markgojs
Version:
Interactive diagrams, charts, and graphs, such as trees, flowcharts, orgcharts, UML, BPMN, or business diagrams
374 lines (311 loc) • 14 kB
JavaScript
/*
* Copyright (c) 2009, Mozilla Corp
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the <organization> nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY <copyright holder> ''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 <copyright holder> BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Based on sample code from the OpenGL(R) ES 2.0 Programming Guide, which carriers
* the following header:
*
* Book: OpenGL(R) ES 2.0 Programming Guide
* Authors: Aaftab Munshi, Dan Ginsburg, Dave Shreiner
* ISBN-10: 0321502795
* ISBN-13: 9780321502797
* Publisher: Addison-Wesley Professional
* URLs: http://safari.informit.com/9780321563835
* http://www.opengles-book.com
*/
//
// A simple 4x4 Matrix utility class
//
function Matrix4x4() {
this.elements = Array(16);
this.loadIdentity();
}
Matrix4x4.prototype = {
scale: function (sx, sy, sz) {
this.elements[0*4+0] *= sx;
this.elements[0*4+1] *= sx;
this.elements[0*4+2] *= sx;
this.elements[0*4+3] *= sx;
this.elements[1*4+0] *= sy;
this.elements[1*4+1] *= sy;
this.elements[1*4+2] *= sy;
this.elements[1*4+3] *= sy;
this.elements[2*4+0] *= sz;
this.elements[2*4+1] *= sz;
this.elements[2*4+2] *= sz;
this.elements[2*4+3] *= sz;
return this;
},
translate: function (tx, ty, tz) {
this.elements[3*4+0] += this.elements[0*4+0] * tx + this.elements[1*4+0] * ty + this.elements[2*4+0] * tz;
this.elements[3*4+1] += this.elements[0*4+1] * tx + this.elements[1*4+1] * ty + this.elements[2*4+1] * tz;
this.elements[3*4+2] += this.elements[0*4+2] * tx + this.elements[1*4+2] * ty + this.elements[2*4+2] * tz;
this.elements[3*4+3] += this.elements[0*4+3] * tx + this.elements[1*4+3] * ty + this.elements[2*4+3] * tz;
return this;
},
rotate: function (angle, x, y, z) {
var mag = Math.sqrt(x*x + y*y + z*z);
var sinAngle = Math.sin(angle * Math.PI / 180.0);
var cosAngle = Math.cos(angle * Math.PI / 180.0);
if (mag > 0) {
var xx, yy, zz, xy, yz, zx, xs, ys, zs;
var oneMinusCos;
var rotMat;
x /= mag;
y /= mag;
z /= mag;
xx = x * x;
yy = y * y;
zz = z * z;
xy = x * y;
yz = y * z;
zx = z * x;
xs = x * sinAngle;
ys = y * sinAngle;
zs = z * sinAngle;
oneMinusCos = 1.0 - cosAngle;
rotMat = new Matrix4x4();
rotMat.elements[0*4+0] = (oneMinusCos * xx) + cosAngle;
rotMat.elements[0*4+1] = (oneMinusCos * xy) - zs;
rotMat.elements[0*4+2] = (oneMinusCos * zx) + ys;
rotMat.elements[0*4+3] = 0.0;
rotMat.elements[1*4+0] = (oneMinusCos * xy) + zs;
rotMat.elements[1*4+1] = (oneMinusCos * yy) + cosAngle;
rotMat.elements[1*4+2] = (oneMinusCos * yz) - xs;
rotMat.elements[1*4+3] = 0.0;
rotMat.elements[2*4+0] = (oneMinusCos * zx) - ys;
rotMat.elements[2*4+1] = (oneMinusCos * yz) + xs;
rotMat.elements[2*4+2] = (oneMinusCos * zz) + cosAngle;
