s + a20 * c;
- out[9] = a01 * s + a21 * c;
- out[10] = a02 * s + a22 * c;
- out[11] = a03 * s + a23 * c;
- return out;
- }
- /**
- * Rotates a matrix by the given angle around the Z axis
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the matrix to rotate
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat4} out
- */
- function rotateZ(out, a, rad) {
- var s = Math.sin(rad);
- var c = Math.cos(rad);
- var a00 = a[0];
- var a01 = a[1];
- var a02 = a[2];
- var a03 = a[3];
- var a10 = a[4];
- var a11 = a[5];
- var a12 = a[6];
- var a13 = a[7];
- if (a !== out) {
- // If the source and destination differ, copy the unchanged last row
- out[8] = a[8];
- out[9] = a[9];
- out[10] = a[10];
- out[11] = a[11];
- out[12] = a[12];
- out[13] = a[13];
- out[14] = a[14];
- out[15] = a[15];
- } // Perform axis-specific matrix multiplication
- out[0] = a00 * c + a10 * s;
- out[1] = a01 * c + a11 * s;
- out[2] = a02 * c + a12 * s;
- out[3] = a03 * c + a13 * s;
- out[4] = a10 * c - a00 * s;
- out[5] = a11 * c - a01 * s;
- out[6] = a12 * c - a02 * s;
- out[7] = a13 * c - a03 * s;
- return out;
- }
- /**
- * Creates a matrix from a vector translation
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.translate(dest, dest, vec);
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {ReadonlyVec3} v Translation vector
- * @returns {mat4} out
- */
- function fromTranslation$2(out, v) {
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = 1;
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[10] = 1;
- out[11] = 0;
- out[12] = v[0];
- out[13] = v[1];
- out[14] = v[2];
- out[15] = 1;
- return out;
- }
- /**
- * Creates a matrix from a vector scaling
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.scale(dest, dest, vec);
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {ReadonlyVec3} v Scaling vector
- * @returns {mat4} out
- */
- function fromScaling$3(out, v) {
- out[0] = v[0];
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = v[1];
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[10] = v[2];
- out[11] = 0;
- out[12] = 0;
- out[13] = 0;
- out[14] = 0;
- out[15] = 1;
- return out;
- }
- /**
- * Creates a matrix from a given angle around a given axis
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.rotate(dest, dest, rad, axis);
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {Number} rad the angle to rotate the matrix by
- * @param {ReadonlyVec3} axis the axis to rotate around
- * @returns {mat4} out
- */
- function fromRotation$3(out, rad, axis) {
- var x = axis[0],
- y = axis[1],
- z = axis[2];
- var len = Math.hypot(x, y, z);
- var s, c, t;
- if (len < EPSILON) {
- return null;
- }
- len = 1 / len;
- x *= len;
- y *= len;
- z *= len;
- s = Math.sin(rad);
- c = Math.cos(rad);
- t = 1 - c; // Perform rotation-specific matrix multiplication
- out[0] = x * x * t + c;
- out[1] = y * x * t + z * s;
- out[2] = z * x * t - y * s;
- out[3] = 0;
- out[4] = x * y * t - z * s;
- out[5] = y * y * t + c;
- out[6] = z * y * t + x * s;
- out[7] = 0;
- out[8] = x * z * t + y * s;
- out[9] = y * z * t - x * s;
- out[10] = z * z * t + c;
- out[11] = 0;
- out[12] = 0;
- out[13] = 0;
- out[14] = 0;
- out[15] = 1;
- return out;
- }
- /**
- * Creates a matrix from the given angle around the X axis
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.rotateX(dest, dest, rad);
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat4} out
- */
- function fromXRotation(out, rad) {
- var s = Math.sin(rad);
- var c = Math.cos(rad); // Perform axis-specific matrix multiplication
- out[0] = 1;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = c;
- out[6] = s;
- out[7] = 0;
- out[8] = 0;
- out[9] = -s;
- out[10] = c;
- out[11] = 0;
- out[12] = 0;
- out[13] = 0;
- out[14] = 0;
- out[15] = 1;
- return out;
- }
- /**
- * Creates a matrix from the given angle around the Y axis
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.rotateY(dest, dest, rad);
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat4} out
- */
- function fromYRotation(out, rad) {
- var s = Math.sin(rad);
- var c = Math.cos(rad); // Perform axis-specific matrix multiplication
- out[0] = c;
- out[1] = 0;
- out[2] = -s;
- out[3] = 0;
- out[4] = 0;
- out[5] = 1;
- out[6] = 0;
- out[7] = 0;
- out[8] = s;
- out[9] = 0;
- out[10] = c;
- out[11] = 0;
- out[12] = 0;
- out[13] = 0;
- out[14] = 0;
- out[15] = 1;
- return out;
- }
- /**
- * Creates a matrix from the given angle around the Z axis
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.rotateZ(dest, dest, rad);
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {Number} rad the angle to rotate the matrix by
- * @returns {mat4} out
- */
- function fromZRotation(out, rad) {
- var s = Math.sin(rad);
- var c = Math.cos(rad); // Perform axis-specific matrix multiplication
- out[0] = c;
- out[1] = s;
- out[2] = 0;
- out[3] = 0;
- out[4] = -s;
- out[5] = c;
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[10] = 1;
- out[11] = 0;
- out[12] = 0;
- out[13] = 0;
- out[14] = 0;
- out[15] = 1;
- return out;
- }
- /**
- * Creates a matrix from a quaternion rotation and vector translation
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.translate(dest, vec);
- * let quatMat = mat4.create();
- * quat4.toMat4(quat, quatMat);
- * mat4.multiply(dest, quatMat);
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {quat4} q Rotation quaternion
- * @param {ReadonlyVec3} v Translation vector
- * @returns {mat4} out
- */
- function fromRotationTranslation(out, q, v) {
- // Quaternion math
- var x = q[0],
- y = q[1],
- z = q[2],
- w = q[3];
- var x2 = x + x;
- var y2 = y + y;
- var z2 = z + z;
- var xx = x * x2;
- var xy = x * y2;
- var xz = x * z2;
- var yy = y * y2;
- var yz = y * z2;
- var zz = z * z2;
- var wx = w * x2;
- var wy = w * y2;
- var wz = w * z2;
- out[0] = 1 - (yy + zz);
- out[1] = xy + wz;
- out[2] = xz - wy;
- out[3] = 0;
- out[4] = xy - wz;
- out[5] = 1 - (xx + zz);
- out[6] = yz + wx;
- out[7] = 0;
- out[8] = xz + wy;
- out[9] = yz - wx;
- out[10] = 1 - (xx + yy);
- out[11] = 0;
- out[12] = v[0];
- out[13] = v[1];
- out[14] = v[2];
- out[15] = 1;
- return out;
- }
- /**
- * Creates a new mat4 from a dual quat.
- *
- * @param {mat4} out Matrix
- * @param {ReadonlyQuat2} a Dual Quaternion
- * @returns {mat4} mat4 receiving operation result
- */
- function fromQuat2(out, a) {
- var translation = new ARRAY_TYPE(3);
- var bx = -a[0],
- by = -a[1],
- bz = -a[2],
- bw = a[3],
- ax = a[4],
- ay = a[5],
- az = a[6],
- aw = a[7];
- var magnitude = bx * bx + by * by + bz * bz + bw * bw; //Only scale if it makes sense
- if (magnitude > 0) {
- translation[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2 / magnitude;
- translation[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2 / magnitude;
- translation[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2 / magnitude;
- } else {
- translation[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2;
- translation[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2;
- translation[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2;
- }
- fromRotationTranslation(out, a, translation);
- return out;
- }
- /**
- * Returns the translation vector component of a transformation
- * matrix. If a matrix is built with fromRotationTranslation,
- * the returned vector will be the same as the translation vector
- * originally supplied.
- * @param {vec3} out Vector to receive translation component
- * @param {ReadonlyMat4} mat Matrix to be decomposed (input)
- * @return {vec3} out
- */
- function getTranslation(out, mat) {
- out[0] = mat[12];
- out[1] = mat[13];
- out[2] = mat[14];
- return out;
- }
- /**
- * Returns the scaling factor component of a transformation
- * matrix. If a matrix is built with fromRotationTranslationScale
- * with a normalized Quaternion paramter, the returned vector will be
- * the same as the scaling vector
- * originally supplied.
- * @param {vec3} out Vector to receive scaling factor component
- * @param {ReadonlyMat4} mat Matrix to be decomposed (input)
- * @return {vec3} out
- */
- function getScaling(out, mat) {
- var m11 = mat[0];
- var m12 = mat[1];
- var m13 = mat[2];
- var m21 = mat[4];
- var m22 = mat[5];
- var m23 = mat[6];
- var m31 = mat[8];
- var m32 = mat[9];
- var m33 = mat[10];
- out[0] = Math.hypot(m11, m12, m13);
- out[1] = Math.hypot(m21, m22, m23);
- out[2] = Math.hypot(m31, m32, m33);
- return out;
- }
- /**
- * Returns a quaternion representing the rotational component
- * of a transformation matrix. If a matrix is built with
- * fromRotationTranslation, the returned quaternion will be the
- * same as the quaternion originally supplied.
- * @param {quat} out Quaternion to receive the rotation component
- * @param {ReadonlyMat4} mat Matrix to be decomposed (input)
- * @return {quat} out
- */
- function getRotation(out, mat) {
- var scaling = new ARRAY_TYPE(3);
- getScaling(scaling, mat);
- var is1 = 1 / scaling[0];
- var is2 = 1 / scaling[1];
- var is3 = 1 / scaling[2];
- var sm11 = mat[0] * is1;
- var sm12 = mat[1] * is2;
- var sm13 = mat[2] * is3;
- var sm21 = mat[4] * is1;
- var sm22 = mat[5] * is2;
- var sm23 = mat[6] * is3;
- var sm31 = mat[8] * is1;
- var sm32 = mat[9] * is2;
- var sm33 = mat[10] * is3;
- var trace = sm11 + sm22 + sm33;
- var S = 0;
- if (trace > 0) {
- S = Math.sqrt(trace + 1.0) * 2;
- out[3] = 0.25 * S;
- out[0] = (sm23 - sm32) / S;
- out[1] = (sm31 - sm13) / S;
- out[2] = (sm12 - sm21) / S;
- } else if (sm11 > sm22 && sm11 > sm33) {
- S = Math.sqrt(1.0 + sm11 - sm22 - sm33) * 2;
- out[3] = (sm23 - sm32) / S;
- out[0] = 0.25 * S;
- out[1] = (sm12 + sm21) / S;
- out[2] = (sm31 + sm13) / S;
- } else if (sm22 > sm33) {
- S = Math.sqrt(1.0 + sm22 - sm11 - sm33) * 2;
- out[3] = (sm31 - sm13) / S;
- out[0] = (sm12 + sm21) / S;
- out[1] = 0.25 * S;
- out[2] = (sm23 + sm32) / S;
- } else {
- S = Math.sqrt(1.0 + sm33 - sm11 - sm22) * 2;
- out[3] = (sm12 - sm21) / S;
- out[0] = (sm31 + sm13) / S;
- out[1] = (sm23 + sm32) / S;
- out[2] = 0.25 * S;
- }
- return out;
- }
- /**
- * Creates a matrix from a quaternion rotation, vector translation and vector scale
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.translate(dest, vec);
- * let quatMat = mat4.create();
- * quat4.toMat4(quat, quatMat);
- * mat4.multiply(dest, quatMat);
- * mat4.scale(dest, scale)
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {quat4} q Rotation quaternion
- * @param {ReadonlyVec3} v Translation vector
- * @param {ReadonlyVec3} s Scaling vector
- * @returns {mat4} out
- */
- function fromRotationTranslationScale(out, q, v, s) {
- // Quaternion math
- var x = q[0],
- y = q[1],
- z = q[2],
- w = q[3];
- var x2 = x + x;
- var y2 = y + y;
- var z2 = z + z;
- var xx = x * x2;
- var xy = x * y2;
- var xz = x * z2;
- var yy = y * y2;
- var yz = y * z2;
- var zz = z * z2;
- var wx = w * x2;
- var wy = w * y2;
- var wz = w * z2;
- var sx = s[0];
- var sy = s[1];
- var sz = s[2];
- out[0] = (1 - (yy + zz)) * sx;
- out[1] = (xy + wz) * sx;
- out[2] = (xz - wy) * sx;
- out[3] = 0;
- out[4] = (xy - wz) * sy;
- out[5] = (1 - (xx + zz)) * sy;
- out[6] = (yz + wx) * sy;
- out[7] = 0;
- out[8] = (xz + wy) * sz;
- out[9] = (yz - wx) * sz;
- out[10] = (1 - (xx + yy)) * sz;
- out[11] = 0;
- out[12] = v[0];
- out[13] = v[1];
- out[14] = v[2];
- out[15] = 1;
- return out;
- }
- /**
- * Creates a matrix from a quaternion rotation, vector translation and vector scale, rotating and scaling around the given origin
- * This is equivalent to (but much faster than):
- *
- * mat4.identity(dest);
- * mat4.translate(dest, vec);
- * mat4.translate(dest, origin);
- * let quatMat = mat4.create();
- * quat4.toMat4(quat, quatMat);
- * mat4.multiply(dest, quatMat);
- * mat4.scale(dest, scale)
- * mat4.translate(dest, negativeOrigin);
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {quat4} q Rotation quaternion
- * @param {ReadonlyVec3} v Translation vector
- * @param {ReadonlyVec3} s Scaling vector
- * @param {ReadonlyVec3} o The origin vector around which to scale and rotate
- * @returns {mat4} out
- */
- function fromRotationTranslationScaleOrigin(out, q, v, s, o) {
- // Quaternion math
- var x = q[0],
- y = q[1],
- z = q[2],
- w = q[3];
- var x2 = x + x;
- var y2 = y + y;
- var z2 = z + z;
- var xx = x * x2;
- var xy = x * y2;
- var xz = x * z2;
- var yy = y * y2;
- var yz = y * z2;
- var zz = z * z2;
- var wx = w * x2;
- var wy = w * y2;
- var wz = w * z2;
- var sx = s[0];
- var sy = s[1];
- var sz = s[2];
- var ox = o[0];
- var oy = o[1];
- var oz = o[2];
- var out0 = (1 - (yy + zz)) * sx;
- var out1 = (xy + wz) * sx;
- var out2 = (xz - wy) * sx;
- var out4 = (xy - wz) * sy;
- var out5 = (1 - (xx + zz)) * sy;
- var out6 = (yz + wx) * sy;
- var out8 = (xz + wy) * sz;
- var out9 = (yz - wx) * sz;
- var out10 = (1 - (xx + yy)) * sz;
- out[0] = out0;
- out[1] = out1;
- out[2] = out2;
- out[3] = 0;
- out[4] = out4;
- out[5] = out5;
- out[6] = out6;
- out[7] = 0;
- out[8] = out8;
- out[9] = out9;
- out[10] = out10;
- out[11] = 0;
- out[12] = v[0] + ox - (out0 * ox + out4 * oy + out8 * oz);
- out[13] = v[1] + oy - (out1 * ox + out5 * oy + out9 * oz);
- out[14] = v[2] + oz - (out2 * ox + out6 * oy + out10 * oz);
- out[15] = 1;
- return out;
- }
- /**
- * Calculates a 4x4 matrix from the given quaternion
- *
- * @param {mat4} out mat4 receiving operation result
- * @param {ReadonlyQuat} q Quaternion to create matrix from
- *
- * @returns {mat4} out
- */
- function fromQuat$1(out, q) {
- var x = q[0],
- y = q[1],
- z = q[2],
- w = q[3];
- var x2 = x + x;
- var y2 = y + y;
- var z2 = z + z;
- var xx = x * x2;
- var yx = y * x2;
- var yy = y * y2;
- var zx = z * x2;
- var zy = z * y2;
- var zz = z * z2;
- var wx = w * x2;
- var wy = w * y2;
- var wz = w * z2;
- out[0] = 1 - yy - zz;
- out[1] = yx + wz;
- out[2] = zx - wy;
- out[3] = 0;
- out[4] = yx - wz;
- out[5] = 1 - xx - zz;
- out[6] = zy + wx;
- out[7] = 0;
- out[8] = zx + wy;
- out[9] = zy - wx;
- out[10] = 1 - xx - yy;
- out[11] = 0;
- out[12] = 0;
- out[13] = 0;
- out[14] = 0;
- out[15] = 1;
- return out;
- }
- /**
- * Generates a frustum matrix with the given bounds
- *
- * @param {mat4} out mat4 frustum matrix will be written into
- * @param {Number} left Left bound of the frustum
- * @param {Number} right Right bound of the frustum
- * @param {Number} bottom Bottom bound of the frustum
- * @param {Number} top Top bound of the frustum
- * @param {Number} near Near bound of the frustum
- * @param {Number} far Far bound of the frustum
- * @returns {mat4} out
- */
- function frustum(out, left, right, bottom, top, near, far) {
- var rl = 1 / (right - left);
- var tb = 1 / (top - bottom);
- var nf = 1 / (near - far);
- out[0] = near * 2 * rl;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = near * 2 * tb;
- out[6] = 0;
- out[7] = 0;
- out[8] = (right + left) * rl;
- out[9] = (top + bottom) * tb;
- out[10] = (far + near) * nf;
- out[11] = -1;
- out[12] = 0;
- out[13] = 0;
- out[14] = far * near * 2 * nf;
- out[15] = 0;
- return out;
- }
- /**
- * Generates a perspective projection matrix with the given bounds.
