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mjs.js
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mjs.js
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/*
* Copyright (c) 2010 Mozilla Corporation
* Copyright (c) 2010 Vladimir Vukicevic
* Modifications 2014 Lucas Doyle
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/
//
// #mjs
//
// https://github.com/Stonelinks/mjs
//
// Vector and Matrix math utilities for JavaScript, optimized for WebGL.
//
// amd support
define([], function() {
//
// ##Constant: MJS_VERSION
//
// mjs version number encoded as a string
//
const MJS_VERSION = '0.0.5';
//
// ##Constant: MJS_FLOAT_ARRAY_TYPE
//
// The base float array type. By default, WebGLFloatArray.
//
// mjs can work with any array-like elements, but if an array
// creation is requested, it will create an array of the type
// MJS_FLOAT_ARRAY_TYPE. Also, the builtin constants such as (M4x4.I)
// will be of this type.
//
const MJS_FLOAT_ARRAY_TYPE = Float64Array;
function MathUtils_assert(cond, msg) {
if (!cond)
throw "Assertion failed: " + msg;
}
//
// #Class V3
//
// Methods for working with 3-element vectors. A vector is represented by a 3-element array.
// Any valid JavaScript array type may be used, but if new
// vectors are created they are created using the configured MJS_FLOAT_ARRAY_TYPE.
//
var V3 = { };
V3._temp1 = new MJS_FLOAT_ARRAY_TYPE(3);
V3._temp2 = new MJS_FLOAT_ARRAY_TYPE(3);
V3._temp3 = new MJS_FLOAT_ARRAY_TYPE(3);
if (MJS_FLOAT_ARRAY_TYPE == Array) {
V3.x = [1.0, 0.0, 0.0];
V3.y = [0.0, 1.0, 0.0];
V3.z = [0.0, 0.0, 1.0];
V3.$ = function V3_$(x, y, z) {
return [x, y, z];
};
V3.clone = function V3_clone(a) {
MathUtils_assert(a.length == 3, "a.length == 3");
return [a[0], a[1], a[2]];
};
} else {
V3.x = new MJS_FLOAT_ARRAY_TYPE([1.0, 0.0, 0.0]);
V3.y = new MJS_FLOAT_ARRAY_TYPE([0.0, 1.0, 0.0]);
V3.z = new MJS_FLOAT_ARRAY_TYPE([0.0, 0.0, 1.0]);
//
// ##Function: V3.$
//
// Creates a new 3-element vector with the given values.
//
// **Parameters:**
//
// - **x, y, z** - the 3 elements of the new vector.
//
// **Returns:**
//
// A new vector containing with the given argument values.
//
V3.$ = function V3_$(x, y, z) {
return new MJS_FLOAT_ARRAY_TYPE([x, y, z]);
};
//
// ##Function: V3.clone
//
// Clone the given 3-element vector.
//
// **Parameters:**
//
// - **a** - the 3-element vector to clone
//
// **Returns:**
//
// A new vector with the same values as the passed-in one.
//
V3.clone = function V3_clone(a) {
MathUtils_assert(a.length == 3, "a.length == 3");
return new MJS_FLOAT_ARRAY_TYPE(a);
};
}
V3.u = V3.x;
V3.v = V3.y;
//
// ##Function: V3.add
//
// Perform r = a + b.
//
// **Parameters:**
//
// - **a** - the first vector operand
// - **b** - the second vector operand
// - **r** - optional vector to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3-element vector with the result.
//
V3.add = function V3_add(a, b, r) {
MathUtils_assert(a.length == 3, "a.length == 3");
MathUtils_assert(b.length == 3, "b.length == 3");
MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(3);
r[0] = a[0] + b[0];
r[1] = a[1] + b[1];
r[2] = a[2] + b[2];
return r;
};
//
// ##Function: V3.sub
//
// Perform
// r = a - b.
//
// **Parameters:**
//
// - **a** - the first vector operand
// - **b** - the second vector operand
// - **r** - optional vector to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3-element vector with the result.