rotMat.elements[2*4+3] = 0.0;
rotMat.elements[3*4+0] = 0.0;
rotMat.elements[3*4+1] = 0.0;
rotMat.elements[3*4+2] = 0.0;
rotMat.elements[3*4+3] = 1.0;
rotMat = rotMat.multiply(this);
this.elements = rotMat.elements;
}
return this;
},
frustum: function (left, right, bottom, top, nearZ, farZ) {
var deltaX = right - left;
var deltaY = top - bottom;
var deltaZ = farZ - nearZ;
var frust;
if ( (nearZ <= 0.0) || (farZ <= 0.0) ||
(deltaX <= 0.0) || (deltaY <= 0.0) || (deltaZ <= 0.0) )
return this;
frust = new Matrix4x4();
frust.elements[0*4+0] = 2.0 * nearZ / deltaX;
frust.elements[0*4+1] = frust.elements[0*4+2] = frust.elements[0*4+3] = 0.0;
frust.elements[1*4+1] = 2.0 * nearZ / deltaY;
frust.elements[1*4+0] = frust.elements[1*4+2] = frust.elements[1*4+3] = 0.0;
frust.elements[2*4+0] = (right + left) / deltaX;
frust.elements[2*4+1] = (top + bottom) / deltaY;
frust.elements[2*4+2] = -(nearZ + farZ) / deltaZ;
frust.elements[2*4+3] = -1.0;
frust.elements[3*4+2] = -2.0 * nearZ * farZ / deltaZ;
frust.elements[3*4+0] = frust.elements[3*4+1] = frust.elements[3*4+3] = 0.0;
frust = frust.multiply(this);
this.elements = frust.elements;
return this;
},
perspective: function (fovy, aspect, nearZ, farZ) {
var frustumH = Math.tan(fovy / 360.0 * Math.PI) * nearZ;
var frustumW = frustumH * aspect;
return this.frustum(-frustumW, frustumW, -frustumH, frustumH, nearZ, farZ);
},
ortho: function (left, right, bottom, top, nearZ, farZ) {
var deltaX = right - left;
var deltaY = top - bottom;
var deltaZ = farZ - nearZ;
var ortho = new Matrix4x4();
if ( (deltaX == 0.0) || (deltaY == 0.0) || (deltaZ == 0.0) )
return this;
ortho.elements[0*4+0] = 2.0 / deltaX;
ortho.elements[3*4+0] = -(right + left) / deltaX;
ortho.elements[1*4+1] = 2.0 / deltaY;
ortho.elements[3*4+1] = -(top + bottom) / deltaY;
ortho.elements[2*4+2] = -2.0 / deltaZ;
ortho.elements[3*4+2] = -(nearZ + farZ) / deltaZ;
ortho = ortho.multiply(this);
this.elements = ortho.elements;
return this;
},
multiply: function (right) {
var tmp = new Matrix4x4();
for (var i = 0; i < 4; i++) {
tmp.elements[i*4+0] =
(this.elements[i*4+0] * right.elements[0*4+0]) +
(this.elements[i*4+1] * right.elements[1*4+0]) +
(this.elements[i*4+2] * right.elements[2*4+0]) +
(this.elements[i*4+3] * right.elements[3*4+0]) ;
tmp.elements[i*4+1] =
(this.elements[i*4+0] * right.elements[0*4+1]) +
(this.elements[i*4+1] * right.elements[1*4+1]) +
(this.elements[i*4+2] * right.elements[2*4+1]) +
(this.elements[i*4+3] * right.elements[3*4+1]) ;
tmp.elements[i*4+2] =
(this.elements[i*4+0] * right.elements[0*4+2]) +
(this.elements[i*4+1] * right.elements[1*4+2]) +
(this.elements[i*4+2] * right.elements[2*4+2]) +
(this.elements[i*4+3] * right.elements[3*4+2]) ;
tmp.elements[i*4+3] =
(this.elements[i*4+0] * right.elements[0*4+3]) +
(this.elements[i*4+1] * right.elements[1*4+3]) +
(this.elements[i*4+2] * right.elements[2*4+3]) +
