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J3DIMath.js
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J3DIMath.js
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/*
* Copyright (C) 2009 Apple Inc. All Rights Reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. 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.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``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 APPLE INC. OR
* CONTRIBUTORS 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.
*/
// J3DI (Jedi) - A support library for WebGL.
/*
J3DI Math Classes. Currently includes:
J3DIMatrix4 - A 4x4 Matrix
*/
/*
J3DIMatrix4 class
This class implements a 4x4 matrix. It has functions which duplicate the
functionality of the OpenGL matrix stack and glut functions. On browsers
that support it, CSSMatrix is used to accelerate operations.
IDL:
[
Constructor(in J3DIMatrix4 matrix), // copy passed matrix into new J3DIMatrix4
Constructor(in sequence<float> array) // create new J3DIMatrix4 with 16 floats (column major)
Constructor() // create new J3DIMatrix4 with identity matrix
]
interface J3DIMatrix4 {
void load(in J3DIMatrix4 matrix); // copy the values from the passed matrix
void load(in sequence<float> array); // copy 16 floats into the matrix
sequence<float> getAsArray(); // return the matrix as an array of 16 floats
Float32Array getAsFloat32Array(); // return the matrix as a Float32Array with 16 values
void setUniform(in WebGLRenderingContext ctx, // Send the matrix to the passed uniform location in the passed context
in WebGLUniformLocation loc,
in boolean transpose);
void makeIdentity(); // replace the matrix with identity
void transpose(); // replace the matrix with its transpose
void invert(); // replace the matrix with its inverse
void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
void translate(in J3DIVector3 v); // multiply the matrix by passed translation values on the right
void scale(in float x, in float y, in float z); // multiply the matrix by passed scale values on the right
void scale(in J3DIVector3 v); // multiply the matrix by passed scale values on the right
void rotate(in float angle, // multiply the matrix by passed rotation values on the right
in float x, in float y, in float z); // (angle is in degrees)
void rotate(in float angle, in J3DIVector3 v); // multiply the matrix by passed rotation values on the right
// (angle is in degrees)
void multiply(in CanvasMatrix matrix); // multiply the matrix by the passed matrix on the right
void divide(in float divisor); // divide the matrix by the passed divisor
void ortho(in float left, in float right, // multiply the matrix by the passed ortho values on the right
in float bottom, in float top,
in float near, in float far);
void frustum(in float left, in float right, // multiply the matrix by the passed frustum values on the right
in float bottom, in float top,
in float near, in float far);
void perspective(in float fovy, in float aspect, // multiply the matrix by the passed perspective values on the right
in float zNear, in float zFar);
void lookat(in J3DIVector3 eye, // multiply the matrix by the passed lookat values on the right
in J3DIVector3 center, in J3DIVector3 up);