//
V3.sub = function V3_sub(a, b, r) {
MathUtils_assert(a.length == 3, "a.length == 3");
MathUtils_assert(b.length == 3, "b.length == 3");
MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(3);
r[0] = a[0] - b[0];
r[1] = a[1] - b[1];
r[2] = a[2] - b[2];
return r;
};
//
// ##Function: V3.neg
//
// Perform
// r = - a.
//
// **Parameters:**
//
// - **a** - the vector operand
// - **r** - optional vector to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3-element vector with the result.
//
V3.neg = function V3_neg(a, r) {
MathUtils_assert(a.length == 3, "a.length == 3");
MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(3);
r[0] = - a[0];
r[1] = - a[1];
r[2] = - a[2];
return r;
};
//
// ##Function: V3.direction
//
// Perform
// r = (a - b) / |a - b|. The result is the normalized
// direction from a to b.
//
// **Parameters:**
//
// - **a** - the first vector operand
// - **b** - the second vector operand
// - **r** - optional vector to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3-element vector with the result.
//
V3.direction = function V3_direction(a, b, r) {
MathUtils_assert(a.length == 3, "a.length == 3");
MathUtils_assert(b.length == 3, "b.length == 3");
MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(3);
return V3.normalize(V3.sub(a, b, r), r);
};
//
// ##Function: V3.length
//
// Perform r = |a|.
//
// **Parameters:**
//
// - **a** - the vector operand
//
// **Returns:**
//
// The length of the given vector.
//
V3.length = function V3_length(a) {
MathUtils_assert(a.length == 3, "a.length == 3");
return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
};
//
// ##Function: V3.lengthSquard
//
// Perform r = |a|*|a|.
//
// **Parameters:**
//
// - **a** - the vector operand
//
// **Returns:**
//
// The square of the length of the given vector.
//
V3.lengthSquared = function V3_lengthSquared(a) {
MathUtils_assert(a.length == 3, "a.length == 3");
return a[0]*a[0] + a[1]*a[1] + a[2]*a[2];
};
//
// ##Function: V3.normalize
//
// Perform r = a / |a|.
//
// **Parameters:**
//
// - **a** - the vector operand
// - **r** - optional vector to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3-element vector with the result.
//
V3.normalize = function V3_normalize(a, r) {
MathUtils_assert(a.length == 3, "a.length == 3");
MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(3);
var im = 1.0 / V3.length(a);
r[0] = a[0] * im;
r[1] = a[1] * im;
r[2] = a[2] * im;
return r;
};
//
// ##Function: V3.scale
//
// Perform r = a * k.
//
// **Parameters:**
//
// - **a** - the vector operand
// - **k** - a scalar value
// - **r** - optional vector to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3-element vector with the result.
//
V3.scale = function V3_scale(a, k, r) {
MathUtils_assert(a.length == 3, "a.length == 3");
MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(3);
r[0] = a[0] * k;
r[1] = a[1] * k;
r[2] = a[2] * k;
return r;
};
//
// ##Function: V3.dot
//
// Perform
// r = dot(a, b).
//
// **Parameters:**
//
// - **a** - the first vector operand
// - **b** - the second vector operand
//
// **Returns:**
//
// The dot product of a and b.
//
V3.dot = function V3_dot(a, b) {
MathUtils_assert(a.length == 3, "a.length == 3");
MathUtils_assert(b.length == 3, "b.length == 3");
return a[0] * b[0] +
a[1] * b[1] +
a[2] * b[2];
};
//
// ##Function: V3.cross
//
// Perform r = a x b.
//
// **Parameters:**
//
// - **a** - the first vector operand
// - **b** - the second vector operand
// - **r** - optional vector to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3-element vector with the result.
//
V3.cross = function V3_cross(a, b, r) {
MathUtils_assert(a.length == 3, "a.length == 3");
MathUtils_assert(b.length == 3, "b.length == 3");
MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(3);
r[0] = a[1]*b[2] - a[2]*b[1];
r[1] = a[2]*b[0] - a[0]*b[2];
r[2] = a[0]*b[1] - a[1]*b[0];
return r;
};
//
// ##Function: V3.mul4x4
//
// Perform
// r = m * v.
//
// **Parameters:**
//
// - **m** - the 4x4 matrix operand
// - **v** - the 3-element vector operand
// - **r** - optional vector to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3-element vector with the result.
