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alchemist/js/J3DIMath.js
lhark a3979b9300 Ajout de transformations, css bootstrap 
Les fichiers de resources ont été bougés dans leur dossiers
propres (css, js, fonts).
La position de la souris dans le canvas est maintenant correcte quelle
que soit la position du canvas dans la page.
2017-12-09 23:53:20 -05:00

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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 (row 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 J3DVector3 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 J3DVector3 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 J3DVector3 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 J3DVector3 eye, // multiply the matrix by the passed lookat
in J3DVector3 center, in J3DVector3 up); // values on the right
bool decompose(in J3DVector3 translate, // decompose the matrix into the passed vector
in J3DVector3 rotate,
in J3DVector3 scale,
in J3DVector3 skew,
in sequence<float> perspective);
}
[
Constructor(in J3DVector3 vector), // copy passed vector into new J3DVector3
Constructor(in sequence<float> array) // create new J3DVector3 with 3 floats from array
Constructor(in float x, in float y, in float z) // create new J3DVector3 with 3 floats
Constructor() // create new J3DVector3 with (0,0,0)
]
interface J3DVector3 {
void load(in J3DVector3 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 matrix as a Float32Array with 16 values
void multMatrix(in J3DIMatrix4 matrix); // multiply the vector by the passed matrix (on the right)
float vectorLength(); // return the length of the vector
float dot(); // return the dot product of the vector
void cross(in J3DVector3 v); // replace the vector with 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;
}
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.transpose();
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)
- b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4)
+ c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4)
- d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
}
J3DIMatrix4.prototype._makeAdjoint = 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;
// 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]+"]";
}
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