diff --git a/index.html b/index.html index 3064545..5ead984 100644 --- a/index.html +++ b/index.html @@ -36,6 +36,7 @@ --> + diff --git a/lib/gl-matrix.js b/lib/gl-matrix.js new file mode 100644 index 0000000..932bed2 --- /dev/null +++ b/lib/gl-matrix.js @@ -0,0 +1,7620 @@ + +/*! +@fileoverview gl-matrix - High performance matrix and vector operations +@author Brandon Jones +@author Colin MacKenzie IV +@version 3.1.0 + +Copyright (c) 2015-2019, 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 {Type} 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({ + 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 {mat2} 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 {mat2} 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 {mat2} 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 {mat2} 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 {mat2} 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 {mat2} 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 {mat2} a the first operand + * @param {mat2} 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 {mat2} 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 {mat2} a the matrix to rotate + * @param {vec2} 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 {vec2} 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 {mat2} 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 {mat2} 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 {mat2} L the lower triangular matrix + * @param {mat2} D the diagonal matrix + * @param {mat2} U the upper triangular matrix + * @param {mat2} 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 {mat2} a the first operand + * @param {mat2} 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 {mat2} a the first operand + * @param {mat2} 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 {mat2} a The first matrix. + * @param {mat2} 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 {mat2} a The first matrix. + * @param {mat2} 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 {mat2} 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 {mat2} a the first operand + * @param {mat2} 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({ + 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: + * 
+   * [a, b, c,
+   *  d, tx, ty]
+   *
+ * This is a short form for the 3x3 matrix: + * 
+   * [a, b, 0,
+   *  c, d, 0,
+   *  tx, ty, 1]
+   *
+ * 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 {mat2d} 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 {mat2d} 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 {mat2d} 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 {mat2d} 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 {mat2d} a the first operand + * @param {mat2d} 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 {mat2d} 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 {mat2d} a the matrix to translate + * @param {vec2} 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 {mat2d} a the matrix to translate + * @param {vec2} 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 {vec2} 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 {vec2} 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 {mat2d} 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 {mat2d} 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 {mat2d} a the first operand + * @param {mat2d} 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 {mat2d} a the first operand + * @param {mat2d} 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 {mat2d} 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 {mat2d} a the first operand + * @param {mat2d} 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 {mat2d} a The first matrix. + * @param {mat2d} 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 {mat2d} a The first matrix. + * @param {mat2d} 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({ + 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 {mat4} 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 {mat3} 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 {mat3} 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 {mat3} 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 {mat3} 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 {mat3} 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 {mat3} 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 {mat3} a the first operand + * @param {mat3} 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 {mat3} a the matrix to translate + * @param {vec2} 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 {mat3} 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 {mat3} a the matrix to rotate + * @param {vec2} 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 {vec2} 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 {vec2} 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 {mat2d} 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 {quat} 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 {mat4} 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 {mat3} 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 {mat3} 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 {mat3} a the first operand + * @param {mat3} 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 {mat3} a the first operand + * @param {mat3} 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 {mat3} 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 {mat3} a the first operand + * @param {mat3} 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 {mat3} a The first matrix. + * @param {mat3} 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 {mat3} a The first matrix. + * @param {mat3} 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({ + 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
Format: column-major, when typed out it looks like row-major
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 {mat4} 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 {mat4} 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 {mat4} 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 {mat4} 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 {mat4} 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 {mat4} 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 {mat4} a the first operand + * @param {mat4} 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 {mat4} a the matrix to translate + * @param {vec3} 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 {mat4} a the matrix to scale + * @param {vec3} 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 {mat4} a the matrix to rotate + * @param {Number} rad the angle to rotate the matrix by + * @param {vec3} 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 {mat4} 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 {mat4} 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 {mat4} 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 {vec3} 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 {vec3} 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 {vec3} 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 {vec3} 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 {quat2} 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 {mat4} 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 {mat4} 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 {mat4} 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 {vec3} v Translation vector + * @param {vec3} 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 {vec3} v Translation vector + * @param {vec3} s Scaling vector + * @param {vec3} 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 {quat} 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. + * 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 perspective(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; + } + /** + * 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 + * + * @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 ortho(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; + } + /** + * 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 {vec3} eye Position of the viewer + * @param {vec3} center Point the viewer is looking at + * @param {vec3} 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 {vec3} eye Position of the viewer + * @param {vec3} center Point the viewer is looking at + * @param {vec3} 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 {mat4} 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 {mat4} a the matrix to calculate Frobenius norm of + * @returns {Number} Frobenius norm + */ + + function frob$3(a) { + return Math.hypot(a[0], a[1], 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 {mat4} a the first operand + * @param {mat4} 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 {mat4} a the first operand + * @param {mat4} 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 {mat4} 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 {mat4} a the first operand + * @param {mat4} 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 {mat4} a The first matrix. + * @param {mat4} 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 {mat4} a The first matrix. + * @param {mat4} 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({ + 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, + perspective: perspective, + perspectiveFromFieldOfView: perspectiveFromFieldOfView, + ortho: ortho, + 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 {vec3} 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 {vec3} 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 {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} 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 {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} 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 {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} 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 {vec3} 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 {vec3} 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 {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} b the second operand + * @param {vec3} c the third operand + * @param {vec3} 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 {vec3} a the first operand + * @param {vec3} b the second operand + * @param {vec3} c the third operand + * @param {vec3} 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 {vec3} a the vector to transform + * @param {mat4} 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 {vec3} a the vector to transform + * @param {mat3} 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 {vec3} a the vector to transform + * @param {quat} 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 {vec3} a The vec3 point to rotate + * @param {vec3} b The origin of the rotation + * @param {Number} c The angle of rotation + * @returns {vec3} out + */ + + function rotateX$1(out, a, b, c) { + 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(c) - p[2] * Math.sin(c); + r[2] = p[1] * Math.sin(c) + p[2] * Math.cos(c); //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 {vec3} a The vec3 point to rotate + * @param {vec3} b The origin of the rotation + * @param {Number} c The angle of rotation + * @returns {vec3} out + */ + + function rotateY$1(out, a, b, c) { + 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(c) + p[0] * Math.cos(c); + r[1] = p[1]; + r[2] = p[2] * Math.cos(c) - p[0] * Math.sin(c); //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 {vec3} a The vec3 point to rotate + * @param {vec3} b The origin of the rotation + * @param {Number} c The angle of rotation + * @returns {vec3} out + */ + + function rotateZ$1(out, a, b, c) { + 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(c) - p[1] * Math.sin(c); + r[1] = p[0] * Math.sin(c) + p[1] * Math.cos(c); + 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 {vec3} a The first operand + * @param {vec3} b The second operand + * @returns {Number} The angle in radians + */ + + function angle(a, b) { + var tempA = fromValues$4(a[0], a[1], a[2]); + var tempB = fromValues$4(b[0], b[1], b[2]); + normalize(tempA, tempA); + normalize(tempB, tempB); + var cosine = dot(tempA, tempB); + + if (cosine > 1.0) { + return 0; + } else if (cosine < -1.0) { + return Math.PI; + } else { + return Math.acos(cosine); + } + } + /** + * 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 {vec3} 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 {vec3} a The first vector. + * @param {vec3} 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 {vec3} a The first vector. + * @param {vec3} 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({ + 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 {vec4} 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 {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} 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 {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} 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 {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} 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 {vec4} 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 {vec4} 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 {vec4} 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 {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} result the receiving vector + * @param {vec4} U the first vector + * @param {vec4} V the second vector + * @param {vec4} 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 {vec4} a the first operand + * @param {vec4} 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 {vec4} a the vector to transform + * @param {mat4} 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 {vec4} a the vector to transform + * @param {quat} 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 {vec4} 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 {vec4} a The first vector. + * @param {vec4} 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 {vec4} a The first vector. + * @param {vec4} 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({ + 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 {vec3} 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 {quat} 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 {quat} a Origin unit quaternion + * @param {quat} 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 {quat} a the first operand + * @param {quat} 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 {quat} 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 {quat} 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 {quat} 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 {quat} 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 {quat} 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 {quat} 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 {quat} 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 {quat} a the first operand + * @param {quat} 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 {quat} 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 {quat} 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 {mat3} 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 {quat} 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 {quat} 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 {quat} 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 {quat} a the first operand + * @param {quat} 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 {quat} 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 {quat} a the first operand + * @param {quat} 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 {quat} a the first operand + * @param {quat} 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 {quat} 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 {quat} 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 {quat} 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 {quat} a The first quaternion. + * @param {quat} 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 {quat} a The first vector. + * @param {quat} 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 {vec3} a the initial vector + * @param {vec3} 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 {quat} a the first operand + * @param {quat} b the second operand + * @param {quat} c the third operand + * @param {quat} 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 {vec3} view the vector representing the viewing direction + * @param {vec3} right the vector representing the local "right" direction + * @param {vec3} 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({ + 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
+ * Format: [real, dual]
+ * Quaternion format: XYZW
+ * Make sure to have normalized dual quaternions, otherwise the functions may not work as intended.
