1065 lines
36 KiB
JavaScript
1065 lines
36 KiB
JavaScript
/*
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* Copyright (C) 2009 Apple Inc. All Rights Reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
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* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
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* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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// J3DI (Jedi) - A support library for WebGL.
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/*
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J3DI Math Classes. Currently includes:
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J3DIMatrix4 - A 4x4 Matrix
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*/
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/*
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J3DIMatrix4 class
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This class implements a 4x4 matrix. It has functions which duplicate the
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functionality of the OpenGL matrix stack and glut functions. On browsers
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that support it, CSSMatrix is used to accelerate operations.
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IDL:
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[
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Constructor(in J3DIMatrix4 matrix), // copy passed matrix into new J3DIMatrix4
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Constructor(in sequence<float> array) // create new J3DIMatrix4 with 16 floats (row major)
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Constructor() // create new J3DIMatrix4 with identity matrix
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]
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interface J3DIMatrix4 {
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void load(in J3DIMatrix4 matrix); // copy the values from the passed matrix
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void load(in sequence<float> array); // copy 16 floats into the matrix
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sequence<float> getAsArray(); // return the matrix as an array of 16 floats
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Float32Array getAsFloat32Array(); // return the matrix as a Float32Array with 16 values
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void setUniform(in WebGLRenderingContext ctx, // Send the matrix to the passed uniform location in the passed context
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in WebGLUniformLocation loc,
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in boolean transpose);
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void makeIdentity(); // replace the matrix with identity
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void transpose(); // replace the matrix with its transpose
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void invert(); // replace the matrix with its inverse
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void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
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void translate(in J3DVector3 v); // multiply the matrix by passed translation values on the right
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void scale(in float x, in float y, in float z); // multiply the matrix by passed scale values on the right
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void scale(in J3DVector3 v); // multiply the matrix by passed scale values on the right
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void rotate(in float angle, // multiply the matrix by passed rotation values on the right
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in float x, in float y, in float z); // (angle is in degrees)
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void rotate(in float angle, in J3DVector3 v); // multiply the matrix by passed rotation values on the right
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// (angle is in degrees)
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void multiply(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the right
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void divide(in float divisor); // divide the matrix by the passed divisor
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void ortho(in float left, in float right, // multiply the matrix by the passed ortho values on the right
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in float bottom, in float top,
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in float near, in float far);
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void frustum(in float left, in float right, // multiply the matrix by the passed frustum values on the right
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in float bottom, in float top,
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in float near, in float far);
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void perspective(in float fovy, in float aspect, // multiply the matrix by the passed perspective values on the right
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in float zNear, in float zFar);
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void lookat(in J3DVector3 eye, // multiply the matrix by the passed lookat
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in J3DVector3 center, in J3DVector3 up); // values on the right
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bool decompose(in J3DVector3 translate, // decompose the matrix into the passed vector
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in J3DVector3 rotate,
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in J3DVector3 scale,
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in J3DVector3 skew,
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in sequence<float> perspective);
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}
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[
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Constructor(in J3DVector3 vector), // copy passed vector into new J3DVector3
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Constructor(in sequence<float> array) // create new J3DVector3 with 3 floats from array
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Constructor(in float x, in float y, in float z) // create new J3DVector3 with 3 floats
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Constructor() // create new J3DVector3 with (0,0,0)
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]
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interface J3DVector3 {
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void load(in J3DVector3 vector); // copy the values from the passed vector
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void load(in sequence<float> array); // copy 3 floats into the vector from array
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void load(in float x, in float y, in float z); // copy 3 floats into the vector
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sequence<float> getAsArray(); // return the vector as an array of 3 floats
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Float32Array getAsFloat32Array(); // return the matrix as a Float32Array with 16 values
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void multMatrix(in J3DIMatrix4 matrix); // multiply the vector by the passed matrix (on the right)
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float vectorLength(); // return the length of the vector
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float dot(); // return the dot product of the vector
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void cross(in J3DVector3 v); // replace the vector with vector x v
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void divide(in float divisor); // divide the vector by the passed divisor
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}
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*/
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J3DIHasCSSMatrix = false;
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J3DIHasCSSMatrixCopy = false;
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/*
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if ("WebKitCSSMatrix" in window && ("media" in window && window.media.matchMedium("(-webkit-transform-3d)")) ||
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("styleMedia" in window && window.styleMedia.matchMedium("(-webkit-transform-3d)"))) {
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J3DIHasCSSMatrix = true;
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if ("copy" in WebKitCSSMatrix.prototype)
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J3DIHasCSSMatrixCopy = true;
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}
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*/
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// console.log("J3DIHasCSSMatrix="+J3DIHasCSSMatrix);
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// console.log("J3DIHasCSSMatrixCopy="+J3DIHasCSSMatrixCopy);
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//
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// J3DIMatrix4
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//
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J3DIMatrix4 = function(m)
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{
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if (J3DIHasCSSMatrix)
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this.$matrix = new WebKitCSSMatrix;
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else
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this.$matrix = new Object;
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if (typeof m == 'object') {
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if ("length" in m && m.length >= 16) {
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this.load(m);
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return;
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}
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else if (m instanceof J3DIMatrix4) {
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this.load(m);
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return;
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}
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}
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this.makeIdentity();
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}
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J3DIMatrix4.prototype.load = function()
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{
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if (arguments.length == 1 && typeof arguments[0] == 'object') {
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var matrix;
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if (arguments[0] instanceof J3DIMatrix4) {
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matrix = arguments[0].$matrix;
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this.$matrix.m11 = matrix.m11;