- * The near/far clip planes correspond to a normalized device coordinate Z range of [-1, 1],
- * which matches WebGL/OpenGL's clip volume.
- * Passing null/undefined/no value for far will generate infinite projection matrix.
- *
- * @param {mat4} out mat4 frustum matrix will be written into
- * @param {number} fovy Vertical field of view in radians
- * @param {number} aspect Aspect ratio. typically viewport width/height
- * @param {number} near Near bound of the frustum
- * @param {number} far Far bound of the frustum, can be null or Infinity
- * @returns {mat4} out
- */
- function perspectiveNO(out, fovy, aspect, near, far) {
- var f = 1.0 / Math.tan(fovy / 2),
- nf;
- out[0] = f / aspect;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = f;
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[11] = -1;
- out[12] = 0;
- out[13] = 0;
- out[15] = 0;
- if (far != null && far !== Infinity) {
- nf = 1 / (near - far);
- out[10] = (far + near) * nf;
- out[14] = 2 * far * near * nf;
- } else {
- out[10] = -1;
- out[14] = -2 * near;
- }
- return out;
- }
- /**
- * Alias for {@link mat4.perspectiveNO}
- * @function
- */
- var perspective = perspectiveNO;
- /**
- * Generates a perspective projection matrix suitable for WebGPU with the given bounds.
- * The near/far clip planes correspond to a normalized device coordinate Z range of [0, 1],
- * which matches WebGPU/Vulkan/DirectX/Metal's clip volume.
- * Passing null/undefined/no value for far will generate infinite projection matrix.
- *
- * @param {mat4} out mat4 frustum matrix will be written into
- * @param {number} fovy Vertical field of view in radians
- * @param {number} aspect Aspect ratio. typically viewport width/height
- * @param {number} near Near bound of the frustum
- * @param {number} far Far bound of the frustum, can be null or Infinity
- * @returns {mat4} out
- */
- function perspectiveZO(out, fovy, aspect, near, far) {
- var f = 1.0 / Math.tan(fovy / 2),
- nf;
- out[0] = f / aspect;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = f;
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[11] = -1;
- out[12] = 0;
- out[13] = 0;
- out[15] = 0;
- if (far != null && far !== Infinity) {
- nf = 1 / (near - far);
- out[10] = far * nf;
- out[14] = far * near * nf;
- } else {
- out[10] = -1;
- out[14] = -near;
- }
- return out;
- }
- /**
- * Generates a perspective projection matrix with the given field of view.
- * This is primarily useful for generating projection matrices to be used
- * with the still experiemental WebVR API.
- *
- * @param {mat4} out mat4 frustum matrix will be written into
- * @param {Object} fov Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees
- * @param {number} near Near bound of the frustum
- * @param {number} far Far bound of the frustum
- * @returns {mat4} out
- */
- function perspectiveFromFieldOfView(out, fov, near, far) {
- var upTan = Math.tan(fov.upDegrees * Math.PI / 180.0);
- var downTan = Math.tan(fov.downDegrees * Math.PI / 180.0);
- var leftTan = Math.tan(fov.leftDegrees * Math.PI / 180.0);
- var rightTan = Math.tan(fov.rightDegrees * Math.PI / 180.0);
- var xScale = 2.0 / (leftTan + rightTan);
- var yScale = 2.0 / (upTan + downTan);
- out[0] = xScale;
- out[1] = 0.0;
- out[2] = 0.0;
- out[3] = 0.0;
- out[4] = 0.0;
- out[5] = yScale;
- out[6] = 0.0;
- out[7] = 0.0;
- out[8] = -((leftTan - rightTan) * xScale * 0.5);
- out[9] = (upTan - downTan) * yScale * 0.5;
- out[10] = far / (near - far);
- out[11] = -1.0;
- out[12] = 0.0;
- out[13] = 0.0;
- out[14] = far * near / (near - far);
- out[15] = 0.0;
- return out;
- }
- /**
- * Generates a orthogonal projection matrix with the given bounds.
- * The near/far clip planes correspond to a normalized device coordinate Z range of [-1, 1],
- * which matches WebGL/OpenGL's clip volume.
- *
- * @param {mat4} out mat4 frustum matrix will be written into
- * @param {number} left Left bound of the frustum
- * @param {number} right Right bound of the frustum
- * @param {number} bottom Bottom bound of the frustum
- * @param {number} top Top bound of the frustum
- * @param {number} near Near bound of the frustum
- * @param {number} far Far bound of the frustum
- * @returns {mat4} out
- */
- function orthoNO(out, left, right, bottom, top, near, far) {
- var lr = 1 / (left - right);
- var bt = 1 / (bottom - top);
- var nf = 1 / (near - far);
- out[0] = -2 * lr;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = -2 * bt;
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[10] = 2 * nf;
- out[11] = 0;
- out[12] = (left + right) * lr;
- out[13] = (top + bottom) * bt;
- out[14] = (far + near) * nf;
- out[15] = 1;
- return out;
- }
- /**
- * Alias for {@link mat4.orthoNO}
- * @function
- */
- var ortho = orthoNO;
- /**
- * Generates a orthogonal projection matrix with the given bounds.
- * The near/far clip planes correspond to a normalized device coordinate Z range of [0, 1],
- * which matches WebGPU/Vulkan/DirectX/Metal's clip volume.
- *
- * @param {mat4} out mat4 frustum matrix will be written into
- * @param {number} left Left bound of the frustum
- * @param {number} right Right bound of the frustum
- * @param {number} bottom Bottom bound of the frustum
- * @param {number} top Top bound of the frustum
- * @param {number} near Near bound of the frustum
- * @param {number} far Far bound of the frustum
- * @returns {mat4} out
- */
- function orthoZO(out, left, right, bottom, top, near, far) {
- var lr = 1 / (left - right);
- var bt = 1 / (bottom - top);
- var nf = 1 / (near - far);
- out[0] = -2 * lr;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- out[4] = 0;
- out[5] = -2 * bt;
- out[6] = 0;
- out[7] = 0;
- out[8] = 0;
- out[9] = 0;
- out[10] = nf;
- out[11] = 0;
- out[12] = (left + right) * lr;
- out[13] = (top + bottom) * bt;
- out[14] = near * nf;
- out[15] = 1;
- return out;
- }
- /**
- * Generates a look-at matrix with the given eye position, focal point, and up axis.
- * If you want a matrix that actually makes an object look at another object, you should use targetTo instead.
- *
- * @param {mat4} out mat4 frustum matrix will be written into
- * @param {ReadonlyVec3} eye Position of the viewer
- * @param {ReadonlyVec3} center Point the viewer is looking at
- * @param {ReadonlyVec3} up vec3 pointing up
- * @returns {mat4} out
- */
- function lookAt(out, eye, center, up) {
- var x0, x1, x2, y0, y1, y2, z0, z1, z2, len;
- var eyex = eye[0];
- var eyey = eye[1];
- var eyez = eye[2];
- var upx = up[0];
- var upy = up[1];
- var upz = up[2];
- var centerx = center[0];
- var centery = center[1];
- var centerz = center[2];
- if (Math.abs(eyex - centerx) < EPSILON && Math.abs(eyey - centery) < EPSILON && Math.abs(eyez - centerz) < EPSILON) {
- return identity$3(out);
- }
- z0 = eyex - centerx;
- z1 = eyey - centery;
- z2 = eyez - centerz;
- len = 1 / Math.hypot(z0, z1, z2);
- z0 *= len;
- z1 *= len;
- z2 *= len;
- x0 = upy * z2 - upz * z1;
- x1 = upz * z0 - upx * z2;
- x2 = upx * z1 - upy * z0;
- len = Math.hypot(x0, x1, x2);
- if (!len) {
- x0 = 0;
- x1 = 0;
- x2 = 0;
- } else {
- len = 1 / len;
- x0 *= len;
- x1 *= len;
- x2 *= len;
- }
- y0 = z1 * x2 - z2 * x1;
- y1 = z2 * x0 - z0 * x2;
- y2 = z0 * x1 - z1 * x0;
- len = Math.hypot(y0, y1, y2);
- if (!len) {
- y0 = 0;
- y1 = 0;
- y2 = 0;
- } else {
- len = 1 / len;
- y0 *= len;
- y1 *= len;
- y2 *= len;
- }
- out[0] = x0;
- out[1] = y0;
- out[2] = z0;
- out[3] = 0;
- out[4] = x1;
- out[5] = y1;
- out[6] = z1;
- out[7] = 0;
- out[8] = x2;
- out[9] = y2;
- out[10] = z2;
- out[11] = 0;
- out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
- out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
- out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
- out[15] = 1;
- return out;
- }
- /**
- * Generates a matrix that makes something look at something else.
- *
- * @param {mat4} out mat4 frustum matrix will be written into
- * @param {ReadonlyVec3} eye Position of the viewer
- * @param {ReadonlyVec3} center Point the viewer is looking at
- * @param {ReadonlyVec3} up vec3 pointing up
- * @returns {mat4} out
- */
- function targetTo(out, eye, target, up) {
- var eyex = eye[0],
- eyey = eye[1],
- eyez = eye[2],
- upx = up[0],
- upy = up[1],
- upz = up[2];
- var z0 = eyex - target[0],
- z1 = eyey - target[1],
- z2 = eyez - target[2];
- var len = z0 * z0 + z1 * z1 + z2 * z2;
- if (len > 0) {
- len = 1 / Math.sqrt(len);
- z0 *= len;
- z1 *= len;
- z2 *= len;
- }
- var x0 = upy * z2 - upz * z1,
- x1 = upz * z0 - upx * z2,
- x2 = upx * z1 - upy * z0;
- len = x0 * x0 + x1 * x1 + x2 * x2;
- if (len > 0) {
- len = 1 / Math.sqrt(len);
- x0 *= len;
- x1 *= len;
- x2 *= len;
- }
- out[0] = x0;
- out[1] = x1;
- out[2] = x2;
- out[3] = 0;
- out[4] = z1 * x2 - z2 * x1;
- out[5] = z2 * x0 - z0 * x2;
- out[6] = z0 * x1 - z1 * x0;
- out[7] = 0;
- out[8] = z0;
- out[9] = z1;
- out[10] = z2;
- out[11] = 0;
- out[12] = eyex;
- out[13] = eyey;
- out[14] = eyez;
- out[15] = 1;
- return out;
- }
- /**
- * Returns a string representation of a mat4
- *
- * @param {ReadonlyMat4} a matrix to represent as a string
- * @returns {String} string representation of the matrix
- */
- function str$3(a) {
- return "mat4(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ", " + a[4] + ", " + a[5] + ", " + a[6] + ", " + a[7] + ", " + a[8] + ", " + a[9] + ", " + a[10] + ", " + a[11] + ", " + a[12] + ", " + a[13] + ", " + a[14] + ", " + a[15] + ")";
- }
- /**
- * Returns Frobenius norm of a mat4
- *
- * @param {ReadonlyMat4} a the matrix to calculate Frobenius norm of
- * @returns {Number} Frobenius norm
- */
- function frob$3(a) {
- return Math.hypot(a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], a[11], a[12], a[13], a[14], a[15]);
- }
- /**
- * Adds two mat4's
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the first operand
- * @param {ReadonlyMat4} b the second operand
- * @returns {mat4} out
- */
- function add$3(out, a, b) {
- out[0] = a[0] + b[0];
- out[1] = a[1] + b[1];
- out[2] = a[2] + b[2];
- out[3] = a[3] + b[3];
- out[4] = a[4] + b[4];
- out[5] = a[5] + b[5];
- out[6] = a[6] + b[6];
- out[7] = a[7] + b[7];
- out[8] = a[8] + b[8];
- out[9] = a[9] + b[9];
- out[10] = a[10] + b[10];
- out[11] = a[11] + b[11];
- out[12] = a[12] + b[12];
- out[13] = a[13] + b[13];
- out[14] = a[14] + b[14];
- out[15] = a[15] + b[15];
- return out;
- }
- /**
- * Subtracts matrix b from matrix a
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the first operand
- * @param {ReadonlyMat4} b the second operand
- * @returns {mat4} out
- */
- function subtract$3(out, a, b) {
- out[0] = a[0] - b[0];
- out[1] = a[1] - b[1];
- out[2] = a[2] - b[2];
- out[3] = a[3] - b[3];
- out[4] = a[4] - b[4];
- out[5] = a[5] - b[5];
- out[6] = a[6] - b[6];
- out[7] = a[7] - b[7];
- out[8] = a[8] - b[8];
- out[9] = a[9] - b[9];
- out[10] = a[10] - b[10];
- out[11] = a[11] - b[11];
- out[12] = a[12] - b[12];
- out[13] = a[13] - b[13];
- out[14] = a[14] - b[14];
- out[15] = a[15] - b[15];
- return out;
- }
- /**
- * Multiply each element of the matrix by a scalar.
- *
- * @param {mat4} out the receiving matrix
- * @param {ReadonlyMat4} a the matrix to scale
- * @param {Number} b amount to scale the matrix's elements by
- * @returns {mat4} out
- */
- function multiplyScalar$3(out, a, b) {
- out[0] = a[0] * b;
- out[1] = a[1] * b;
- out[2] = a[2] * b;
- out[3] = a[3] * b;
- out[4] = a[4] * b;
- out[5] = a[5] * b;
- out[6] = a[6] * b;
- out[7] = a[7] * b;
- out[8] = a[8] * b;
- out[9] = a[9] * b;
- out[10] = a[10] * b;
- out[11] = a[11] * b;
- out[12] = a[12] * b;
- out[13] = a[13] * b;
- out[14] = a[14] * b;
- out[15] = a[15] * b;
- return out;
- }
- /**
- * Adds two mat4's after multiplying each element of the second operand by a scalar value.
- *
- * @param {mat4} out the receiving vector
- * @param {ReadonlyMat4} a the first operand
- * @param {ReadonlyMat4} b the second operand
- * @param {Number} scale the amount to scale b's elements by before adding
- * @returns {mat4} out
- */
- function multiplyScalarAndAdd$3(out, a, b, scale) {
- out[0] = a[0] + b[0] * scale;
- out[1] = a[1] + b[1] * scale;
- out[2] = a[2] + b[2] * scale;
- out[3] = a[3] + b[3] * scale;
- out[4] = a[4] + b[4] * scale;
- out[5] = a[5] + b[5] * scale;
- out[6] = a[6] + b[6] * scale;
- out[7] = a[7] + b[7] * scale;
- out[8] = a[8] + b[8] * scale;
- out[9] = a[9] + b[9] * scale;
- out[10] = a[10] + b[10] * scale;
- out[11] = a[11] + b[11] * scale;
- out[12] = a[12] + b[12] * scale;
- out[13] = a[13] + b[13] * scale;
- out[14] = a[14] + b[14] * scale;
- out[15] = a[15] + b[15] * scale;
- return out;
- }
- /**
- * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyMat4} a The first matrix.
- * @param {ReadonlyMat4} b The second matrix.
- * @returns {Boolean} True if the matrices are equal, false otherwise.
- */
- function exactEquals$3(a, b) {
- 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] && a[6] === b[6] && a[7] === b[7] && a[8] === b[8] && a[9] === b[9] && a[10] === b[10] && a[11] === b[11] && a[12] === b[12] && a[13] === b[13] && a[14] === b[14] && a[15] === b[15];
- }
- /**
- * Returns whether or not the matrices have approximately the same elements in the same position.
- *
- * @param {ReadonlyMat4} a The first matrix.
- * @param {ReadonlyMat4} b The second matrix.
- * @returns {Boolean} True if the matrices are equal, false otherwise.
