/* -*- Mode: javascript; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- */ /* vim: set ts=2 et sw=2 tw=80: */ /***** BEGIN LICENSE BLOCK ***** * Version: MPL 1.1/GPL 2.0/LGPL 2.1 * * The contents of this file are subject to the Mozilla Public License Version * 1.1 (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * http://www.mozilla.org/MPL/ * * Software distributed under the License is distributed on an "AS IS" basis, * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License * for the specific language governing rights and limitations under the * License. * * The Original Code is Tilt: A WebGL-based 3D visualization of a webpage. * * The Initial Developer of the Original Code is * Mozilla Foundation. * Portions created by the Initial Developer are Copyright (C) 2011 * the Initial Developer. All Rights Reserved. * * Contributor(s): * Victor Porof (original author) * * Alternatively, the contents of this file may be used under the terms of * either the GNU General Public License Version 2 or later (the "GPL"), or * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), * in which case the provisions of the GPL or the LGPL are applicable instead * of those above. If you wish to allow use of your version of this file only * under the terms of either the GPL or the LGPL, and not to allow others to * use your version of this file under the terms of the MPL, indicate your * decision by deleting the provisions above and replace them with the notice * and other provisions required by the LGPL or the GPL. If you do not delete * the provisions above, a recipient may use your version of this file under * the terms of any one of the MPL, the GPL or the LGPL. * ***** END LICENSE BLOCK *****/ /*global Components, TiltUtils */ "use strict"; const Cu = Components.utils; Cu.import("resource:///modules/devtools/TiltUtils.jsm"); let EXPORTED_SYMBOLS = ["EPSILON", "TiltMath", "vec3", "mat3", "mat4", "quat4"]; /** * Module containing high performance matrix and vector operations for WebGL. * Inspired by glMatrix, version 0.9.6, (c) 2011 Brandon Jones. */ const EPSILON = 0.01; const PI_OVER_180 = Math.PI / 180; const INV_PI_OVER_180 = 180 / Math.PI; const FIFTEEN_OVER_225 = 15 / 225; const ONE_OVER_255 = 1 / 255; /** * vec3 - 3 Dimensional Vector. */ let vec3 = { /** * Creates a new instance of a vec3 using the Float32Array type. * Any array containing at least 3 numeric elements can serve as a vec3. * * @param {Array} aVec * optional, vec3 containing values to initialize with * * @return {Array} a new instance of a vec3 */ create: function V3_create(aVec) { let dest = new Float32Array(3); if (aVec) { vec3.set(aVec, dest); } else { vec3.zero(dest); } return dest; }, /** * Copies the values of one vec3 to another. * * @param {Array} aVec * vec3 containing values to copy * @param {Array} aDest * vec3 receiving copied values * * @return {Array} the destination vec3 receiving copied values */ set: function V3_set(aVec, aDest) { aDest[0] = aVec[0]; aDest[1] = aVec[1]; aDest[2] = aVec[2] || 0; return aDest; }, /** * Sets a vec3 to an zero vector. * * @param {Array} aDest * vec3 to set * * @return {Array} the same vector */ zero: function V3_zero(aDest) { aDest[0] = 0; aDest[1] = 0; aDest[2] = 0; return aDest; }, /** * Performs a vector addition. * * @param {Array} aVec * vec3, first operand * @param {Array} aVec2 * vec3, second operand * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, first operand otherwise */ add: function V3_add(aVec, aVec2, aDest) { if (!aDest) { aDest = aVec; } aDest[0] = aVec[0] + aVec2[0]; aDest[1] = aVec[1] + aVec2[1]; aDest[2] = aVec[2] + aVec2[2]; return aDest; }, /** * Performs a vector subtraction. * * @param {Array} aVec * vec3, first operand * @param {Array} aVec2 * vec3, second operand * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, first operand otherwise */ subtract: function V3_subtract(aVec, aVec2, aDest) { if (!aDest) { aDest = aVec; } aDest[0] = aVec[0] - aVec2[0]; aDest[1] = aVec[1] - aVec2[1]; aDest[2] = aVec[2] - aVec2[2]; return aDest; }, /** * Negates the components of a vec3. * * @param {Array} aVec * vec3 to negate * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, first operand otherwise */ negate: function V3_negate(aVec, aDest) { if (!aDest) { aDest = aVec; } aDest[0] = -aVec[0]; aDest[1] = -aVec[1]; aDest[2] = -aVec[2]; return aDest; }, /** * Multiplies the components of a vec3 by a scalar value. * * @param {Array} aVec * vec3 to scale * @param {Number} aVal * numeric value to scale by * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, first operand otherwise */ scale: function V3_scale(aVec, aVal, aDest) { if (!aDest) { aDest = aVec; } aDest[0] = aVec[0] * aVal; aDest[1] = aVec[1] * aVal; aDest[2] = aVec[2] * aVal; return aDest; }, /** * Generates a unit vector of the same direction as the provided vec3. * If vector length is 0, returns [0, 0, 0]. * * @param {Array} aVec * vec3 to normalize * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, first operand otherwise */ normalize: function V3_normalize(aVec, aDest) { if (!aDest) { aDest = aVec; } let x = aVec[0]; let y = aVec[1]; let z = aVec[2]; let len = Math.sqrt(x * x + y * y + z * z); if (Math.abs(len) < EPSILON) { aDest[0] = 0; aDest[1] = 0; aDest[2] = 0; return aDest; } len = 1 / len; aDest[0] = x * len; aDest[1] = y * len; aDest[2] = z * len; return aDest; }, /** * Generates the cross product of two vectors. * * @param {Array} aVec * vec3, first operand * @param {Array} aVec2 * vec3, second operand * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, first operand otherwise */ cross: function V3_cross(aVec, aVec2, aDest) { if (!aDest) { aDest = aVec; } let x = aVec[0]; let y = aVec[1]; let z = aVec[2]; let x2 = aVec2[0]; let y2 = aVec2[1]; let z2 = aVec2[2]; aDest[0] = y * z2 - z * y2; aDest[1] = z * x2 - x * z2; aDest[2] = x * y2 - y * x2; return aDest; }, /** * Caclulate the dot product of two vectors. * * @param {Array} aVec * vec3, first operand * @param {Array} aVec2 * vec3, second operand * * @return {Array} dot product of the first and second operand */ dot: function V3_dot(aVec, aVec2) { return aVec[0] * aVec2[0] + aVec[1] * aVec2[1] + aVec[2] * aVec2[2]; }, /** * Caclulate the length of a vec3. * * @param {Array} aVec * vec3 to calculate length of * * @return {Array} length of the vec3 */ length: function V3_length(aVec) { let x = aVec[0]; let y = aVec[1]; let z = aVec[2]; return Math.sqrt(x * x + y * y + z * z); }, /** * Generates a unit vector pointing from one vector to another. * * @param {Array} aVec * origin vec3 * @param {Array} aVec2 * vec3 to point to * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, first operand otherwise */ direction: function V3_direction(aVec, aVec2, aDest) { if (!aDest) { aDest = aVec; } let x = aVec[0] - aVec2[0]; let y = aVec[1] - aVec2[1]; let z = aVec[2] - aVec2[2]; let len = Math.sqrt(x * x + y * y + z * z); if (Math.abs(len) < EPSILON) { aDest[0] = 0; aDest[1] = 0; aDest[2] = 0; return aDest; } len = 1 / len; aDest[0] = x * len; aDest[1] = y * len; aDest[2] = z * len; return aDest; }, /** * Performs a linear interpolation between two vec3. * * @param {Array} aVec * first vector * @param {Array} aVec2 * second vector * @param {Number} aLerp * interpolation amount between the two inputs * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, first operand otherwise */ lerp: function V3_lerp(aVec, aVec2, aLerp, aDest) { if (!aDest) { aDest = aVec; } aDest[0] = aVec[0] + aLerp * (aVec2[0] - aVec[0]); aDest[1] = aVec[1] + aLerp * (aVec2[1] - aVec[1]); aDest[2] = aVec[2] + aLerp * (aVec2[2] - aVec[2]); return aDest; }, /** * Projects a 3D point on a 2D screen plane. * * @param {Array} aP * the [x, y, z] coordinates of the point to project * @param {Array} aViewport * the viewport [x, y, width, height] coordinates * @param {Array} aMvMatrix * the model view matrix * @param {Array} aProjMatrix * the projection matrix * @param {Array} aDest * optional parameter, the array to write the values to * * @return {Array} the projected coordinates */ project: function V3_project(aP, aViewport, aMvMatrix, aProjMatrix, aDest) { /*jshint undef: false */ let mvpMatrix = new Float32Array(16); let coordinates = new Float32Array(4); // compute the perspective * model view matrix mat4.multiply(aProjMatrix, aMvMatrix, mvpMatrix); // now transform that vector into homogenous coordinates coordinates[0] = aP[0]; coordinates[1] = aP[1]; coordinates[2] = aP[2]; coordinates[3] = 1; mat4.multiplyVec4(mvpMatrix, coordinates); // transform the homogenous coordinates into screen space coordinates[0] /= coordinates[3]; coordinates[0] *= aViewport[2] * 0.5; coordinates[0] += aViewport[2] * 0.5; coordinates[1] /= coordinates[3]; coordinates[1] *= -aViewport[3] * 0.5; coordinates[1] += aViewport[3] * 0.5; coordinates[2] = 0; if (!aDest) { vec3.set(coordinates, aP); } else { vec3.set(coordinates, aDest); } return coordinates; }, /** * Unprojects a 2D point to 3D space. * * @param {Array} aP * the [x, y, z] coordinates of the point to unproject; * the z value should range between 0 and 1, as clipping plane * @param {Array} aViewport * the viewport [x, y, width, height] coordinates * @param {Array} aMvMatrix * the model view matrix * @param {Array} aProjMatrix * the projection matrix * @param {Array} aDest * optional parameter, the array to write the values to * * @return {Array} the unprojected coordinates */ unproject: function V3_unproject( aP, aViewport, aMvMatrix, aProjMatrix, aDest) { /*jshint undef: false */ let mvpMatrix = new Float32Array(16); let coordinates = new Float32Array(4); // compute the inverse of the perspective * model view matrix mat4.multiply(aProjMatrix, aMvMatrix, mvpMatrix); mat4.inverse(mvpMatrix); // transformation of normalized coordinates (-1 to 1) coordinates[0] = +((aP[0] - aViewport[0]) / aViewport[2] * 2 - 1); coordinates[1] = -((aP[1] - aViewport[1]) / aViewport[3] * 2 - 1); coordinates[2] = 2 * aP[2] - 1; coordinates[3] = 1; // now transform that vector into space coordinates mat4.multiplyVec4(mvpMatrix, coordinates); // invert to normalize x, y, and z values coordinates[3] = 1 / coordinates[3]; coordinates[0] *= coordinates[3]; coordinates[1] *= coordinates[3]; coordinates[2] *= coordinates[3]; if (!aDest) { vec3.set(coordinates, aP); } else { vec3.set(coordinates, aDest); } return coordinates; }, /** * Create a ray between two points using the current model view & projection * matrices. This is useful when creating a ray destined for 3D picking. * * @param {Array} aP0 * the [x, y, z] coordinates of the first point * @param {Array} aP1 * the [x, y, z] coordinates of the second point * @param {Array} aViewport * the viewport [x, y, width, height] coordinates * @param {Array} aMvMatrix * the model view matrix * @param {Array} aProjMatrix * the projection matrix * * @return {Object} a ray object containing the direction vector between * the two unprojected points, the position and the lookAt */ createRay: function V3_createRay(aP0, aP1, aViewport, aMvMatrix, aProjMatrix) { // unproject the two points vec3.unproject(aP0, aViewport, aMvMatrix, aProjMatrix, aP0); vec3.unproject(aP1, aViewport, aMvMatrix, aProjMatrix, aP1); return { origin: aP0, direction: vec3.normalize(vec3.subtract(aP1, aP0)) }; }, /** * Returns a string representation of a vector. * * @param {Array} aVec * vec3 to represent as a string * * @return {String} representation of the vector */ str: function V3_str(aVec) { return '[' + aVec[0] + ", " + aVec[1] + ", " + aVec[2] + ']'; } }; /** * mat3 - 3x3 Matrix. */ let mat3 = { /** * Creates a new instance of a mat3 using the Float32Array array type. * Any array containing at least 9 numeric elements can serve as a mat3. * * @param {Array} aMat * optional, mat3 containing values to initialize with * * @return {Array} a new instance of a mat3 */ create: function M3_create(aMat) { let dest = new Float32Array(9); if (aMat) { mat3.set(aMat, dest); } else { mat3.identity(dest); } return dest; }, /** * Copies the values of one mat3 to another. * * @param {Array} aMat * mat3 containing values to copy * @param {Array} aDest * mat3 receiving copied values * * @return {Array} the destination mat3 receiving copied values */ set: function M3_set(aMat, aDest) { aDest[0] = aMat[0]; aDest[1] = aMat[1]; aDest[2] = aMat[2]; aDest[3] = aMat[3]; aDest[4] = aMat[4]; aDest[5] = aMat[5]; aDest[6] = aMat[6]; aDest[7] = aMat[7]; aDest[8] = aMat[8]; return aDest; }, /** * Sets a mat3 to an identity matrix. * * @param {Array} aDest * mat3 to set * * @return {Array} the same matrix */ identity: function M3_identity(aDest) { aDest[0] = 1; aDest[1] = 0; aDest[2] = 0; aDest[3] = 0; aDest[4] = 1; aDest[5] = 0; aDest[6] = 0; aDest[7] = 0; aDest[8] = 1; return aDest; }, /** * Transposes a mat3 (flips the values over the diagonal). * * @param {Array} aMat * mat3 to transpose * @param {Array} aDest * optional, mat3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat3 if specified, first operand otherwise */ transpose: function M3_transpose(aMat, aDest) { if (!aDest || aMat === aDest) { let a01 = aMat[1]; let a02 = aMat[2]; let a12 = aMat[5]; aMat[1] = aMat[3]; aMat[2] = aMat[6]; aMat[3] = a01; aMat[5] = aMat[7]; aMat[6] = a02; aMat[7] = a12; return