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this.$matrix.m12 = matrix.m12;
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this.$matrix.m13 = matrix.m13;
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this.$matrix.m14 = matrix.m14;
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this.$matrix.m21 = matrix.m21;
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this.$matrix.m22 = matrix.m22;
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this.$matrix.m23 = matrix.m23;
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this.$matrix.m24 = matrix.m24;
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this.$matrix.m31 = matrix.m31;
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this.$matrix.m32 = matrix.m32;
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this.$matrix.m33 = matrix.m33;
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this.$matrix.m34 = matrix.m34;
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this.$matrix.m41 = matrix.m41;
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this.$matrix.m42 = matrix.m42;
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this.$matrix.m43 = matrix.m43;
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this.$matrix.m44 = matrix.m44;
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return;
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}
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else
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matrix = arguments[0];
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if ("length" in matrix && matrix.length >= 16) {
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this.$matrix.m11 = matrix[0];
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this.$matrix.m12 = matrix[1];
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this.$matrix.m13 = matrix[2];
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this.$matrix.m14 = matrix[3];
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this.$matrix.m21 = matrix[4];
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this.$matrix.m22 = matrix[5];
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this.$matrix.m23 = matrix[6];
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this.$matrix.m24 = matrix[7];
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this.$matrix.m31 = matrix[8];
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this.$matrix.m32 = matrix[9];
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this.$matrix.m33 = matrix[10];
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this.$matrix.m34 = matrix[11];
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this.$matrix.m41 = matrix[12];
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this.$matrix.m42 = matrix[13];
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this.$matrix.m43 = matrix[14];
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this.$matrix.m44 = matrix[15];
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return;
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}
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}
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this.makeIdentity();
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}
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J3DIMatrix4.prototype.getAsArray = function()
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{
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return [
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this.$matrix.m11, this.$matrix.m12, this.$matrix.m13, this.$matrix.m14,
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this.$matrix.m21, this.$matrix.m22, this.$matrix.m23, this.$matrix.m24,
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this.$matrix.m31, this.$matrix.m32, this.$matrix.m33, this.$matrix.m34,
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this.$matrix.m41, this.$matrix.m42, this.$matrix.m43, this.$matrix.m44
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];
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}
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J3DIMatrix4.prototype.getAsFloat32Array = function()
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{
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if (J3DIHasCSSMatrixCopy) {
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var array = new Float32Array(16);
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this.$matrix.copy(array);
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return array;
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}
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return new Float32Array(this.getAsArray());
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}
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J3DIMatrix4.prototype.setUniform = function(ctx, loc, transpose)
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{
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if (J3DIMatrix4.setUniformArray == undefined) {
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J3DIMatrix4.setUniformWebGLArray = new Float32Array(16);
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J3DIMatrix4.setUniformArray = new Array(16);
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}
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if (J3DIHasCSSMatrixCopy)
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this.$matrix.copy(J3DIMatrix4.setUniformWebGLArray);
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else {
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J3DIMatrix4.setUniformArray[0] = this.$matrix.m11;
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J3DIMatrix4.setUniformArray[1] = this.$matrix.m12;
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J3DIMatrix4.setUniformArray[2] = this.$matrix.m13;
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J3DIMatrix4.setUniformArray[3] = this.$matrix.m14;
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J3DIMatrix4.setUniformArray[4] = this.$matrix.m21;
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J3DIMatrix4.setUniformArray[5] = this.$matrix.m22;
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J3DIMatrix4.setUniformArray[6] = this.$matrix.m23;
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J3DIMatrix4.setUniformArray[7] = this.$matrix.m24;
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J3DIMatrix4.setUniformArray[8] = this.$matrix.m31;
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J3DIMatrix4.setUniformArray[9] = this.$matrix.m32;
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J3DIMatrix4.setUniformArray[10] = this.$matrix.m33;
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J3DIMatrix4.setUniformArray[11] = this.$matrix.m34;
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J3DIMatrix4.setUniformArray[12] = this.$matrix.m41;
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J3DIMatrix4.setUniformArray[13] = this.$matrix.m42;
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J3DIMatrix4.setUniformArray[14] = this.$matrix.m43;
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J3DIMatrix4.setUniformArray[15] = this.$matrix.m44;
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J3DIMatrix4.setUniformWebGLArray.set(J3DIMatrix4.setUniformArray);
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}
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ctx.uniformMatrix4fv(loc, transpose, J3DIMatrix4.setUniformWebGLArray);
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}
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J3DIMatrix4.prototype.makeIdentity = function()
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{
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this.$matrix.m11 = 1;
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this.$matrix.m12 = 0;
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this.$matrix.m13 = 0;
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this.$matrix.m14 = 0;
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this.$matrix.m21 = 0;
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this.$matrix.m22 = 1;
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this.$matrix.m23 = 0;
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this.$matrix.m24 = 0;
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this.$matrix.m31 = 0;
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this.$matrix.m32 = 0;
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this.$matrix.m33 = 1;
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this.$matrix.m34 = 0;
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this.$matrix.m41 = 0;
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this.$matrix.m42 = 0;
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this.$matrix.m43 = 0;
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this.$matrix.m44 = 1;
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}
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J3DIMatrix4.prototype.transpose = function()
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{
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var tmp = this.$matrix.m12;
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this.$matrix.m12 = this.$matrix.m21;
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this.$matrix.m21 = tmp;
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tmp = this.$matrix.m13;
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this.$matrix.m13 = this.$matrix.m31;
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this.$matrix.m31 = tmp;
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tmp = this.$matrix.m14;
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this.$matrix.m14 = this.$matrix.m41;
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this.$matrix.m41 = tmp;
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tmp = this.$matrix.m23;
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this.$matrix.m23 = this.$matrix.m32;
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this.$matrix.m32 = tmp;
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tmp = this.$matrix.m24;
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this.$matrix.m24 = this.$matrix.m42;
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this.$matrix.m42 = tmp;
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tmp = this.$matrix.m34;
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this.$matrix.m34 = this.$matrix.m43;
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this.$matrix.m43 = tmp;
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}
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J3DIMatrix4.prototype.invert = function()
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{
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if (J3DIHasCSSMatrix) {
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this.$matrix = this.$matrix.inverse();
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return;
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}
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// Calculate the 4x4 determinant
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// If the determinant is zero,
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// then the inverse matrix is not unique.
