/* * Copyright (c) 2009, Mozilla Corp * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * Neither the name of the nor the * names of its contributors may be used to endorse or promote products * derived from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY ''AS IS'' AND ANY * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE * DISCLAIMED. IN NO EVENT SHALL BE LIABLE FOR ANY * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* * Based on sample code from the OpenGL(R) ES 2.0 Programming Guide, which carriers * the following header: * * Book: OpenGL(R) ES 2.0 Programming Guide * Authors: Aaftab Munshi, Dan Ginsburg, Dave Shreiner * ISBN-10: 0321502795 * ISBN-13: 9780321502797 * Publisher: Addison-Wesley Professional * URLs: http://safari.informit.com/9780321563835 * http://www.opengles-book.com */ // // A simple 4x4 Matrix utility class // function Matrix4x4() { this.elements = Array(16); this.loadIdentity(); } Matrix4x4.prototype = { scale: function (sx, sy, sz) { this.elements[0*4+0] *= sx; this.elements[0*4+1] *= sx; this.elements[0*4+2] *= sx; this.elements[0*4+3] *= sx; this.elements[1*4+0] *= sy; this.elements[1*4+1] *= sy; this.elements[1*4+2] *= sy; this.elements[1*4+3] *= sy; this.elements[2*4+0] *= sz; this.elements[2*4+1] *= sz; this.elements[2*4+2] *= sz; this.elements[2*4+3] *= sz; return this; }, translate: function (tx, ty, tz) { this.elements[3*4+0] += this.elements[0*4+0] * tx + this.elements[1*4+0] * ty + this.elements[2*4+0] * tz; this.elements[3*4+1] += this.elements[0*4+1] * tx + this.elements[1*4+1] * ty + this.elements[2*4+1] * tz; this.elements[3*4+2] += this.elements[0*4+2] * tx + this.elements[1*4+2] * ty + this.elements[2*4+2] * tz; this.elements[3*4+3] += this.elements[0*4+3] * tx + this.elements[1*4+3] * ty + this.elements[2*4+3] * tz; return this; }, rotate: function (angle, x, y, z) { var mag = Math.sqrt(x*x + y*y + z*z); var sinAngle = Math.sin(angle * Math.PI / 180.0); var cosAngle = Math.cos(angle * Math.PI / 180.0); if (mag > 0) { var xx, yy, zz, xy, yz, zx, xs, ys, zs; var oneMinusCos; var rotMat; x /= mag; y /= mag; z /= mag; xx = x * x; yy = y * y; zz = z * z; xy = x * y; yz = y * z; zx = z * x; xs = x * sinAngle; ys = y * sinAngle; zs = z * sinAngle; oneMinusCos = 1.0 - cosAngle; rotMat = new Matrix4x4(); rotMat.elements[0*4+0] = (oneMinusCos * xx) + cosAngle; rotMat.elements[0*4+1] = (oneMinusCos * xy) - zs; rotMat.elements[0*4+2] = (oneMinusCos * zx) + ys; rotMat.elements[0*4+3] = 0.0; rotMat.elements[1*4+0] = (oneMinusCos * xy) + zs; rotMat.elements[1*4+1] = (oneMinusCos * yy) + cosAngle; rotMat.elements[1*4+2] = (oneMinusCos * yz) - xs; rotMat.elements[1*4+3] = 0.0; rotMat.elements[2*4+0] = (oneMinusCos * zx) - ys; rotMat.elements[2*4+1] = (oneMinusCos * yz) + xs; rotMat.elements[2*4+2] = (oneMinusCos * zz) + cosAngle; rotMat.elements[2*4+3] = 