// The 4-element result vector is divided by the w component
// and returned as a 3-element vector.
//
V3.mul4x4 = function V3_mul4x4(m, v, r) {
MathUtils_assert(m.length == 16, "m.length == 16");
MathUtils_assert(v.length == 3, "v.length == 3");
MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
var w;
var tmp = V3._temp1;
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(3);
tmp[0] = m[ 3];
tmp[1] = m[ 7];
tmp[2] = m[11];
w = V3.dot(v, tmp) + m[15];
tmp[0] = m[ 0];
tmp[1] = m[ 4];
tmp[2] = m[ 8];
r[0] = (V3.dot(v, tmp) + m[12])/w;
tmp[0] = m[ 1];
tmp[1] = m[ 5];
tmp[2] = m[ 9];
r[1] = (V3.dot(v, tmp) + m[13])/w;
tmp[0] = m[ 2];
tmp[1] = m[ 6];
tmp[2] = m[10];
r[2] = (V3.dot(v, tmp) + m[14])/w;
return r;
};
//
// #Class M4x4
//
// Methods for working with 4x4 matrices. A matrix is represented by a 16-element array
// in column-major order. Any valid JavaScript array type may be used, but if new
// matrices are created they are created using the configured MJS_FLOAT_ARRAY_TYPE.
//
var M4x4 = { };
M4x4._temp1 = new MJS_FLOAT_ARRAY_TYPE(16);
M4x4._temp2 = new MJS_FLOAT_ARRAY_TYPE(16);
if (MJS_FLOAT_ARRAY_TYPE == Array) {
M4x4.I = [1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0];
M4x4.$ = function M4x4_$(m00, m01, m02, m03,
m04, m05, m06, m07,
m08, m09, m10, m11,
m12, m13, m14, m15)
{
return [m00, m01, m02, m03,
m04, m05, m06, m07,
m08, m09, m10, m11,
m12, m13, m14, m15];
};
M4x4.clone = function M4x4_clone(m) {
MathUtils_assert(m.length == 16, "m.length == 16");
return new [m[0], m[1], m[2], m[3],
m[4], m[5], m[6], m[7],
m[8], m[9], m[10], m[11],
m[12], m[13], m[14], m[15]];
};
} else {
M4x4.I = new MJS_FLOAT_ARRAY_TYPE([1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0]);
//
// ##Function: M4x4.$
//
// Creates a new 4x4 matrix with the given values.
//
// **Parameters:**
//
// - **m00..m15** - the 16 elements of the new matrix.
//
// **Returns:**
//
// A new matrix filled with the given argument values.
//
M4x4.$ = function M4x4_$(m00, m01, m02, m03,
m04, m05, m06, m07,
m08, m09, m10, m11,
m12, m13, m14, m15)
{
return new MJS_FLOAT_ARRAY_TYPE([m00, m01, m02, m03,
m04, m05, m06, m07,
m08, m09, m10, m11,
m12, m13, m14, m15]);
};
//
// ##Function: M4x4.clone
//
// Clone the given 4x4 matrix.
//
// **Parameters:**
//
// - **m** - the 4x4 matrix to clone
//
// **Returns:**
//
// A new matrix with the same values as the passed-in one.
//
M4x4.clone = function M4x4_clone(m) {
MathUtils_assert(m.length == 16, "m.length == 16");
return new MJS_FLOAT_ARRAY_TYPE(m);
};
}
M4x4.identity = M4x4.I;
//
// ##Function: M4x4.topLeft3x3
//
// Return the top left 3x3 matrix from the given 4x4 matrix m.
//
// **Parameters:**
//
// - **m** - the matrix
// - **r** - optional 3x3 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3x3 matrix with the result.
//
M4x4.topLeft3x3 = function M4x4_topLeft3x3(m, r) {
MathUtils_assert(m.length == 16, "m.length == 16");
MathUtils_assert(r == undefined || r.length == 9, "r == undefined || r.length == 9");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(9);
r[0] = m[0]; r[1] = m[1]; r[2] = m[2];
r[3] = m[4]; r[4] = m[5]; r[5] = m[6];
r[6] = m[8]; r[7] = m[9]; r[8] = m[10];
return r;
};
//
// ##Function: M4x4.inverseOrthonormal
//
// Computes the inverse of the given matrix m, assuming that
// the matrix is orthonormal.