(this.elements[i*4+3] * right.elements[3*4+3]) ;
}
this.elements = tmp.elements;
return this;
},
copy: function () {
var tmp = new Matrix4x4();
for (var i = 0; i < 16; i++) {
tmp.elements[i] = this.elements[i];
}
return tmp;
},
get: function (row, col) {
return this.elements[4*row+col];
},
// In-place inversion
invert: function () {
var tmp_0 = this.get(2,2) * this.get(3,3);
var tmp_1 = this.get(3,2) * this.get(2,3);
var tmp_2 = this.get(1,2) * this.get(3,3);
var tmp_3 = this.get(3,2) * this.get(1,3);
var tmp_4 = this.get(1,2) * this.get(2,3);
var tmp_5 = this.get(2,2) * this.get(1,3);
var tmp_6 = this.get(0,2) * this.get(3,3);
var tmp_7 = this.get(3,2) * this.get(0,3);
var tmp_8 = this.get(0,2) * this.get(2,3);
var tmp_9 = this.get(2,2) * this.get(0,3);
var tmp_10 = this.get(0,2) * this.get(1,3);
var tmp_11 = this.get(1,2) * this.get(0,3);
var tmp_12 = this.get(2,0) * this.get(3,1);
var tmp_13 = this.get(3,0) * this.get(2,1);
var tmp_14 = this.get(1,0) * this.get(3,1);
var tmp_15 = this.get(3,0) * this.get(1,1);
var tmp_16 = this.get(1,0) * this.get(2,1);
var tmp_17 = this.get(2,0) * this.get(1,1);
var tmp_18 = this.get(0,0) * this.get(3,1);
var tmp_19 = this.get(3,0) * this.get(0,1);
var tmp_20 = this.get(0,0) * this.get(2,1);
var tmp_21 = this.get(2,0) * this.get(0,1);
var tmp_22 = this.get(0,0) * this.get(1,1);
var tmp_23 = this.get(1,0) * this.get(0,1);
var t0 = ((tmp_0 * this.get(1,1) + tmp_3 * this.get(2,1) + tmp_4 * this.get(3,1)) -
(tmp_1 * this.get(1,1) + tmp_2 * this.get(2,1) + tmp_5 * this.get(3,1)));
var t1 = ((tmp_1 * this.get(0,1) + tmp_6 * this.get(2,1) + tmp_9 * this.get(3,1)) -
(tmp_0 * this.get(0,1) + tmp_7 * this.get(2,1) + tmp_8 * this.get(3,1)));
var t2 = ((tmp_2 * this.get(0,1) + tmp_7 * this.get(1,1) + tmp_10 * this.get(3,1)) -
(tmp_3 * this.get(0,1) + tmp_6 * this.get(1,1) + tmp_11 * this.get(3,1)));
var t3 = ((tmp_5 * this.get(0,1) + tmp_8 * this.get(1,1) + tmp_11 * this.get(2,1)) -
(tmp_4 * this.get(0,1) + tmp_9 * this.get(1,1) + tmp_10 * this.get(2,1)));
var d = 1.0 / (this.get(0,0) * t0 + this.get(1,0) * t1 + this.get(2,0) * t2 + this.get(3,0) * t3);
var out_00 = d * t0;
var out_01 = d * t1;
var out_02 = d * t2;
var out_03 = d * t3;
var out_10 = d * ((tmp_1 * this.get(1,0) + tmp_2 * this.get(2,0) + tmp_5 * this.get(3,0)) -
(tmp_0 * this.get(1,0) + tmp_3 * this.get(2,0) + tmp_4 * this.get(3,0)));
var out_11 = d * ((tmp_0 * this.get(0,0) + tmp_7 * this.get(2,0) + tmp_8 * this.get(3,0)) -
(tmp_1 * this.get(0,0) + tmp_6 * this.get(2,0) + tmp_9 * this.get(3,0)));
var out_12 = d * ((tmp_3 * this.get(0,0) + tmp_6 * this.get(1,0) + tmp_11 * this.get(3,0)) -
(tmp_2 * this.get(0,0) + tmp_7 * this.get(1,0) + tmp_10 * this.get(3,0)));
var out_13 = d * ((tmp_4 * this.get(0,0) + tmp_9 * this.get(1,0) + tmp_10 * this.get(2,0)) -
(tmp_5 * this.get(0,0) + tmp_8 * this.get(1,0) + tmp_11 * this.get(2,0)));