aMat; } aDest[0] = aMat[0]; aDest[1] = aMat[3]; aDest[2] = aMat[6]; aDest[3] = aMat[1]; aDest[4] = aMat[4]; aDest[5] = aMat[7]; aDest[6] = aMat[2]; aDest[7] = aMat[5]; aDest[8] = aMat[8]; return aDest; }, /** * Copies the elements of a mat3 into the upper 3x3 elements of a mat4. * * @param {Array} aMat * mat3 containing values to copy * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat3 if specified, first operand otherwise */ toMat4: function M3_toMat4(aMat, aDest) { if (!aDest) { aDest = new Float32Array(16); } aDest[0] = aMat[0]; aDest[1] = aMat[1]; aDest[2] = aMat[2]; aDest[3] = 0; aDest[4] = aMat[3]; aDest[5] = aMat[4]; aDest[6] = aMat[5]; aDest[7] = 0; aDest[8] = aMat[6]; aDest[9] = aMat[7]; aDest[10] = aMat[8]; aDest[11] = 0; aDest[12] = 0; aDest[13] = 0; aDest[14] = 0; aDest[15] = 1; return aDest; }, /** * Returns a string representation of a 3x3 matrix. * * @param {Array} aMat * mat3 to represent as a string * * @return {String} representation of the matrix */ str: function M3_str(aMat) { return "[" + aMat[0] + ", " + aMat[1] + ", " + aMat[2] + ", " + aMat[3] + ", " + aMat[4] + ", " + aMat[5] + ", " + aMat[6] + ", " + aMat[7] + ", " + aMat[8] + "]"; } }; /** * mat4 - 4x4 Matrix. */ let mat4 = { /** * Creates a new instance of a mat4 using the default Float32Array type. * Any array containing at least 16 numeric elements can serve as a mat4. * * @param {Array} aMat * optional, mat4 containing values to initialize with * * @return {Array} a new instance of a mat4 */ create: function M4_create(aMat) { let dest = new Float32Array(16); if (aMat) { mat4.set(aMat, dest); } else { mat4.identity(dest); } return dest; }, /** * Copies the values of one mat4 to another * * @param {Array} aMat * mat4 containing values to copy * @param {Array} aDest * mat4 receiving copied values * * @return {Array} the destination mat4 receiving copied values */ set: function M4_set(aMat, aDest) { aDest[0] = aMat[0]; aDest[1] = aMat[1]; aDest[2] = aMat[2]; aDest[3] = aMat[3]; aDest[4] = aMat[4]; aDest[5] = aMat[5]; aDest[6] = aMat[6]; aDest[7] = aMat[7]; aDest[8] = aMat[8]; aDest[9] = aMat[9]; aDest[10] = aMat[10]; aDest[11] = aMat[11]; aDest[12] = aMat[12]; aDest[13] = aMat[13]; aDest[14] = aMat[14]; aDest[15] = aMat[15]; return aDest; }, /** * Sets a mat4 to an identity matrix. * * @param {Array} aDest * mat4 to set * * @return {Array} the same matrix */ identity: function M4_identity(aDest) { aDest[0] = 1; aDest[1] = 0; aDest[2] = 0; aDest[3] = 0; aDest[4] = 0; aDest[5] = 1; aDest[6] = 0; aDest[7] = 0; aDest[8] = 0; aDest[9] = 0; aDest[10] = 1; aDest[11] = 0; aDest[12] = 0; aDest[13] = 0; aDest[14] = 0; aDest[15] = 1; return aDest; }, /** * Transposes a mat4 (flips the values over the diagonal). * * @param {Array} aMat * mat4 to transpose * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ transpose: function M4_transpose(aMat, aDest) { if (!aDest || aMat === aDest) { let a01 = aMat[1]; let a02 = aMat[2]; let a03 = aMat[3]; let a12 = aMat[6]; let a13 = aMat[7]; let a23 = aMat[11]; aMat[1] = aMat[4]; aMat[2] = aMat[8]; aMat[3] = aMat[12]; aMat[4] = a01; aMat[6] = aMat[9]; aMat[7] = aMat[13]; aMat[8] = a02; aMat[9] = a12; aMat[11] = aMat[14]; aMat[12] = a03; aMat[13] = a13; aMat[14] = a23; return aMat; } aDest[0] = aMat[0]; aDest[1] = aMat[4]; aDest[2] = aMat[8]; aDest[3] = aMat[12]; aDest[4] = aMat[1]; aDest[5] = aMat[5]; aDest[6] = aMat[9]; aDest[7] = aMat[13]; aDest[8] = aMat[2]; aDest[9] = aMat[6]; aDest[10] = aMat[10]; aDest[11] = aMat[14]; aDest[12] = aMat[3]; aDest[13] = aMat[7]; aDest[14] = aMat[11]; aDest[15] = aMat[15]; return aDest; }, /** * Calculate the determinant of a mat4. * * @param {Array} aMat * mat4 to calculate determinant of * * @return {Number} determinant of the matrix */ determinant: function M4_determinant(mat) { let a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3]; let a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7]; let a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11]; let a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15]; return a30 * a21 * a12 * a03 - a20 * a31 * a12 * a03 - a30 * a11 * a22 * a03 + a10 * a31 * a22 * a03 + a20 * a11 * a32 * a03 - a10 * a21 * a32 * a03 - a30 * a21 * a02 * a13 + a20 * a31 * a02 * a13 + a30 * a01 * a22 * a13 - a00 * a31 * a22 * a13 - a20 * a01 * a32 * a13 + a00 * a21 * a32 * a13 + a30 * a11 * a02 * a23 - a10 * a31 * a02 * a23 - a30 * a01 * a12 * a23 + a00 * a31 * a12 * a23 + a10 * a01 * a32 * a23 - a00 * a11 * a32 * a23 - a20 * a11 * a02 * a33 + a10 * a21 * a02 * a33 + a20 * a01 * a12 * a33 - a00 * a21 * a12 * a33 - a10 * a01 * a22 * a33 + a00 * a11 * a22 * a33; }, /** * Calculate the inverse of a mat4. * * @param {Array} aMat * mat4 to calculate inverse of * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ inverse: function M4_inverse(aMat, aDest) { if (!aDest) { aDest = aMat; } let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3]; let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7]; let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11]; let a30 = aMat[12], a31 = aMat[13], a32 = aMat[14], a33 = aMat[15]; let b00 = a00 * a11 - a01 * a10; let b01 = a00 * a12 - a02 * a10; let b02 = a00 * a13 - a03 * a10; let b03 = a01 * a12 - a02 * a11; let b04 = a01 * a13 - a03 * a11; let b05 = a02 * a13 - a03 * a12; let b06 = a20 * a31 - a21 * a30; let b07 = a20 * a32 - a22 * a30; let b08 = a20 * a33 - a23 * a30; let b09 = a21 * a32 - a22 * a31; let b10 = a21 * a33 - a23 * a31; let b11 = a22 * a33 - a23 * a32; let id = 1 / ((b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06) || EPSILON); aDest[0] = ( a11 * b11 - a12 * b10 + a13 * b09) * id; aDest[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * id; aDest[2] = ( a31 * b05 - a32 * b04 + a33 * b03) * id; aDest[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * id; aDest[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * id; aDest[5] = ( a00 * b11 - a02 * b08 + a03 * b07) * id; aDest[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * id; aDest[7] = ( a20 * b05 - a22 * b02 + a23 * b01) * id; aDest[8] = ( a10 * b10 - a11 * b08 + a13 * b06) * id; aDest[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * id; aDest[10] = ( a30 * b04 - a31 * b02 + a33 * b00) * id; aDest[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * id; aDest[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * id; aDest[13] = ( a00 * b09 - a01 * b07 + a02 * b06) * id; aDest[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * id; aDest[15] = ( a20 * b03 - a21 * b01 + a22 * b00) * id; return