- */
- function equals$4(a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3];
- var a4 = a[4],
- a5 = a[5],
- a6 = a[6],
- a7 = a[7];
- var a8 = a[8],
- a9 = a[9],
- a10 = a[10],
- a11 = a[11];
- var a12 = a[12],
- a13 = a[13],
- a14 = a[14],
- a15 = a[15];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3];
- var b4 = b[4],
- b5 = b[5],
- b6 = b[6],
- b7 = b[7];
- var b8 = b[8],
- b9 = b[9],
- b10 = b[10],
- b11 = b[11];
- var b12 = b[12],
- b13 = b[13],
- b14 = b[14],
- b15 = b[15];
- return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) && Math.abs(a8 - b8) <= EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8)) && Math.abs(a9 - b9) <= EPSILON * Math.max(1.0, Math.abs(a9), Math.abs(b9)) && Math.abs(a10 - b10) <= EPSILON * Math.max(1.0, Math.abs(a10), Math.abs(b10)) && Math.abs(a11 - b11) <= EPSILON * Math.max(1.0, Math.abs(a11), Math.abs(b11)) && Math.abs(a12 - b12) <= EPSILON * Math.max(1.0, Math.abs(a12), Math.abs(b12)) && Math.abs(a13 - b13) <= EPSILON * Math.max(1.0, Math.abs(a13), Math.abs(b13)) && Math.abs(a14 - b14) <= EPSILON * Math.max(1.0, Math.abs(a14), Math.abs(b14)) && Math.abs(a15 - b15) <= EPSILON * Math.max(1.0, Math.abs(a15), Math.abs(b15));
- }
- /**
- * Alias for {@link mat4.multiply}
- * @function
- */
- var mul$3 = multiply$3;
- /**
- * Alias for {@link mat4.subtract}
- * @function
- */
- var sub$3 = subtract$3;
- var mat4 = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create$3,
- clone: clone$3,
- copy: copy$3,
- fromValues: fromValues$3,
- set: set$3,
- identity: identity$3,
- transpose: transpose$2,
- invert: invert$3,
- adjoint: adjoint$2,
- determinant: determinant$3,
- multiply: multiply$3,
- translate: translate$2,
- scale: scale$3,
- rotate: rotate$3,
- rotateX: rotateX,
- rotateY: rotateY,
- rotateZ: rotateZ,
- fromTranslation: fromTranslation$2,
- fromScaling: fromScaling$3,
- fromRotation: fromRotation$3,
- fromXRotation: fromXRotation,
- fromYRotation: fromYRotation,
- fromZRotation: fromZRotation,
- fromRotationTranslation: fromRotationTranslation,
- fromQuat2: fromQuat2,
- getTranslation: getTranslation,
- getScaling: getScaling,
- getRotation: getRotation,
- fromRotationTranslationScale: fromRotationTranslationScale,
- fromRotationTranslationScaleOrigin: fromRotationTranslationScaleOrigin,
- fromQuat: fromQuat$1,
- frustum: frustum,
- perspectiveNO: perspectiveNO,
- perspective: perspective,
- perspectiveZO: perspectiveZO,
- perspectiveFromFieldOfView: perspectiveFromFieldOfView,
- orthoNO: orthoNO,
- ortho: ortho,
- orthoZO: orthoZO,
- lookAt: lookAt,
- targetTo: targetTo,
- str: str$3,
- frob: frob$3,
- add: add$3,
- subtract: subtract$3,
- multiplyScalar: multiplyScalar$3,
- multiplyScalarAndAdd: multiplyScalarAndAdd$3,
- exactEquals: exactEquals$3,
- equals: equals$4,
- mul: mul$3,
- sub: sub$3
- });
- /**
- * 3 Dimensional Vector
- * @module vec3
- */
- /**
- * Creates a new, empty vec3
- *
- * @returns {vec3} a new 3D vector
- */
- function create$4() {
- var out = new ARRAY_TYPE(3);
- if (ARRAY_TYPE != Float32Array) {
- out[0] = 0;
- out[1] = 0;
- out[2] = 0;
- }
- return out;
- }
- /**
- * Creates a new vec3 initialized with values from an existing vector
- *
- * @param {ReadonlyVec3} a vector to clone
- * @returns {vec3} a new 3D vector
- */
- function clone$4(a) {
- var out = new ARRAY_TYPE(3);
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- return out;
- }
- /**
- * Calculates the length of a vec3
- *
- * @param {ReadonlyVec3} a vector to calculate length of
- * @returns {Number} length of a
- */
- function length(a) {
- var x = a[0];
- var y = a[1];
- var z = a[2];
- return Math.hypot(x, y, z);
- }
- /**
- * Creates a new vec3 initialized with the given values
- *
- * @param {Number} x X component
- * @param {Number} y Y component
- * @param {Number} z Z component
- * @returns {vec3} a new 3D vector
- */
- function fromValues$4(x, y, z) {
- var out = new ARRAY_TYPE(3);
- out[0] = x;
- out[1] = y;
- out[2] = z;
- return out;
- }
- /**
- * Copy the values from one vec3 to another
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the source vector
- * @returns {vec3} out
- */
- function copy$4(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- return out;
- }
- /**
- * Set the components of a vec3 to the given values
- *
- * @param {vec3} out the receiving vector
- * @param {Number} x X component
- * @param {Number} y Y component
- * @param {Number} z Z component
- * @returns {vec3} out
- */
- function set$4(out, x, y, z) {
- out[0] = x;
- out[1] = y;
- out[2] = z;
- return out;
- }
- /**
- * Adds two vec3's
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {vec3} out
- */
- function add$4(out, a, b) {
- out[0] = a[0] + b[0];
- out[1] = a[1] + b[1];
- out[2] = a[2] + b[2];
- return out;
- }
- /**
- * Subtracts vector b from vector a
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {vec3} out
- */
- function subtract$4(out, a, b) {
- out[0] = a[0] - b[0];
- out[1] = a[1] - b[1];
- out[2] = a[2] - b[2];
- return out;
- }
- /**
- * Multiplies two vec3's
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {vec3} out
- */
- function multiply$4(out, a, b) {
- out[0] = a[0] * b[0];
- out[1] = a[1] * b[1];
- out[2] = a[2] * b[2];
- return out;
- }
- /**
- * Divides two vec3's
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {vec3} out
- */
- function divide(out, a, b) {
- out[0] = a[0] / b[0];
- out[1] = a[1] / b[1];
- out[2] = a[2] / b[2];
- return out;
- }
- /**
- * Math.ceil the components of a vec3
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a vector to ceil
- * @returns {vec3} out
- */
- function ceil(out, a) {
- out[0] = Math.ceil(a[0]);
- out[1] = Math.ceil(a[1]);
- out[2] = Math.ceil(a[2]);
- return out;
- }
- /**
- * Math.floor the components of a vec3
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a vector to floor
- * @returns {vec3} out
- */
- function floor(out, a) {
- out[0] = Math.floor(a[0]);
- out[1] = Math.floor(a[1]);
- out[2] = Math.floor(a[2]);
- return out;
- }
- /**
- * Returns the minimum of two vec3's
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {vec3} out
- */
- function min(out, a, b) {
- out[0] = Math.min(a[0], b[0]);
- out[1] = Math.min(a[1], b[1]);
- out[2] = Math.min(a[2], b[2]);
- return out;
- }
- /**
- * Returns the maximum of two vec3's
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {vec3} out
- */
- function max(out, a, b) {
- out[0] = Math.max(a[0], b[0]);
- out[1] = Math.max(a[1], b[1]);
- out[2] = Math.max(a[2], b[2]);
- return out;
- }
- /**
- * Math.round the components of a vec3
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a vector to round
- * @returns {vec3} out
- */
- function round(out, a) {
- out[0] = Math.round(a[0]);
- out[1] = Math.round(a[1]);
- out[2] = Math.round(a[2]);
- return out;
- }
- /**
- * Scales a vec3 by a scalar number
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the vector to scale
- * @param {Number} b amount to scale the vector by
- * @returns {vec3} out
- */
- function scale$4(out, a, b) {
- out[0] = a[0] * b;
- out[1] = a[1] * b;
- out[2] = a[2] * b;
- return out;
- }
- /**
- * Adds two vec3's after scaling the second operand by a scalar value
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @param {Number} scale the amount to scale b by before adding
- * @returns {vec3} out
- */
- function scaleAndAdd(out, a, b, scale) {
- out[0] = a[0] + b[0] * scale;
- out[1] = a[1] + b[1] * scale;
- out[2] = a[2] + b[2] * scale;
- return out;
- }
- /**
- * Calculates the euclidian distance between two vec3's
- *
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {Number} distance between a and b
- */
- function distance(a, b) {
- var x = b[0] - a[0];
- var y = b[1] - a[1];
- var z = b[2] - a[2];
- return Math.hypot(x, y, z);
- }
- /**
- * Calculates the squared euclidian distance between two vec3's
- *
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {Number} squared distance between a and b
- */
- function squaredDistance(a, b) {
- var x = b[0] - a[0];
- var y = b[1] - a[1];
- var z = b[2] - a[2];
- return x * x + y * y + z * z;
- }
- /**
- * Calculates the squared length of a vec3
- *
- * @param {ReadonlyVec3} a vector to calculate squared length of
- * @returns {Number} squared length of a
- */
- function squaredLength(a) {
- var x = a[0];
- var y = a[1];
- var z = a[2];
- return x * x + y * y + z * z;
- }
- /**
- * Negates the components of a vec3
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a vector to negate
- * @returns {vec3} out
- */
- function negate(out, a) {
- out[0] = -a[0];
- out[1] = -a[1];
- out[2] = -a[2];
- return out;
- }
- /**
- * Returns the inverse of the components of a vec3
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a vector to invert
- * @returns {vec3} out
- */
- function inverse(out, a) {
- out[0] = 1.0 / a[0];
- out[1] = 1.0 / a[1];
- out[2] = 1.0 / a[2];
- return out;
- }
- /**
- * Normalize a vec3
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a vector to normalize
- * @returns {vec3} out
- */
- function normalize(out, a) {
- var x = a[0];
- var y = a[1];
- var z = a[2];
- var len = x * x + y * y + z * z;
- if (len > 0) {
- //TODO: evaluate use of glm_invsqrt here?
- len = 1 / Math.sqrt(len);
- }
- out[0] = a[0] * len;
- out[1] = a[1] * len;
- out[2] = a[2] * len;
- return out;
- }
- /**
- * Calculates the dot product of two vec3's
- *
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {Number} dot product of a and b
- */
- function dot(a, b) {
- return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
- }
- /**
- * Computes the cross product of two vec3's
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @returns {vec3} out
- */
- function cross(out, a, b) {
- var ax = a[0],
- ay = a[1],
- az = a[2];
- var bx = b[0],
- by = b[1],
- bz = b[2];
- out[0] = ay * bz - az * by;
- out[1] = az * bx - ax * bz;
- out[2] = ax * by - ay * bx;
- return out;
- }
- /**
- * Performs a linear interpolation between two vec3's
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {vec3} out
- */
- function lerp(out, a, b, t) {
- var ax = a[0];
- var ay = a[1];
- var az = a[2];
- out[0] = ax + t * (b[0] - ax);
- out[1] = ay + t * (b[1] - ay);
- out[2] = az + t * (b[2] - az);
- return out;
- }
- /**
- * Performs a hermite interpolation with two control points
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @param {ReadonlyVec3} c the third operand
- * @param {ReadonlyVec3} d the fourth operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {vec3} out
- */
- function hermite(out, a, b, c, d, t) {
- var factorTimes2 = t * t;
- var factor1 = factorTimes2 * (2 * t - 3) + 1;
- var factor2 = factorTimes2 * (t - 2) + t;
- var factor3 = factorTimes2 * (t - 1);
- var factor4 = factorTimes2 * (3 - 2 * t);
- out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4;
- out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4;
- out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4;
- return out;
- }
- /**
- * Performs a bezier interpolation with two control points
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the first operand
- * @param {ReadonlyVec3} b the second operand
- * @param {ReadonlyVec3} c the third operand
- * @param {ReadonlyVec3} d the fourth operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {vec3} out
- */
- function bezier(out, a, b, c, d, t) {
- var inverseFactor = 1 - t;
- var inverseFactorTimesTwo = inverseFactor * inverseFactor;
- var factorTimes2 = t * t;
- var factor1 = inverseFactorTimesTwo * inverseFactor;
- var factor2 = 3 * t * inverseFactorTimesTwo;
- var factor3 = 3 * factorTimes2 * inverseFactor;
- var factor4 = factorTimes2 * t;
- out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4;
- out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4;
- out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4;
- return out;
- }
- /**
- * Generates a random vector with the given scale
- *
- * @param {vec3} out the receiving vector
- * @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned
- * @returns {vec3} out
- */
- function random(out, scale) {
- scale = scale || 1.0;
- var r = RANDOM() * 2.0 * Math.PI;
- var z = RANDOM() * 2.0 - 1.0;
- var zScale = Math.sqrt(1.0 - z * z) * scale;
- out[0] = Math.cos(r) * zScale;
- out[1] = Math.sin(r) * zScale;
- out[2] = z * scale;
- return out;
- }
- /**
- * Transforms the vec3 with a mat4.
- * 4th vector component is implicitly '1'
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the vector to transform
- * @param {ReadonlyMat4} m matrix to transform with
- * @returns {vec3} out
- */
- function transformMat4(out, a, m) {
- var x = a[0],
- y = a[1],
- z = a[2];
- var w = m[3] * x + m[7] * y + m[11] * z + m[15];
- w = w || 1.0;
- out[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;
- out[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;
- out[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;
- return out;
- }
- /**
- * Transforms the vec3 with a mat3.
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the vector to transform
- * @param {ReadonlyMat3} m the 3x3 matrix to transform with
- * @returns {vec3} out
- */
- function transformMat3(out, a, m) {
- var x = a[0],
- y = a[1],
- z = a[2];
- out[0] = x * m[0] + y * m[3] + z * m[6];
- out[1] = x * m[1] + y * m[4] + z * m[7];
- out[2] = x * m[2] + y * m[5] + z * m[8];
- return out;
- }
- /**
- * Transforms the vec3 with a quat
- * Can also be used for dual quaternions. (Multiply it with the real part)
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec3} a the vector to transform
- * @param {ReadonlyQuat} q quaternion to transform with
- * @returns {vec3} out
- */
- function transformQuat(out, a, q) {
- // benchmarks: https://jsperf.com/quaternion-transform-vec3-implementations-fixed
- var qx = q[0],
- qy = q[1],
- qz = q[2],
- qw = q[3];
- var x = a[0],
- y = a[1],
- z = a[2]; // var qvec = [qx, qy, qz];
- // var uv = vec3.cross([], qvec, a);
- var uvx = qy * z - qz * y,
- uvy = qz * x - qx * z,
- uvz = qx * y - qy * x; // var uuv = vec3.cross([], qvec, uv);
- var uuvx = qy * uvz - qz * uvy,
- uuvy = qz * uvx - qx * uvz,
- uuvz = qx * uvy - qy * uvx; // vec3.scale(uv, uv, 2 * w);
- var w2 = qw * 2;
- uvx *= w2;
- uvy *= w2;
- uvz *= w2; // vec3.scale(uuv, uuv, 2);
- uuvx *= 2;
- uuvy *= 2;
- uuvz *= 2; // return vec3.add(out, a, vec3.add(out, uv, uuv));
- out[0] = x + uvx + uuvx;
- out[1] = y + uvy + uuvy;
- out[2] = z + uvz + uuvz;
- return out;
- }
- /**
- * Rotate a 3D vector around the x-axis
- * @param {vec3} out The receiving vec3
- * @param {ReadonlyVec3} a The vec3 point to rotate
- * @param {ReadonlyVec3} b The origin of the rotation
- * @param {Number} rad The angle of rotation in radians
- * @returns {vec3} out
- */
- function rotateX$1(out, a, b, rad) {
- var p = [],
- r = []; //Translate point to the origin
- p[0] = a[0] - b[0];
- p[1] = a[1] - b[1];
- p[2] = a[2] - b[2]; //perform rotation
- r[0] = p[0];
- r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);
- r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad); //translate to correct position
- out[0] = r[0] + b[0];
- out[1] = r[1] + b[1];
- out[2] = r[2] + b[2];
- return out;
- }
- /**
- * Rotate a 3D vector around the y-axis
- * @param {vec3} out The receiving vec3
- * @param {ReadonlyVec3} a The vec3 point to rotate
- * @param {ReadonlyVec3} b The origin of the rotation
- * @param {Number} rad The angle of rotation in radians
- * @returns {vec3} out
- */
- function rotateY$1(out, a, b, rad) {
- var p = [],
- r = []; //Translate point to the origin
- p[0] = a[0] - b[0];
- p[1] = a[1] - b[1];
- p[2] = a[2] - b[2]; //perform rotation
- r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);
- r[1] = p[1];
- r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad); //translate to correct position
- out[0] = r[0] + b[0];
- out[1] = r[1] + b[1];
- out[2] = r[2] + b[2];
- return out;
- }
- /**
- * Rotate a 3D vector around the z-axis
- * @param {vec3} out The receiving vec3
- * @param {ReadonlyVec3} a The vec3 point to rotate
- * @param {ReadonlyVec3} b The origin of the rotation
- * @param {Number} rad The angle of rotation in radians
- * @returns {vec3} out
- */
- function rotateZ$1(out, a, b, rad) {
- var p = [],
- r = []; //Translate point to the origin
- p[0] = a[0] - b[0];
- p[1] = a[1] - b[1];
- p[2] = a[2] - b[2]; //perform rotation
- r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);
- r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);
- r[2] = p[2]; //translate to correct position
- out[0] = r[0] + b[0];
- out[1] = r[1] + b[1];
- out[2] = r[2] + b[2];
- return out;
- }
- /**
- * Get the angle between two 3D vectors
- * @param {ReadonlyVec3} a The first operand
- * @param {ReadonlyVec3} b The second operand
- * @returns {Number} The angle in radians
- */
- function angle(a, b) {
- var ax = a[0],
- ay = a[1],
- az = a[2],
- bx = b[0],
- by = b[1],
- bz = b[2],
- mag1 = Math.sqrt(ax * ax + ay * ay + az * az),
- mag2 = Math.sqrt(bx * bx + by * by + bz * bz),
- mag = mag1 * mag2,
- cosine = mag && dot(a, b) / mag;
- return Math.acos(Math.min(Math.max(cosine, -1), 1));
- }
- /**
- * Set the components of a vec3 to zero
- *
- * @param {vec3} out the receiving vector
- * @returns {vec3} out
- */
- function zero(out) {
- out[0] = 0.0;
- out[1] = 0.0;
- out[2] = 0.0;
- return out;
- }
- /**
- * Returns a string representation of a vector
- *
- * @param {ReadonlyVec3} a vector to represent as a string
- * @returns {String} string representation of the vector
- */
- function str$4(a) {
- return "vec3(" + a[0] + ", " + a[1] + ", " + a[2] + ")";
- }
- /**
- * Returns whether or not the vectors have exactly the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyVec3} a The first vector.