var out_20 = d * ((tmp_12 * this.get(1,3) + tmp_15 * this.get(2,3) + tmp_16 * this.get(3,3)) -
(tmp_13 * this.get(1,3) + tmp_14 * this.get(2,3) + tmp_17 * this.get(3,3)));
var out_21 = d * ((tmp_13 * this.get(0,3) + tmp_18 * this.get(2,3) + tmp_21 * this.get(3,3)) -
(tmp_12 * this.get(0,3) + tmp_19 * this.get(2,3) + tmp_20 * this.get(3,3)));
var out_22 = d * ((tmp_14 * this.get(0,3) + tmp_19 * this.get(1,3) + tmp_22 * this.get(3,3)) -
(tmp_15 * this.get(0,3) + tmp_18 * this.get(1,3) + tmp_23 * this.get(3,3)));
var out_23 = d * ((tmp_17 * this.get(0,3) + tmp_20 * this.get(1,3) + tmp_23 * this.get(2,3)) -
(tmp_16 * this.get(0,3) + tmp_21 * this.get(1,3) + tmp_22 * this.get(2,3)));
var out_30 = d * ((tmp_14 * this.get(2,2) + tmp_17 * this.get(3,2) + tmp_13 * this.get(1,2)) -
(tmp_16 * this.get(3,2) + tmp_12 * this.get(1,2) + tmp_15 * this.get(2,2)));
var out_31 = d * ((tmp_20 * this.get(3,2) + tmp_12 * this.get(0,2) + tmp_19 * this.get(2,2)) -
(tmp_18 * this.get(2,2) + tmp_21 * this.get(3,2) + tmp_13 * this.get(0,2)));
var out_32 = d * ((tmp_18 * this.get(1,2) + tmp_23 * this.get(3,2) + tmp_15 * this.get(0,2)) -
(tmp_22 * this.get(3,2) + tmp_14 * this.get(0,2) + tmp_19 * this.get(1,2)));
var out_33 = d * ((tmp_22 * this.get(2,2) + tmp_16 * this.get(0,2) + tmp_21 * this.get(1,2)) -
(tmp_20 * this.get(1,2) + tmp_23 * this.get(2,2) + tmp_17 * this.get(0,2)));
this.elements[0*4+0] = out_00;
this.elements[0*4+1] = out_01;
this.elements[0*4+2] = out_02;
this.elements[0*4+3] = out_03;
this.elements[1*4+0] = out_10;
this.elements[1*4+1] = out_11;
this.elements[1*4+2] = out_12;
this.elements[1*4+3] = out_13;
this.elements[2*4+0] = out_20;
this.elements[2*4+1] = out_21;
this.elements[2*4+2] = out_22;
this.elements[2*4+3] = out_23;
this.elements[3*4+0] = out_30;
this.elements[3*4+1] = out_31;
this.elements[3*4+2] = out_32;
this.elements[3*4+3] = out_33;
return this;
},
// Returns new matrix which is the inverse of this
inverse: function () {
var tmp = this.copy();
return tmp.invert();
},
// In-place transpose
transpose: function () {
var tmp = this.elements[0*4+1];
this.elements[0*4+1] = this.elements[1*4+0];
this.elements[1*4+0] = tmp;
tmp = this.elements[0*4+2];
this.elements[0*4+2] = this.elements[2*4+0];
this.elements[2*4+0] = tmp;
tmp = this.elements[0*4+3];
this.elements[0*4+3] = this.elements[3*4+0];
this.elements[3*4+0] = tmp;
tmp = this.elements[1*4+2];
this.elements[1*4+2] = this.elements[2*4+1];
this.elements[2*4+1] = tmp;
tmp = this.elements[1*4+3];
this.elements[1*4+3] = this.elements[3*4+1];
this.elements[3*4+1] = tmp;
tmp = this.elements[2*4+3];
this.elements[2*4+3] = this.elements[3*4+2];
this.elements[3*4+2] = tmp;
return this;
},
loadIdentity: function () {
for (var i = 0; i < 16; i++)
this.elements[i] = 0;
this.elements[0*4+0] = 1.0;
this.elements[1*4+1] = 1.0;
this.elements[2*4+2] = 1.0;
this.elements[3*4+3] = 1.0;
return this;
}
};