diff options
Diffstat (limited to 'o3d/samples/o3djs/math.js')
| -rw-r--r-- | o3d/samples/o3djs/math.js | 3100 |
1 files changed, 1808 insertions, 1292 deletions
diff --git a/o3d/samples/o3djs/math.js b/o3d/samples/o3djs/math.js index e840f23..c37ccb2 100644 --- a/o3d/samples/o3djs/math.js +++ b/o3d/samples/o3djs/math.js @@ -35,21 +35,20 @@ * It adds them to the "math" module on the o3djs object. * * o3djs.math supports a row-major and a column-major mode. In both - * modes, vectors are stored as arrays of numbers, and matrices are stored as - * arrays of arrays of numbers. + * modes, vectors are stored as arrays of numbers, and matrices are also. * * In row-major mode: * - * - Rows of a matrix are sub-arrays. - * - Individual entries of a matrix M get accessed in M[row][column] fashion. - * - Tuples of coordinates are interpreted as row-vectors. + * - Rows of a matrix are neighboring <dimension> elements in the array. + * - Entries of a matrix M get accessed in M[row*dimension+column] fashion. + * - Tuples of coordinates adjacent are interpreted as row-vectors. * - A vector v gets transformed by a matrix M by multiplying in the order v*M. * * In column-major mode: * - * - Columns of a matrix are sub-arrays. - * - Individual entries of a matrix M get accessed in M[column][row] fashion. - * - Tuples of coordinates are interpreted as column-vectors. + * - Columns of a matrix are neighboring <dimension> elements in the array. + * - Entries of a matrix M get accessed in M[column*dimension+row] fashion. + * - Tuples of coordinates adjacent are interpreted as column-vectors. * - A matrix M transforms a vector v by multiplying in the order M*v. * * When a function in o3djs.math requires separate row-major and @@ -96,123 +95,483 @@ * mean all sample code will work even if a line is added which switches major * modes, but it does mean that calls to o3djs still do what they are supposed * to. - * */ -o3djs.provide('o3djs.math'); + +var use_plugin_math = false; + +if ((typeof o3d != 'undefined') && o3d && o3d.Transform && + o3d.Transform.makeIdentityMatrix4_) { + o3djs.provide('o3djs.math'); +} else { + use_plugin_math = true; + o3djs.require('o3djs.plugin_math'); +} + +o3djs.provide("o3djs.flat_math"); /** - * A module for math for o3djs.math. + * A module for math functions where a matrix is represented as a flat + * (1-dimensional) array. * @namespace */ -o3djs.math = o3djs.math || {}; +o3djs.flat_math = o3djs.flat_math || {}; /** * A random seed for the pseudoRandom function. * @private * @type {number} */ -o3djs.math.randomSeed_ = 0; +o3djs.flat_math.randomSeed_ = 0; /** * A constant for the pseudoRandom function * @private * @type {number} */ -o3djs.math.RANDOM_RANGE_ = Math.pow(2, 32); +o3djs.flat_math.RANDOM_RANGE_ = Math.pow(2, 32); /** * Functions which deal with 4-by-4 transformation matrices are kept in their * own namespsace. * @namespace */ -o3djs.math.matrix4 = o3djs.math.matrix4 || {}; +o3djs.flat_math.matrix4 = o3djs.flat_math.matrix4 || {}; /** * Functions that are specifically row major are kept in their own namespace. * @namespace */ -o3djs.math.rowMajor = o3djs.math.rowMajor || {}; +o3djs.flat_math.rowMajor = o3djs.flat_math.rowMajor || {}; /** * Functions that are specifically column major are kept in their own namespace. * @namespace */ -o3djs.math.columnMajor = o3djs.math.columnMajor || {}; +o3djs.flat_math.columnMajor = o3djs.flat_math.columnMajor || {}; /** * Functions that do error checking are stored in their own namespace. * @namespace */ -o3djs.math.errorCheck = o3djs.math.errorCheck || {}; +o3djs.flat_math.errorCheck = o3djs.flat_math.errorCheck || {}; /** * Functions that do no error checking and have a separate version that does in - * o3djs.math.errorCheck are stored in their own namespace. + * o3djs.flat_math.errorCheck are stored in their own namespace. * @namespace */ -o3djs.math.errorCheckFree = o3djs.math.errorCheckFree || {}; +o3djs.flat_math.errorCheckFree = o3djs.flat_math.errorCheckFree || {}; /** - * An Array of 2 floats - * @type {(!Array.<number>|!o3d.Float2)} + * An Float32Array of 2 floats + * @type {(!Float32Array.<number>|!o3d.Float2)} */ -o3djs.math.Vector2 = goog.typedef; +o3djs.flat_math.Vector2 = goog.typedef; /** - * An Array of 3 floats - * @type {(!Array.