- * @param {ReadonlyVec3} b The second vector.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
- */
- function exactEquals$4(a, b) {
- return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];
- }
- /**
- * Returns whether or not the vectors have approximately the same elements in the same position.
- *
- * @param {ReadonlyVec3} a The first vector.
- * @param {ReadonlyVec3} b The second vector.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
- */
- function equals$5(a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2];
- return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2));
- }
- /**
- * Alias for {@link vec3.subtract}
- * @function
- */
- var sub$4 = subtract$4;
- /**
- * Alias for {@link vec3.multiply}
- * @function
- */
- var mul$4 = multiply$4;
- /**
- * Alias for {@link vec3.divide}
- * @function
- */
- var div = divide;
- /**
- * Alias for {@link vec3.distance}
- * @function
- */
- var dist = distance;
- /**
- * Alias for {@link vec3.squaredDistance}
- * @function
- */
- var sqrDist = squaredDistance;
- /**
- * Alias for {@link vec3.length}
- * @function
- */
- var len = length;
- /**
- * Alias for {@link vec3.squaredLength}
- * @function
- */
- var sqrLen = squaredLength;
- /**
- * Perform some operation over an array of vec3s.
- *
- * @param {Array} a the array of vectors to iterate over
- * @param {Number} stride Number of elements between the start of each vec3. If 0 assumes tightly packed
- * @param {Number} offset Number of elements to skip at the beginning of the array
- * @param {Number} count Number of vec3s to iterate over. If 0 iterates over entire array
- * @param {Function} fn Function to call for each vector in the array
- * @param {Object} [arg] additional argument to pass to fn
- * @returns {Array} a
- * @function
- */
- var forEach = function () {
- var vec = create$4();
- return function (a, stride, offset, count, fn, arg) {
- var i, l;
- if (!stride) {
- stride = 3;
- }
- if (!offset) {
- offset = 0;
- }
- if (count) {
- l = Math.min(count * stride + offset, a.length);
- } else {
- l = a.length;
- }
- for (i = offset; i < l; i += stride) {
- vec[0] = a[i];
- vec[1] = a[i + 1];
- vec[2] = a[i + 2];
- fn(vec, vec, arg);
- a[i] = vec[0];
- a[i + 1] = vec[1];
- a[i + 2] = vec[2];
- }
- return a;
- };
- }();
- var vec3 = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create$4,
- clone: clone$4,
- length: length,
- fromValues: fromValues$4,
- copy: copy$4,
- set: set$4,
- add: add$4,
- subtract: subtract$4,
- multiply: multiply$4,
- divide: divide,
- ceil: ceil,
- floor: floor,
- min: min,
- max: max,
- round: round,
- scale: scale$4,
- scaleAndAdd: scaleAndAdd,
- distance: distance,
- squaredDistance: squaredDistance,
- squaredLength: squaredLength,
- negate: negate,
- inverse: inverse,
- normalize: normalize,
- dot: dot,
- cross: cross,
- lerp: lerp,
- hermite: hermite,
- bezier: bezier,
- random: random,
- transformMat4: transformMat4,
- transformMat3: transformMat3,
- transformQuat: transformQuat,
- rotateX: rotateX$1,
- rotateY: rotateY$1,
- rotateZ: rotateZ$1,
- angle: angle,
- zero: zero,
- str: str$4,
- exactEquals: exactEquals$4,
- equals: equals$5,
- sub: sub$4,
- mul: mul$4,
- div: div,
- dist: dist,
- sqrDist: sqrDist,
- len: len,
- sqrLen: sqrLen,
- forEach: forEach
- });
- /**
- * 4 Dimensional Vector
- * @module vec4
- */
- /**
- * Creates a new, empty vec4
- *
- * @returns {vec4} a new 4D vector
- */
- function create$5() {
- var out = new ARRAY_TYPE(4);
- if (ARRAY_TYPE != Float32Array) {
- out[0] = 0;
- out[1] = 0;
- out[2] = 0;
- out[3] = 0;
- }
- return out;
- }
- /**
- * Creates a new vec4 initialized with values from an existing vector
- *
- * @param {ReadonlyVec4} a vector to clone
- * @returns {vec4} a new 4D vector
- */
- function clone$5(a) {
- var out = new ARRAY_TYPE(4);
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- return out;
- }
- /**
- * Creates a new vec4 initialized with the given values
- *
- * @param {Number} x X component
- * @param {Number} y Y component
- * @param {Number} z Z component
- * @param {Number} w W component
- * @returns {vec4} a new 4D vector
- */
- function fromValues$5(x, y, z, w) {
- var out = new ARRAY_TYPE(4);
- out[0] = x;
- out[1] = y;
- out[2] = z;
- out[3] = w;
- return out;
- }
- /**
- * Copy the values from one vec4 to another
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the source vector
- * @returns {vec4} out
- */
- function copy$5(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- return out;
- }
- /**
- * Set the components of a vec4 to the given values
- *
- * @param {vec4} out the receiving vector
- * @param {Number} x X component
- * @param {Number} y Y component
- * @param {Number} z Z component
- * @param {Number} w W component
- * @returns {vec4} out
- */
- function set$5(out, x, y, z, w) {
- out[0] = x;
- out[1] = y;
- out[2] = z;
- out[3] = w;
- return out;
- }
- /**
- * Adds two vec4's
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {vec4} out
- */
- function add$5(out, a, b) {
- out[0] = a[0] + b[0];
- out[1] = a[1] + b[1];
- out[2] = a[2] + b[2];
- out[3] = a[3] + b[3];
- return out;
- }
- /**
- * Subtracts vector b from vector a
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {vec4} out
- */
- function subtract$5(out, a, b) {
- out[0] = a[0] - b[0];
- out[1] = a[1] - b[1];
- out[2] = a[2] - b[2];
- out[3] = a[3] - b[3];
- return out;
- }
- /**
- * Multiplies two vec4's
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {vec4} out
- */
- function multiply$5(out, a, b) {
- out[0] = a[0] * b[0];
- out[1] = a[1] * b[1];
- out[2] = a[2] * b[2];
- out[3] = a[3] * b[3];
- return out;
- }
- /**
- * Divides two vec4's
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {vec4} out
- */
- function divide$1(out, a, b) {
- out[0] = a[0] / b[0];
- out[1] = a[1] / b[1];
- out[2] = a[2] / b[2];
- out[3] = a[3] / b[3];
- return out;
- }
- /**
- * Math.ceil the components of a vec4
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a vector to ceil
- * @returns {vec4} out
- */
- function ceil$1(out, a) {
- out[0] = Math.ceil(a[0]);
- out[1] = Math.ceil(a[1]);
- out[2] = Math.ceil(a[2]);
- out[3] = Math.ceil(a[3]);
- return out;
- }
- /**
- * Math.floor the components of a vec4
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a vector to floor
- * @returns {vec4} out
- */
- function floor$1(out, a) {
- out[0] = Math.floor(a[0]);
- out[1] = Math.floor(a[1]);
- out[2] = Math.floor(a[2]);
- out[3] = Math.floor(a[3]);
- return out;
- }
- /**
- * Returns the minimum of two vec4's
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {vec4} out
- */
- function min$1(out, a, b) {
- out[0] = Math.min(a[0], b[0]);
- out[1] = Math.min(a[1], b[1]);
- out[2] = Math.min(a[2], b[2]);
- out[3] = Math.min(a[3], b[3]);
- return out;
- }
- /**
- * Returns the maximum of two vec4's
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {vec4} out
- */
- function max$1(out, a, b) {
- out[0] = Math.max(a[0], b[0]);
- out[1] = Math.max(a[1], b[1]);
- out[2] = Math.max(a[2], b[2]);
- out[3] = Math.max(a[3], b[3]);
- return out;
- }
- /**
- * Math.round the components of a vec4
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a vector to round
- * @returns {vec4} out
- */
- function round$1(out, a) {
- out[0] = Math.round(a[0]);
- out[1] = Math.round(a[1]);
- out[2] = Math.round(a[2]);
- out[3] = Math.round(a[3]);
- return out;
- }
- /**
- * Scales a vec4 by a scalar number
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the vector to scale
- * @param {Number} b amount to scale the vector by
- * @returns {vec4} out
- */
- function scale$5(out, a, b) {
- out[0] = a[0] * b;
- out[1] = a[1] * b;
- out[2] = a[2] * b;
- out[3] = a[3] * b;
- return out;
- }
- /**
- * Adds two vec4's after scaling the second operand by a scalar value
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @param {Number} scale the amount to scale b by before adding
- * @returns {vec4} out
- */
- function scaleAndAdd$1(out, a, b, scale) {
- out[0] = a[0] + b[0] * scale;
- out[1] = a[1] + b[1] * scale;
- out[2] = a[2] + b[2] * scale;
- out[3] = a[3] + b[3] * scale;
- return out;
- }
- /**
- * Calculates the euclidian distance between two vec4's
- *
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {Number} distance between a and b
- */
- function distance$1(a, b) {
- var x = b[0] - a[0];
- var y = b[1] - a[1];
- var z = b[2] - a[2];
- var w = b[3] - a[3];
- return Math.hypot(x, y, z, w);
- }
- /**
- * Calculates the squared euclidian distance between two vec4's
- *
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {Number} squared distance between a and b
- */
- function squaredDistance$1(a, b) {
- var x = b[0] - a[0];
- var y = b[1] - a[1];
- var z = b[2] - a[2];
- var w = b[3] - a[3];
- return x * x + y * y + z * z + w * w;
- }
- /**
- * Calculates the length of a vec4
- *
- * @param {ReadonlyVec4} a vector to calculate length of
- * @returns {Number} length of a
- */
- function length$1(a) {
- var x = a[0];
- var y = a[1];
- var z = a[2];
- var w = a[3];
- return Math.hypot(x, y, z, w);
- }
- /**
- * Calculates the squared length of a vec4
- *
- * @param {ReadonlyVec4} a vector to calculate squared length of
- * @returns {Number} squared length of a
- */
- function squaredLength$1(a) {
- var x = a[0];
- var y = a[1];
- var z = a[2];
- var w = a[3];
- return x * x + y * y + z * z + w * w;
- }
- /**
- * Negates the components of a vec4
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a vector to negate
- * @returns {vec4} out
- */
- function negate$1(out, a) {
- out[0] = -a[0];
- out[1] = -a[1];
- out[2] = -a[2];
- out[3] = -a[3];
- return out;
- }
- /**
- * Returns the inverse of the components of a vec4
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a vector to invert
- * @returns {vec4} out
- */
- function inverse$1(out, a) {
- out[0] = 1.0 / a[0];
- out[1] = 1.0 / a[1];
- out[2] = 1.0 / a[2];
- out[3] = 1.0 / a[3];
- return out;
- }
- /**
- * Normalize a vec4
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a vector to normalize
- * @returns {vec4} out
- */
- function normalize$1(out, a) {
- var x = a[0];
- var y = a[1];
- var z = a[2];
- var w = a[3];
- var len = x * x + y * y + z * z + w * w;
- if (len > 0) {
- len = 1 / Math.sqrt(len);
- }
- out[0] = x * len;
- out[1] = y * len;
- out[2] = z * len;
- out[3] = w * len;
- return out;
- }
- /**
- * Calculates the dot product of two vec4's
- *
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @returns {Number} dot product of a and b
- */
- function dot$1(a, b) {
- return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3];
- }
- /**
- * Returns the cross-product of three vectors in a 4-dimensional space
- *
- * @param {ReadonlyVec4} result the receiving vector
- * @param {ReadonlyVec4} U the first vector
- * @param {ReadonlyVec4} V the second vector
- * @param {ReadonlyVec4} W the third vector
- * @returns {vec4} result
- */
- function cross$1(out, u, v, w) {
- var A = v[0] * w[1] - v[1] * w[0],
- B = v[0] * w[2] - v[2] * w[0],
- C = v[0] * w[3] - v[3] * w[0],
- D = v[1] * w[2] - v[2] * w[1],
- E = v[1] * w[3] - v[3] * w[1],
- F = v[2] * w[3] - v[3] * w[2];
- var G = u[0];
- var H = u[1];
- var I = u[2];
- var J = u[3];
- out[0] = H * F - I * E + J * D;
- out[1] = -(G * F) + I * C - J * B;
- out[2] = G * E - H * C + J * A;
- out[3] = -(G * D) + H * B - I * A;
- return out;
- }
- /**
- * Performs a linear interpolation between two vec4's
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the first operand
- * @param {ReadonlyVec4} b the second operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {vec4} out
- */
- function lerp$1(out, a, b, t) {
- var ax = a[0];
- var ay = a[1];
- var az = a[2];
- var aw = a[3];
- out[0] = ax + t * (b[0] - ax);
- out[1] = ay + t * (b[1] - ay);
- out[2] = az + t * (b[2] - az);
- out[3] = aw + t * (b[3] - aw);
- return out;
- }
- /**
- * Generates a random vector with the given scale
- *
- * @param {vec4} out the receiving vector
- * @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned
- * @returns {vec4} out
- */
- function random$1(out, scale) {
- scale = scale || 1.0; // Marsaglia, George. Choosing a Point from the Surface of a
- // Sphere. Ann. Math. Statist. 43 (1972), no. 2, 645--646.
- // http://projecteuclid.org/euclid.aoms/1177692644;
- var v1, v2, v3, v4;
- var s1, s2;
- do {
- v1 = RANDOM() * 2 - 1;
- v2 = RANDOM() * 2 - 1;
- s1 = v1 * v1 + v2 * v2;
- } while (s1 >= 1);
- do {
- v3 = RANDOM() * 2 - 1;
- v4 = RANDOM() * 2 - 1;
- s2 = v3 * v3 + v4 * v4;
- } while (s2 >= 1);
- var d = Math.sqrt((1 - s1) / s2);
- out[0] = scale * v1;
- out[1] = scale * v2;
- out[2] = scale * v3 * d;
- out[3] = scale * v4 * d;
- return out;
- }
- /**
- * Transforms the vec4 with a mat4.
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the vector to transform
- * @param {ReadonlyMat4} m matrix to transform with
- * @returns {vec4} out
- */
- function transformMat4$1(out, a, m) {
- var x = a[0],
- y = a[1],
- z = a[2],
- w = a[3];
- out[0] = m[0] * x + m[4] * y + m[8] * z + m[12] * w;
- out[1] = m[1] * x + m[5] * y + m[9] * z + m[13] * w;
- out[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;
- out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;
- return out;
- }
- /**
- * Transforms the vec4 with a quat
- *
- * @param {vec4} out the receiving vector
- * @param {ReadonlyVec4} a the vector to transform
- * @param {ReadonlyQuat} q quaternion to transform with
- * @returns {vec4} out
- */
- function transformQuat$1(out, a, q) {
- var x = a[0],
- y = a[1],
- z = a[2];
- var qx = q[0],
- qy = q[1],
- qz = q[2],
- qw = q[3]; // calculate quat * vec
- var ix = qw * x + qy * z - qz * y;
- var iy = qw * y + qz * x - qx * z;
- var iz = qw * z + qx * y - qy * x;
- var iw = -qx * x - qy * y - qz * z; // calculate result * inverse quat
- out[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
- out[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
- out[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
- out[3] = a[3];
- return out;
- }
- /**
- * Set the components of a vec4 to zero
- *
- * @param {vec4} out the receiving vector
- * @returns {vec4} out
- */
- function zero$1(out) {
- out[0] = 0.0;
- out[1] = 0.0;
- out[2] = 0.0;
- out[3] = 0.0;
- return out;
- }
- /**
- * Returns a string representation of a vector
- *
- * @param {ReadonlyVec4} a vector to represent as a string
- * @returns {String} string representation of the vector
- */
- function str$5(a) {
- return "vec4(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ")";
- }
- /**
- * Returns whether or not the vectors have exactly the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyVec4} a The first vector.