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var det = this._determinant4x4();
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if (Math.abs(det) < 1e-8)
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return null;
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this._makeAdjoint();
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// Scale the adjoint matrix to get the inverse
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this.$matrix.m11 /= det;
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this.$matrix.m12 /= det;
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this.$matrix.m13 /= det;
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this.$matrix.m14 /= det;
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this.$matrix.m21 /= det;
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this.$matrix.m22 /= det;
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this.$matrix.m23 /= det;
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this.$matrix.m24 /= det;
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this.$matrix.m31 /= det;
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this.$matrix.m32 /= det;
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this.$matrix.m33 /= det;
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this.$matrix.m34 /= det;
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this.$matrix.m41 /= det;
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this.$matrix.m42 /= det;
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this.$matrix.m43 /= det;
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this.$matrix.m44 /= det;
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}
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J3DIMatrix4.prototype.translate = function(x,y,z)
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{
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if (typeof x == 'object' && "length" in x) {
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var t = x;
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x = t[0];
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y = t[1];
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z = t[2];
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}
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else {
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if (x == undefined)
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x = 0;
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if (y == undefined)
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y = 0;
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if (z == undefined)
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z = 0;
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}
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if (J3DIHasCSSMatrix) {
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this.$matrix = this.$matrix.translate(x, y, z);
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return;
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}
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var matrix = new J3DIMatrix4();
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matrix.$matrix.m41 = x;
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matrix.$matrix.m42 = y;
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matrix.$matrix.m43 = z;
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this.multiply(matrix);
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}
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J3DIMatrix4.prototype.scale = function(x,y,z)
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{
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if (typeof x == 'object' && "length" in x) {
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var t = x;
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x = t[0];
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y = t[1];
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z = t[2];
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}
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else {
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if (x == undefined)
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x = 1;
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if (z == undefined) {
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if (y == undefined) {
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y = x;
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z = x;
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}
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else
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z = 1;
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}
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else if (y == undefined)
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y = x;
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}
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if (J3DIHasCSSMatrix) {
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this.$matrix = this.$matrix.scale(x, y, z);
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return;
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}
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var matrix = new J3DIMatrix4();
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matrix.$matrix.m11 = x;
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matrix.$matrix.m22 = y;