aDest; }, /** * Copies the upper 3x3 elements of a mat4 into another mat4. * * @param {Array} aMat * mat4 containing values to copy * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ toRotationMat: function M4_toRotationMat(aMat, aDest) { if (!aDest) { aDest = new Float32Array(16); } aDest[0] = aMat[0]; aDest[1] = aMat[1]; aDest[2] = aMat[2]; aDest[3] = aMat[3]; aDest[4] = aMat[4]; aDest[5] = aMat[5]; aDest[6] = aMat[6]; aDest[7] = aMat[7]; aDest[8] = aMat[8]; aDest[9] = aMat[9]; aDest[10] = aMat[10]; aDest[11] = aMat[11]; aDest[12] = 0; aDest[13] = 0; aDest[14] = 0; aDest[15] = 1; return aDest; }, /** * Copies the upper 3x3 elements of a mat4 into a mat3. * * @param {Array} aMat * mat4 containing values to copy * @param {Array} aDest * optional, mat3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat3 if specified, first operand otherwise */ toMat3: function M4_toMat3(aMat, aDest) { if (!aDest) { aDest = new Float32Array(9); } aDest[0] = aMat[0]; aDest[1] = aMat[1]; aDest[2] = aMat[2]; aDest[3] = aMat[4]; aDest[4] = aMat[5]; aDest[5] = aMat[6]; aDest[6] = aMat[8]; aDest[7] = aMat[9]; aDest[8] = aMat[10]; return aDest; }, /** * Calculate the inverse of the upper 3x3 elements of a mat4 and copies * the result into a mat3. The resulting matrix is useful for calculating * transformed normals. * * @param {Array} aMat * mat4 containing values to invert and copy * @param {Array} aDest * optional, mat3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat3 if specified, first operand otherwise */ toInverseMat3: function M4_toInverseMat3(aMat, aDest) { if (!aDest) { aDest = new Float32Array(9); } let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2]; let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6]; let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10]; let b01 = a22 * a11 - a12 * a21; let b11 = -a22 * a10 + a12 * a20; let b21 = a21 * a10 - a11 * a20; let id = 1 / ((a00 * b01 + a01 * b11 + a02 * b21) || EPSILON); aDest[0] = b01 * id; aDest[1] = (-a22 * a01 + a02 * a21) * id; aDest[2] = ( a12 * a01 - a02 * a11) * id; aDest[3] = b11 * id; aDest[4] = ( a22 * a00 - a02 * a20) * id; aDest[5] = (-a12 * a00 + a02 * a10) * id; aDest[6] = b21 * id; aDest[7] = (-a21 * a00 + a01 * a20) * id; aDest[8] = ( a11 * a00 - a01 * a10) * id; return aDest; }, /** * Performs a matrix multiplication. * * @param {Array} aMat * first operand * @param {Array} aMat2 * second operand * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ multiply: function M4_multiply(aMat, aMat2, aDest) { if (!aDest) { aDest = aMat; } let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3]; let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7]; let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11]; let a30 = aMat[12], a31 = aMat[13], a32 = aMat[14], a33 = aMat[15]; let b00 = aMat2[0], b01 = aMat2[1], b02 = aMat2[2], b03 = aMat2[3]; let b10 = aMat2[4], b11 = aMat2[5], b12 = aMat2[6], b13 = aMat2[7]; let b20 = aMat2[8], b21 = aMat2[9], b22 = aMat2[10], b23 = aMat2[11]; let b30 = aMat2[12], b31 = aMat2[13], b32 = aMat2[14], b33 = aMat2[15]; aDest[0] = b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30; aDest[1] = b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31; aDest[2] = b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32; aDest[3] = b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33; aDest[4] = b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30; aDest[5] = b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31; aDest[6] = b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32; aDest[7] = b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33; aDest[8] = b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30; aDest[9] = b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31; aDest[10] = b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32; aDest[11] = b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33; aDest[12] = b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30; aDest[13] = b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31; aDest[14] = b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32; aDest[15] = b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33; return aDest; }, /** * Transforms a vec3 with the given matrix. * 4th vector component is implicitly 1. * * @param {Array} aMat * mat4 to transform the vector with * @param {Array} aVec * vec3 to transform * @param {Array} aDest * optional, vec3 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, aVec operand otherwise */ multiplyVec3: function M4_multiplyVec3(aMat, aVec, aDest) { if (!aDest) { aDest = aVec; } let x = aVec[0]; let y = aVec[1]; let z = aVec[2]; aDest[0] = aMat[0] * x + aMat[4] * y + aMat[8] * z + aMat[12]; aDest[1] = aMat[1] * x + aMat[5] * y + aMat[9] * z + aMat[13]; aDest[2] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14]; return aDest; }, /** * Transforms a vec4 with the given matrix. * * @param {Array} aMat * mat4 to transform the vector with * @param {Array} aVec * vec4 to transform * @param {Array} aDest * optional, vec4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination vec4 if specified, vec4 operand otherwise */ multiplyVec4: function M4_multiplyVec4(aMat, aVec, aDest) { if (!aDest) { aDest = aVec; } let x = aVec[0]; let y = aVec[1]; let z = aVec[2]; let w = aVec[3]; aDest[0] = aMat[0] * x + aMat[4] * y + aMat[8] * z + aMat[12] * w; aDest[1] = aMat[1] * x + aMat[5] * y + aMat[9] * z + aMat[13] * w; aDest[2] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14] * w; aDest[3] = aMat[3] * x + aMat[7] * y + aMat[11] * z + aMat[15] * w; return aDest; }, /** * Translates a matrix by the given vector. * * @param {Array} aMat * mat4 to translate * @param {Array} aVec * vec3 specifying the translation * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ translate: function M4_translate(aMat, aVec, aDest) { let x = aVec[0]; let y = aVec[1]; let z = aVec[2]; if (!aDest || aMat === aDest) { aMat[12] = aMat[0] * x + aMat[4] * y + aMat[8] * z + aMat[12]; aMat[13] = aMat[1] * x + aMat[5] * y + aMat[9] * z + aMat[13]; aMat[14] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14]; aMat[15] = aMat[3] * x + aMat[7] * y + aMat[11] * z + aMat[15]; return aMat; } let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3]; let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7]; let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11]; aDest[0] = a00; aDest[1] = a01; aDest[2] = a02; aDest[3] = a03; aDest[4] = a10; aDest[5] = a11; aDest[6] = a12; aDest[7] = a13; aDest[8] = a20; aDest[9] = a21; aDest[10] = a22; aDest[11] = a23; aDest[12] = a00 * x + a10 * y + a20 * z + aMat[12]; aDest[13] = a01 * x + a11 * y + a21 * z + aMat[13]; aDest[14] = a02 * x + a12 * y + a22 * z + aMat[14]; aDest[15] = a03 * x + a13 * y + a23 * z + aMat[15]; return aDest; }, /** * Scales a matrix by the given vector. * * @param {Array} aMat * mat4 to translate * @param {Array} aVec * vec3 specifying the scale on each axis * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ scale: function M4_scale(aMat, aVec, aDest) { let x = aVec[0]; let y = aVec[1]; let z = aVec[2]; if (!aDest || aMat === aDest) { aMat[0] *= x; aMat[1] *= x; aMat[2] *= x; aMat[3] *= x; aMat[4] *= y; aMat[5] *= y; aMat[6] *= y; aMat[7] *= y; aMat[8] *= z; aMat[9] *= z; aMat[10] *= z; aMat[11] *= z; return aMat; } aDest[0] = aMat[0] * x; aDest[1] = aMat[1] * x; aDest[2] = aMat[2] * x; aDest[3] = aMat[3] * x; aDest[4] = aMat[4] * y; aDest[5] = aMat[5] * y; aDest[6] = aMat[6] * y; aDest[7] = aMat[7] * y; aDest[8] = aMat[8] * z; aDest[9] = aMat[9] * z; aDest[10] = aMat[10] * z; aDest[11] = aMat[11] * z; aDest[12] = aMat[12]; aDest[13] = aMat[13]; aDest[14] = aMat[14]; aDest[15] = aMat[15]; return aDest; }, /** * Rotates a matrix by the given angle around the specified axis. * If rotating around a primary axis (x, y, z) one of the specialized * rotation functions should be used instead for performance, * * @param {Array} aMat * mat4 to rotate * @param {Number} aAngle * the angle (in radians) to rotate * @param {Array} aAxis * vec3 representing the axis to rotate around * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ rotate: function M4_rotate(aMat, aAngle, aAxis, aDest) { let x = aAxis[0]; let y = aAxis[1]; let z = aAxis[2]; let len = 1 / (Math.sqrt(x * x + y * y + z * z) || EPSILON); x *= len; y *= len; z *= len; let s = Math.sin(aAngle); let c = Math.cos(aAngle); let t = 1 - c; let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3]; let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7]; let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11]; let b00 = x * x * t + c, b01 = y * x * t + z * s, b02 = z * x * t - y * s; let b10 = x * y * t - z * s, b11 = y * y * t + c, b12 = z * y * t + x * s; let b20 = x * z * t + y * s, b21 = y * z * t - x * s, b22 = z * z * t + c; if (!aDest) { aDest = aMat; } else if (aMat !== aDest) { aDest[12] = aMat[12]; aDest[13] = aMat[13]; aDest[14] = aMat[14]; aDest[15] = aMat[15]; } aDest[0] = a00 * b00 + a10 * b01 + a20 * b02; aDest[1] = a01 * b00 + a11 * b01 + a21 * b02; aDest[2] = a02 * b00 + a12 * b01 + a22 * b02; aDest[3] = a03 * b00 + a13 * b01 + a23 * b02; aDest[4] = a00 * b10 + a10 * b11 + a20 * b12; aDest[5] = a01 * b10 + a11 * b11 + a21 * b12; aDest[6] = a02 * b10 + a12 * b11 + a22 * b12; aDest[7] = a03 * b10 + a13 * b11 + a23 * b12; aDest[8] = a00 * b20 + a10 * b21 + a20 * b22; aDest[9] = a01 * b20 + a11 * b21 + a21 * b22; aDest[10] = a02 * b20 + a12 * b21 + a22 * b22; aDest[11] = a03 * b20 + a13 * b21 + a23 * b22; return aDest; }, /** * Rotates a matrix by the given angle around the X axis. * * @param {Array} aMat * mat4 to rotate * @param {Number} aAngle * the angle (in radians) to rotate * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ rotateX: function M4_rotateX(aMat, aAngle, aDest) { let s = Math.sin(aAngle); let c = Math.cos(aAngle); let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7]; let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11]; if (!aDest) { aDest = aMat; } else if (aMat !== aDest) { aDest[0] = aMat[0]; aDest[1] = aMat[1]; aDest[2] = aMat[2]; aDest[3] = aMat[3]; aDest[12] = aMat[12]; aDest[13] = aMat[13]; aDest[14] = aMat[14]; aDest[15] = aMat[15]; } aDest[4] = a10 * c + a20 * s; aDest[5] = a11 * c + a21 * s; aDest[6] = a12 * c + a22 * s; aDest[7] = a13 * c + a23 * s; aDest[8] = a10 * -s + a20 * c; aDest[9] = a11 * -s + a21 * c; aDest[10] = a12 * -s + a22 * c; aDest[11] = a13 * -s + a23 * c; return aDest; }, /** * Rotates a matrix by the given angle around the Y axix. * * @param {Array} aMat * mat4 to rotate * @param {Number} aAngle * the angle (in radians) to rotate * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ rotateY: function M4_rotateY(aMat, aAngle, aDest) { let s = Math.sin(aAngle); let c = Math.cos(aAngle); let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3]; let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11]; if (!aDest) { aDest = aMat; } else if (aMat !== aDest) { aDest[4] = aMat[4]; aDest[5] = aMat[5]; aDest[6] = aMat[6]; aDest[7] = aMat[7]; aDest[12] = aMat[12]; aDest[13] = aMat[13]; aDest[14] = aMat[14]; aDest[15] = aMat[15]; } aDest[0] = a00 * c + a20 * -s; aDest[1] = a01 * c + a21 * -s; aDest[2] = a02 * c + a22 * -s; aDest[3] = a03 * c + a23 * -s; aDest[8] = a00 * s + a20 * c; aDest[9] = a01 * s + a21 * c; aDest[10] = a02 * s + a22 * c; aDest[11] = a03 * s + a23 * c; return aDest; }, /** * Rotates a matrix by the given angle around the Z axix. * * @param {Array} aMat * mat4 to rotate * @param {Number} aAngle * the angle (in radians) to rotate * @param {Array} aDest * optional, mat4 receiving operation result * if not specified result is written to the first operand * * @return {Array} the destination mat4 if specified, first operand otherwise */ rotateZ: function M4_rotateZ(aMat, aAngle, aDest) { let s = Math.sin(aAngle); let c = Math.cos(aAngle); let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3]; let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7]; if (!aDest) { aDest = aMat; } else if (aMat !== aDest) { aDest[8] = aMat[8]; aDest[9] = aMat[9]; aDest[10] = aMat[10]; aDest[11] = aMat[11]; aDest[12] = aMat[12]; aDest[13] = aMat[13]; aDest[14] = aMat[14]; aDest[15] = aMat[15]; } aDest[0] = a00 * c + a10 * s; aDest[1] = a01 * c + a11 * s; aDest[2] = a02 * c + a12 * s; aDest[3] = a03 * c + a13 * s; aDest[4] = a00 * -s + a10 * c; aDest[5] = a01 * -s + a11 * c; aDest[6] = a02 * -s + a12 * c; aDest[7] = a03 * -s + a13 * c; return aDest; }, /** * Generates a frustum matrix with the given bounds. * * @param {Number} aLeft * scalar, left bound of the frustum * @param {Number} aRight * scalar, right bound of the frustum * @param {Number} aBottom * scalar, bottom bound of the frustum * @param {Number} aTop * scalar, top bound of the frustum * @param {Number} aNear * scalar, near bound of the frustum * @param {Number} aFar * scalar, far bound of the frustum * @param {Array} aDest * optional, mat4 frustum matrix will be written into * if not specified result is written to a new mat4 * * @return {Array} the destination mat4 if specified, a new mat4 otherwise */ frustum: function M4_frustum( aLeft, aRight, aBottom, aTop, aNear, aFar, aDest) { if (!aDest) { aDest = new Float32Array(16); } let rl = (aRight - aLeft); let tb = (aTop - aBottom); let fn = (aFar - aNear); aDest[0] = (aNear * 2) / rl; aDest[1] = 0; aDest[2] = 0; aDest[3] = 0; aDest[4] = 0; aDest[5] = (aNear * 2) / tb; aDest[6] = 0; aDest[7] = 0; aDest[8] = (aRight + aLeft) / rl; aDest[9] = (aTop + aBottom) / tb; aDest[10] = -(aFar + aNear) / fn; aDest[11] = -1; aDest[12] = 0; aDest[13] = 0; aDest[14] = -(aFar * aNear * 2) / fn; aDest[15] = 0; return aDest; }, /** * Generates a perspective projection matrix with the given bounds. * * @param {Number} aFovy * scalar, vertical field of view (degrees) * @param {Number} aAspect * scalar, aspect ratio (typically viewport width/height) * @param {Number} aNear * scalar, near bound of the frustum * @param {Number} aFar * scalar, far bound of the frustum * @param {Array} aDest * optional, mat4 frustum matrix will be written into * if not specified result is written to a new mat4 * * @return {Array} the destination mat4 if specified, a new mat4 otherwise */ perspective: function M4_perspective( aFovy, aAspect, aNear, aFar, aDest, aFlip) { let upper = aNear * Math.tan(aFovy * 0.00872664626); // PI * 180 / 2 let right = upper * aAspect; let top = upper * (aFlip || 1); return mat4.frustum(-right, right, -top, top, aNear, aFar, aDest); }, /** * Generates a orthogonal projection matrix with the given bounds. * * @param {Number} aLeft * scalar, left bound of the frustum * @param {Number} aRight * scalar, right bound of the frustum * @param {Number} aBottom * scalar, bottom bound of the frustum * @param {Number} aTop * scalar, top bound of the frustum * @param {Number} aNear * scalar, near bound of the frustum * @param {Number} aFar * scalar, far bound of the frustum * @param {Array} aDest * optional, mat4 frustum matrix will be written into * if not specified result is written to a new mat4 * * @return {Array} the destination mat4 if specified, a new mat4 otherwise */ ortho: function M4_ortho(aLeft, aRight, aBottom, aTop, aNear, aFar, aDest) { if (!aDest) { aDest = new Float32Array(16); } let rl = (aRight - aLeft); let tb = (aTop - aBottom); let fn = (aFar - aNear); aDest[0] = 2 / rl; aDest[1] = 0; aDest[2] = 0; aDest[3] = 0; aDest[4] = 0; aDest[5] = 2 / tb; aDest[6] = 0; aDest[7] = 0; aDest[8] = 0; aDest[9] = 0; aDest[10] = -2 / fn; aDest[11] = 0; aDest[12] = -(aLeft + aRight) / rl; aDest[13] = -(aTop + aBottom) / tb; aDest[14] = -(aFar + aNear) / fn; aDest[15] = 1; return aDest; }, /** * Generates a look-at matrix with the given eye position, focal point, and * up axis. * * @param {Array} aEye * vec3, position of the viewer * @param {Array} aCenter * vec3, point the viewer is looking at * @param {Array} aUp * vec3 pointing up * @param {Array} aDest * optional, mat4 frustum matrix will be written into * if not specified result is written to a new mat4 * * @return {Array} the destination mat4 if specified, a new mat4 otherwise */ lookAt: function M4_lookAt(aEye, aCenter, aUp, aDest) { if (!aDest) { aDest = new Float32Array(16); } let eyex = aEye[0]; let eyey = aEye[1]; let eyez = aEye[2]; let upx = aUp[0]; let upy = aUp[1]; let upz = aUp[2]; let centerx = aCenter[0]; let centery = aCenter[1]; let centerz = aCenter[2]; let z0 = eyex - aCenter[0]; let z1 = eyey - aCenter[1]; let z2 = eyez - aCenter[2]; let len = 1 / (Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2) || EPSILON); z0 *= len; z1 *= len; z2 *= len; let x0 = upy * z2 - upz * z1; let x1 = upz * z0 - upx * z2; let x2 = upx * z1 - upy * z0; len = 1 / (Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2) || EPSILON); x0 *= len; x1 *= len; x2 *= len; let y0 = z1 * x2 - z2 * x1; let y1 = z2 * x0 - z0 * x2; let y2 = z0 * x1 - z1 * x0; len = 1 / (Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2) || EPSILON); y0 *= len; y1 *= len; y2 *= len; aDest[0] = x0; aDest[1] = y0; aDest[2] = z0; aDest[3] = 0; aDest[4] = x1; aDest[5] = y1; aDest[6] = z1; aDest[7] = 0; aDest[8] = x2; aDest[9] = y2; aDest[10] = z2; aDest[11] = 0; aDest[12] = -(x0 * eyex + x1 * eyey + x2 * eyez); aDest[13] = -(y0 * eyex + y1 * eyey + y2 * eyez); aDest[14] = -(z0 * eyex + z1 * eyey + z2 * eyez); aDest[15] = 1; return aDest; }, /** * Returns a string representation of a 4x4 matrix. * * @param {Array} aMat * mat4 to represent as a string * * @return {String} representation of the matrix */ str: function M4_str(mat) { return "[" + mat[0] + ", " + mat[1] + ", " + mat[2] + ", " + mat[3] + ", "+ mat[4] + ", " + mat[5] + ", " + mat[6] + ", " + mat[7] + ", "+ mat[8] + ", " + mat[9] + ", " + mat[10] + ", " + mat[11] + ", "+ mat[12] + ", " + mat[13] + ", " + mat[14] + ", " + mat[15] + "]"; } }; /** * quat4 - Quaternion. */ let quat4 = { /** * Creates a new instance of a quat4 using the default Float32Array type. * Any array containing at least 4 numeric elements can serve as a quat4. * * @param {Array} aQuat * optional, quat4 containing values to initialize with * * @return {Array} a new instance of a quat4 */ create: function Q4_create(aQuat) { let dest = new Float32Array(4); if (aQuat) { quat4.set(aQuat, dest); } else { quat4.identity(dest); } return dest; }, /** * Copies the values of one quat4 to another. * * @param {Array} aQuat * quat4 containing values to copy * @param {Array} aDest * quat4 receiving copied values * * @return {Array} the destination quat4 receiving copied values */ set: function Q4_set(aQuat, aDest) { aDest[0] = aQuat[0]; aDest[1] = aQuat[1]; aDest[2] = aQuat[2]; aDest[3] = aQuat[3]; return aDest; }, /** * Sets a quat4 to an identity quaternion. * * @param {Array} aDest * quat4 to set * * @return {Array} the same quaternion */ identity: function Q4_identity(aDest) { aDest[0] = 0; aDest[1] = 0; aDest[2] = 0; aDest[3] = 1; return aDest; }, /** * Calculate the W component of a quat4 from the X, Y, and Z components. * Assumes that quaternion is 1 unit in length. * Any existing W component will be ignored. * * @param {Array} aQuat * quat4 to calculate W component of * @param {Array} aDest * optional, quat4 receiving calculated values * if not specified result is written to the first operand * * @return {Array} the destination quat if specified, first operand otherwise */ calculateW: function Q4_calculateW(aQuat, aDest) { if (!aDest) { aDest = aQuat; } let x = aQuat[0]; let y = aQuat[1]; let z = aQuat[2]; aDest[0] = x; aDest[1] = y; aDest[2] = z; aDest[3] = -Math.sqrt(Math.abs(1 - x * x - y * y - z * z)); return aDest; }, /** * Calculate the inverse of a quat4. * * @param {Array} aQuat * quat4 to calculate the inverse of * @param {Array} aDest * optional, quat4 receiving the