<number>|!o3d.Float3)} + * An Float32Array of 3 floats + * @type {(!Float32Array.<number>|!o3d.Float3)} */ -o3djs.math.Vector3 = goog.typedef; +o3djs.flat_math.Vector3 = goog.typedef; /** - * An Array of 4 floats - * @type {(!Array.<number>|!o3d.Float4)} + * An Float32Array of 4 floats + * @type {(!Float32Array.<number>|!o3d.Float4)} */ -o3djs.math.Vector4 = goog.typedef; +o3djs.flat_math.Vector4 = goog.typedef; -/** - * An Array of floats. - * @type {!Array.<number>} - */ -o3djs.math.Vector = goog.typedef; /** * A 1x1 Matrix of floats - * @type {!Array.<!Array.<number>>} + * @type {!Array.<number>} */ -o3djs.math.Matrix1 = goog.typedef; +o3djs.flat_math.Matrix1 = goog.typedef; /** * A 2x2 Matrix of floats - * @type {!Array.<!Array.<number>>} + * @type {!Array.<number>} */ -o3djs.math.Matrix2 = goog.typedef; +o3djs.flat_math.Matrix2 = goog.typedef; /** * A 3x3 Matrix of floats - * @type {!Array.<!Array.<number>>} + * @type {!Array.<number>} */ -o3djs.math.Matrix3 = goog.typedef; +o3djs.flat_math.Matrix3 = goog.typedef; /** * A 4x4 Matrix of floats - * @type {(!Array.<!Array.<number>>|!o3d.Matrix4)} + * @type {(!Array.<number>|!o3d.Matrix4)} + */ +o3djs.flat_math.Matrix4 = goog.typedef; + +o3djs.flat_math.useFloat32Array_ = false; + +/** + * A arbitrary size Matrix of floats + * @type {(!Array.<number>|!o3d.Matrix4)} */ -o3djs.math.Matrix4 = goog.typedef; +o3djs.flat_math.Matrix = goog.typedef; + +/** + * A arbitrary size Matrix of floats + * @type {(!Array.<number>)} + */ +o3djs.flat_math.Vector = goog.typedef; + + +/** + * Namespace for Float32Array specific math functions + */ +o3djs.flat_math.Float32Array = {}; + +/** + * A arbitrary size Matrix of floats + * @type {(!Array.<number>|!o3d.Matrix4)} + */ +o3djs.flat_math.Float32Array.Matrix = + (use_plugin_math ? goog.typedef : Float32Array); +/** + * An Float32Array of floats. + * @type {!Array.<number>} + */ +o3djs.flat_math.Float32Array.Vector = + (use_plugin_math ? goog.typedef : Float32Array); + +/** + * If 16 arguments, this returns a 4x4 matrix + * with values set to the passed in arguments + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [0][2] element + * @param {number} d [0][3] element + * @param {number} e [1][0] element + * @param {number} f [1][1] element + * @param {number} g [1][2] element + * @param {number} h [1][3] element + * @param {number} i [2][0] element + * @param {number} j [2][1] element + * @param {number} k [2][2] element + * @param {number} l [2][3] element + * @param {number} m [3][0] element + * @param {number} n [3][1] element + * @param {number} o [3][2] element + * @param {number} p [3][3] element + * + * If 9 arguments returns a 3x3 matrix + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [0][2] element + * @param {number} d [1][0] element + * @param {number} e [1][1] element + * @param {number} f [1][2] element + * @param {number} g [2][0] element + * @param {number} h [2][1] element + * @param {number} i [2][2] element + + * If 4 arguments returns a 2x2 matrix + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [1][0] element + * @param {number} d [1][1] element + * @returns {!o3djs.flat_math.Matrix} + */ +o3djs.flat_math.Float32Array.makeMatrix = function( + a, b, c, d, + e, f, g, h, + i, j, k, l, + m, n, o, p) { + if (p === undefined) { + if (i === undefined) { + var retval = new Float32Array(4); + retval[0] = a; + retval[1] = b; + retval[2] = c; + retval[3] = d; + return retval; + } + var retval = new Float32Array(9); + retval[0] = a; + retval[1] = b; + retval[2] = c; + retval[3] = d; + retval[4] = e; + retval[5] = f; + retval[6] = g; + retval[7] = h; + retval[8] = i; + return retval; + } + var retval = new Float32Array(16); + retval[0] = a; + retval[1] = b; + retval[2] = c; + retval[3] = d; + retval[4] = e; + retval[5] = f; + retval[6] = g; + retval[7] = h; + retval[8] = i; + retval[9] = j; + retval[10] = k; + retval[11] = l; + retval[12] = m; + retval[13] = n; + retval[14] = o; + retval[15] = p; + return retval; +}; + +/** + * returns a 2x2 matrix + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [1][0] element + * @param {number} d [1][1] element + * @returns {!o3djs.flat_math.Matrix} + */ +o3djs.flat_math.Float32Array.makeMatrix2 = function(a,b, + c,d) { + var retval = new