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matrix.$matrix.m33 = z;
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this.multiply(matrix);
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}
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J3DIMatrix4.prototype.rotate = function(angle,x,y,z)
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{
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// Forms are (angle, x,y,z), (angle,vector), (angleX, angleY, angleZ), (angle)
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if (typeof x == 'object' && "length" in x) {
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var t = x;
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x = t[0];
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y = t[1];
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z = t[2];
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}
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else {
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if (arguments.length == 1) {
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x = 0;
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y = 0;
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z = 1;
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}
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else if (arguments.length == 3) {
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this.rotate(angle, 1,0,0); // about X axis
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this.rotate(x, 0,1,0); // about Y axis
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this.rotate(y, 0,0,1); // about Z axis
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return;
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}
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}
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if (J3DIHasCSSMatrix) {
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this.$matrix = this.$matrix.rotateAxisAngle(x, y, z, angle);
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return;
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}
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// angles are in degrees. Switch to radians
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angle = angle / 180 * Math.PI;
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angle /= 2;
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var sinA = Math.sin(angle);
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var cosA = Math.cos(angle);
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var sinA2 = sinA * sinA;
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// normalize
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var len = Math.sqrt(x * x + y * y + z * z);
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if (len == 0) {
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// bad vector, just use something reasonable
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x = 0;
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y = 0;
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z = 1;
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} else if (len != 1) {
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x /= len;
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y /= len;
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z /= len;
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}
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var mat = new J3DIMatrix4();
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// optimize case where axis is along major axis
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if (x == 1 && y == 0 && z == 0) {
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mat.$matrix.m11 = 1;
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mat.$matrix.m12 = 0;
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mat.$matrix.m13 = 0;
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mat.$matrix.m21 = 0;
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mat.$matrix.m22 = 1 - 2 * sinA2;
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mat.$matrix.m23 = 2 * sinA * cosA;
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mat.$matrix.m31 = 0;
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mat.$matrix.m32 = -2 * sinA * cosA;
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mat.$matrix.m33 = 1 - 2 * sinA2;
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mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
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mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
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mat.$matrix.m44 = 1;
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} else if (x == 0 && y == 1 && z == 0) {
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mat.$matrix.m11 = 1 - 2 * sinA2;
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mat.$matrix.m12 = 0;
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mat.$matrix.m13 = -2 * sinA * cosA;
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mat.$matrix.m21 = 0;
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mat.$matrix.m22 = 1;
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mat.$matrix.m23 = 0;
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mat.$matrix.m31 = 2 * sinA * cosA;
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mat.$matrix.m32 = 0;
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mat.$matrix.m33 = 1 - 2 * sinA2;