bool decompose(in J3DIVector3 translate, // decompose the matrix into the passed vectors
in J3DIVector3 rotate,
in J3DIVector3 scale,
in J3DIVector3 skew,
in sequence<float> perspective);
}
[
Constructor(in J3DIVector3 vector), // copy passed vector into new J3DIVector3
Constructor(in sequence<float> array) // create new J3DIVector3 with 3 floats from array
Constructor(in float x, in float y, in float z) // create new J3DIVector3 with 3 floats
Constructor() // create new J3DIVector3 with (0,0,0)
]
interface J3DIVector3 {
void load(in J3DIVector3 vector); // copy the values from the passed vector
void load(in sequence<float> array); // copy 3 floats into the vector from array
void load(in float x, in float y, in float z); // copy 3 floats into the vector
sequence<float> getAsArray(); // return the vector as an array of 3 floats
Float32Array getAsFloat32Array(); // return the vector as a Float32Array with 3 values
void multVecMatrix(in J3DIMatrix4 matrix); // transform the vector with the passed matrix containing a homogenous coordinate transform
float vectorLength(); // return the length of the vector
float dot(in J3DIVector3 v); // return the dot product vector . v
void cross(in J3DIVector3 v); // replace the vector with cross product vector x v
void divide(in float divisor); // divide the vector by the passed divisor
}
*/
J3DIHasCSSMatrix = false;
J3DIHasCSSMatrixCopy = false;
/*
if ("WebKitCSSMatrix" in window && ("media" in window && window.media.matchMedium("(-webkit-transform-3d)")) ||
("styleMedia" in window && window.styleMedia.matchMedium("(-webkit-transform-3d)"))) {
J3DIHasCSSMatrix = true;
if ("copy" in WebKitCSSMatrix.prototype)
J3DIHasCSSMatrixCopy = true;
}
*/
// console.log("J3DIHasCSSMatrix="+J3DIHasCSSMatrix);
// console.log("J3DIHasCSSMatrixCopy="+J3DIHasCSSMatrixCopy);
//
// J3DIMatrix4
//
J3DIMatrix4 = function(m)
{
if (J3DIHasCSSMatrix)
this.$matrix = new WebKitCSSMatrix;
else
this.$matrix = new Object;
if (typeof m == 'object') {
if ("length" in m && m.length >= 16) {
this.load(m);
return;
}
else if (m instanceof J3DIMatrix4) {
this.load(m);
return;
}
}
this.makeIdentity();
}
J3DIMatrix4.prototype.load = function()
{
if (arguments.length == 1 && typeof arguments[0] == 'object') {
var matrix;
if (arguments[0] instanceof J3DIMatrix4) {
matrix = arguments[0].$matrix;
this.$matrix.m11 = matrix.m11;
this.$matrix.m12 = matrix.m12;
this.$matrix.m13 = matrix.m13;
this.$matrix.m14 = matrix.m14;
this.$matrix.m21 = matrix.m21;
this.$matrix.m22 = matrix.m22;
this.$matrix.m23 = matrix.m23;
this.$matrix.m24 = matrix.m24;
this.$matrix.m31 = matrix.m31;
this.$matrix.m32 = matrix.m32;
this.$matrix.m33 = matrix.m33;
this.$matrix.m34 = matrix.m34;
this.$matrix.m41 = matrix.m41;
this.$matrix.m42 = matrix.m42;
this.$matrix.m43 = matrix.m43;
this.$matrix.m44 = matrix.m44;
return;
}
else
matrix = arguments[0];
if ("length" in matrix && matrix.length >= 16) {
this.$matrix.m11 = matrix[0];
this.$matrix.m12 = matrix[1];
this.$matrix.m13 = matrix[2];
this.$matrix.m14 = matrix[3];
this.$matrix.m21 = matrix[4];
this.$matrix.m22 = matrix[5];
this.$matrix.m23 = matrix[6];
this.$matrix.m24 = matrix[7];
this.$matrix.m31 = matrix[8];
this.$matrix.m32 = matrix[9];