Float32Array(4); + retval[0] = a; + retval[1] = b; + retval[2] = c; + retval[3] = d; + return retval; +}; + +/** + * If returns a 3x3 matrix + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [0][2] element + * @param {number} d [1][0] element + * @param {number} e [1][1] element + * @param {number} f [1][2] element + * @param {number} g [2][0] element + * @param {number} h [2][1] element + * @param {number} i [2][2] element + * @return {!o3djs.flat_math.Matrix} the matrix of the above elements + */ +o3djs.flat_math.Float32Array.makeMatrix3 = function( + a, b, c, + d, e, f, + g, h, i) { + var retval = new Float32Array(9); + retval[0] = a; + retval[1] = b; + retval[2] = c; + retval[3] = d; + retval[4] = e; + retval[5] = f; + retval[6] = g; + retval[7] = h; + retval[8] = i; + return retval; +}; + +/** + * returns a 4x4 matrix + * with values set to the passed in arguments + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [0][2] element + * @param {number} d [0][3] element + * @param {number} e [1][0] element + * @param {number} f [1][1] element + * @param {number} g [1][2] element + * @param {number} h [1][3] element + * @param {number} i [2][0] element + * @param {number} j [2][1] element + * @param {number} k [2][2] element + * @param {number} l [2][3] element + * @param {number} m [3][0] element + * @param {number} n [3][1] element + * @param {number} o [3][2] element + * @param {number} p [3][3] element + * @returns {o3djs.flat_math.Matrix} comprised of the above elements + */ +o3djs.flat_math.Float32Array.makeMatrix4 = function( + a, b, c, d, + e, f, g, h, + i, j, k, l, + m, n, o, p) { + var retval = new Float32Array(16); + retval[0] = a; + retval[1] = b; + retval[2] = c; + retval[3] = d; + retval[4] = e; + retval[5] = f; + retval[6] = g; + retval[7] = h; + retval[8] = i; + retval[9] = j; + retval[10] = k; + retval[11] = l; + retval[12] = m; + retval[13] = n; + retval[14] = o; + retval[15] = p; + return retval; +}; + +/** + * Namespace for Array specific math functions + */ +o3djs.flat_math.Array={}; /** * A arbitrary size Matrix of floats * @type {(!Array.<!Array.<number>>|!o3d.Matrix4)} */ -o3djs.math.Matrix = goog.typedef; +o3djs.flat_math.Array.Matrix = (use_plugin_math ? goog.typedef: Array); + +/** + * An Float32Array of floats. + * @type {!Float32Array.<number>} + */ +o3djs.flat_math.Array.Vector = (use_plugin_math ? goog.typedef: Array); + +/** + * If 16 arguments, this returns a 4x4 matrix + * with values set to the passed in arguments + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [0][2] element + * @param {number} d [0][3] element + * @param {number} e [1][0] element + * @param {number} f [1][1] element + * @param {number} g [1][2] element + * @param {number} h [1][3] element + * @param {number} i [2][0] element + * @param {number} j [2][1] element + * @param {number} k [2][2] element + * @param {number} l [2][3] element + * @param {number} m [3][0] element + * @param {number} n [3][1] element + * @param {number} o [3][2] element + * @param {number} p [3][3] element + * + * If 9 arguments returns a 3x3 matrix + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [0][2] element + * @param {number} d [1][0] element + * @param {number} e [1][1] element + * @param {number} f [1][2] element + * @param {number} g [2][0] element + * @param {number} h [2][1] element + * @param {number} i [2][2] element + + * If 4 arguments returns a 2x2 matrix + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [1][0] element + * @param {number} d [1][1] element + * @returns {!o3djs.flat_math.Matrix} + */ +o3djs.flat_math.Array.makeMatrix = function( + a, b, c, d, + e, f, g, h, + i, j, k, l, + m, n, o, p) { + if (p === undefined) { + if (i === undefined) { + return [a,b,c,d]; + } + return [a, b, c, d, e, f, g, h, i]; + } + return [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p]; +}; + +/** + * returns a 2x2 matrix + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [1][0] element + * @param {number} d [1][1] element + * @returns {!o3djs.flat_math.Matrix} + */ +o3djs.flat_math.Array.makeMatrix2 = function(a, b, c, d) { + return [a, b, c, d]; +}; + +/** + * If returns a 3x3 matrix + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [0][2] element + * @param {number} d [1][0] element + * @param {number} e [1][1] element + * @param {number} f [1][2] element + * @param {number} g [2][0] element + * @param {number} h [2][1] element + * @param {number} i [2][2] element + * @return {!o3djs.flat_math.Matrix} the matrix of the above elements + */ +o3djs.flat_math.Array.makeMatrix3 = function( + a, b, c, + d, e, f, + g, h, i) { + return [a, b, c, d, e, f, g, h, i]; +}; + +/** + * returns a 4x4 matrix + * with values set to the passed in arguments + * @param {number} a [0][0] element + * @param {number} b [0][1] element + * @param {number} c [0][2] element + * @param {number} d [0][3] element + * @param {number} e [1][0] element + * @param {number} f [1][1] element + * @param {number} g [1][2] element + * @param {number} h [1][3] element + * @param {number} i [2][0] element + * @param {number} j [2][1] element + * @param {number} k [2][2] element + * @param {number} l [2][3] element + * @param {number} m [3][0] element + * @param {number} n [3][1] element + * @param {number} o [3][2] element + * @param {number} p [3][3] element + * @returns {o3djs.flat_math.Matrix} comprised of the above elements + */ +o3djs.flat_math.Array.makeMatrix4 = function( + a, b, c, d, + e, f, g, h, + i, j, k, l, + m, n, o, p) { + return [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p]; +}; + +if (o3djs.flat_math.useFloat32Array_) { + o3djs.flat_math.Matrix = o3djs.flat_math.Float32Array.Matrix; + o3djs.flat_math.Vector = o3djs.flat_math.Float32Array.Vector; + for (var i in o3djs.flat_math.Float32Array) { + if (o3djs.flat_math.Float32Array[i].call) + o3djs.flat_math[i]=o3djs.flat_math.Float32Array[i]; + } +} else { + o3djs.flat_math.Matrix = o3djs.flat_math.Array.Matrix; + o3djs.flat_math.Vector = o3djs.flat_math.Array.Vector; + for (var i in o3djs.flat_math.Array) { + if (o3djs.flat_math.Array[i].call) + o3djs.flat_math[i]=o3djs.flat_math.Array[i]; + } +} + + + /** * Returns a deterministic pseudorandom number between 0 and 1 * @return {number} a random number between 0 and 1 */ -o3djs.math.pseudoRandom = function() { - var math = o3djs.math; +o3djs.flat_math.pseudoRandom = function() { + var math = o3djs.flat_math; return (math.randomSeed_ = (134775813 * math.randomSeed_ + 1) % math.RANDOM_RANGE_) / math.RANDOM_RANGE_; @@ -221,8 +580,8 @@ o3djs.math.pseudoRandom = function() { /** * Resets the pseudoRandom function sequence. */ -o3djs.math.resetPseudoRandom = function() { - o3djs.math.randomSeed_ = 0; +o3djs.flat_math.resetPseudoRandom = function() { + o3djs.flat_math.randomSeed_ = 0; }; /** @@ -230,7 +589,7 @@ o3djs.math.resetPseudoRandom = function() { * @param {number} degrees A value in degrees. * @return {number} the value in radians. */ -o3djs.math.degToRad = function(degrees) { +o3djs.flat_math.degToRad = function(degrees) { return degrees * Math.PI / 180; }; @@ -239,7 +598,7 @@ o3djs.math.degToRad = function(degrees) { * @param {number} radians A value in radians. * @return {number} the value in degrees. */ -o3djs.math.radToDeg = function(radians) { +o3djs.flat_math.radToDeg = function(radians) { return radians * 180 / Math.PI; }; @@ -252,19 +611,19 @@ o3djs.math.radToDeg = function(radians) { * @param {number} t Interpolation coefficient. * @return {number} The weighted sum of a and b. */ -o3djs.math.lerpScalar = function(a, b, t) { +o3djs.flat_math.lerpScalar = function(a, b, t) { return (1 - t) * a + t * b; }; /** * Adds two vectors; assumes a and b have the same dimension. - * @param {!o3djs.math.Vector} a Operand vector. - * @param {!o3djs.math.Vector} b Operand vector. - * @return {!o3djs.math.Vector} The sum of a and b. + * @param {!o3djs.flat_math.Vector} a Operand vector. + * @param {!o3djs.flat_math.Vector} b Operand vector. + * @return {!o3djs.flat_math.Vector} The sum of a and b. */ -o3djs.math.addVector = function(a, b) { - var r = []; +o3djs.flat_math.addVector = function(a, b) { var aLength = a.length; + var r = new o3djs.flat_math.Vector(aLength); for (var i = 0; i < aLength; ++i) r[i] = a[i] + b[i]; return r; @@ -272,30 +631,43 @@ o3djs.math.addVector = function(a, b) { /** * Subtracts two vectors. - * @param {!o3djs.math.Vector} a Operand vector. - * @param {!o3djs.math.Vector} b Operand vector. - * @return {!o3djs.math.Vector} The difference of a and b. + * @param {!o3djs.flat_math.Vector} a