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mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
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mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
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mat.$matrix.m44 = 1;
|
|
} else if (x == 0 && y == 0 && z == 1) {
|
|
mat.$matrix.m11 = 1 - 2 * sinA2;
|
|
mat.$matrix.m12 = 2 * sinA * cosA;
|
|
mat.$matrix.m13 = 0;
|
|
mat.$matrix.m21 = -2 * sinA * cosA;
|
|
mat.$matrix.m22 = 1 - 2 * sinA2;
|
|
mat.$matrix.m23 = 0;
|
|
mat.$matrix.m31 = 0;
|
|
mat.$matrix.m32 = 0;
|
|
mat.$matrix.m33 = 1;
|
|
mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
|
|
mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
|
|
mat.$matrix.m44 = 1;
|
|
} else {
|
|
var x2 = x*x;
|
|
var y2 = y*y;
|
|
var z2 = z*z;
|
|
|
|
mat.$matrix.m11 = 1 - 2 * (y2 + z2) * sinA2;
|
|
mat.$matrix.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
|
|
mat.$matrix.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
|
|
mat.$matrix.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
|
|
mat.$matrix.m22 = 1 - 2 * (z2 + x2) * sinA2;
|
|
mat.$matrix.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
|
|
mat.$matrix.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
|
|
mat.$matrix.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
|
|
mat.$matrix.m33 = 1 - 2 * (x2 + y2) * sinA2;
|
|
mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
|
|
mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
|
|
mat.$matrix.m44 = 1;
|
|
}
|
|
this.multiply(mat);
|
|
}
|
|
|
|
J3DIMatrix4.prototype.multiply = function(mat)
|
|
{
|
|
if (J3DIHasCSSMatrix) {
|
|
this.$matrix = this.$matrix.multiply(mat.$matrix);
|
|
return;
|
|
}
|
|
|
|
var m11 = (mat.$matrix.m11 * this.$matrix.m11 + mat.$matrix.m12 * this.$matrix.m21
|
|
+ mat.$matrix.m13 * this.$matrix.m31 + mat.$matrix.m14 * this.$matrix.m41);
|
|
var m12 = (mat.$matrix.m11 * this.$matrix.m12 + mat.$matrix.m12 * this.$matrix.m22
|
|
+ mat.$matrix.m13 * this.$matrix.m32 + mat.$matrix.m14 * this.$matrix.m42);
|
|
var m13 = (mat.$matrix.m11 * this.$matrix.m13 + mat.$matrix.m12 * this.$matrix.m23
|
|
+ mat.$matrix.m13 * this.$matrix.m33 + mat.$matrix.m14 * this.$matrix.m43);
|
|
var m14 = (mat.$matrix.m11 * this.$matrix.m14 + mat.$matrix.m12 * this.$matrix.m24
|
|
+ mat.$matrix.m13 * this.$matrix.m34 + mat.$matrix.m14 * this.$matrix.m44);
|
|
|
|
var m21 = (mat.$matrix.m21 * this.$matrix.m11 + mat.$matrix.m22 * this.$matrix.m21
|
|
+ mat.$matrix.m23 * this.$matrix.m31 + mat.$matrix.m24 * this.$matrix.m41);
|
|
var m22 = (mat.$matrix.m21 * this.$matrix.m12 + mat.$matrix.m22 * this.$matrix.m22
|
|
+ mat.$matrix.m23 * this.$matrix.m32 + mat.$matrix.m24 * this.$matrix.m42);
|
|
var m23 = (mat.$matrix.m21 * this.$matrix.m13 + mat.$matrix.m22 * this.$matrix.m23
|
|
+ mat.$matrix.m23 * this.$matrix.m33 + mat.$matrix.m24 * this.$matrix.m43);
|
|
var m24 = (mat.$matrix.m21 * this.$matrix.m14 + mat.$matrix.m22 * this.$matrix.m24
|
|
+ mat.$matrix.m23 * this.$matrix.m34 + mat.$matrix.m24 * this.$matrix.m44);
|
|
|
|
var m31 = (mat.$matrix.m31 * this.$matrix.m11 + mat.$matrix.m32 * this.$matrix.m21
|
|
+ mat.$matrix.m33 * this.$matrix.m31 + mat.$matrix.m34 * this.$matrix.m41);
|
|
var m32 = (mat.$matrix.m31 * this.$matrix.m12 + mat.$matrix.m32 * this.$matrix.m22
|
|
+ mat.$matrix.m33 * this.$matrix.m32 + mat.$matrix.m34 * this.$matrix.m42);
|
|
var m33 = (mat.$matrix.m31 * this.$matrix.m13 + mat.$matrix.m32 * this.$matrix.m23
|
|
+ mat.$matrix.m33 * this.$matrix.m33 + mat.$matrix.m34 * this.$matrix.m43);
|
|
var m34 = (mat.$matrix.m31 * this.$matrix.m14 + mat.$matrix.m32 * this.$matrix.m24
|
|
+ mat.$matrix.m33 * this.$matrix.m34 + mat.$matrix.m34 * this.$matrix.m44);
|
|
|
|
var m41 = (mat.$matrix.m41 * this.$matrix.m11 + mat.$matrix.m42 * this.$matrix.m21
|
|
+ mat.$matrix.m43 * this.$matrix.m31 + mat.$matrix.m44 * this.$matrix.m41);
|
|
var m42 = (mat.$matrix.m41 * this.$matrix.m12 + mat.$matrix.m42 * this.$matrix.m22
|
|
+ mat.$matrix.m43 * this.$matrix.m32 + mat.$matrix.m44 * this.$matrix.m42);
|
|
var m43 = (mat.$matrix.m41 * this.$matrix.m13 + mat.$matrix.m42 * this.$matrix.m23
|
|
+ mat.$matrix.m43 * this.$matrix.m33 + mat.$matrix.m44 * this.$matrix.m43);
|
|
var m44 = (mat.$matrix.m41 * this.$matrix.m14 + mat.$matrix.m42 * this.$matrix.m24
|
|
+ mat.$matrix.m43 * this.$matrix.m34 + mat.$matrix.m44 * this.$matrix.m44);
|
|
|
|
this.$matrix.m11 = m11;
|
|
this.$matrix.m12 = m12;
|
|
this.$matrix.m13 = m13;
|
|
this.$matrix.m14 = m14;
|
|
|
|
this.$matrix.m21 = m21;
|
|
this.$matrix.m22 = m22;
|
|
this.$matrix.m23 = m23;
|
|
this.$matrix.m24 = m24;
|
|
|
|
this.$matrix.m31 = m31;
|
|
this.$matrix.m32 = m32;
|
|
this.$matrix.m33 = m33;
|
|
this.$matrix.m34 = m34;
|
|
|
|
this.$matrix.m41 = m41;
|
|
this.$matrix.m42 = m42;
|
|
this.$matrix.m43 = m43;
|
|
this.$matrix.m44 = m44;
|
|
}
|
|
|
|
J3DIMatrix4.prototype.divide = function(divisor)
|
|
{
|
|
this.$matrix.m11 /= divisor;
|
|
this.$matrix.m12 /= divisor;
|
|
this.$matrix.m13 /= divisor;
|
|
this.$matrix.m14 /= divisor;
|
|
|
|
this.$matrix.m21 /= divisor;
|
|
this.$matrix.m22 /= divisor;
|
|
this.$matrix.m23 /= divisor;
|
|
this.$matrix.m24 /= divisor;
|
|
|
|
this.$matrix.m31 /= divisor;
|
|
this.$matrix.m32 /= divisor;
|
|
this.$matrix.m33 /= divisor;
|
|
this.$matrix.m34 /= divisor;
|
|
|
|
this.$matrix.m41 /= divisor;
|
|
this.$matrix.m42 /= divisor;
|
|
this.$matrix.m43 /= divisor;
|
|
this.$matrix.m44 /= divisor;
|
|
|
|
}
|
|
|
|
J3DIMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