0.0; rotMat.elements[3*4+0] = 0.0; rotMat.elements[3*4+1] = 0.0; rotMat.elements[3*4+2] = 0.0; rotMat.elements[3*4+3] = 1.0; rotMat = rotMat.multiply(this); this.elements = rotMat.elements; } return this; }, frustum: function (left, right, bottom, top, nearZ, farZ) { var deltaX = right - left; var deltaY = top - bottom; var deltaZ = farZ - nearZ; var frust; if ( (nearZ <= 0.0) || (farZ <= 0.0) || (deltaX <= 0.0) || (deltaY <= 0.0) || (deltaZ <= 0.0) ) return this; frust = new Matrix4x4(); frust.elements[0*4+0] = 2.0 * nearZ / deltaX; frust.elements[0*4+1] = frust.elements[0*4+2] = frust.elements[0*4+3] = 0.0; frust.elements[1*4+1] = 2.0 * nearZ / deltaY; frust.elements[1*4+0] = frust.elements[1*4+2] = frust.elements[1*4+3] = 0.0; frust.elements[2*4+0] = (right + left) / deltaX; frust.elements[2*4+1] = (top + bottom) / deltaY; frust.elements[2*4+2] = -(nearZ + farZ) / deltaZ; frust.elements[2*4+3] = -1.0; frust.elements[3*4+2] = -2.0 * nearZ * farZ / deltaZ; frust.elements[3*4+0] = frust.elements[3*4+1] = frust.elements[3*4+3] = 0.0; frust = frust.multiply(this); this.elements = frust.elements; return this; }, perspective: function (fovy, aspect, nearZ, farZ) { var frustumH = Math.tan(fovy / 360.0 * Math.PI) * nearZ; var frustumW = frustumH * aspect; return this.frustum(-frustumW, frustumW, -frustumH, frustumH, nearZ, farZ); }, ortho: function (left, right, bottom, top, nearZ, farZ) { var deltaX = right - left; var deltaY = top - bottom; var deltaZ = farZ - nearZ; var ortho = new Matrix4x4(); if ( (deltaX == 0.0) || (deltaY == 0.0) || (deltaZ == 0.0) ) return this; ortho.elements[0*4+0] = 2.0 / deltaX; ortho.elements[3*4+0] = -(right + left) / deltaX; ortho.elements[1*4+1] = 2.0 / deltaY; ortho.elements[3*4+1] = -(top + bottom) / deltaY; ortho.elements[2*4+2] = -2.0 / deltaZ; ortho.elements[3*4+2] = -(nearZ + farZ) / deltaZ; ortho = ortho.multiply(this); this.elements = ortho.elements; return this; }, multiply: function (right) { var tmp = new Matrix4x4(); for (var i = 0; i < 4; i++) { tmp.elements[i*4+0] = (this.elements[i*4+0] * right.elements[0*4+0]) + (this.elements[i*4+1] * right.elements[1*4+0]) + (this.elements[i*4+2] * right.elements[2*4+0]) + (this.elements[i*4+3] * right.elements[3*4+0]) ; tmp.elements[i*4+1] = (this.elements[i*4+0] * right.elements[0*4+1]) + (this.elements[i*4+1] * right.elements[1*4+1]) + (this.elements[i*4+2] * right.elements[2*4+1]) + (this.elements[i*4+3] * right.elements[3*4+1]) ; tmp.elements[i*4+2] = (this.elements[i*4+0] * right.elements[0*4+2]) + (this.elements[i*4+1] * right.elements[1*4+2]) + (this.elements[i*4+2] * right.elements[2*4+2]) + (this.elements[i*4+3] * right.elements[3*4+2]) ; tmp.elements[i*4+3] = (this.elements[i*4+0] * right.elements[0*4+3]) + (this.elements[i*4+1] * right.elements[1*4+3]) + (this.elements[i*4+2] * right.elements[2*4+3]) + (this.elements[i*4+3] * right.elements[3*4+3]) ; } this.elements = tmp.elements; return this; }, copy: function () { var tmp = new Matrix4x4(); for (var i = 0; i < 16; i++) { tmp.elements[i] = this.elements[i]; } return tmp; }, get: function (row, col) { return this.elements[4*row+col]; }, // In-place inversion invert: function () { var tmp_0 = this.get(2,2) * this.get(3,3); var tmp_1 = this.get(3,2) * this.get(2,3); var tmp_2 = this.get(1,2) * this.get(3,3); var tmp_3 = this.get(3,2) * this.get(1,3); var tmp_4 = this.get(1,2) * this.get(2,3); var tmp_5 = this.get(2,2) * this.get(1,3); var tmp_6 = this.get(0,2) * this.get(3,3); var tmp_7 = this.get(3,2) * this.get(0,3); var tmp_8 = this.get(0,2) * this.get(2,3); var tmp_9 = this.get(2,2) * this.get(0,3); var tmp_10 = this.get(0,2) * this.get(1,3); var tmp_11 = this.get(1,2) * this.get(0,3); var tmp_12 = this.get(2,0) * this.get(3,1); var tmp_13 = this.get(3,0) * this.get(2,1); var tmp_14 = this.get(1,0) * this.get(3,1); var tmp_15 = this.get(3,0) * this.get(1,1); var tmp_16 = this.get(1,0) * this.get(2,1); var tmp_17 = this.get(2,0) * this.get(1,1); var tmp_18 = this.get(0,0) * this.get(3,1); var tmp_19 = this.get(3,0) * this.get(0,1); var tmp_20 = this.get(0,0) * this.get(2,1); var tmp_21 = this.get(2,0) * this.get(0,1); var tmp_22 = this.get(0,0) * this.get(1,1); var tmp_23 = this.get(1,0) * this.get(0,1); var t0 = ((tmp_0 * this.get(1,1) + tmp_3 * this.get(2,1) + tmp_4 * this.get(3,1)) - (tmp_1 * this.get(1,1) + tmp_2 * this.get(2,1) + tmp_5 * this.get(3,1))); var t1 = ((tmp_1 * this.get(0,1) + tmp_6 * this.get(2,1) + tmp_9 * this.get(3,1)) - (tmp_0 * this.get(0,1) + tmp_7 * this.get(2,1) + tmp_8 * this.get(3,1))); var t2 = ((tmp_2 * this.get(0,1) + tmp_7 * this.get(1,1) + tmp_10 * this.get(3,1)) - (tmp_3 * this.get(0,1) + tmp_6 * this.get(1,1) + tmp_11 * this.get(3,1))); var t3 = ((tmp_5 * this.get(0,1) + tmp_8 * this.get(1,1) + tmp_11 * this.get(2,1)) - (tmp_4 * this.get(0,1) + tmp_9 * this.get(1,1) + tmp_10 * this.get(2,1))); var d = 1.0 / (this.get(0,0) * t0 + this.get(1,0) * t1 + this.get(2,0) * t2 + this.get(3,0) * t3); var out_00 = d * t0; var out_01 = d * t1; var out_02 = d * t2; var out_03 = d * t3; var out_10 = d * ((tmp_1 * this.get(1,0) + tmp_2 * this.get(2,0) + tmp_5 * this.get(3,0)) - (tmp_0 * this.get(1,0) + tmp_3 * this.get(2,0) + tmp_4 * this.get(3,0))); var out_11 = d * ((tmp_0 * this.get(0,0) + tmp_7 * this.get(2,0) + tmp_8 * this.get(3,0)) - (tmp_1 * this.get(0,0) + tmp_6 * this.get(2,0) + tmp_9 * this.get(3,0))); var out_12 = d * ((tmp_3 * this.get(0,0) + tmp_6 * this.get(1,0) + tmp_11 * this.get(3,0)) - (tmp_2 * this.get(0,0) + tmp_7 * this.get(1,0) + tmp_10 * this.get(3,0))); var out_13 = d * ((tmp_4 * this.get(0,0) + tmp_9 * this.get(1,0) + tmp_10 * this.get(2,0)) - (tmp_5 * this.get(0,0) + tmp_8 * this.get(1,0) + tmp_11 * this.get(2,0))); var out_20 = d * ((tmp_12 * this.get(1,3) + tmp_15 * this.get(2,3) + tmp_16 * this.get(3,3)) - (tmp_13 * this.get(1,3) + tmp_14 * this.get(2,3) + tmp_17 * this.get(3,3))); var out_21 = d * ((tmp_13 * this.get(0,3) + tmp_18 * this.get(2,3) + tmp_21 * this.get(3,3)) - (tmp_12 * this.get(0,3) + tmp_19 * this.get(2,3) + tmp_20 * this.get(3,3))); var out_22 = d * ((tmp_14 * this.get(0,3) + tmp_19 * this.get(1,3) + tmp_22 * this.get(3,3)) - (tmp_15 * this.get(0,3) + tmp_18 * this.get(1,3) + tmp_23 * this.get(3,3))); var out_23 = d * ((tmp_17 * this.get(0,3) + tmp_20 * this.get(1,3) + tmp_23 * this.get(2,3)) - (tmp_16 * this.get(0,3) + tmp_21 * this.get(1,3) + tmp_22 * this.get(2,3))); var out_30 = d * ((tmp_14 * this.get(2,2) + tmp_17 * this.get(3,2) + tmp_13 * this.get(1,2)) - (tmp_16 * this.get(3,2) + tmp_12 * this.get(1,2) + tmp_15 * this.get(2,2))); var out_31 = d * ((tmp_20 * this.get(3,2) + tmp_12 * this.get(0,2) + tmp_19 * this.get(2,2)) - (tmp_18 * this.get(2,2) + tmp_21 * this.get(3,2) + tmp_13 * this.get(0,2))); var out_32 = d * ((tmp_18 * this.get(1,2) + tmp_23 * this.get(3,2) + tmp_15 * this.get(0,2)) - (tmp_22 * this.get(3,2) + tmp_14 * this.get(0,2) + tmp_19 * this.get(1,2))); var out_33 = d * ((tmp_22 * this.get(2,2) + tmp_16 * this.get(0,2) + tmp_21 * this.get(1,2)) - (tmp_20 * this.get(1,2) + tmp_23 * this.get(2,2) + tmp_17 * this.get(0,2))); this.elements[0*4+0] = out_00; this.elements[0*4+1] = out_01; this.elements[0*4+2] = out_02; this.elements[0*4+3] = out_03; this.elements[1*4+0] = out_10; this.elements[1*4+1] = out_11; this.elements[1*4+2] = out_12; this.elements[1*4+3] = out_13; this.elements[2*4+0] = out_20; this.elements[2*4+1] = out_21; this.elements[2*4+2] = out_22; this.elements[2*4+3] = out_23; this.elements[3*4+0] = out_30; this.elements[3*4+1] = out_31; this.elements[3*4+2] = out_32; this.elements[3*4+3] = out_33; return this; }, // Returns new matrix which is the inverse of this inverse: function () { var tmp = this.copy(); return tmp.invert(); }, // In-place transpose transpose: function () { var tmp = this.elements[0*4+1]; this.elements[0*4+1] = this.elements[1*4+0]; this.elements[1*4+0] = tmp; tmp = this.elements[0*4+2]; this.elements[0*4+2] = this.elements[2*4+0]; this.elements[2*4+0] = tmp; tmp = this.elements[0*4+3]; this.elements[0*4+3] = this.elements[3*4+0]; this.elements[3*4+0] = tmp; tmp = this.elements[1*4+2]; this.elements[1*4+2] = this.elements[2*4+1]; this.elements[2*4+1] = tmp; tmp = this.elements[1*4+3]; this.elements[1*4+3] = this.elements[3*4+1]; this.elements[3*4+1] = tmp; tmp = this.elements[2*4+3]; this.elements[2*4+3] = this.elements[3*4+2]; this.elements[3*4+2] = tmp; return this; }, loadIdentity: function () { for (var i = 0; i < 16; i++) this.elements[i] = 0; this.elements[0*4+0] = 1.0; this.elements[1*4+1] = 1.0; this.elements[2*4+2] = 1.0; this.elements[3*4+3] = 1.0; return this; } };