this.$matrix.m33 = matrix[10];
this.$matrix.m34 = matrix[11];
this.$matrix.m41 = matrix[12];
this.$matrix.m42 = matrix[13];
this.$matrix.m43 = matrix[14];
this.$matrix.m44 = matrix[15];
return;
}
}
this.makeIdentity();
}
J3DIMatrix4.prototype.getAsArray = function()
{
return [
this.$matrix.m11, this.$matrix.m12, this.$matrix.m13, this.$matrix.m14,
this.$matrix.m21, this.$matrix.m22, this.$matrix.m23, this.$matrix.m24,
this.$matrix.m31, this.$matrix.m32, this.$matrix.m33, this.$matrix.m34,
this.$matrix.m41, this.$matrix.m42, this.$matrix.m43, this.$matrix.m44
];
}
J3DIMatrix4.prototype.getAsFloat32Array = function()
{
if (J3DIHasCSSMatrixCopy) {
var array = new Float32Array(16);
this.$matrix.copy(array);
return array;
}
return new Float32Array(this.getAsArray());
}
J3DIMatrix4.prototype.setUniform = function(ctx, loc, transpose)
{
if (J3DIMatrix4.setUniformArray == undefined) {
J3DIMatrix4.setUniformWebGLArray = new Float32Array(16);
J3DIMatrix4.setUniformArray = new Array(16);
}
if (J3DIHasCSSMatrixCopy)
this.$matrix.copy(J3DIMatrix4.setUniformWebGLArray);
else {
J3DIMatrix4.setUniformArray[0] = this.$matrix.m11;
J3DIMatrix4.setUniformArray[1] = this.$matrix.m12;
J3DIMatrix4.setUniformArray[2] = this.$matrix.m13;
J3DIMatrix4.setUniformArray[3] = this.$matrix.m14;
J3DIMatrix4.setUniformArray[4] = this.$matrix.m21;
J3DIMatrix4.setUniformArray[5] = this.$matrix.m22;
J3DIMatrix4.setUniformArray[6] = this.$matrix.m23;
J3DIMatrix4.setUniformArray[7] = this.$matrix.m24;
J3DIMatrix4.setUniformArray[8] = this.$matrix.m31;
J3DIMatrix4.setUniformArray[9] = this.$matrix.m32;
J3DIMatrix4.setUniformArray[10] = this.$matrix.m33;
J3DIMatrix4.setUniformArray[11] = this.$matrix.m34;
J3DIMatrix4.setUniformArray[12] = this.$matrix.m41;
J3DIMatrix4.setUniformArray[13] = this.$matrix.m42;
J3DIMatrix4.setUniformArray[14] = this.$matrix.m43;
J3DIMatrix4.setUniformArray[15] = this.$matrix.m44;
J3DIMatrix4.setUniformWebGLArray.set(J3DIMatrix4.setUniformArray);
}
ctx.uniformMatrix4fv(loc, transpose, J3DIMatrix4.setUniformWebGLArray);
}
J3DIMatrix4.prototype.makeIdentity = function()
{
this.$matrix.m11 = 1;
this.$matrix.m12 = 0;
this.$matrix.m13 = 0;
this.$matrix.m14 = 0;
this.$matrix.m21 = 0;
this.$matrix.m22 = 1;
this.$matrix.m23 = 0;
this.$matrix.m24 = 0;
this.$matrix.m31 = 0;
this.$matrix.m32 = 0;
this.$matrix.m33 = 1;
this.$matrix.m34 = 0;
this.$matrix.m41 = 0;
this.$matrix.m42 = 0;
this.$matrix.m43 = 0;
this.$matrix.m44 = 1;
}
J3DIMatrix4.prototype.transpose = function()
{
var tmp = this.$matrix.m12;
this.$matrix.m12 = this.$matrix.m21;
this.$matrix.m21 = tmp;
tmp = this.$matrix.m13;
this.$matrix.m13 = this.$matrix.m31;
this.$matrix.m31 = tmp;
tmp = this.$matrix.m14;
this.$matrix.m14 = this.$matrix.m41;
this.$matrix.m41 = tmp;
tmp = this.$matrix.m23;
this.$matrix.m23 = this.$matrix.m32;
this.$matrix.m32 = tmp;
tmp = this.$matrix.m24;
this.$matrix.m24 = this.$matrix.m42;
this.$matrix.m42 = tmp;
tmp = this.$matrix.m34;
this.$matrix.m34 = this.$matrix.m43;
this.$matrix.m43 = tmp;
}
J3DIMatrix4.prototype.invert = function()
{
if (J3DIHasCSSMatrix) {
this.$matrix = this.$matrix.inverse();
return;
}
// Calculate the 4x4 determinant
// If the determinant is zero,
// then the inverse matrix is not unique.