|
|
{
|
|
var tx = (left + right) / (left - right);
|
|
var ty = (top + bottom) / (top - bottom);
|
|
var tz = (far + near) / (far - near);
|
|
|
|
var matrix = new J3DIMatrix4();
|
|
matrix.$matrix.m11 = 2 / (left - right);
|
|
matrix.$matrix.m12 = 0;
|
|
matrix.$matrix.m13 = 0;
|
|
matrix.$matrix.m14 = 0;
|
|
matrix.$matrix.m21 = 0;
|
|
matrix.$matrix.m22 = 2 / (top - bottom);
|
|
matrix.$matrix.m23 = 0;
|
|
matrix.$matrix.m24 = 0;
|
|
matrix.$matrix.m31 = 0;
|
|
matrix.$matrix.m32 = 0;
|
|
matrix.$matrix.m33 = -2 / (far - near);
|
|
matrix.$matrix.m34 = 0;
|
|
matrix.$matrix.m41 = tx;
|
|
matrix.$matrix.m42 = ty;
|
|
matrix.$matrix.m43 = tz;
|
|
matrix.$matrix.m44 = 1;
|
|
|
|
this.multiply(matrix);
|
|
}
|
|
|
|
J3DIMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
|
|
{
|
|
var matrix = new J3DIMatrix4();
|
|
var A = (right + left) / (right - left);
|
|
var B = (top + bottom) / (top - bottom);
|
|
var C = -(far + near) / (far - near);
|
|
var D = -(2 * far * near) / (far - near);
|
|
|
|
matrix.$matrix.m11 = (2 * near) / (right - left);
|
|
matrix.$matrix.m12 = 0;
|
|
matrix.$matrix.m13 = 0;
|
|
matrix.$matrix.m14 = 0;
|
|
|
|
matrix.$matrix.m21 = 0;
|
|
matrix.$matrix.m22 = 2 * near / (top - bottom);
|
|
matrix.$matrix.m23 = 0;
|
|
matrix.$matrix.m24 = 0;
|
|
|
|
matrix.$matrix.m31 = A;
|
|
matrix.$matrix.m32 = B;
|
|
matrix.$matrix.m33 = C;
|
|
matrix.$matrix.m34 = -1;
|
|
|
|
matrix.$matrix.m41 = 0;
|
|
matrix.$matrix.m42 = 0;
|
|
matrix.$matrix.m43 = D;
|
|
matrix.$matrix.m44 = 0;
|
|
|
|
this.multiply(matrix);
|
|
}
|
|
|
|
J3DIMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
|
|
{
|
|
var top = Math.tan(fovy * Math.PI / 360) * zNear;
|
|
var bottom = -top;
|
|
var left = aspect * bottom;
|
|
var right = aspect * top;
|
|
this.frustum(left, right, bottom, top, zNear, zFar);
|
|
}
|
|
|
|
J3DIMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
|
|
{
|
|
if (typeof eyez == 'object' && "length" in eyez) {
|
|
var t = eyez;
|
|
upx = t[0];
|
|
upy = t[1];
|
|
upz = t[2];
|
|
|
|
t = eyey;
|
|
centerx = t[0];
|
|
centery = t[1];
|
|
centerz = t[2];
|
|
|
|
t = eyex;
|
|
eyex = t[0];
|
|
eyey = t[1];
|
|
eyez = t[2];
|
|
}
|
|
|
|
var matrix = new J3DIMatrix4();
|
|
|
|
// Make rotation matrix
|
|
|
|
// Z vector
|
|
var zx = eyex - centerx;
|
|
var zy = eyey - centery;
|
|
var zz = eyez - centerz;
|
|
var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
|
|
if (mag) {
|
|
zx /= mag;
|
|
zy /= mag;
|
|
zz /= mag;
|
|
}
|
|
|
|
// Y vector
|
|
var yx = upx;
|
|
var yy = upy;
|
|
var yz = upz;
|
|
|
|
// X vector = Y cross Z
|
|
xx = yy * zz - yz * zy;
|
|
xy = -yx * zz + yz * zx;
|
|
xz = yx * zy - yy * zx;
|
|
|
|
// Recompute Y = Z cross X
|
|
yx = zy * xz - zz * xy;
|
|
yy = -zx * xz + zz * xx;
|
|
yx = zx * xy - zy * xx;
|
|
|
|
// cross product gives area of parallelogram, which is < 1.0 for
|
|
// non-perpendicular unit-length vectors; so normalize x, y here
|
|
|
|
mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
|
|
if (mag) {
|
|
xx /= mag;
|
|
xy /= mag;
|
|
xz /= mag;
|
|
}
|
|
|
|
mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
|
|
if (mag) {
|
|
yx /= mag;
|
|
yy /= mag;
|
|
yz /= mag;
|
|
}
|
|
|
|
matrix.$matrix.m11 = xx;
|
|
matrix.$matrix.m12 = xy;
|
|
matrix.$matrix.m13 = xz;
|
|
matrix.$matrix.m14 = 0;
|
|
|
|
matrix.$matrix.m21 = yx;
|
|
matrix.$matrix.m22 = yy;
|
|
matrix.$matrix.m23 = yz;
|
|
matrix.$matrix.m24 = 0;
|
|
|
|
matrix.$matrix.m31 = zx;
|
|
matrix.$matrix.m32 = zy;
|
|
matrix.$matrix.m33 = zz;
|
|
matrix.$matrix.m34 = 0;
|
|
|
|
matrix.$matrix.m41 = 0;
|
|
matrix.$matrix.m42 = 0;
|
|
matrix.$matrix.m43 = 0;
|
|
matrix.$matrix.m44 = 1;
|
|
matrix.translate(-eyex, -eyey, -eyez);
|
|
|
|
this.multiply(matrix);
|
|
}
|
|
|
|
// Returns true on success, false otherwise. All params are Array objects
|
|
J3DIMatrix4.prototype.decompose = function(_translate, _rotate, _scale, _skew, _perspective)
|
|
{
|
|
// Normalize the matrix.
|
|
if (this.$matrix.m44 == 0)
|
|
return false;
|
|
|
|
// Gather the params
|
|
var translate, rotate, scale, skew, perspective;
|
|
|
|
var translate = (_translate == undefined || !("length" in _translate)) ? new J3DIVector3 : _translate;
|
|
var rotate = (_rotate == undefined || !("length" in _rotate)) ? new J3DIVector3 : _rotate;
|
|
var scale = (_scale == undefined || !("length" in _scale)) ? new J3DIVector3 : _scale;
|
|
var skew = (_skew == undefined || !("length" in _skew)) ? new J3DIVector3 : _skew;
|
|
var perspective = (_perspective == undefined || !("length" in _perspective)) ? new Array(4) : _perspective;
|
|
|
|
var matrix = new J3DIMatrix4(this);
|
|
|
|
matrix.divide(matrix.$matrix.m44);
|
|
|
|
// perspectiveMatrix is used to solve for perspective, but it also provides
|
|
// an easy way to test for singularity of the upper 3x3 component.
|
|
var perspectiveMatrix = new J3DIMatrix4(matrix);
|
|
|
|
perspectiveMatrix.$matrix.m14 = 0;
|
|
perspectiveMatrix.$matrix.m24 = 0;
|
|
perspectiveMatrix.$matrix.m34 = 0;
|
|
perspectiveMatrix.$matrix.m44 = 1;
|
|
|
|
if (perspectiveMatrix._determinant4x4() == 0)
|
|
return false;
|
|
|
|
// First, isolate perspective.
|
|
if (matrix.$matrix.m14 != 0 || matrix.$matrix.m24 != 0 || matrix.$matrix.m34 != 0) {
|
|
// rightHandSide is the right hand side of the equation.
|
|
var rightHandSide = [ matrix.$matrix.m14, matrix.$matrix.m24, matrix.$matrix.m34, matrix.$matrix.m44 ];
|
|
|
|
// Solve the equation by inverting perspectiveMatrix and multiplying
|
|
// rightHandSide by the inverse.