- * @param {ReadonlyVec4} b The second vector.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
- */
- function exactEquals$5(a, b) {
- return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];
- }
- /**
- * Returns whether or not the vectors have approximately the same elements in the same position.
- *
- * @param {ReadonlyVec4} a The first vector.
- * @param {ReadonlyVec4} b The second vector.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
- */
- function equals$6(a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3];
- return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3));
- }
- /**
- * Alias for {@link vec4.subtract}
- * @function
- */
- var sub$5 = subtract$5;
- /**
- * Alias for {@link vec4.multiply}
- * @function
- */
- var mul$5 = multiply$5;
- /**
- * Alias for {@link vec4.divide}
- * @function
- */
- var div$1 = divide$1;
- /**
- * Alias for {@link vec4.distance}
- * @function
- */
- var dist$1 = distance$1;
- /**
- * Alias for {@link vec4.squaredDistance}
- * @function
- */
- var sqrDist$1 = squaredDistance$1;
- /**
- * Alias for {@link vec4.length}
- * @function
- */
- var len$1 = length$1;
- /**
- * Alias for {@link vec4.squaredLength}
- * @function
- */
- var sqrLen$1 = squaredLength$1;
- /**
- * Perform some operation over an array of vec4s.
- *
- * @param {Array} a the array of vectors to iterate over
- * @param {Number} stride Number of elements between the start of each vec4. If 0 assumes tightly packed
- * @param {Number} offset Number of elements to skip at the beginning of the array
- * @param {Number} count Number of vec4s to iterate over. If 0 iterates over entire array
- * @param {Function} fn Function to call for each vector in the array
- * @param {Object} [arg] additional argument to pass to fn
- * @returns {Array} a
- * @function
- */
- var forEach$1 = function () {
- var vec = create$5();
- return function (a, stride, offset, count, fn, arg) {
- var i, l;
- if (!stride) {
- stride = 4;
- }
- if (!offset) {
- offset = 0;
- }
- if (count) {
- l = Math.min(count * stride + offset, a.length);
- } else {
- l = a.length;
- }
- for (i = offset; i < l; i += stride) {
- vec[0] = a[i];
- vec[1] = a[i + 1];
- vec[2] = a[i + 2];
- vec[3] = a[i + 3];
- fn(vec, vec, arg);
- a[i] = vec[0];
- a[i + 1] = vec[1];
- a[i + 2] = vec[2];
- a[i + 3] = vec[3];
- }
- return a;
- };
- }();
- var vec4 = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create$5,
- clone: clone$5,
- fromValues: fromValues$5,
- copy: copy$5,
- set: set$5,
- add: add$5,
- subtract: subtract$5,
- multiply: multiply$5,
- divide: divide$1,
- ceil: ceil$1,
- floor: floor$1,
- min: min$1,
- max: max$1,
- round: round$1,
- scale: scale$5,
- scaleAndAdd: scaleAndAdd$1,
- distance: distance$1,
- squaredDistance: squaredDistance$1,
- length: length$1,
- squaredLength: squaredLength$1,
- negate: negate$1,
- inverse: inverse$1,
- normalize: normalize$1,
- dot: dot$1,
- cross: cross$1,
- lerp: lerp$1,
- random: random$1,
- transformMat4: transformMat4$1,
- transformQuat: transformQuat$1,
- zero: zero$1,
- str: str$5,
- exactEquals: exactEquals$5,
- equals: equals$6,
- sub: sub$5,
- mul: mul$5,
- div: div$1,
- dist: dist$1,
- sqrDist: sqrDist$1,
- len: len$1,
- sqrLen: sqrLen$1,
- forEach: forEach$1
- });
- /**
- * Quaternion
- * @module quat
- */
- /**
- * Creates a new identity quat
- *
- * @returns {quat} a new quaternion
- */
- function create$6() {
- var out = new ARRAY_TYPE(4);
- if (ARRAY_TYPE != Float32Array) {
- out[0] = 0;
- out[1] = 0;
- out[2] = 0;
- }
- out[3] = 1;
- return out;
- }
- /**
- * Set a quat to the identity quaternion
- *
- * @param {quat} out the receiving quaternion
- * @returns {quat} out
- */
- function identity$4(out) {
- out[0] = 0;
- out[1] = 0;
- out[2] = 0;
- out[3] = 1;
- return out;
- }
- /**
- * Sets a quat from the given angle and rotation axis,
- * then returns it.
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyVec3} axis the axis around which to rotate
- * @param {Number} rad the angle in radians
- * @returns {quat} out
- **/
- function setAxisAngle(out, axis, rad) {
- rad = rad * 0.5;
- var s = Math.sin(rad);
- out[0] = s * axis[0];
- out[1] = s * axis[1];
- out[2] = s * axis[2];
- out[3] = Math.cos(rad);
- return out;
- }
- /**
- * Gets the rotation axis and angle for a given
- * quaternion. If a quaternion is created with
- * setAxisAngle, this method will return the same
- * values as providied in the original parameter list
- * OR functionally equivalent values.
- * Example: The quaternion formed by axis [0, 0, 1] and
- * angle -90 is the same as the quaternion formed by
- * [0, 0, 1] and 270. This method favors the latter.
- * @param {vec3} out_axis Vector receiving the axis of rotation
- * @param {ReadonlyQuat} q Quaternion to be decomposed
- * @return {Number} Angle, in radians, of the rotation
- */
- function getAxisAngle(out_axis, q) {
- var rad = Math.acos(q[3]) * 2.0;
- var s = Math.sin(rad / 2.0);
- if (s > EPSILON) {
- out_axis[0] = q[0] / s;
- out_axis[1] = q[1] / s;
- out_axis[2] = q[2] / s;
- } else {
- // If s is zero, return any axis (no rotation - axis does not matter)
- out_axis[0] = 1;
- out_axis[1] = 0;
- out_axis[2] = 0;
- }
- return rad;
- }
- /**
- * Gets the angular distance between two unit quaternions
- *
- * @param {ReadonlyQuat} a Origin unit quaternion
- * @param {ReadonlyQuat} b Destination unit quaternion
- * @return {Number} Angle, in radians, between the two quaternions
- */
- function getAngle(a, b) {
- var dotproduct = dot$2(a, b);
- return Math.acos(2 * dotproduct * dotproduct - 1);
- }
- /**
- * Multiplies two quat's
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a the first operand
- * @param {ReadonlyQuat} b the second operand
- * @returns {quat} out
- */
- function multiply$6(out, a, b) {
- var ax = a[0],
- ay = a[1],
- az = a[2],
- aw = a[3];
- var bx = b[0],
- by = b[1],
- bz = b[2],
- bw = b[3];
- out[0] = ax * bw + aw * bx + ay * bz - az * by;
- out[1] = ay * bw + aw * by + az * bx - ax * bz;
- out[2] = az * bw + aw * bz + ax * by - ay * bx;
- out[3] = aw * bw - ax * bx - ay * by - az * bz;
- return out;
- }
- /**
- * Rotates a quaternion by the given angle about the X axis
- *
- * @param {quat} out quat receiving operation result
- * @param {ReadonlyQuat} a quat to rotate
- * @param {number} rad angle (in radians) to rotate
- * @returns {quat} out
- */
- function rotateX$2(out, a, rad) {
- rad *= 0.5;
- var ax = a[0],
- ay = a[1],
- az = a[2],
- aw = a[3];
- var bx = Math.sin(rad),
- bw = Math.cos(rad);
- out[0] = ax * bw + aw * bx;
- out[1] = ay * bw + az * bx;
- out[2] = az * bw - ay * bx;
- out[3] = aw * bw - ax * bx;
- return out;
- }
- /**
- * Rotates a quaternion by the given angle about the Y axis
- *
- * @param {quat} out quat receiving operation result
- * @param {ReadonlyQuat} a quat to rotate
- * @param {number} rad angle (in radians) to rotate
- * @returns {quat} out
- */
- function rotateY$2(out, a, rad) {
- rad *= 0.5;
- var ax = a[0],
- ay = a[1],
- az = a[2],
- aw = a[3];
- var by = Math.sin(rad),
- bw = Math.cos(rad);
- out[0] = ax * bw - az * by;
- out[1] = ay * bw + aw * by;
- out[2] = az * bw + ax * by;
- out[3] = aw * bw - ay * by;
- return out;
- }
- /**
- * Rotates a quaternion by the given angle about the Z axis
- *
- * @param {quat} out quat receiving operation result
- * @param {ReadonlyQuat} a quat to rotate
- * @param {number} rad angle (in radians) to rotate
- * @returns {quat} out
- */
- function rotateZ$2(out, a, rad) {
- rad *= 0.5;
- var ax = a[0],
- ay = a[1],
- az = a[2],
- aw = a[3];
- var bz = Math.sin(rad),
- bw = Math.cos(rad);
- out[0] = ax * bw + ay * bz;
- out[1] = ay * bw - ax * bz;
- out[2] = az * bw + aw * bz;
- out[3] = aw * bw - az * bz;
- return out;
- }
- /**
- * Calculates the W component of a quat from the X, Y, and Z components.
- * Assumes that quaternion is 1 unit in length.
- * Any existing W component will be ignored.
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a quat to calculate W component of
- * @returns {quat} out
- */
- function calculateW(out, a) {
- var x = a[0],
- y = a[1],
- z = a[2];
- out[0] = x;
- out[1] = y;
- out[2] = z;
- out[3] = Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
- return out;
- }
- /**
- * Calculate the exponential of a unit quaternion.
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a quat to calculate the exponential of
- * @returns {quat} out
- */
- function exp(out, a) {
- var x = a[0],
- y = a[1],
- z = a[2],
- w = a[3];
- var r = Math.sqrt(x * x + y * y + z * z);
- var et = Math.exp(w);
- var s = r > 0 ? et * Math.sin(r) / r : 0;
- out[0] = x * s;
- out[1] = y * s;
- out[2] = z * s;
- out[3] = et * Math.cos(r);
- return out;
- }
- /**
- * Calculate the natural logarithm of a unit quaternion.
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a quat to calculate the exponential of
- * @returns {quat} out
- */
- function ln(out, a) {
- var x = a[0],
- y = a[1],
- z = a[2],
- w = a[3];
- var r = Math.sqrt(x * x + y * y + z * z);
- var t = r > 0 ? Math.atan2(r, w) / r : 0;
- out[0] = x * t;
- out[1] = y * t;
- out[2] = z * t;
- out[3] = 0.5 * Math.log(x * x + y * y + z * z + w * w);
- return out;
- }
- /**
- * Calculate the scalar power of a unit quaternion.
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a quat to calculate the exponential of
- * @param {Number} b amount to scale the quaternion by
- * @returns {quat} out
- */
- function pow(out, a, b) {
- ln(out, a);
- scale$6(out, out, b);
- exp(out, out);
- return out;
- }
- /**
- * Performs a spherical linear interpolation between two quat
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a the first operand
- * @param {ReadonlyQuat} b the second operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {quat} out
- */
- function slerp(out, a, b, t) {
- // benchmarks:
- // http://jsperf.com/quaternion-slerp-implementations
- var ax = a[0],
- ay = a[1],
- az = a[2],
- aw = a[3];
- var bx = b[0],
- by = b[1],
- bz = b[2],
- bw = b[3];
- var omega, cosom, sinom, scale0, scale1; // calc cosine
- cosom = ax * bx + ay * by + az * bz + aw * bw; // adjust signs (if necessary)
- if (cosom < 0.0) {
- cosom = -cosom;
- bx = -bx;
- by = -by;
- bz = -bz;
- bw = -bw;
- } // calculate coefficients
- if (1.0 - cosom > EPSILON) {
- // standard case (slerp)
- omega = Math.acos(cosom);
- sinom = Math.sin(omega);
- scale0 = Math.sin((1.0 - t) * omega) / sinom;
- scale1 = Math.sin(t * omega) / sinom;
- } else {
- // "from" and "to" quaternions are very close
- // ... so we can do a linear interpolation
- scale0 = 1.0 - t;
- scale1 = t;
- } // calculate final values
- out[0] = scale0 * ax + scale1 * bx;
- out[1] = scale0 * ay + scale1 * by;
- out[2] = scale0 * az + scale1 * bz;
- out[3] = scale0 * aw + scale1 * bw;
- return out;
- }
- /**
- * Generates a random unit quaternion
- *
- * @param {quat} out the receiving quaternion
- * @returns {quat} out
- */
- function random$2(out) {
- // Implementation of http://planning.cs.uiuc.edu/node198.html
- // TODO: Calling random 3 times is probably not the fastest solution
- var u1 = RANDOM();
- var u2 = RANDOM();
- var u3 = RANDOM();
- var sqrt1MinusU1 = Math.sqrt(1 - u1);
- var sqrtU1 = Math.sqrt(u1);
- out[0] = sqrt1MinusU1 * Math.sin(2.0 * Math.PI * u2);
- out[1] = sqrt1MinusU1 * Math.cos(2.0 * Math.PI * u2);
- out[2] = sqrtU1 * Math.sin(2.0 * Math.PI * u3);
- out[3] = sqrtU1 * Math.cos(2.0 * Math.PI * u3);
- return out;
- }
- /**
- * Calculates the inverse of a quat
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a quat to calculate inverse of
- * @returns {quat} out
- */
- function invert$4(out, a) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3];
- var dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;
- var invDot = dot ? 1.0 / dot : 0; // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0
- out[0] = -a0 * invDot;
- out[1] = -a1 * invDot;
- out[2] = -a2 * invDot;
- out[3] = a3 * invDot;
- return out;
- }
- /**
- * Calculates the conjugate of a quat
- * If the quaternion is normalized, this function is faster than quat.inverse and produces the same result.
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a quat to calculate conjugate of
- * @returns {quat} out
- */
- function conjugate(out, a) {
- out[0] = -a[0];
- out[1] = -a[1];
- out[2] = -a[2];
- out[3] = a[3];
- return out;
- }
- /**
- * Creates a quaternion from the given 3x3 rotation matrix.
- *
- * NOTE: The resultant quaternion is not normalized, so you should be sure
- * to renormalize the quaternion yourself where necessary.
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyMat3} m rotation matrix
- * @returns {quat} out
- * @function
- */
- function fromMat3(out, m) {
- // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
- // article "Quaternion Calculus and Fast Animation".
- var fTrace = m[0] + m[4] + m[8];
- var fRoot;
- if (fTrace > 0.0) {
- // |w| > 1/2, may as well choose w > 1/2
- fRoot = Math.sqrt(fTrace + 1.0); // 2w
- out[3] = 0.5 * fRoot;
- fRoot = 0.5 / fRoot; // 1/(4w)
- out[0] = (m[5] - m[7]) * fRoot;
- out[1] = (m[6] - m[2]) * fRoot;
- out[2] = (m[1] - m[3]) * fRoot;
- } else {
- // |w| <= 1/2
- var i = 0;
- if (m[4] > m[0]) i = 1;
- if (m[8] > m[i * 3 + i]) i = 2;
- var j = (i + 1) % 3;
- var k = (i + 2) % 3;
- fRoot = Math.sqrt(m[i * 3 + i] - m[j * 3 + j] - m[k * 3 + k] + 1.0);
- out[i] = 0.5 * fRoot;
- fRoot = 0.5 / fRoot;
- out[3] = (m[j * 3 + k] - m[k * 3 + j]) * fRoot;
- out[j] = (m[j * 3 + i] + m[i * 3 + j]) * fRoot;
- out[k] = (m[k * 3 + i] + m[i * 3 + k]) * fRoot;
- }
- return out;
- }
- /**
- * Creates a quaternion from the given euler angle x, y, z.
- *
- * @param {quat} out the receiving quaternion
- * @param {x} Angle to rotate around X axis in degrees.
- * @param {y} Angle to rotate around Y axis in degrees.
- * @param {z} Angle to rotate around Z axis in degrees.