//
// **Parameters:**
//
// - **m** - the matrix
// - **r** - optional 4x4 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 4x4 matrix with the result.
//
M4x4.inverseOrthonormal = function M4x4_inverseOrthonormal(m, r) {
MathUtils_assert(m.length == 16, "m.length == 16");
MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
MathUtils_assert(m != r, "m != r");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(16);
M4x4.transpose(m, r);
var t = [m[12], m[13], m[14]];
r[3] = r[7] = r[11] = 0;
r[12] = -V3.dot([r[0], r[4], r[8]], t);
r[13] = -V3.dot([r[1], r[5], r[9]], t);
r[14] = -V3.dot([r[2], r[6], r[10]], t);
return r;
};
//
// ##Function: M4x4.inverseTo3x3
//
// Computes the inverse of the given matrix m, but calculates
// only the top left 3x3 values of the result.
//
// **Parameters:**
//
// - **m** - the matrix
// - **r** - optional 3x3 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 3x3 matrix with the result.
//
M4x4.inverseTo3x3 = function M4x4_inverseTo3x3(m, r) {
MathUtils_assert(m.length == 16, "m.length == 16");
MathUtils_assert(r == undefined || r.length == 9, "r == undefined || r.length == 9");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(9);
var a11 = m[10]*m[5]-m[6]*m[9],
a21 = -m[10]*m[1]+m[2]*m[9],
a31 = m[6]*m[1]-m[2]*m[5],
a12 = -m[10]*m[4]+m[6]*m[8],
a22 = m[10]*m[0]-m[2]*m[8],
a32 = -m[6]*m[0]+m[2]*m[4],
a13 = m[9]*m[4]-m[5]*m[8],
a23 = -m[9]*m[0]+m[1]*m[8],
a33 = m[5]*m[0]-m[1]*m[4];
var det = m[0]*(a11) + m[1]*(a12) + m[2]*(a13);
if (det == 0) // no inverse
throw "matrix not invertible";
var idet = 1.0 / det;
r[0] = idet*a11;
r[1] = idet*a21;
r[2] = idet*a31;
r[3] = idet*a12;
r[4] = idet*a22;
r[5] = idet*a32;
r[6] = idet*a13;
r[7] = idet*a23;
r[8] = idet*a33;
return r;
};
//
// ##Function: M4x4.makeFrustum
//
// Creates a matrix for a projection frustum with the given parameters.
//
// **Parameters:**
//
// - **left** - the left coordinate of the frustum
// - **right** - the right coordinate of the frustum
// - **bottom** - the bottom coordinate of the frustum
// - **top** - the top coordinate of the frustum
// - **znear** - the near z distance of the frustum
// - **zfar** - the far z distance of the frustum
// - **r** - optional 4x4 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after creating the projection matrix.
// Otherwise, returns a new 4x4 matrix.
//
M4x4.makeFrustum = function M4x4_makeFrustum(left, right, bottom, top, znear, zfar, r) {
MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(16);
var X = 2*znear/(right-left);
var Y = 2*znear/(top-bottom);
var A = (right+left)/(right-left);
var B = (top+bottom)/(top-bottom);
var C = -(zfar+znear)/(zfar-znear);
var D = -2*zfar*znear/(zfar-znear);
r[0] = 2*znear/(right-left);
r[1] = 0;
r[2] = 0;
r[3] = 0;
r[4] = 0;
r[5] = 2*znear/(top-bottom);
r[6] = 0;
r[7] = 0;
r[8] = (right+left)/(right-left);
r[9] = (top+bottom)/(top-bottom);
r[10] = -(zfar+znear)/(zfar-znear);
r[11] = -1;
r[12] = 0;
r[13] = 0;
r[14] = -2*zfar*znear/(zfar-znear);
r[15] = 0;
return r;
};
//
// ##Function: M4x4.makePerspective
//
// Creates a matrix for a perspective projection with the given parameters.