|
|
var inversePerspectiveMatrix = new J3DIMatrix4(perspectiveMatrix);
|
|
inversePerspectiveMatrix.invert();
|
|
var transposedInversePerspectiveMatrix = new J3DIMatrix4(inversePerspectiveMatrix);
|
|
transposedInversePerspectiveMatrix.transpose();
|
|
transposedInversePerspectiveMatrix.multVecMatrix(perspective, rightHandSide);
|
|
|
|
// Clear the perspective partition
|
|
matrix.$matrix.m14 = matrix.$matrix.m24 = matrix.$matrix.m34 = 0
|
|
matrix.$matrix.m44 = 1;
|
|
}
|
|
else {
|
|
// No perspective.
|
|
perspective[0] = perspective[1] = perspective[2] = 0;
|
|
perspective[3] = 1;
|
|
}
|
|
|
|
// Next take care of translation
|
|
translate[0] = matrix.$matrix.m41
|
|
matrix.$matrix.m41 = 0
|
|
translate[1] = matrix.$matrix.m42
|
|
matrix.$matrix.m42 = 0
|
|
translate[2] = matrix.$matrix.m43
|
|
matrix.$matrix.m43 = 0
|
|
|
|
// Now get scale and shear. 'row' is a 3 element array of 3 component vectors
|
|
var row0 = new J3DIVector3(matrix.$matrix.m11, matrix.$matrix.m12, matrix.$matrix.m13);
|
|
var row1 = new J3DIVector3(matrix.$matrix.m21, matrix.$matrix.m22, matrix.$matrix.m23);
|
|
var row2 = new J3DIVector3(matrix.$matrix.m31, matrix.$matrix.m32, matrix.$matrix.m33);
|
|
|
|
// Compute X scale factor and normalize first row.
|
|
scale[0] = row0.vectorLength();
|
|
row0.divide(scale[0]);
|
|
|
|
// Compute XY shear factor and make 2nd row orthogonal to 1st.
|
|
skew[0] = row0.dot(row1);
|
|
row1.combine(row0, 1.0, -skew[0]);
|
|
|
|
// Now, compute Y scale and normalize 2nd row.
|
|
scale[1] = row1.vectorLength();
|
|
row1.divide(scale[1]);
|
|
skew[0] /= scale[1];
|
|
|
|
// Compute XZ and YZ shears, orthogonalize 3rd row
|
|
skew[1] = row1.dot(row2);
|
|
row2.combine(row0, 1.0, -skew[1]);
|
|
skew[2] = row1.dot(row2);
|
|
row2.combine(row1, 1.0, -skew[2]);
|
|
|
|
// Next, get Z scale and normalize 3rd row.
|
|
scale[2] = row2.vectorLength();
|
|
row2.divide(scale[2]);
|
|
skew[1] /= scale[2];
|
|
skew[2] /= scale[2];
|
|
|
|
// At this point, the matrix (in rows) is orthonormal.
|
|
// Check for a coordinate system flip. If the determinant
|
|
// is -1, then negate the matrix and the scaling factors.
|
|
var pdum3 = new J3DIVector3(row1);
|
|
pdum3.cross(row2);
|
|
if (row0.dot(pdum3) < 0) {
|
|
for (i = 0; i < 3; i++) {
|
|
scale[i] *= -1;
|
|
row[0][i] *= -1;
|
|
row[1][i] *= -1;
|
|
row[2][i] *= -1;
|
|
}
|
|
}
|
|
|
|
// Now, get the rotations out
|
|
rotate[1] = Math.asin(-row0[2]);
|
|
if (Math.cos(rotate[1]) != 0) {
|
|
rotate[0] = Math.atan2(row1[2], row2[2]);
|
|
rotate[2] = Math.atan2(row0[1], row0[0]);
|
|
}
|
|
else {
|
|
rotate[0] = Math.atan2(-row2[0], row1[1]);
|
|
rotate[2] = 0;
|
|
}
|
|
|
|
// Convert rotations to degrees
|
|
var rad2deg = 180 / Math.PI;
|
|
rotate[0] *= rad2deg;
|
|
rotate[1] *= rad2deg;
|
|
rotate[2] *= rad2deg;
|
|
|
|
return true;
|
|
}
|
|
|
|
J3DIMatrix4.prototype._determinant2x2 = function(a, b, c, d)
|
|
{
|
|
return a * d - b * c;
|
|
}
|
|
|
|
J3DIMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
|
|
{
|
|
return a1 * this._determinant2x2(b2, b3, c2, c3)
|
|
- b1 * this._determinant2x2(a2, a3, c2, c3)
|
|
+ c1 * this._determinant2x2(a2, a3, b2, b3);
|
|
}
|
|
|
|
J3DIMatrix4.prototype._determinant4x4 = function()
|
|
{
|
|
var a1 = this.$matrix.m11;
|
|
var b1 = this.$matrix.m12;
|
|
var c1 = this.$matrix.m13;
|
|
var d1 = this.$matrix.m14;
|
|
|
|
var a2 = this.$matrix.m21;
|
|
var b2 = this.$matrix.m22;
|
|
var c2 = this.$matrix.m23;
|
|
var d2 = this.$matrix.m24;
|
|
|
|
var a3 = this.$matrix.m31;
|
|
var b3 = this.$matrix.m32;
|
|
var c3 = this.$matrix.m33;
|
|
var d3 = this.$matrix.m34;
|
|
|
|
var a4 = this.$matrix.m41;
|
|
var b4 = this.$matrix.m42;
|
|
var c4 = this.$matrix.m43;
|
|
var d4 = this.$matrix.m44;
|
|
|
|
return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4)
|
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- b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4)
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+ c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4)
|
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- d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
|
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}
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|
|
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J3DIMatrix4.prototype._makeAdjoint = function()
|
|
{
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var a1 = this.$matrix.m11;
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var b1 = this.$matrix.m12;
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var c1 = this.$matrix.m13;