- * @returns {quat} out
- * @function
- */
- function fromEuler(out, x, y, z) {
- var halfToRad = 0.5 * Math.PI / 180.0;
- x *= halfToRad;
- y *= halfToRad;
- z *= halfToRad;
- var sx = Math.sin(x);
- var cx = Math.cos(x);
- var sy = Math.sin(y);
- var cy = Math.cos(y);
- var sz = Math.sin(z);
- var cz = Math.cos(z);
- out[0] = sx * cy * cz - cx * sy * sz;
- out[1] = cx * sy * cz + sx * cy * sz;
- out[2] = cx * cy * sz - sx * sy * cz;
- out[3] = cx * cy * cz + sx * sy * sz;
- return out;
- }
- /**
- * Returns a string representation of a quatenion
- *
- * @param {ReadonlyQuat} a vector to represent as a string
- * @returns {String} string representation of the vector
- */
- function str$6(a) {
- return "quat(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ")";
- }
- /**
- * Creates a new quat initialized with values from an existing quaternion
- *
- * @param {ReadonlyQuat} a quaternion to clone
- * @returns {quat} a new quaternion
- * @function
- */
- var clone$6 = clone$5;
- /**
- * Creates a new quat initialized with the given values
- *
- * @param {Number} x X component
- * @param {Number} y Y component
- * @param {Number} z Z component
- * @param {Number} w W component
- * @returns {quat} a new quaternion
- * @function
- */
- var fromValues$6 = fromValues$5;
- /**
- * Copy the values from one quat to another
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a the source quaternion
- * @returns {quat} out
- * @function
- */
- var copy$6 = copy$5;
- /**
- * Set the components of a quat to the given values
- *
- * @param {quat} out the receiving quaternion
- * @param {Number} x X component
- * @param {Number} y Y component
- * @param {Number} z Z component
- * @param {Number} w W component
- * @returns {quat} out
- * @function
- */
- var set$6 = set$5;
- /**
- * Adds two quat's
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a the first operand
- * @param {ReadonlyQuat} b the second operand
- * @returns {quat} out
- * @function
- */
- var add$6 = add$5;
- /**
- * Alias for {@link quat.multiply}
- * @function
- */
- var mul$6 = multiply$6;
- /**
- * Scales a quat by a scalar number
- *
- * @param {quat} out the receiving vector
- * @param {ReadonlyQuat} a the vector to scale
- * @param {Number} b amount to scale the vector by
- * @returns {quat} out
- * @function
- */
- var scale$6 = scale$5;
- /**
- * Calculates the dot product of two quat's
- *
- * @param {ReadonlyQuat} a the first operand
- * @param {ReadonlyQuat} b the second operand
- * @returns {Number} dot product of a and b
- * @function
- */
- var dot$2 = dot$1;
- /**
- * Performs a linear interpolation between two quat's
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a the first operand
- * @param {ReadonlyQuat} b the second operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {quat} out
- * @function
- */
- var lerp$2 = lerp$1;
- /**
- * Calculates the length of a quat
- *
- * @param {ReadonlyQuat} a vector to calculate length of
- * @returns {Number} length of a
- */
- var length$2 = length$1;
- /**
- * Alias for {@link quat.length}
- * @function
- */
- var len$2 = length$2;
- /**
- * Calculates the squared length of a quat
- *
- * @param {ReadonlyQuat} a vector to calculate squared length of
- * @returns {Number} squared length of a
- * @function
- */
- var squaredLength$2 = squaredLength$1;
- /**
- * Alias for {@link quat.squaredLength}
- * @function
- */
- var sqrLen$2 = squaredLength$2;
- /**
- * Normalize a quat
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a quaternion to normalize
- * @returns {quat} out
- * @function
- */
- var normalize$2 = normalize$1;
- /**
- * Returns whether or not the quaternions have exactly the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyQuat} a The first quaternion.
- * @param {ReadonlyQuat} b The second quaternion.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
- */
- var exactEquals$6 = exactEquals$5;
- /**
- * Returns whether or not the quaternions have approximately the same elements in the same position.
- *
- * @param {ReadonlyQuat} a The first vector.
- * @param {ReadonlyQuat} b The second vector.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
- */
- var equals$7 = equals$6;
- /**
- * Sets a quaternion to represent the shortest rotation from one
- * vector to another.
- *
- * Both vectors are assumed to be unit length.
- *
- * @param {quat} out the receiving quaternion.
- * @param {ReadonlyVec3} a the initial vector
- * @param {ReadonlyVec3} b the destination vector
- * @returns {quat} out
- */
- var rotationTo = function () {
- var tmpvec3 = create$4();
- var xUnitVec3 = fromValues$4(1, 0, 0);
- var yUnitVec3 = fromValues$4(0, 1, 0);
- return function (out, a, b) {
- var dot$1 = dot(a, b);
- if (dot$1 < -0.999999) {
- cross(tmpvec3, xUnitVec3, a);
- if (len(tmpvec3) < 0.000001) cross(tmpvec3, yUnitVec3, a);
- normalize(tmpvec3, tmpvec3);
- setAxisAngle(out, tmpvec3, Math.PI);
- return out;
- } else if (dot$1 > 0.999999) {
- out[0] = 0;
- out[1] = 0;
- out[2] = 0;
- out[3] = 1;
- return out;
- } else {
- cross(tmpvec3, a, b);
- out[0] = tmpvec3[0];
- out[1] = tmpvec3[1];
- out[2] = tmpvec3[2];
- out[3] = 1 + dot$1;
- return normalize$2(out, out);
- }
- };
- }();
- /**
- * Performs a spherical linear interpolation with two control points
- *
- * @param {quat} out the receiving quaternion
- * @param {ReadonlyQuat} a the first operand
- * @param {ReadonlyQuat} b the second operand
- * @param {ReadonlyQuat} c the third operand
- * @param {ReadonlyQuat} d the fourth operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {quat} out
- */
- var sqlerp = function () {
- var temp1 = create$6();
- var temp2 = create$6();
- return function (out, a, b, c, d, t) {
- slerp(temp1, a, d, t);
- slerp(temp2, b, c, t);
- slerp(out, temp1, temp2, 2 * t * (1 - t));
- return out;
- };
- }();
- /**
- * Sets the specified quaternion with values corresponding to the given
- * axes. Each axis is a vec3 and is expected to be unit length and
- * perpendicular to all other specified axes.
- *
- * @param {ReadonlyVec3} view the vector representing the viewing direction
- * @param {ReadonlyVec3} right the vector representing the local "right" direction
- * @param {ReadonlyVec3} up the vector representing the local "up" direction
- * @returns {quat} out
- */
- var setAxes = function () {
- var matr = create$2();
- return function (out, view, right, up) {
- matr[0] = right[0];
- matr[3] = right[1];
- matr[6] = right[2];
- matr[1] = up[0];
- matr[4] = up[1];
- matr[7] = up[2];
- matr[2] = -view[0];
- matr[5] = -view[1];
- matr[8] = -view[2];
- return normalize$2(out, fromMat3(out, matr));
- };
- }();
- var quat = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create$6,
- identity: identity$4,
- setAxisAngle: setAxisAngle,
- getAxisAngle: getAxisAngle,
- getAngle: getAngle,
- multiply: multiply$6,
- rotateX: rotateX$2,
- rotateY: rotateY$2,
- rotateZ: rotateZ$2,
- calculateW: calculateW,
- exp: exp,
- ln: ln,
- pow: pow,
- slerp: slerp,
- random: random$2,
- invert: invert$4,
- conjugate: conjugate,
- fromMat3: fromMat3,
- fromEuler: fromEuler,
- str: str$6,
- clone: clone$6,
- fromValues: fromValues$6,
- copy: copy$6,
- set: set$6,
- add: add$6,
- mul: mul$6,
- scale: scale$6,
- dot: dot$2,
- lerp: lerp$2,
- length: length$2,
- len: len$2,
- squaredLength: squaredLength$2,
- sqrLen: sqrLen$2,
- normalize: normalize$2,
- exactEquals: exactEquals$6,
- equals: equals$7,
- rotationTo: rotationTo,
- sqlerp: sqlerp,
- setAxes: setAxes
- });
- /**
- * Dual Quaternion<br>
- * Format: [real, dual]<br>
- * Quaternion format: XYZW<br>
- * Make sure to have normalized dual quaternions, otherwise the functions may not work as intended.<br>
- * @module quat2
- */
- /**
- * Creates a new identity dual quat
- *
- * @returns {quat2} a new dual quaternion [real -> rotation, dual -> translation]
- */
- function create$7() {
- var dq = new ARRAY_TYPE(8);
- if (ARRAY_TYPE != Float32Array) {
- dq[0] = 0;
- dq[1] = 0;
- dq[2] = 0;
- dq[4] = 0;
- dq[5] = 0;
- dq[6] = 0;
- dq[7] = 0;
- }
- dq[3] = 1;
- return dq;
- }
- /**
- * Creates a new quat initialized with values from an existing quaternion
- *
- * @param {ReadonlyQuat2} a dual quaternion to clone
- * @returns {quat2} new dual quaternion
- * @function
- */
- function clone$7(a) {
- var dq = new ARRAY_TYPE(8);
- dq[0] = a[0];
- dq[1] = a[1];
- dq[2] = a[2];
- dq[3] = a[3];
- dq[4] = a[4];
- dq[5] = a[5];
- dq[6] = a[6];
- dq[7] = a[7];
- return dq;
- }
- /**
- * Creates a new dual quat initialized with the given values
- *
- * @param {Number} x1 X component
- * @param {Number} y1 Y component
- * @param {Number} z1 Z component
- * @param {Number} w1 W component
- * @param {Number} x2 X component
- * @param {Number} y2 Y component
- * @param {Number} z2 Z component
- * @param {Number} w2 W component
- * @returns {quat2} new dual quaternion
- * @function
- */
- function fromValues$7(x1, y1, z1, w1, x2, y2, z2, w2) {
- var dq = new ARRAY_TYPE(8);
- dq[0] = x1;
- dq[1] = y1;
- dq[2] = z1;
- dq[3] = w1;
- dq[4] = x2;
- dq[5] = y2;
- dq[6] = z2;
- dq[7] = w2;
- return dq;
- }
- /**
- * Creates a new dual quat from the given values (quat and translation)
- *
- * @param {Number} x1 X component
- * @param {Number} y1 Y component
- * @param {Number} z1 Z component
- * @param {Number} w1 W component
- * @param {Number} x2 X component (translation)
- * @param {Number} y2 Y component (translation)
- * @param {Number} z2 Z component (translation)
- * @returns {quat2} new dual quaternion
- * @function
- */
- function fromRotationTranslationValues(x1, y1, z1, w1, x2, y2, z2) {
- var dq = new ARRAY_TYPE(8);
- dq[0] = x1;
- dq[1] = y1;
- dq[2] = z1;
- dq[3] = w1;
- var ax = x2 * 0.5,
- ay = y2 * 0.5,
- az = z2 * 0.5;
- dq[4] = ax * w1 + ay * z1 - az * y1;
- dq[5] = ay * w1 + az * x1 - ax * z1;
- dq[6] = az * w1 + ax * y1 - ay * x1;
- dq[7] = -ax * x1 - ay * y1 - az * z1;
- return dq;
- }
- /**
- * Creates a dual quat from a quaternion and a translation
- *
- * @param {ReadonlyQuat2} dual quaternion receiving operation result
- * @param {ReadonlyQuat} q a normalized quaternion
- * @param {ReadonlyVec3} t tranlation vector
- * @returns {quat2} dual quaternion receiving operation result
- * @function
- */
- function fromRotationTranslation$1(out, q, t) {
- var ax = t[0] * 0.5,
- ay = t[1] * 0.5,
- az = t[2] * 0.5,
- bx = q[0],
- by = q[1],
- bz = q[2],
- bw = q[3];
- out[0] = bx;
- out[1] = by;
- out[2] = bz;
- out[3] = bw;
- out[4] = ax * bw + ay * bz - az * by;
- out[5] = ay * bw + az * bx - ax * bz;
- out[6] = az * bw + ax * by - ay * bx;
- out[7] = -ax * bx - ay * by - az * bz;
- return out;
- }
- /**
- * Creates a dual quat from a translation
- *
- * @param {ReadonlyQuat2} dual quaternion receiving operation result
- * @param {ReadonlyVec3} t translation vector
- * @returns {quat2} dual quaternion receiving operation result
- * @function
- */
- function fromTranslation$3(out, t) {
- out[0] = 0;
- out[1] = 0;
- out[2] = 0;
- out[3] = 1;
- out[4] = t[0] * 0.5;
- out[5] = t[1] * 0.5;
- out[6] = t[2] * 0.5;
- out[7] = 0;
- return out;
- }
- /**
- * Creates a dual quat from a quaternion
- *
- * @param {ReadonlyQuat2} dual quaternion receiving operation result
- * @param {ReadonlyQuat} q the quaternion
- * @returns {quat2} dual quaternion receiving operation result
- * @function
- */
- function fromRotation$4(out, q) {
- out[0] = q[0];
- out[1] = q[1];
- out[2] = q[2];
- out[3] = q[3];
- out[4] = 0;
- out[5] = 0;
- out[6] = 0;
- out[7] = 0;
- return out;
- }
- /**
- * Creates a new dual quat from a matrix (4x4)
- *
- * @param {quat2} out the dual quaternion
- * @param {ReadonlyMat4} a the matrix
- * @returns {quat2} dual quat receiving operation result
- * @function
- */
- function fromMat4$1(out, a) {
- //TODO Optimize this
- var outer = create$6();
- getRotation(outer, a);
- var t = new ARRAY_TYPE(3);
- getTranslation(t, a);
- fromRotationTranslation$1(out, outer, t);
- return out;
- }
- /**
- * Copy the values from one dual quat to another
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the source dual quaternion
- * @returns {quat2} out
- * @function
- */
- function copy$7(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- out[2] = a[2];
- out[3] = a[3];
- out[4] = a[4];
- out[5] = a[5];
- out[6] = a[6];
- out[7] = a[7];
- return out;
- }
- /**
- * Set a dual quat to the identity dual quaternion
- *
- * @param {quat2} out the receiving quaternion
- * @returns {quat2} out
- */
- function identity$5(out) {
- out[0] = 0;
- out[1] = 0;
- out[2] = 0;
- out[3] = 1;
- out[4] = 0;
- out[5] = 0;
- out[6] = 0;
- out[7] = 0;
- return out;
- }
- /**
- * Set the components of a dual quat to the given values
- *
- * @param {quat2} out the receiving quaternion
- * @param {Number} x1 X component
- * @param {Number} y1 Y component
- * @param {Number} z1 Z component
- * @param {Number} w1 W component
- * @param {Number} x2 X component
- * @param {Number} y2 Y component
- * @param {Number} z2 Z component
- * @param {Number} w2 W component
- * @returns {quat2} out
- * @function
- */
- function set$7(out, x1, y1, z1, w1, x2, y2, z2, w2) {
- out[0] = x1;
- out[1] = y1;
- out[2] = z1;
- out[3] = w1;
- out[4] = x2;
- out[5] = y2;
- out[6] = z2;
- out[7] = w2;
- return out;
- }
- /**
- * Gets the real part of a dual quat
- * @param {quat} out real part
- * @param {ReadonlyQuat2} a Dual Quaternion
- * @return {quat} real part
- */
- var getReal = copy$6;
- /**
- * Gets the dual part of a dual quat
- * @param {quat} out dual part
- * @param {ReadonlyQuat2} a Dual Quaternion
- * @return {quat} dual part
- */
- function getDual(out, a) {
- out[0] = a[4];
- out[1] = a[5];
- out[2] = a[6];
- out[3] = a[7];
- return out;
- }
- /**
- * Set the real component of a dual quat to the given quaternion
- *
- * @param {quat2} out the receiving quaternion
- * @param {ReadonlyQuat} q a quaternion representing the real part