var det = this._determinant4x4();
if (Math.abs(det) < 1e-8)
return null;
this._makeAdjoint();
// Scale the adjoint matrix to get the inverse
this.$matrix.m11 /= det;
this.$matrix.m12 /= det;
this.$matrix.m13 /= det;
this.$matrix.m14 /= det;
this.$matrix.m21 /= det;
this.$matrix.m22 /= det;
this.$matrix.m23 /= det;
this.$matrix.m24 /= det;
this.$matrix.m31 /= det;
this.$matrix.m32 /= det;
this.$matrix.m33 /= det;
this.$matrix.m34 /= det;
this.$matrix.m41 /= det;
this.$matrix.m42 /= det;
this.$matrix.m43 /= det;
this.$matrix.m44 /= det;
}
J3DIMatrix4.prototype.translate = function(x,y,z)
{
if (typeof x == 'object' && "length" in x) {
var t = x;
x = t[0];
y = t[1];
z = t[2];
}
else {
if (x == undefined)
x = 0;
if (y == undefined)
y = 0;
if (z == undefined)
z = 0;
}
if (J3DIHasCSSMatrix) {
this.$matrix = this.$matrix.translate(x, y, z);
return;
}
var matrix = new J3DIMatrix4();
matrix.$matrix.m41 = x;
matrix.$matrix.m42 = y;
matrix.$matrix.m43 = z;
this.multiply(matrix);
}
J3DIMatrix4.prototype.scale = function(x,y,z)
{
if (typeof x == 'object' && "length" in x) {
var t = x;
x = t[0];
y = t[1];
z = t[2];
}
else {
if (x == undefined)
x = 1;
if (z == undefined) {
if (y == undefined) {
y = x;
z = x;
}
else
z = 1;
}
else if (y == undefined)
y = x;
}
if (J3DIHasCSSMatrix) {
this.$matrix = this.$matrix.scale(x, y, z);
return;
}
var matrix = new J3DIMatrix4();
matrix.$matrix.m11 = x;
matrix.$matrix.m22 = y;
matrix.$matrix.m33 = z;
this.multiply(matrix);
}
J3DIMatrix4.prototype.rotate = function(angle,x,y,z)
{
// Forms are (angle, x,y,z), (angle,vector), (angleX, angleY, angleZ), (angle)
if (typeof x == 'object' && "length" in x) {
var t = x;
x = t[0];
y = t[1];
z = t[2];
}
else {
if (arguments.length == 1) {
x = 0;
y = 0;
z = 1;
}
else if (arguments.length == 3) {
this.rotate(angle, 1,0,0); // about X axis
this.rotate(x, 0,1,0); // about Y axis
this.rotate(y, 0,0,1); // about Z axis
return;
}
}
if (J3DIHasCSSMatrix) {
this.$matrix = this.$matrix.rotateAxisAngle(x, y, z, angle);
return;
}
// angles are in degrees. Switch to radians
angle = angle / 180 * Math.PI;
angle /= 2;
var sinA = Math.sin(angle);
var cosA = Math.cos(angle);
var sinA2 = sinA * sinA;
// normalize
var len = Math.sqrt(x * x + y * y + z * z);
if (len == 0) {
// bad vector, just use something reasonable
x = 0;
y = 0;
z = 1;
} else if (len != 1) {
x /= len;
y /= len;
z /= len;
}
var mat = new J3DIMatrix4();
// optimize case where axis is along major axis
if (x == 1 && y == 0 && z == 0) {
mat.$matrix.m11 = 1;
mat.$matrix.m12 = 0;
mat.$matrix.m13 = 0;
mat.$matrix.m21 = 0;
mat.$matrix.m22 = 1 - 2 * sinA2;
mat.$matrix.m23 = 2 * sinA * cosA;
mat.$matrix.m31 = 0;
mat.$matrix.m32 = -2 * sinA * cosA;
mat.$matrix.m33 = 1 - 2 * sinA2;
mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
mat.$matrix.m44 = 1;
} else if (x == 0 && y == 1 && z == 0) {
mat.$matrix.m11 = 1 - 2 * sinA2;
mat.$matrix.m12 = 0;
mat.$matrix.m13 = -2 * sinA * cosA;
mat.$matrix.m21 = 0;
mat.$matrix.m22 = 1;
mat.$matrix.m23 = 0;
mat.$matrix.m31 = 2 * sinA * cosA;
mat.$matrix.m32 = 0;
mat.$matrix.m33 = 1 - 2 * sinA2;
mat.$matrix.m14 = mat.$matrix.m24 = mat.$matrix.m34 = 0;
mat.$matrix.m41 = mat.$matrix.m42 = mat.$matrix.m43 = 0;
mat.$matrix.m44 = 1;
} else if (x == 0 && y == 0 && z == 1) {
mat.$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;
}
// Note that m12 is the value in the first column and second row, etc.