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var d1 = this.$matrix.m14;
|
|
|
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var a2 = this.$matrix.m21;
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var b2 = this.$matrix.m22;
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var c2 = this.$matrix.m23;
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var d2 = this.$matrix.m24;
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|
|
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var a3 = this.$matrix.m31;
|
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var b3 = this.$matrix.m32;
|
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var c3 = this.$matrix.m33;
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var d3 = this.$matrix.m34;
|
|
|
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var a4 = this.$matrix.m41;
|
|
var b4 = this.$matrix.m42;
|
|
var c4 = this.$matrix.m43;
|
|
var d4 = this.$matrix.m44;
|
|
|
|
// Row column labeling reversed since we transpose rows & columns
|
|
this.$matrix.m11 = this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
|
|
this.$matrix.m21 = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
|
|
this.$matrix.m31 = this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
|
|
this.$matrix.m41 = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
|
|
|
|
this.$matrix.m12 = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
|
|
this.$matrix.m22 = this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
|
|
this.$matrix.m32 = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
|
|
this.$matrix.m42 = this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
|
|
|
|
this.$matrix.m13 = this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
|
|
this.$matrix.m23 = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
|
|
this.$matrix.m33 = this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
|
|
this.$matrix.m43 = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
|
|
|
|
this.$matrix.m14 = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
|
|
this.$matrix.m24 = this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
|
|
this.$matrix.m34 = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
|
|
this.$matrix.m44 = this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
|
|
}
|
|
|
|
//
|
|
// J3DIVector3
|
|
//
|
|
J3DIVector3 = function(x,y,z)
|
|
{
|
|
this.load(x,y,z);
|
|
}
|
|
|
|
J3DIVector3.prototype.load = function(x,y,z)
|
|
{
|
|
if (typeof x == 'object' && "length" in x) {
|
|
this[0] = x[0];
|
|
this[1] = x[1];
|
|
this[2] = x[2];
|
|
}
|
|
else if (typeof x == 'number') {
|
|
this[0] = x;
|
|
this[1] = y;
|
|
this[2] = z;
|
|
}
|
|
else {
|
|
this[0] = 0;
|
|
this[1] = 0;
|
|
this[2] = 0;
|
|
}
|
|
}
|
|
|
|
J3DIVector3.prototype.getAsArray = function()
|
|
{
|
|
return [ this[0], this[1], this[2] ];
|
|
}
|
|
|
|
J3DIVector3.prototype.getAsFloat32Array = function()
|
|
{
|
|
return new Float32Array(this.getAsArray());
|
|
}
|
|
|
|
J3DIVector3.prototype.vectorLength = function()
|
|
{
|
|
return Math.sqrt(this[0] * this[0] + this[1] * this[1] + this[2] * this[2]);
|
|
}
|
|
|
|
J3DIVector3.prototype.divide = function(divisor)
|
|
{
|
|
this[0] /= divisor; this[1] /= divisor; this[2] /= divisor;
|
|
}
|
|
|
|
J3DIVector3.prototype.cross = function(v)
|
|
{
|
|
this[0] = this[1] * v[2] - this[2] * v[1];
|
|
this[1] = -this[0] * v[2] + this[2] * v[0];
|
|
this[2] = this[0] * v[1] - this[1] * v[0];
|
|
}
|
|
|
|
J3DIVector3.prototype.dot = function(v)
|
|
{
|
|
return this[0] * v[0] + this[1] * v[1] + this[2] * v[2];
|
|
}
|
|
|
|
J3DIVector3.prototype.combine = function(v, ascl, bscl)
|
|
{
|
|
this[0] = (ascl * this[0]) + (bscl * v[0]);
|
|
this[1] = (ascl * this[1]) + (bscl * v[1]);
|
|
this[2] = (ascl * this[2]) + (bscl * v[2]);
|
|
}
|
|
|
|
J3DIVector3.prototype.multVecMatrix = function(matrix)
|
|
{
|
|
var x = this[0];
|
|
var y = this[1];
|
|
var z = this[2];
|
|
|
|
this[0] = matrix.$matrix.m41 + x * matrix.$matrix.m11 + y * matrix.$matrix.m21 + z * matrix.$matrix.m31;
|
|
this[1] = matrix.$matrix.m42 + x * matrix.$matrix.m12 + y * matrix.$matrix.m22 + z * matrix.$matrix.m32;
|
|
this[2] = matrix.$matrix.m43 + x * matrix.$matrix.m13 + y * matrix.$matrix.m23 + z * matrix.$matrix.m33;
|
|
var w = matrix.$matrix.m44 + x * matrix.$matrix.m14 + y * matrix.$matrix.m24 + z * matrix.$matrix.m34;
|
|
if (w != 1 && w != 0) {
|
|
this[0] /= w;
|
|
this[1] /= w;
|
|
this[2] /= w;
|
|
}
|
|
}
|
|
|
|
J3DIVector3.prototype.toString = function()
|
|
{
|
|
return "["+this[0]+","+this[1]+","+this[2]+"]";
|
|
}
|