- * @returns {quat2} out
- * @function
- */
- var setReal = copy$6;
- /**
- * Set the dual component of a dual quat to the given quaternion
- *
- * @param {quat2} out the receiving quaternion
- * @param {ReadonlyQuat} q a quaternion representing the dual part
- * @returns {quat2} out
- * @function
- */
- function setDual(out, q) {
- out[4] = q[0];
- out[5] = q[1];
- out[6] = q[2];
- out[7] = q[3];
- return out;
- }
- /**
- * Gets the translation of a normalized dual quat
- * @param {vec3} out translation
- * @param {ReadonlyQuat2} a Dual Quaternion to be decomposed
- * @return {vec3} translation
- */
- function getTranslation$1(out, a) {
- var ax = a[4],
- ay = a[5],
- az = a[6],
- aw = a[7],
- bx = -a[0],
- by = -a[1],
- bz = -a[2],
- bw = a[3];
- out[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2;
- out[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2;
- out[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2;
- return out;
- }
- /**
- * Translates a dual quat by the given vector
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the dual quaternion to translate
- * @param {ReadonlyVec3} v vector to translate by
- * @returns {quat2} out
- */
- function translate$3(out, a, v) {
- var ax1 = a[0],
- ay1 = a[1],
- az1 = a[2],
- aw1 = a[3],
- bx1 = v[0] * 0.5,
- by1 = v[1] * 0.5,
- bz1 = v[2] * 0.5,
- ax2 = a[4],
- ay2 = a[5],
- az2 = a[6],
- aw2 = a[7];
- out[0] = ax1;
- out[1] = ay1;
- out[2] = az1;
- out[3] = aw1;
- out[4] = aw1 * bx1 + ay1 * bz1 - az1 * by1 + ax2;
- out[5] = aw1 * by1 + az1 * bx1 - ax1 * bz1 + ay2;
- out[6] = aw1 * bz1 + ax1 * by1 - ay1 * bx1 + az2;
- out[7] = -ax1 * bx1 - ay1 * by1 - az1 * bz1 + aw2;
- return out;
- }
- /**
- * Rotates a dual quat around the X axis
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the dual quaternion to rotate
- * @param {number} rad how far should the rotation be
- * @returns {quat2} out
- */
- function rotateX$3(out, a, rad) {
- var bx = -a[0],
- by = -a[1],
- bz = -a[2],
- bw = a[3],
- ax = a[4],
- ay = a[5],
- az = a[6],
- aw = a[7],
- ax1 = ax * bw + aw * bx + ay * bz - az * by,
- ay1 = ay * bw + aw * by + az * bx - ax * bz,
- az1 = az * bw + aw * bz + ax * by - ay * bx,
- aw1 = aw * bw - ax * bx - ay * by - az * bz;
- rotateX$2(out, a, rad);
- bx = out[0];
- by = out[1];
- bz = out[2];
- bw = out[3];
- out[4] = ax1 * bw + aw1 * bx + ay1 * bz - az1 * by;
- out[5] = ay1 * bw + aw1 * by + az1 * bx - ax1 * bz;
- out[6] = az1 * bw + aw1 * bz + ax1 * by - ay1 * bx;
- out[7] = aw1 * bw - ax1 * bx - ay1 * by - az1 * bz;
- return out;
- }
- /**
- * Rotates a dual quat around the Y axis
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the dual quaternion to rotate
- * @param {number} rad how far should the rotation be
- * @returns {quat2} out
- */
- function rotateY$3(out, a, rad) {
- var bx = -a[0],
- by = -a[1],
- bz = -a[2],
- bw = a[3],
- ax = a[4],
- ay = a[5],
- az = a[6],
- aw = a[7],
- ax1 = ax * bw + aw * bx + ay * bz - az * by,
- ay1 = ay * bw + aw * by + az * bx - ax * bz,
- az1 = az * bw + aw * bz + ax * by - ay * bx,
- aw1 = aw * bw - ax * bx - ay * by - az * bz;
- rotateY$2(out, a, rad);
- bx = out[0];
- by = out[1];
- bz = out[2];
- bw = out[3];
- out[4] = ax1 * bw + aw1 * bx + ay1 * bz - az1 * by;
- out[5] = ay1 * bw + aw1 * by + az1 * bx - ax1 * bz;
- out[6] = az1 * bw + aw1 * bz + ax1 * by - ay1 * bx;
- out[7] = aw1 * bw - ax1 * bx - ay1 * by - az1 * bz;
- return out;
- }
- /**
- * Rotates a dual quat around the Z axis
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the dual quaternion to rotate
- * @param {number} rad how far should the rotation be
- * @returns {quat2} out
- */
- function rotateZ$3(out, a, rad) {
- var bx = -a[0],
- by = -a[1],
- bz = -a[2],
- bw = a[3],
- ax = a[4],
- ay = a[5],
- az = a[6],
- aw = a[7],
- ax1 = ax * bw + aw * bx + ay * bz - az * by,
- ay1 = ay * bw + aw * by + az * bx - ax * bz,
- az1 = az * bw + aw * bz + ax * by - ay * bx,
- aw1 = aw * bw - ax * bx - ay * by - az * bz;
- rotateZ$2(out, a, rad);
- bx = out[0];
- by = out[1];
- bz = out[2];
- bw = out[3];
- out[4] = ax1 * bw + aw1 * bx + ay1 * bz - az1 * by;
- out[5] = ay1 * bw + aw1 * by + az1 * bx - ax1 * bz;
- out[6] = az1 * bw + aw1 * bz + ax1 * by - ay1 * bx;
- out[7] = aw1 * bw - ax1 * bx - ay1 * by - az1 * bz;
- return out;
- }
- /**
- * Rotates a dual quat by a given quaternion (a * q)
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the dual quaternion to rotate
- * @param {ReadonlyQuat} q quaternion to rotate by
- * @returns {quat2} out
- */
- function rotateByQuatAppend(out, a, q) {
- var qx = q[0],
- qy = q[1],
- qz = q[2],
- qw = q[3],
- ax = a[0],
- ay = a[1],
- az = a[2],
- aw = a[3];
- out[0] = ax * qw + aw * qx + ay * qz - az * qy;
- out[1] = ay * qw + aw * qy + az * qx - ax * qz;
- out[2] = az * qw + aw * qz + ax * qy - ay * qx;
- out[3] = aw * qw - ax * qx - ay * qy - az * qz;
- ax = a[4];
- ay = a[5];
- az = a[6];
- aw = a[7];
- out[4] = ax * qw + aw * qx + ay * qz - az * qy;
- out[5] = ay * qw + aw * qy + az * qx - ax * qz;
- out[6] = az * qw + aw * qz + ax * qy - ay * qx;
- out[7] = aw * qw - ax * qx - ay * qy - az * qz;
- return out;
- }
- /**
- * Rotates a dual quat by a given quaternion (q * a)
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat} q quaternion to rotate by
- * @param {ReadonlyQuat2} a the dual quaternion to rotate
- * @returns {quat2} out
- */
- function rotateByQuatPrepend(out, q, a) {
- var qx = q[0],
- qy = q[1],
- qz = q[2],
- qw = q[3],
- bx = a[0],
- by = a[1],
- bz = a[2],
- bw = a[3];
- out[0] = qx * bw + qw * bx + qy * bz - qz * by;
- out[1] = qy * bw + qw * by + qz * bx - qx * bz;
- out[2] = qz * bw + qw * bz + qx * by - qy * bx;
- out[3] = qw * bw - qx * bx - qy * by - qz * bz;
- bx = a[4];
- by = a[5];
- bz = a[6];
- bw = a[7];
- out[4] = qx * bw + qw * bx + qy * bz - qz * by;
- out[5] = qy * bw + qw * by + qz * bx - qx * bz;
- out[6] = qz * bw + qw * bz + qx * by - qy * bx;
- out[7] = qw * bw - qx * bx - qy * by - qz * bz;
- return out;
- }
- /**
- * Rotates a dual quat around a given axis. Does the normalisation automatically
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the dual quaternion to rotate
- * @param {ReadonlyVec3} axis the axis to rotate around
- * @param {Number} rad how far the rotation should be
- * @returns {quat2} out
- */
- function rotateAroundAxis(out, a, axis, rad) {
- //Special case for rad = 0
- if (Math.abs(rad) < EPSILON) {
- return copy$7(out, a);
- }
- var axisLength = Math.hypot(axis[0], axis[1], axis[2]);
- rad = rad * 0.5;
- var s = Math.sin(rad);
- var bx = s * axis[0] / axisLength;
- var by = s * axis[1] / axisLength;
- var bz = s * axis[2] / axisLength;
- var bw = Math.cos(rad);
- var ax1 = a[0],
- ay1 = a[1],
- az1 = a[2],
- aw1 = a[3];
- out[0] = ax1 * bw + aw1 * bx + ay1 * bz - az1 * by;
- out[1] = ay1 * bw + aw1 * by + az1 * bx - ax1 * bz;
- out[2] = az1 * bw + aw1 * bz + ax1 * by - ay1 * bx;
- out[3] = aw1 * bw - ax1 * bx - ay1 * by - az1 * bz;
- var ax = a[4],
- ay = a[5],
- az = a[6],
- aw = a[7];
- out[4] = ax * bw + aw * bx + ay * bz - az * by;
- out[5] = ay * bw + aw * by + az * bx - ax * bz;
- out[6] = az * bw + aw * bz + ax * by - ay * bx;
- out[7] = aw * bw - ax * bx - ay * by - az * bz;
- return out;
- }
- /**
- * Adds two dual quat's
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the first operand
- * @param {ReadonlyQuat2} b the second operand
- * @returns {quat2} out
- * @function
- */
- function add$7(out, a, b) {
- out[0] = a[0] + b[0];
- out[1] = a[1] + b[1];
- out[2] = a[2] + b[2];
- out[3] = a[3] + b[3];
- out[4] = a[4] + b[4];
- out[5] = a[5] + b[5];
- out[6] = a[6] + b[6];
- out[7] = a[7] + b[7];
- return out;
- }
- /**
- * Multiplies two dual quat's
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a the first operand
- * @param {ReadonlyQuat2} b the second operand
- * @returns {quat2} out
- */
- function multiply$7(out, a, b) {
- var ax0 = a[0],
- ay0 = a[1],
- az0 = a[2],
- aw0 = a[3],
- bx1 = b[4],
- by1 = b[5],
- bz1 = b[6],
- bw1 = b[7],
- ax1 = a[4],
- ay1 = a[5],
- az1 = a[6],
- aw1 = a[7],
- bx0 = b[0],
- by0 = b[1],
- bz0 = b[2],
- bw0 = b[3];
- out[0] = ax0 * bw0 + aw0 * bx0 + ay0 * bz0 - az0 * by0;
- out[1] = ay0 * bw0 + aw0 * by0 + az0 * bx0 - ax0 * bz0;
- out[2] = az0 * bw0 + aw0 * bz0 + ax0 * by0 - ay0 * bx0;
- out[3] = aw0 * bw0 - ax0 * bx0 - ay0 * by0 - az0 * bz0;
- out[4] = ax0 * bw1 + aw0 * bx1 + ay0 * bz1 - az0 * by1 + ax1 * bw0 + aw1 * bx0 + ay1 * bz0 - az1 * by0;
- out[5] = ay0 * bw1 + aw0 * by1 + az0 * bx1 - ax0 * bz1 + ay1 * bw0 + aw1 * by0 + az1 * bx0 - ax1 * bz0;
- out[6] = az0 * bw1 + aw0 * bz1 + ax0 * by1 - ay0 * bx1 + az1 * bw0 + aw1 * bz0 + ax1 * by0 - ay1 * bx0;
- out[7] = aw0 * bw1 - ax0 * bx1 - ay0 * by1 - az0 * bz1 + aw1 * bw0 - ax1 * bx0 - ay1 * by0 - az1 * bz0;
- return out;
- }
- /**
- * Alias for {@link quat2.multiply}
- * @function
- */
- var mul$7 = multiply$7;
- /**
- * Scales a dual quat by a scalar number
- *
- * @param {quat2} out the receiving dual quat
- * @param {ReadonlyQuat2} a the dual quat to scale
- * @param {Number} b amount to scale the dual quat by
- * @returns {quat2} out
- * @function
- */
- function scale$7(out, a, b) {
- out[0] = a[0] * b;
- out[1] = a[1] * b;
- out[2] = a[2] * b;
- out[3] = a[3] * b;
- out[4] = a[4] * b;
- out[5] = a[5] * b;
- out[6] = a[6] * b;
- out[7] = a[7] * b;
- return out;
- }
- /**
- * Calculates the dot product of two dual quat's (The dot product of the real parts)
- *
- * @param {ReadonlyQuat2} a the first operand
- * @param {ReadonlyQuat2} b the second operand
- * @returns {Number} dot product of a and b
- * @function
- */
- var dot$3 = dot$2;
- /**
- * Performs a linear interpolation between two dual quats's
- * NOTE: The resulting dual quaternions won't always be normalized (The error is most noticeable when t = 0.5)
- *
- * @param {quat2} out the receiving dual quat
- * @param {ReadonlyQuat2} a the first operand
- * @param {ReadonlyQuat2} b the second operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {quat2} out
- */
- function lerp$3(out, a, b, t) {
- var mt = 1 - t;
- if (dot$3(a, b) < 0) t = -t;
- out[0] = a[0] * mt + b[0] * t;
- out[1] = a[1] * mt + b[1] * t;
- out[2] = a[2] * mt + b[2] * t;
- out[3] = a[3] * mt + b[3] * t;
- out[4] = a[4] * mt + b[4] * t;
- out[5] = a[5] * mt + b[5] * t;
- out[6] = a[6] * mt + b[6] * t;
- out[7] = a[7] * mt + b[7] * t;
- return out;
- }
- /**
- * Calculates the inverse of a dual quat. If they are normalized, conjugate is cheaper
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a dual quat to calculate inverse of
- * @returns {quat2} out
- */
- function invert$5(out, a) {
- var sqlen = squaredLength$3(a);
- out[0] = -a[0] / sqlen;
- out[1] = -a[1] / sqlen;
- out[2] = -a[2] / sqlen;
- out[3] = a[3] / sqlen;
- out[4] = -a[4] / sqlen;
- out[5] = -a[5] / sqlen;
- out[6] = -a[6] / sqlen;
- out[7] = a[7] / sqlen;
- return out;
- }
- /**
- * Calculates the conjugate of a dual quat
- * If the dual quaternion is normalized, this function is faster than quat2.inverse and produces the same result.
- *
- * @param {quat2} out the receiving quaternion
- * @param {ReadonlyQuat2} a quat to calculate conjugate of
- * @returns {quat2} out
- */
- function conjugate$1(out, a) {
- out[0] = -a[0];
- out[1] = -a[1];
- out[2] = -a[2];
- out[3] = a[3];
- out[4] = -a[4];
- out[5] = -a[5];
- out[6] = -a[6];
- out[7] = a[7];
- return out;
- }
- /**
- * Calculates the length of a dual quat
- *
- * @param {ReadonlyQuat2} a dual quat to calculate length of
- * @returns {Number} length of a
- * @function
- */
- var length$3 = length$2;
- /**
- * Alias for {@link quat2.length}
- * @function
- */
- var len$3 = length$3;
- /**
- * Calculates the squared length of a dual quat
- *
- * @param {ReadonlyQuat2} a dual quat to calculate squared length of
- * @returns {Number} squared length of a
- * @function
- */
- var squaredLength$3 = squaredLength$2;
- /**
- * Alias for {@link quat2.squaredLength}
- * @function
- */
- var sqrLen$3 = squaredLength$3;
- /**
- * Normalize a dual quat
- *
- * @param {quat2} out the receiving dual quaternion
- * @param {ReadonlyQuat2} a dual quaternion to normalize
- * @returns {quat2} out
- * @function
- */
- function normalize$3(out, a) {
- var magnitude = squaredLength$3(a);
- if (magnitude > 0) {
- magnitude = Math.sqrt(magnitude);
- var a0 = a[0] / magnitude;
- var a1 = a[1] / magnitude;
- var a2 = a[2] / magnitude;
- var a3 = a[3] / magnitude;
- var b0 = a[4];
- var b1 = a[5];
- var b2 = a[6];
- var b3 = a[7];
- var a_dot_b = a0 * b0 + a1 * b1 + a2 * b2 + a3 * b3;
- out[0] = a0;
- out[1] = a1;
- out[2] = a2;
- out[3] = a3;
- out[4] = (b0 - a0 * a_dot_b) / magnitude;
- out[5] = (b1 - a1 * a_dot_b) / magnitude;
- out[6] = (b2 - a2 * a_dot_b) / magnitude;
- out[7] = (b3 - a3 * a_dot_b) / magnitude;
- }
- return out;
- }
- /**
- * Returns a string representation of a dual quatenion
- *
- * @param {ReadonlyQuat2} a dual quaternion to represent as a string
- * @returns {String} string representation of the dual quat
- */
- function str$7(a) {
- return "quat2(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ", " + a[4] + ", " + a[5] + ", " + a[6] + ", " + a[7] + ")";
- }
- /**
- * Returns whether or not the dual quaternions have exactly the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyQuat2} a the first dual quaternion.
- * @param {ReadonlyQuat2} b the second dual quaternion.
- * @returns {Boolean} true if the dual quaternions are equal, false otherwise.
- */
- function exactEquals$7(a, b) {
- 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] && a[6] === b[6] && a[7] === b[7];
- }
- /**
- * Returns whether or not the dual quaternions have approximately the same elements in the same position.
- *
- * @param {ReadonlyQuat2} a the first dual quat.
- * @param {ReadonlyQuat2} b the second dual quat.
- * @returns {Boolean} true if the dual quats are equal, false otherwise.