//
// **Parameters:**
//
// - **fovy** - field of view in the y axis, in degrees
// - **aspect** - aspect ratio
// - **znear** - the near z distance of the projection
// - **zfar** - the far z distance of the projection
// - **r** - optional 4x4 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after creating the projection matrix.
// Otherwise, returns a new 4x4 matrix.
//
M4x4.makePerspective = function M4x4_makePerspective (fovy, aspect, znear, zfar, r) {
MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
var ymax = znear * Math.tan(fovy * Math.PI / 360.0);
var ymin = -ymax;
var xmin = ymin * aspect;
var xmax = ymax * aspect;
return M4x4.makeFrustum(xmin, xmax, ymin, ymax, znear, zfar, r);
};
//
// ##Function: M4x4.makeOrtho
//
// Creates a matrix for an orthogonal frustum projection with the given parameters.
//
// **Parameters:**
//
// - **left** - the left coordinate of the frustum
// - **right** - the right coordinate of the frustum
// - **bottom** - the bottom coordinate of the frustum
// - **top** - the top coordinate of the frustum
// - **znear** - the near z distance of the frustum
// - **zfar** - the far z distance of the frustum
// - **r** - optional 4x4 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after creating the projection matrix.
// Otherwise, returns a new 4x4 matrix.
//
M4x4.makeOrtho = function M4x4_makeOrtho (left, right, bottom, top, znear, zfar, r) {
MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(16);
var tX = -(right+left)/(right-left);
var tY = -(top+bottom)/(top-bottom);
var tZ = -(zfar+znear)/(zfar-znear);
var X = 2 / (right-left);
var Y = 2 / (top-bottom);
var Z = -2 / (zfar-znear);
r[0] = 2 / (right-left);
r[1] = 0;
r[2] = 0;
r[3] = 0;
r[4] = 0;
r[5] = 2 / (top-bottom);
r[6] = 0;
r[7] = 0;
r[8] = 0;
r[9] = 0;
r[10] = -2 / (zfar-znear);
r[11] = 0;
r[12] = -(right+left)/(right-left);
r[13] = -(top+bottom)/(top-bottom);
r[14] = -(zfar+znear)/(zfar-znear);
r[15] = 1;
return r;
};
//
// ##Function: M4x4.makeOrtho
//
// Creates a matrix for a 2D orthogonal frustum projection with the given parameters.
// znear and zfar are assumed to be -1 and 1, respectively.
//
// **Parameters:**
//
// - **left** - the left coordinate of the frustum
// - **right** - the right coordinate of the frustum
// - **bottom** - the bottom coordinate of the frustum
// - **top** - the top coordinate of the frustum
// - **r** - optional 4x4 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after creating the projection matrix.
// Otherwise, returns a new 4x4 matrix.
//
M4x4.makeOrtho2D = function M4x4_makeOrtho2D (left, right, bottom, top, r) {
MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
return M4x4.makeOrtho(left, right, bottom, top, -1, 1, r);
};
//
// ##Function: M4x4.mul
//
// Performs r = a * b.
//
// **Parameters:**
//
// - **a** - the first matrix operand
// - **b** - the second matrix operand
// - **r** - optional 4x4 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 4x4 matrix with the result.
//
M4x4.mul = function M4x4_mul(a, b, r) {
MathUtils_assert(a.length == 16, "a.length == 16");
MathUtils_assert(b.length == 16, "b.length == 16");
MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
MathUtils_assert(a != r && b != r, "a != r && b != r");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(16);
var a11 = a[0];
var a21 = a[1];
var a31 = a[2];
var a41 = a[3];
var a12 = a[4];
var a22 = a[5];
var a32 = a[6];
var a42 = a[7];
var a13 = a[8];
var a23 = a[9];
var a33 = a[10];
var a43 = a[11];
var a14 = a[12];
var a24 = a[13];
var a34 = a[14];
var a44 = a[15];
var b11 = b[0];
var b21 = b[1];
var b31 = b[2];
var b41 = b[3];
var b12 = b[4];
var b22 = b[5];
var b32 = b[6];
var b42 = b[7];
var b13 = b[8];
var b23 = b[9];
var b33 = b[10];
var b43 = b[11];
var b14 = b[12];
var b24 = b[13];
var b34 = b[14];
var b44 = b[15];
r[0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
r[1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
r[2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
r[3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
r[4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
r[5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
r[6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
r[7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
r[8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
r[9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
r[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
r[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
r[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
r[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
r[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
r[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
return r;
};
//
// ##Function: M4x4.mulOffset
//
// Performs r' = a * b, where r' is the 16 elements of r starting at element o.