Operand vector. + * @param {!o3djs.flat_math.Vector} b Operand vector. + * @return {!o3djs.flat_math.Vector} The difference of a and b. */ -o3djs.math.subVector = function(a, b) { - var r = []; +o3djs.flat_math.subVector = function(a, b) { var aLength = a.length; + var r = new o3djs.flat_math.Vector(aLength); for (var i = 0; i < aLength; ++i) r[i] = a[i] - b[i]; return r; }; /** + * Subtracts two 3d vectors. + * @param {!o3djs.flat_math.Vector3} a Operand vector. + * @param {!o3djs.flat_math.Vector3} b Operand vector. + * @return {!o3djs.flat_math.Vector3} The difference of a and b. + */ +o3djs.flat_math.subVector3 = function(a, b) { + var r = new o3djs.flat_math.Vector(3); + for (var i = 0; i < 3; ++i) + r[i] = a[i] - b[i]; + return r; +}; + +/** * Performs linear interpolation on two vectors. * Given vectors a and b and interpolation coefficient t, returns * (1 - t) * a + t * b. - * @param {!o3djs.math.Vector} a Operand vector. - * @param {!o3djs.math.Vector} b Operand vector. + * @param {!o3djs.flat_math.Vector} a Operand vector. + * @param {!o3djs.flat_math.Vector} b Operand vector. * @param {number} t Interpolation coefficient. - * @return {!o3djs.math.Vector} The weighted sum of a and b. + * @return {!o3djs.flat_math.Vector} The weighted sum of a and b. */ -o3djs.math.lerpVector = function(a, b, t) { - var r = []; +o3djs.flat_math.lerpVector = function(a, b, t) { var aLength = a.length; + var r = new o3djs.flat_math.Vector(aLength); for (var i = 0; i < aLength; ++i) r[i] = (1 - t) * a[i] + t * b[i]; return r; @@ -308,7 +680,7 @@ o3djs.math.lerpVector = function(a, b, t) { * @param {number} opt_rangeStart start of range. Default = 0. * @return {number} Clamp modded value. */ -o3djs.math.modClamp = function(v, range, opt_rangeStart) { +o3djs.flat_math.modClamp = function(v, range, opt_rangeStart) { var start = opt_rangeStart || 0; if (range < 0.00001) { return start; @@ -332,9 +704,9 @@ o3djs.math.modClamp = function(v, range, opt_rangeStart) { * @param {number} range Range of circle. * @return {number} lerped result. */ -o3djs.math.lerpCircular = function(a, b, t, range) { - a = o3djs.math.modClamp(a, range); - b = o3djs.math.modClamp(b, range); +o3djs.flat_math.lerpCircular = function(a, b, t, range) { + a = o3djs.flat_math.modClamp(a, range); + b = o3djs.flat_math.modClamp(b, range); var delta = b - a; if (Math.abs(delta) > range * 0.5) { if (delta > 0) { @@ -343,7 +715,7 @@ o3djs.math.lerpCircular = function(a, b, t, range) { b += range; } } - return o3djs.math.modClamp(o3djs.math.lerpScalar(a, b, t), range); + return o3djs.flat_math.modClamp(o3djs.flat_math.lerpScalar(a, b, t), range); }; /** @@ -353,17 +725,17 @@ o3djs.math.lerpCircular = function(a, b, t, range) { * @param {number} t Amount to lerp (0 to 1). * @return {number} lerped result. */ -o3djs.math.lerpRadian = function(a, b, t) { - return o3djs.math.lerpCircular(a, b, t, Math.PI * 2); +o3djs.flat_math.lerpRadian = function(a, b, t) { + return o3djs.flat_math.lerpCircular(a, b, t, Math.PI * 2); }; /** * Divides a vector by a scalar. - * @param {!o3djs.math.Vector} v The vector. + * @param {!o3djs.flat_math.Vector} v The vector. * @param {number} k The scalar. - * @return {!o3djs.math.Vector} v The vector v divided by k. + * @return {!o3djs.flat_math.Vector} v The vector v divided by k. */ -o3djs.math.divVectorScalar = function(v, k) { +o3djs.flat_math.divVectorScalar = function(v, k) { var r = []; var vLength = v.length; for (var i = 0; i < vLength; ++i) @@ -374,11 +746,11 @@ o3djs.math.divVectorScalar = function(v, k) { /** * Computes the dot product of two vectors; assumes that a and b have * the same dimension. - * @param {!o3djs.math.Vector} a Operand vector. - * @param {!o3djs.math.Vector} b Operand vector. + * @param {!o3djs.flat_math.Vector} a Operand vector. + * @param {!o3djs.flat_math.Vector} b Operand vector. * @return {number} The dot product of a and b. */ -o3djs.math.dot = function(a, b) { +o3djs.flat_math.dot = function(a, b) { var r = 0.0; var aLength = a.length; for (var i = 0; i < aLength; ++i) @@ -389,23 +761,25 @@ o3djs.math.dot = function(a, b) { /** * Computes the cross product of two vectors; assumes both vectors have * three entries. - * @param {!o3djs.math.Vector} a Operand vector. - * @param {!o3djs.math.Vector} b Operand vector. - * @return {!o3djs.math.Vector} The vector a cross b. - */ -o3djs.math.cross = function(a, b) { - return [a[1] * b[2] - a[2] * b[1], - a[2] * b[0] - a[0] * b[2], - a[0] * b[1] - a[1] * b[0]]; + * @param {!o3djs.flat_math.Vector} a Operand vector. + * @param {!o3djs.flat_math.Vector} b Operand vector. + * @return {!o3djs.flat_math.Vector} The vector a cross b. + */ +o3djs.flat_math.cross = function(a, b) { + var r = new o3djs.flat_math.Vector(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; }; /** * Computes the Euclidean length of a vector, i.e. the square root of the * sum of the squares of the entries. - * @param {!o3djs.math.Vector} a The vector. + * @param {!o3djs.flat_math.Vector} a The vector. * @return {number} The length of a. */ -o3djs.math.length = function(a) { +o3djs.flat_math.length = function(a) { var r = 0.0; var aLength = a.length; for (var i = 0; i < aLength; ++i) @@ -416,10 +790,10 @@ o3djs.math.length = function(a) { /** * Computes the square of the Euclidean length of a vector, i.e. the sum * of the squares of the entries. - * @param {!o3djs.math.Vector} a The vector. + * @param {!o3djs.flat_math.Vector} a The vector. * @return {number} The square of the length of a. */ -o3djs.math.lengthSquared = function(a) { +o3djs.flat_math.lengthSquared = function(a) { var r = 0.0; var aLength = a.length; for (var i = 0; i < aLength; ++i) @@ -429,11 +803,11 @@ o3djs.math.lengthSquared = function(a) { /** * Computes the Euclidean distance between two vectors. - * @param {!o3djs.math.Vector} a A vector. - * @param {!o3djs.math.Vector} b A vector. + * @param {!o3djs.flat_math.Vector} a A vector. + * @param {!o3djs.flat_math.Vector} b A vector. * @return {number} The distance between a and b. */ -o3djs.math.distance = function(a, b) { +o3djs.flat_math.distance = function(a, b) { var r = 0.0; var aLength = a.length; for (var i = 0; i < aLength; ++i) { @@ -445,11 +819,11 @@ o3djs.math.distance = function(a, b) { /** * Computes the square of the Euclidean distance between two vectors. - * @param {!o3djs.math.Vector} a A vector. - * @param {!o3djs.math.Vector} b A vector. + * @param {!o3djs.flat_math.Vector} a A vector. + * @param {!o3djs.flat_math.Vector} b A vector. * @return {number} The distance between a and b. */ -o3djs.math.distanceSquared = function(a, b) { +o3djs.flat_math.distanceSquared = function(a, b) { var r = 0.0; var aLength = a.length; for (var i = 0; i < aLength; ++i) { @@ -461,59 +835,48 @@ o3djs.math.distanceSquared = function(a, b) { /** * Divides a vector by its Euclidean length and returns the quotient. - * @param {!o3djs.math.Vector} a The vector. - * @return {!o3djs.math.Vector} The normalized vector. + * @param {!o3djs.flat_math.Vector} a The vector. + * @return {!o3djs.flat_math.Vector} The normalized vector. */ -o3djs.math.normalize = function(a) { - var r = []; - var n = 0.0; +o3djs.flat_math.normalize = function(a) { var aLength = a.length; - for (var i = 0; i < aLength; ++i) + var r = new o3djs.flat_math.Vector(aLength); + var n = 0.0; + var i; + for (i = 0; i < aLength; ++i) n += a[i] * a[i]; n = Math.sqrt(n); - for (var i = 0; i < aLength; ++i) + for (i = 0; i < aLength; ++i) r[i] = a[i] / n; return r; }; /** * Adds two matrices; assumes a and b are the same size. - * @param {!o3djs.math.Matrix} a Operand matrix. - * @param {!o3djs.math.Matrix} b Operand matrix. - * @return {!o3djs.math.Matrix} The sum of a and b. + * @param {!o3djs.flat_math.Matrix} a Operand matrix. + * @param {!o3djs.flat_math.Matrix} b Operand matrix. + * @return {!o3djs.flat_math.Matrix} The sum of a and b. */ -o3djs.math.addMatrix = function(a, b) { - var r = []; +o3djs.flat_math.addMatrix = function(a, b) { var aLength = a.length; - var a0Length = a[0].length; + var r = new o3djs.flat_math.Matrix(aLength); for (var i = 0; i < aLength; ++i) { - var row = []; - var ai = a[i]; - var bi = b[i]; - for (var j = 0; j < a0Length; ++j) - row[j] = ai[j] + bi[j]; - r[i] = row; + r[i] = a[i] + b[i]; } return r; }; /** * Subtracts two matrices; assumes a and b are the same size. - * @param {!o3djs.math.Matrix} a Operand matrix. - * @param {!o3djs.math.Matrix} b Operand matrix. - * @return {!o3djs.math.Matrix} The sum of a and b. + * @param {!o3djs.flat_math.Matrix} a