- */
- function equals$8(a, b) {
- var a0 = a[0],
- a1 = a[1],
- a2 = a[2],
- a3 = a[3],
- a4 = a[4],
- a5 = a[5],
- a6 = a[6],
- a7 = a[7];
- var b0 = b[0],
- b1 = b[1],
- b2 = b[2],
- b3 = b[3],
- b4 = b[4],
- b5 = b[5],
- b6 = b[6],
- b7 = b[7];
- return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7));
- }
- var quat2 = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create$7,
- clone: clone$7,
- fromValues: fromValues$7,
- fromRotationTranslationValues: fromRotationTranslationValues,
- fromRotationTranslation: fromRotationTranslation$1,
- fromTranslation: fromTranslation$3,
- fromRotation: fromRotation$4,
- fromMat4: fromMat4$1,
- copy: copy$7,
- identity: identity$5,
- set: set$7,
- getReal: getReal,
- getDual: getDual,
- setReal: setReal,
- setDual: setDual,
- getTranslation: getTranslation$1,
- translate: translate$3,
- rotateX: rotateX$3,
- rotateY: rotateY$3,
- rotateZ: rotateZ$3,
- rotateByQuatAppend: rotateByQuatAppend,
- rotateByQuatPrepend: rotateByQuatPrepend,
- rotateAroundAxis: rotateAroundAxis,
- add: add$7,
- multiply: multiply$7,
- mul: mul$7,
- scale: scale$7,
- dot: dot$3,
- lerp: lerp$3,
- invert: invert$5,
- conjugate: conjugate$1,
- length: length$3,
- len: len$3,
- squaredLength: squaredLength$3,
- sqrLen: sqrLen$3,
- normalize: normalize$3,
- str: str$7,
- exactEquals: exactEquals$7,
- equals: equals$8
- });
- /**
- * 2 Dimensional Vector
- * @module vec2
- */
- /**
- * Creates a new, empty vec2
- *
- * @returns {vec2} a new 2D vector
- */
- function create$8() {
- var out = new ARRAY_TYPE(2);
- if (ARRAY_TYPE != Float32Array) {
- out[0] = 0;
- out[1] = 0;
- }
- return out;
- }
- /**
- * Creates a new vec2 initialized with values from an existing vector
- *
- * @param {ReadonlyVec2} a vector to clone
- * @returns {vec2} a new 2D vector
- */
- function clone$8(a) {
- var out = new ARRAY_TYPE(2);
- out[0] = a[0];
- out[1] = a[1];
- return out;
- }
- /**
- * Creates a new vec2 initialized with the given values
- *
- * @param {Number} x X component
- * @param {Number} y Y component
- * @returns {vec2} a new 2D vector
- */
- function fromValues$8(x, y) {
- var out = new ARRAY_TYPE(2);
- out[0] = x;
- out[1] = y;
- return out;
- }
- /**
- * Copy the values from one vec2 to another
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the source vector
- * @returns {vec2} out
- */
- function copy$8(out, a) {
- out[0] = a[0];
- out[1] = a[1];
- return out;
- }
- /**
- * Set the components of a vec2 to the given values
- *
- * @param {vec2} out the receiving vector
- * @param {Number} x X component
- * @param {Number} y Y component
- * @returns {vec2} out
- */
- function set$8(out, x, y) {
- out[0] = x;
- out[1] = y;
- return out;
- }
- /**
- * Adds two vec2's
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {vec2} out
- */
- function add$8(out, a, b) {
- out[0] = a[0] + b[0];
- out[1] = a[1] + b[1];
- return out;
- }
- /**
- * Subtracts vector b from vector a
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {vec2} out
- */
- function subtract$6(out, a, b) {
- out[0] = a[0] - b[0];
- out[1] = a[1] - b[1];
- return out;
- }
- /**
- * Multiplies two vec2's
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {vec2} out
- */
- function multiply$8(out, a, b) {
- out[0] = a[0] * b[0];
- out[1] = a[1] * b[1];
- return out;
- }
- /**
- * Divides two vec2's
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {vec2} out
- */
- function divide$2(out, a, b) {
- out[0] = a[0] / b[0];
- out[1] = a[1] / b[1];
- return out;
- }
- /**
- * Math.ceil the components of a vec2
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a vector to ceil
- * @returns {vec2} out
- */
- function ceil$2(out, a) {
- out[0] = Math.ceil(a[0]);
- out[1] = Math.ceil(a[1]);
- return out;
- }
- /**
- * Math.floor the components of a vec2
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a vector to floor
- * @returns {vec2} out
- */
- function floor$2(out, a) {
- out[0] = Math.floor(a[0]);
- out[1] = Math.floor(a[1]);
- return out;
- }
- /**
- * Returns the minimum of two vec2's
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {vec2} out
- */
- function min$2(out, a, b) {
- out[0] = Math.min(a[0], b[0]);
- out[1] = Math.min(a[1], b[1]);
- return out;
- }
- /**
- * Returns the maximum of two vec2's
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {vec2} out
- */
- function max$2(out, a, b) {
- out[0] = Math.max(a[0], b[0]);
- out[1] = Math.max(a[1], b[1]);
- return out;
- }
- /**
- * Math.round the components of a vec2
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a vector to round
- * @returns {vec2} out
- */
- function round$2(out, a) {
- out[0] = Math.round(a[0]);
- out[1] = Math.round(a[1]);
- return out;
- }
- /**
- * Scales a vec2 by a scalar number
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the vector to scale
- * @param {Number} b amount to scale the vector by
- * @returns {vec2} out
- */
- function scale$8(out, a, b) {
- out[0] = a[0] * b;
- out[1] = a[1] * b;
- return out;
- }
- /**
- * Adds two vec2's after scaling the second operand by a scalar value
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @param {Number} scale the amount to scale b by before adding
- * @returns {vec2} out
- */
- function scaleAndAdd$2(out, a, b, scale) {
- out[0] = a[0] + b[0] * scale;
- out[1] = a[1] + b[1] * scale;
- return out;
- }
- /**
- * Calculates the euclidian distance between two vec2's
- *
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {Number} distance between a and b
- */
- function distance$2(a, b) {
- var x = b[0] - a[0],
- y = b[1] - a[1];
- return Math.hypot(x, y);
- }
- /**
- * Calculates the squared euclidian distance between two vec2's
- *
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {Number} squared distance between a and b
- */
- function squaredDistance$2(a, b) {
- var x = b[0] - a[0],
- y = b[1] - a[1];
- return x * x + y * y;
- }
- /**
- * Calculates the length of a vec2
- *
- * @param {ReadonlyVec2} a vector to calculate length of
- * @returns {Number} length of a
- */
- function length$4(a) {
- var x = a[0],
- y = a[1];
- return Math.hypot(x, y);
- }
- /**
- * Calculates the squared length of a vec2
- *
- * @param {ReadonlyVec2} a vector to calculate squared length of
- * @returns {Number} squared length of a
- */
- function squaredLength$4(a) {
- var x = a[0],
- y = a[1];
- return x * x + y * y;
- }
- /**
- * Negates the components of a vec2
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a vector to negate
- * @returns {vec2} out
- */
- function negate$2(out, a) {
- out[0] = -a[0];
- out[1] = -a[1];
- return out;
- }
- /**
- * Returns the inverse of the components of a vec2
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a vector to invert
- * @returns {vec2} out
- */
- function inverse$2(out, a) {
- out[0] = 1.0 / a[0];
- out[1] = 1.0 / a[1];
- return out;
- }
- /**
- * Normalize a vec2
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a vector to normalize
- * @returns {vec2} out
- */
- function normalize$4(out, a) {
- var x = a[0],
- y = a[1];
- var len = x * x + y * y;
- if (len > 0) {
- //TODO: evaluate use of glm_invsqrt here?
- len = 1 / Math.sqrt(len);
- }
- out[0] = a[0] * len;
- out[1] = a[1] * len;
- return out;
- }
- /**
- * Calculates the dot product of two vec2's
- *
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {Number} dot product of a and b
- */
- function dot$4(a, b) {
- return a[0] * b[0] + a[1] * b[1];
- }
- /**
- * Computes the cross product of two vec2's
- * Note that the cross product must by definition produce a 3D vector
- *
- * @param {vec3} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @returns {vec3} out
- */
- function cross$2(out, a, b) {
- var z = a[0] * b[1] - a[1] * b[0];
- out[0] = out[1] = 0;
- out[2] = z;
- return out;
- }
- /**
- * Performs a linear interpolation between two vec2's
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the first operand
- * @param {ReadonlyVec2} b the second operand
- * @param {Number} t interpolation amount, in the range [0-1], between the two inputs
- * @returns {vec2} out
- */
- function lerp$4(out, a, b, t) {
- var ax = a[0],
- ay = a[1];
- out[0] = ax + t * (b[0] - ax);
- out[1] = ay + t * (b[1] - ay);
- return out;
- }
- /**
- * Generates a random vector with the given scale
- *
- * @param {vec2} out the receiving vector
- * @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned
- * @returns {vec2} out
- */
- function random$3(out, scale) {
- scale = scale || 1.0;
- var r = RANDOM() * 2.0 * Math.PI;
- out[0] = Math.cos(r) * scale;
- out[1] = Math.sin(r) * scale;
- return out;
- }
- /**
- * Transforms the vec2 with a mat2
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the vector to transform
- * @param {ReadonlyMat2} m matrix to transform with
- * @returns {vec2} out
- */
- function transformMat2(out, a, m) {
- var x = a[0],
- y = a[1];
- out[0] = m[0] * x + m[2] * y;
- out[1] = m[1] * x + m[3] * y;
- return out;
- }
- /**
- * Transforms the vec2 with a mat2d
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the vector to transform
- * @param {ReadonlyMat2d} m matrix to transform with
- * @returns {vec2} out
- */
- function transformMat2d(out, a, m) {
- var x = a[0],
- y = a[1];
- out[0] = m[0] * x + m[2] * y + m[4];
- out[1] = m[1] * x + m[3] * y + m[5];
- return out;
- }
- /**
- * Transforms the vec2 with a mat3
- * 3rd vector component is implicitly '1'
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the vector to transform
- * @param {ReadonlyMat3} m matrix to transform with
- * @returns {vec2} out
- */
- function transformMat3$1(out, a, m) {
- var x = a[0],
- y = a[1];
- out[0] = m[0] * x + m[3] * y + m[6];
- out[1] = m[1] * x + m[4] * y + m[7];
- return out;
- }
- /**
- * Transforms the vec2 with a mat4
- * 3rd vector component is implicitly '0'
- * 4th vector component is implicitly '1'
- *
- * @param {vec2} out the receiving vector
- * @param {ReadonlyVec2} a the vector to transform
- * @param {ReadonlyMat4} m matrix to transform with
- * @returns {vec2} out
- */
- function transformMat4$2(out, a, m) {
- var x = a[0];
- var y = a[1];
- out[0] = m[0] * x + m[4] * y + m[12];
- out[1] = m[1] * x + m[5] * y + m[13];
- return out;
- }
- /**
- * Rotate a 2D vector
- * @param {vec2} out The receiving vec2
- * @param {ReadonlyVec2} a The vec2 point to rotate
- * @param {ReadonlyVec2} b The origin of the rotation
- * @param {Number} rad The angle of rotation in radians
- * @returns {vec2} out
- */
- function rotate$4(out, a, b, rad) {
- //Translate point to the origin
- var p0 = a[0] - b[0],
- p1 = a[1] - b[1],
- sinC = Math.sin(rad),
- cosC = Math.cos(rad); //perform rotation and translate to correct position
- out[0] = p0 * cosC - p1 * sinC + b[0];
- out[1] = p0 * sinC + p1 * cosC + b[1];
- return out;
- }
- /**
- * Get the angle between two 2D vectors
- * @param {ReadonlyVec2} a The first operand
- * @param {ReadonlyVec2} b The second operand
- * @returns {Number} The angle in radians
- */
- function angle$1(a, b) {
- var x1 = a[0],
- y1 = a[1],
- x2 = b[0],
- y2 = b[1],
- // mag is the product of the magnitudes of a and b
- mag = Math.sqrt(x1 * x1 + y1 * y1) * Math.sqrt(x2 * x2 + y2 * y2),
- // mag &&.. short circuits if mag == 0
- cosine = mag && (x1 * x2 + y1 * y2) / mag; // Math.min(Math.max(cosine, -1), 1) clamps the cosine between -1 and 1
- return Math.acos(Math.min(Math.max(cosine, -1), 1));
- }
- /**
- * Set the components of a vec2 to zero
- *
- * @param {vec2} out the receiving vector
- * @returns {vec2} out
- */
- function zero$2(out) {
- out[0] = 0.0;
- out[1] = 0.0;
- return out;
- }
- /**
- * Returns a string representation of a vector
- *
- * @param {ReadonlyVec2} a vector to represent as a string
- * @returns {String} string representation of the vector
- */
- function str$8(a) {
- return "vec2(" + a[0] + ", " + a[1] + ")";
- }
- /**
- * Returns whether or not the vectors exactly have the same elements in the same position (when compared with ===)
- *
- * @param {ReadonlyVec2} a The first vector.
- * @param {ReadonlyVec2} b The second vector.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
- */
- function exactEquals$8(a, b) {
- return a[0] === b[0] && a[1] === b[1];
- }
- /**
- * Returns whether or not the vectors have approximately the same elements in the same position.
- *
- * @param {ReadonlyVec2} a The first vector.
- * @param {ReadonlyVec2} b The second vector.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
- */
- function equals$9(a, b) {
- var a0 = a[0],
- a1 = a[1];
- var b0 = b[0],
- b1 = b[1];
- return Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1));
- }
- /**
- * Alias for {@link vec2.length}
- * @function
- */
- var len$4 = length$4;
- /**
- * Alias for {@link vec2.subtract}
- * @function
- */
- var sub$6 = subtract$6;
- /**
- * Alias for {@link vec2.multiply}
- * @function
- */
- var mul$8 = multiply$8;
- /**
- * Alias for {@link vec2.divide}
- * @function
- */
- var div$2 = divide$2;
- /**
- * Alias for {@link vec2.distance}
- * @function
- */
- var dist$2 = distance$2;
- /**
- * Alias for {@link vec2.squaredDistance}
- * @function
- */
- var sqrDist$2 = squaredDistance$2;
- /**
- * Alias for {@link vec2.squaredLength}
- * @function
- */
- var sqrLen$4 = squaredLength$4;
- /**
- * Perform some operation over an array of vec2s.
- *
- * @param {Array} a the array of vectors to iterate over
- * @param {Number} stride Number of elements between the start of each vec2. If 0 assumes tightly packed
- * @param {Number} offset Number of elements to skip at the beginning of the array
- * @param {Number} count Number of vec2s to iterate over. If 0 iterates over entire array
- * @param {Function} fn Function to call for each vector in the array
- * @param {Object} [arg] additional argument to pass to fn
- * @returns {Array} a
- * @function
- */
- var forEach$2 = function () {
- var vec = create$8();
- return function (a, stride, offset, count, fn, arg) {
- var i, l;
- if (!stride) {
- stride = 2;
- }
- if (!offset) {
- offset = 0;
- }
- if (count) {
- l = Math.min(count * stride + offset, a.length);
- } else {
- l = a.length;
- }
- for (i = offset; i < l; i += stride) {
- vec[0] = a[i];
- vec[1] = a[i + 1];
- fn(vec, vec, arg);
- a[i] = vec[0];
- a[i + 1] = vec[1];
- }
- return a;
- };
- }();
- var vec2 = /*#__PURE__*/Object.freeze({
- __proto__: null,
- create: create$8,
- clone: clone$8,
- fromValues: fromValues$8,
- copy: copy$8,
- set: set$8,
- add: add$8,
- subtract: subtract$6,
- multiply: multiply$8,
- divide: divide$2,
- ceil: ceil$2,
- floor: floor$2,
- min: min$2,
- max: max$2,
- round: round$2,
- scale: scale$8,
- scaleAndAdd: scaleAndAdd$2,
- distance: distance$2,
- squaredDistance: squaredDistance$2,
- length: length$4,
- squaredLength: squaredLength$4,
- negate: negate$2,
- inverse: inverse$2,
- normalize: normalize$4,
- dot: dot$4,
- cross: cross$2,
- lerp: lerp$4,
- random: random$3,
- transformMat2: transformMat2,
- transformMat2d: transformMat2d,
- transformMat3: transformMat3$1,
- transformMat4: transformMat4$2,
- rotate: rotate$4,
- angle: angle$1,
- zero: zero$2,
- str: str$8,
- exactEquals: exactEquals$8,
- equals: equals$9,
- len: len$4,
- sub: sub$6,
- mul: mul$8,
- div: div$2,
- dist: dist$2,
- sqrDist: sqrDist$2,
- sqrLen: sqrLen$4,
- forEach: forEach$2
- });
- exports.glMatrix = common;
- exports.mat2 = mat2;
- exports.mat2d = mat2d;
- exports.mat3 = mat3;
- exports.mat4 = mat4;
- exports.quat = quat;
- exports.quat2 = quat2;
- exports.vec2 = vec2;
- exports.vec3 = vec3;
- exports.vec4 = vec4;
- Object.defineProperty(exports, '__esModule', { value: true });
- })));
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