+ * @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 {quat2} 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 {quat2} dual quaternion receiving operation result + * @param {quat} q a normalized quaternion + * @param {vec3} 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 {quat2} dual quaternion receiving operation result + * @param {vec3} 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 {quat2} dual quaternion receiving operation result + * @param {quat} 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 {mat4} 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 {quat2} 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 {quat2} 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 {quat2} 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 {quat} 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 {quat} 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 {quat2} 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 {quat2} a the dual quaternion to translate + * @param {vec3} 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 {quat2} 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 {quat2} 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 {quat2} 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 {quat2} a the dual quaternion to rotate + * @param {quat} 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 {quat} q quaternion to rotate by + * @param {quat2} 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 {quat2} a the dual quaternion to rotate + * @param {vec3} 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 {quat2} a the first operand + * @param {quat2} 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 {quat2} a the first operand + * @param {quat2} 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 {quat2} 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 {quat2} a the first operand + * @param {quat2} 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 {quat2} a the first operand + * @param {quat2} 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 {quat2} 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 {quat2} 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 {quat2} 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 {quat2} 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 {quat2} 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 {quat2} 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 {quat2} a the first dual quaternion. + * @param {quat2} 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 {quat2} a the first dual quat. + * @param {quat2} 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({ + 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 {vec2} 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 {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} 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 {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} 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 {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} 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 {vec2} 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 {vec2} 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 {vec2} 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 {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the first operand + * @param {vec2} 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 {vec2} a the vector to transform + * @param {mat2} 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 {vec2} a the vector to transform + * @param {mat2d} 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 {vec2} a the vector to transform + * @param {mat3} 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 {vec2} a the vector to transform + * @param {mat4} 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 {vec2} a The vec2 point to rotate + * @param {vec2} b The origin of the rotation + * @param {Number} c The angle of rotation + * @returns {vec2} out + */ + + function rotate$4(out, a, b, c) { + //Translate point to the origin + var p0 = a[0] - b[0], + p1 = a[1] - b[1], + sinC = Math.sin(c), + cosC = Math.cos(c); //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 {vec2} a The first operand + * @param {vec2} 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]; + var len1 = x1 * x1 + y1 * y1; + + if (len1 > 0) { + //TODO: evaluate use of glm_invsqrt here? + len1 = 1 / Math.sqrt(len1); + } + + var len2 = x2 * x2 + y2 * y2; + + if (len2 > 0) { + //TODO: evaluate use of glm_invsqrt here? + len2 = 1 / Math.sqrt(len2); + } + + var cosine = (x1 * x2 + y1 * y2) * len1 * len2; + + if (cosine > 1.0) { + return 0; + } else if (cosine < -1.0) { + return Math.PI; + } else { + return Math.acos(cosine); + } + } + /** + * 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 {vec2} 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 {vec2} a The first vector. + * @param {vec2} 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 {vec2} a The first vector. + * @param {vec2} 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({ + 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 }); + +}));