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;
yz = 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);
}
// Decompose the matrix to the passed vectors. Returns true on success, false
// otherwise. All params are Array objects.
// Based on James Arvo: Graphics Gems II section VII. 1 Decomposing a matrix
// into simple transformations. Source code here:
// http://tog.acm.org/resources/GraphicsGems/gemsii/unmatrix.c
// The rotation decomposition code in the book is incorrect, official errata
// is here: http://tog.acm.org/resources/GraphicsGems/Errata.GraphicsGemsII
//
// This code has completely re-derived rotation decomposition since the book
// has different conventions for the handedness of rotations, and the
// explanation in the errata is not very thorough either.
//
// Rotation matrix Rx * Ry * Rz = rotate(A, B, C)
//
// [ 1 0 0 ] [ cos(B) 0 sin(B) ] [ cos(C) -sin(C) 0 ]
// = | 0 cos(A) -sin(A) | * | 0 1 0 | * | sin(C) cos(C) 0 |
// [ 0 sin(A) cos(A) ] [ -sin(B) 0 cos(B) ] [ 0 0 1 ]
//
// [ cos(B)*cos(C) -cos(B)*sin(C) sin(B) ]
// = | sin(A)*sin(B)*cos(C) + cos(A)*sin(C) -sin(A)*sin(B)*sin(C) + cos(A)*cos(C) -sin(A)*cos(B) |
// [ -cos(A)*sin(B)*cos(C) + sin(A)*sin(C) cos(A)*sin(B)*sin(C) + sin(A)*cos(C) cos(A)*cos(B) ]
//
// From here, we easily get B = asin(m31) (note that this class is using
// atypical notation where m31 corresponds to third column and first row, and
// code also uses "row" to mean "column" as it is usually used with matrices).
//
// This corresponds to the matrix above:
// [ m11 m21 m31 ]
// | m12 m22 m32 |
// [ m13 m23 m33 ]
//
// Now, if cos(B) != 0, C is easily derived from m11, m21, and A is equally
// easily derived from m32 and m33:
//
// m32 / m33 = (-sin(A) * cos(B)) / (cos(A) * cos(B))
// -m32 / m33 = sin(A) / cos(A)
// -m32 / m33 = tan(A)
// => A = atan2(-m32, m33)
//
// And similarly for C.
//
// If cos(B) = 0, things get more interesting:
//
// let b = sin(B) = +-1
//
// Let's handle cases where b = 1 and b = -1 separately.
//
// b = 1
// ============================================================================
// m12 + m23 = sin(A) * b * cos(C) + cos(A) * sin(C) + cos(A) * b * sin(C) + sin(A) * cos(C)
// m12 + m23 = sin(A + C) + b * sin(A + C)
// m12 + m23 = (b + 1) * sin(A + C)
// => A = asin((m12 + m23) / (b + 1)) - C
//
// b = -1
// ============================================================================
// m13 + m22 = -cos(A) * b * cos(C) + sin(A) * sin(C) - sin(A) * b * sin(C) + cos(A) * cos(C)
// m13 + m22 = cos(A - C) - b * cos(A - C)
// m13 + m22 = (1 - b) * cos(A - C)
// => A = acos((m13 + m22) / (1 - b)) + C
//
// Technically, these aren't complete solutions for A because of periodicity,
// but we're only interested in one solution.
//
// As long as A is solved as above, C can be chosen arbitrarily. Proof for
// this is omitted.
//
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(row2[0]);
if (Math.cos(rotate[1]) != 0) {
rotate[0] = Math.atan2(-row2[1], row2[2]);
rotate[2] = Math.atan2(-row1[0], row0[0]);
}
else {
rotate[2] = 0; // arbitrary in this case
var b = Math.sin(rotate[1]);
if (b < 0) {
// b == -1
rotate[0] = Math.acos((row0[2] + row1[1]) / (1 - b)) + rotate[2];
} else {
// b == 1
rotate[0] = Math.asin((row1[2] + row0[1]) / (b + 1)) - rotate[2];
}
}
// 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;