inverse values * if not specified result is written to the first operand * * @return {Array} the destination quat if specified, first operand otherwise */ inverse: function Q4_inverse(aQuat, aDest) { if (!aDest) { aDest = aQuat; } aQuat[0] = -aQuat[0]; aQuat[1] = -aQuat[1]; aQuat[2] = -aQuat[2]; return aQuat; }, /** * Generates a unit quaternion of the same direction as the provided quat4. * If quaternion length is 0, returns [0, 0, 0, 0]. * * @param {Array} aQuat * quat4 to normalize * @param {Array} aDest * optional, quat4 receiving the operation result * if not specified result is written to the first operand * * @return {Array} the destination quat if specified, first operand otherwise */ normalize: function Q4_normalize(aQuat, aDest) { if (!aDest) { aDest = aQuat; } let x = aQuat[0]; let y = aQuat[1]; let z = aQuat[2]; let w = aQuat[3]; let len = Math.sqrt(x * x + y * y + z * z + w * w); if (Math.abs(len) < EPSILON) { aDest[0] = 0; aDest[1] = 0; aDest[2] = 0; aDest[3] = 0; return aDest; } len = 1 / len; aDest[0] = x * len; aDest[1] = y * len; aDest[2] = z * len; aDest[3] = w * len; return aDest; }, /** * Calculate the length of a quat4. * * @param {Array} aQuat * quat4 to calculate the length of * * @return {Number} length of the quaternion */ length: function Q4_length(aQuat) { let x = aQuat[0]; let y = aQuat[1]; let z = aQuat[2]; let w = aQuat[3]; return Math.sqrt(x * x + y * y + z * z + w * w); }, /** * Performs a quaternion multiplication. * * @param {Array} aQuat * first operand * @param {Array} aQuat2 * second operand * @param {Array} aDest * optional, quat4 receiving the operation result * if not specified result is written to the first operand * * @return {Array} the destination quat if specified, first operand otherwise */ multiply: function Q4_multiply(aQuat, aQuat2, aDest) { if (!aDest) { aDest = aQuat; } let qax = aQuat[0]; let qay = aQuat[1]; let qaz = aQuat[2]; let qaw = aQuat[3]; let qbx = aQuat2[0]; let qby = aQuat2[1]; let qbz = aQuat2[2]; let qbw = aQuat2[3]; aDest[0] = qax * qbw + qaw * qbx + qay * qbz - qaz * qby; aDest[1] = qay * qbw + qaw * qby + qaz * qbx - qax * qbz; aDest[2] = qaz * qbw + qaw * qbz + qax * qby - qay * qbx; aDest[3] = qaw * qbw - qax * qbx - qay * qby - qaz * qbz; return aDest; }, /** * Transforms a vec3 with the given quaternion. * * @param {Array} aQuat * quat4 to transform the vector with * @param {Array} aVec * vec3 to transform * @param {Array} aDest * optional, vec3 receiving the operation result * if not specified result is written to the first operand * * @return {Array} the destination vec3 if specified, aVec operand otherwise */ multiplyVec3: function Q4_multiplyVec3(aQuat, aVec, aDest) { if (!aDest) { aDest = aVec; } let x = aVec[0]; let y = aVec[1]; let z = aVec[2]; let qx = aQuat[0]; let qy = aQuat[1]; let qz = aQuat[2]; let qw = aQuat[3]; let ix = qw * x + qy * z - qz * y; let iy = qw * y + qz * x - qx * z; let iz = qw * z + qx * y - qy * x; let iw = -qx * x - qy * y - qz * z; aDest[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy; aDest[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz; aDest[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx; return aDest; }, /** * Performs a spherical linear interpolation between two quat4. * * @param {Array} aQuat * first quaternion * @param {Array} aQuat2 * second quaternion * @param {Number} aSlerp * interpolation amount between the two inputs * @param {Array} aDest * optional, quat4 receiving the operation result * if not specified result is written to the first operand * * @return {Array} the destination quat if specified, first operand otherwise */ slerp: function Q4_slerp(aQuat, aQuat2, aSlerp, aDest) { if (!aDest) { aDest = aQuat; } let cosHalfTheta = aQuat[0] * aQuat2[0] + aQuat[1] * aQuat2[1] + aQuat[2] * aQuat2[2] + aQuat[3] * aQuat2[3]; if (Math.abs(cosHalfTheta) >= 1) { aDest[0] = aQuat[0]; aDest[1] = aQuat[1]; aDest[2] = aQuat[2]; aDest[3] = aQuat[3]; return aDest; } let halfTheta = Math.acos(cosHalfTheta); let sinHalfTheta = Math.sqrt(1 - cosHalfTheta * cosHalfTheta); if (Math.abs(sinHalfTheta) < EPSILON) { aDest[0] = (aQuat[0] * 0.5 + aQuat2[0] * 0.5); aDest[1] = (aQuat[1] * 0.5 + aQuat2[1] * 0.5); aDest[2] = (aQuat[2] * 0.5 + aQuat2[2] * 0.5); aDest[3] = (aQuat[3] * 0.5 + aQuat2[3] * 0.5); return aDest; } let ratioA = Math.sin((1 - aSlerp) * halfTheta) / sinHalfTheta; let ratioB = Math.sin(aSlerp * halfTheta) / sinHalfTheta; aDest[0] = (aQuat[0] * ratioA + aQuat2[0] * ratioB); aDest[1] = (aQuat[1] * ratioA + aQuat2[1] * ratioB); aDest[2] = (aQuat[2] * ratioA + aQuat2[2] * ratioB); aDest[3] = (aQuat[3] * ratioA + aQuat2[3] * ratioB); return aDest; }, /** * Calculates a 3x3 matrix from the given quat4. * * @param {Array} aQuat * quat4 to create matrix from * @param {Array} aDest * optional, mat3 receiving the initialization result * if not specified, a new matrix is created * * @return {Array} the destination mat3 if specified, first operand otherwise */ toMat3: function Q4_toMat3(aQuat, aDest) { if (!aDest) { aDest = new Float32Array(9); } let x = aQuat[0]; let y = aQuat[1]; let z = aQuat[2]; let w = aQuat[3]; let x2 = x + x; let y2 = y + y; let z2 = z + z; let xx = x * x2; let xy = x * y2; let xz = x * z2; let yy = y * y2; let yz = y * z2; let zz = z * z2; let wx = w * x2; let wy = w * y2; let wz = w * z2; aDest[0] = 1 - (yy + zz); aDest[1] = xy - wz; aDest[2] = xz + wy; aDest[3] = xy + wz; aDest[4] = 1 - (xx + zz); aDest[5] = yz - wx; aDest[6] = xz - wy; aDest[7] = yz + wx; aDest[8] = 1 - (xx + yy); return aDest; }, /** * Calculates a 4x4 matrix from the given quat4. * * @param {Array} aQuat * quat4 to create matrix from * @param {Array} aDest * optional, mat4 receiving the initialization result * if not specified, a new matrix is created * * @return {Array} the destination mat4 if specified, first operand otherwise */ toMat4: function Q4_toMat4(aQuat, aDest) { if (!aDest) { aDest = new Float32Array(16); } let x = aQuat[0]; let y = aQuat[1]; let z = aQuat[2]; let w = aQuat[3]; let x2 = x + x; let y2 = y + y; let z2 = z + z; let xx = x * x2; let xy = x * y2; let xz = x * z2; let yy = y * y2; let yz = y * z2; let zz = z * z2; let wx = w * x2; let wy = w * y2; let wz = w * z2; aDest[0] = 1 - (yy + zz); aDest[1] = xy - wz; aDest[2] = xz + wy; aDest[3] = 0; aDest[4] = xy + wz; aDest[5] = 1 - (xx + zz); aDest[6] = yz - wx; aDest[7] = 0; aDest[8] = xz - wy; aDest[9] = yz + wx; aDest[10] = 1 - (xx + yy); aDest[11] = 0; aDest[12] = 0; aDest[13] = 0; aDest[14] = 0; aDest[15] = 1; return aDest; }, /** * Creates a rotation quaternion from axis-angle. * This