//
// **Parameters:**
//
// - **a** - the first matrix operand
// - **b** - the second matrix operand
// - **r** - array to store the result in
// - **o** - offset into r at which to start storing results
//
// **Returns:**
//
// r
//
M4x4.mulOffset = function M4x4_mulOffset(a, b, r, o) {
MathUtils_assert(a.length == 16, "a.length == 16");
MathUtils_assert(b.length == 16, "b.length == 16");
var a21 = a[1];
var a31 = a[2];
var a41 = a[3];
var a12 = a[4];
var a22 = a[5];
var a32 = a[6];
var a42 = a[7];
var a13 = a[8];
var a23 = a[9];
var a33 = a[10];
var a43 = a[11];
var a14 = a[12];
var a24 = a[13];
var a34 = a[14];
var a44 = a[15];
var b11 = b[0];
var b21 = b[1];
var b31 = b[2];
var b41 = b[3];
var b12 = b[4];
var b22 = b[5];
var b32 = b[6];
var b42 = b[7];
var b13 = b[8];
var b23 = b[9];
var b33 = b[10];
var b43 = b[11];
var b14 = b[12];
var b24 = b[13];
var b34 = b[14];
var b44 = b[15];
r[o+0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
r[o+1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
r[o+2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
r[o+3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
r[o+4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
r[o+5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
r[o+6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
r[o+7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
r[o+8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
r[o+9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
r[o+10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
r[o+11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
r[o+12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
r[o+13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
r[o+14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
r[o+15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
return r;
};
//
// ##Function: M4x4.mulAffine
//
// Performs r = a * b, assuming a and b are affine (elements 3,7,11,15 = 0,0,0,1)
//
// **Parameters:**
//
// - **a** - the first matrix operand
// - **b** - the second matrix operand
// - **r** - optional 4x4 matrix to store the result in
//
// **Returns:**
//
// If r is specified, returns r after performing the operation.
// Otherwise, returns a new 4x4 matrix with the result.
//
M4x4.mulAffine = function M4x4_mulAffine(a, b, r) {
MathUtils_assert(a.length == 16, "a.length == 16");
MathUtils_assert(b.length == 16, "b.length == 16");
MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
MathUtils_assert(a != r && b != r, "a != r && b != r");
if (r == undefined)
r = new MJS_FLOAT_ARRAY_TYPE(16);
var a11 = a[0];
var a21 = a[1];
var a31 = a[2];
var a12 = a[4];
var a22 = a[5];
var a32 = a[6];
var a13 = a[8];
var a23 = a[9];
var a33 = a[10];
var a14 = a[12];
var a24 = a[13];
var a34 = a[14];
var b11 = b[0];
var b21 = b[1];
var b31 = b[2];
var b12 = b[4];
var b22 = b[5];
var b32 = b[6];
var b13 = b[8];
var b23 = b[9];
var b33 = b[10];
var b14 = b[12];
var b24 = b[13];
var b34 = b[14];
r[0] = a11 * b11 + a12 * b21 + a13 * b31;
r[1] = a21 * b11 + a22 * b21 + a23 * b31;
r[2] = a31 * b11 + a32 * b21 + a33 * b31;
r[3] = 0;
r[4] = a11 * b12 + a12 * b22 + a13 * b32;
r[5] = a21 * b12 + a22 * b22 + a23 * b32;
r[6] = a31 * b12 + a32 * b22 + a33 * b32;
r[7] = 0;
r[8] = a11 * b13 + a12 * b23 + a13 * b33;
r[9] = a21 * b13 + a22 * b23 + a23 * b33;
r[10] = a31 * b13 + a32 * b23 + a33 * b33;
r[11] = 0;
r[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14;
r[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24;
r[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34;
r[15] = 1;
return r;
};