function expects that the axis is a normalized vector. * * @param {Array} aAxis * an array of elements representing the [x, y, z] axis * @param {Number} aAngle * the angle of rotation * @param {Array} aDest * optional, quat4 receiving the initialization result * if not specified, a new quaternion is created * * @return {Array} the quaternion as [x, y, z, w] */ fromAxis: function Q4_fromAxis(aAxis, aAngle, aDest) { if (!aDest) { aDest = new Float32Array(4); } let ang = aAngle * 0.5; let sin = Math.sin(ang); let cos = Math.cos(ang); aDest[0] = aAxis[0] * sin; aDest[1] = aAxis[1] * sin; aDest[2] = aAxis[2] * sin; aDest[3] = cos; return aDest; }, /** * Creates a rotation quaternion from Euler angles. * * @param {Number} aYaw * the yaw angle of rotation * @param {Number} aPitch * the pitch angle of rotation * @param {Number} aRoll * the roll angle of rotation * @param {Array} aDest * optional, quat4 receiving the initialization result * if not specified, a new quaternion is created * * @return {Array} the quaternion as [x, y, z, w] */ fromEuler: function Q4_fromEuler(aYaw, aPitch, aRoll, aDest) { if (!aDest) { aDest = new Float32Array(4); } let x = aPitch * 0.5; let y = aYaw * 0.5; let z = aRoll * 0.5; let sinr = Math.sin(x); let sinp = Math.sin(y); let siny = Math.sin(z); let cosr = Math.cos(x); let cosp = Math.cos(y); let cosy = Math.cos(z); aDest[0] = sinr * cosp * cosy - cosr * sinp * siny; aDest[1] = cosr * sinp * cosy + sinr * cosp * siny; aDest[2] = cosr * cosp * siny - sinr * sinp * cosy; aDest[3] = cosr * cosp * cosy + sinr * sinp * siny; return aDest; }, /** * Returns a string representation of a quaternion. * * @param {Array} aQuat * quat4 to represent as a string * * @return {String} representation of the quaternion */ str: function Q4_str(aQuat) { return "[" + aQuat[0] + ", " + aQuat[1] + ", " + aQuat[2] + ", " + aQuat[3] + "]"; } }; /** * Various algebraic math functions required by the engine. */ let TiltMath = { /** * Helper function, converts degrees to radians. * * @param {Number} aDegrees * the degrees to be converted to radians * * @return {Number} the degrees converted to radians */ radians: function TM_radians(aDegrees) { return aDegrees * PI_OVER_180; }, /** * Helper function, converts radians to degrees. * * @param {Number} aRadians * the radians to be converted to degrees * * @return {Number} the radians converted to degrees */ degrees: function TM_degrees(aRadians) { return aRadians * INV_PI_OVER_180; }, /** * Re-maps a number from one range to another. * * @param {Number} aValue * the number to map * @param {Number} aLow1 * the normal lower bound of the number * @param {Number} aHigh1 * the normal upper bound of the number * @param {Number} aLow2 * the new lower bound of the number * @param {Number} aHigh2 * the new upper bound of the number * * @return {Number} the remapped number */ map: function TM_map(aValue, aLow1, aHigh1, aLow2, aHigh2) { return aLow2 + (aHigh2 - aLow2) * ((aValue - aLow1) / (aHigh1 - aLow1)); }, /** * Returns if number is power of two. * * @param {Number} aNumber * the number to be verified * * @return {Boolean} true if x is power of two */ isPowerOfTwo: function TM_isPowerOfTwo(aNumber) { return !(aNumber & (aNumber - 1)); }, /** * Returns the next closest power of two greater than a number. * * @param {Number} aNumber * the number to be converted * * @return {Number} the next closest power of two for x */ nextPowerOfTwo: function TM_nextPowerOfTwo(aNumber) { --aNumber; for (let i = 1; i < 32; i <<= 1) { aNumber = aNumber | aNumber >> i; } return aNumber + 1; }, /** * A convenient way of limiting values to a set boundary. * * @param {Number} aValue * the number to be limited * @param {Number} aMin * the minimum allowed value for the number * @param {Number} aMax * the maximum allowed value for the number */ clamp: function TM_clamp(aValue, aMin, aMax) { return Math.max(aMin, Math.min(aMax, aValue)); }, /** * Convenient way to clamp a value to 0..1 * * @param {Number} aValue * the number to be limited */ saturate: function TM_saturate(aValue) { return Math.max(0, Math.min(1, aValue)); }, /** * Converts a hex color to rgba. * If the passed param is invalid, it will be converted to [0, 0, 0, 1]; * * @param {String} aColor * color expressed in hex, or using rgb() or rgba() * * @return {Array} with 4 color 0..1 components: [red, green, blue, alpha] */ hex2rgba: (function() { let cache = {}; return function TM_hex2rgba(aColor) { let hex = aColor.charAt(0) === "#" ? aColor.substring(1) : aColor; // check the cache to see if this color wasn't converted already if (cache[hex] !== undefined) { return cache[hex]; } // e.g. "f00" if (hex.length === 3) { let r = parseInt(hex.substring(0, 1), 16) * FIFTEEN_OVER_225; let g = parseInt(hex.substring(1, 2), 16) * FIFTEEN_OVER_225; let b = parseInt(hex.substring(2, 3), 16) * FIFTEEN_OVER_225; return (cache[hex] = [r, g, b, 1]); } // e.g. "f008" if (hex.length === 4) { let r = parseInt(hex.substring(0, 1), 16) * FIFTEEN_OVER_225; let g = parseInt(hex.substring(1, 2), 16) * FIFTEEN_OVER_225; let b = parseInt(hex.substring(2, 3), 16) * FIFTEEN_OVER_225; let a = parseInt(hex.substring(3, 4), 16) * FIFTEEN_OVER_225; return (cache[hex] = [r, g, b, a]); } // e.g. "ff0000" if (hex.length === 6) { let r = parseInt(hex.substring(0, 2), 16) * ONE_OVER_255; let g = parseInt(hex.substring(2, 4), 16) * ONE_OVER_255; let b = parseInt(hex.substring(4, 6), 16) * ONE_OVER_255; let a = 1; return (cache[hex] = [r, g, b, a]); } // e.g "ff0000aa" if (hex.length === 8) { let r = parseInt(hex.substring(0, 2), 16) * ONE_OVER_255; let g = parseInt(hex.substring(2, 4), 16) * ONE_OVER_255; let b = parseInt(hex.substring(4, 6), 16) * ONE_OVER_255; let a = parseInt(hex.substring(6, 8), 16) * ONE_OVER_255; return (cache[hex] = [r, g, b, a]); } // e.g. "rgba(255, 0, 0, 0.5)" if (hex.match("^rgba")) { let rgba = hex.substring(5, hex.length - 1).split(","); rgba[0] *= ONE_OVER_255; rgba[1] *= ONE_OVER_255; rgba[2] *= ONE_OVER_255; // in CSS, the alpha component of rgba() is already in the range 0..1 return (cache[hex] = rgba); } // e.g. "rgb(255, 0, 0)" if (hex.match("^rgb")) { let rgba = hex.substring(4, hex.length - 1).split(","); rgba[0] *= ONE_OVER_255; rgba[1] *= ONE_OVER_255; rgba[2] *= ONE_OVER_255; rgba[3] = 1; return (cache[hex] = rgba); } // your argument is invalid return (cache[hex] = [0, 0, 0, 1]); }; }()) }; // bind the owner object to the necessary functions TiltUtils.bindObjectFunc(vec3); TiltUtils.bindObjectFunc(mat3); TiltUtils.bindObjectFunc(mat4); TiltUtils.bindObjectFunc(quat4); TiltUtils.bindObjectFunc(TiltMath);