Operand matrix. + * @param {!o3djs.flat_math.Matrix} b Operand matrix. + * @return {!o3djs.flat_math.Matrix} The sum of a and b. */ -o3djs.math.subMatrix = function(a, b) { - var r = []; +o3djs.flat_math.subMatrix = function(a, b) { var aLength = a.length; - var a0Length = a[0].length; + var r = new o3djs.flat_math.Matrix(aLength); for (var i = 0; i < aLength; ++i) { - var row = []; - var ai = a[i]; - var bi = b[i]; - for (var j = 0; j < a0Length; ++j) - row[j] = ai[j] - bi[j]; - r[i] = row; + r[i] = a[i] - b[i]; } return r; }; @@ -522,40 +885,31 @@ o3djs.math.subMatrix = function(a, b) { * Performs linear interpolation on two matrices. * Given matrices a and b and interpolation coefficient t, returns * (1 - t) * a + t * b. - * @param {!o3djs.math.Matrix} a Operand matrix. - * @param {!o3djs.math.Matrix} b Operand matrix. + * @param {!o3djs.flat_math.Matrix} a Operand matrix. + * @param {!o3djs.flat_math.Matrix} b Operand matrix. * @param {number} t Interpolation coefficient. - * @return {!o3djs.math.Matrix} The weighted of a and b. + * @return {!o3djs.flat_math.Matrix} Interpolated a and b. */ -o3djs.math.lerpMatrix = function(a, b, t) { - var r = []; +o3djs.flat_math.lerpMatrix = function(a, b, t) { var aLength = a.length; - var a0Length = a[0].length; + var r = new o3djs.flat_math.Matrix(aLength); for (var i = 0; i < aLength; ++i) { - var row = []; - var ai = a[i]; - var bi = b[i]; - for (var j = 0; j < a0Length; ++j) - row[j] = (1 - t) * ai[j] + t * bi[j]; - r[i] = row; + r[i] = (1 - t) * a[i] + t * b[i]; } return r; }; /** - * Divides a matrix by a scalar. - * @param {!o3djs.math.Matrix} m The matrix. - * @param {number} k The scalar. - * @return {!o3djs.math.Matrix} The matrix m divided by k. + * Divides a matrix by a scalar; assumes a and b are the same size. + * @param {!o3djs.flat_math.Matrix} a Operand matrix. + * @param {number} b scalar + * @return {!o3djs.flat_math.Matrix} The division of a by b. */ -o3djs.math.divMatrixScalar = function(m, k) { - var r = []; - var mLength = m.length; - var m0Length = m[0].length; - for (var i = 0; i < mLength; ++i) { - r[i] = []; - for (var j = 0; j < m0Length; ++j) - r[i][j] = m[i][j] / k; +o3djs.flat_math.divMatrixScalar = function(a, b) { + var aLength = a.length; + var r = new o3djs.flat_math.Matrix(aLength); + for (var i = 0; i < aLength; ++i) { + r[i] = a[i] / b; } return r; }; @@ -565,18 +919,18 @@ o3djs.math.divMatrixScalar = function(m, k) { * @param {number} a The scalar. * @return {number} -a. */ -o3djs.math.negativeScalar = function(a) { +o3djs.flat_math.negativeScalar = function(a) { return -a; }; /** * Negates a vector. - * @param {!o3djs.math.Vector} v The vector. - * @return {!o3djs.math.Vector} -v. + * @param {!o3djs.flat_math.Vector} v The vector. + * @return {!o3djs.flat_math.Vector} -v. */ -o3djs.math.negativeVector = function(v) { - var r = []; +o3djs.flat_math.negativeVector = function(v) { var vLength = v.length; + var r = new o3djs.flat_math.Vector(vLength); for (var i = 0; i < vLength; ++i) { r[i] = -v[i]; } @@ -585,17 +939,14 @@ o3djs.math.negativeVector = function(v) { /** * Negates a matrix. - * @param {!o3djs.math.Matrix} m The matrix. - * @return {!o3djs.math.Matrix} -m. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Matrix} -m. */ -o3djs.math.negativeMatrix = function(m) { - var r = []; +o3djs.flat_math.negativeMatrix = function(m) { var mLength = m.length; - var m0Length = m[0].length; + var r = new o3djs.flat_math.Matrix(mLength); for (var i = 0; i < mLength; ++i) { - r[i] = []; - for (var j = 0; j < m0Length; ++j) - r[i][j] = -m[i][j]; + r[i] = -m[i]; } return r; }; @@ -605,57 +956,56 @@ o3djs.math.negativeMatrix = function(m) { * @param {number} a The scalar. * @return {number} a. */ -o3djs.math.copyScalar = function(a) { +o3djs.flat_math.copyScalar = function(a) { return a; }; /** * Copies a vector. - * @param {!o3djs.math.Vector} v The vector. - * @return {!o3djs.math.Vector} A copy of v. + * @param {!o3djs.flat_math.Vector} v The vector. + * @return {!o3djs.flat_math.Vector} A copy of v. */ -o3djs.math.copyVector = function(v) { - var r = []; - for (var i = 0; i < v.length; i++) +o3djs.flat_math.copyVector = function(v) { + var vLength = v.length; + var r = new o3djs.flat_math.Vector(vLength); + for (var i = 0; i < vLength; i++) r[i] = v[i]; return r; }; /** - * Copies a matrix. - * @param {!o3djs.math.Matrix} m The matrix. - * @return {!o3djs.math.Matrix} A copy of m. + * Copies a vector. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Vector} r Set to a copy of v. */ -o3djs.math.copyMatrix = function(m) { - var r = []; - var mLength = m.length; - for (var i = 0; i < mLength; ++i) { - r[i] = []; - for (var j = 0; j < m[i].length; j++) { - r[i][j] = m[i][j]; - } - } - return r; +o3djs.flat_math.copyVectorTo = function(v, r) { + var vLength = v.length; + for (var i = 0; i < vLength; i++) + r[i] = v[i]; }; /** - * Returns the elements of a matrix as a one-dimensional array. The + * Copies a matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Matrix} A copy of m. + */ +o3djs.flat_math.copyMatrix = o3djs.flat_math.copyVector; + +/** + * Copies a matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Matrix} A copy of m. + */ +o3djs.flat_math.copyMatrixTo = o3djs.flat_math.copyVectorTo; + +/** + * Returns the elements of a matrix as a copied one-dimensional array. The * rows or columns (depending on whether the matrix is row-major or * column-major) are concatenated. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @return {!Array.<number>} The matrix's elements as a one-dimensional array. */ -o3djs.math.getMatrixElements = function(m) { - var r = []; - var mLength = m.length; - var k = 0; - for (var i = 0; i < mLength; i++) { - for (var j = 0; j < m[i].length; j++) { - r[k++] = m[i][j]; - } - } - return r; -}; +o3djs.flat_math.getMatrixElements = o3djs.flat_math.copyMatrix; /** * Multiplies two scalars. @@ -663,19 +1013,19 @@ o3djs.math.getMatrixElements = function(m) { * @param {number} b Operand scalar. * @return {number} The product of a and b. */ -o3djs.math.mulScalarScalar = function(a, b) { +o3djs.flat_math.mulScalarScalar = function(a, b) { return a * b; }; /** * Multiplies a scalar by a vector. * @param {number} k The scalar. - * @param {!o3djs.math.Vector} v The vector. - * @return {!o3djs.math.Vector} The product of k and v. + * @param {!o3djs.flat_math.Vector} v The vector. + * @return {!o3djs.flat_math.Vector} The product of k and v. */ -o3djs.math.mulScalarVector = function(k, v) { - var r = []; +o3djs.flat_math.mulScalarVector = function(k, v) { var vLength = v.length; + var r = new o3djs.flat_math.Vector(vLength); for (var i = 0; i < vLength; ++i) { r[i] = k * v[i]; } @@ -684,53 +1034,41 @@ o3djs.math.mulScalarVector = function(k, v) { /** * Multiplies a vector by a scalar. - * @param {!o3djs.math.Vector} v The vector. + * @param {!o3djs.flat_math.Vector} v The vector. * @param {number} k The scalar. - * @return {!o3djs.math.Vector} The product of k and v. + * @return {!o3djs.flat_math.Vector} The product of k and v. */ -o3djs.math.mulVectorScalar = function(v, k) { - return o3djs.math.mulScalarVector(k, v); +o3djs.flat_math.mulVectorScalar = function(v, k) { + return o3djs.flat_math.mulScalarVector(k, v); }; /** * Multiplies a scalar by a matrix. * @param {number} k The scalar. - * @param {!o3djs.math.Matrix} m The matrix. - * @return {!o3djs.math.Matrix} The product of m and k. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Matrix} The product of m and k. */ -o3djs.math.mulScalarMatrix = function(k, m) { - var r = []; - var mLength = m.length; - var m0Length = m[0].length; - for (var i = 0; i < mLength; ++i) { - r[i] = []; - for (var j = 0; j < m0Length; ++j) - r[i][j] = k * m[i][j]; - } - return r; -}; +o3djs.flat_math.mulScalarMatrix = o3djs.flat_math.mulScalarVector; /** * Multiplies a matrix by a scalar. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @param {number} k The scalar. - * @return {!o3djs.math.Matrix} The product of m and k. + * @return {!o3djs.flat_math.Matrix} The product of m and k. */ -o3djs.math.mulMatrixScalar = function(m, k) { - return o3djs.math.mulScalarMatrix(k, m); -}; +o3djs.flat_math.mulMatrixScalar = o3djs.flat_math.mulVectorScalar; /** * Multiplies a vector by another vector (component-wise); assumes a and * b have the same length. - * @param {!o3djs.math.Vector} a Operand vector. - * @param {!o3djs.math.Vector} b Operand vector. - * @return {!o3djs.math.Vector} The vector of products of entries of a and + * @param {!o3djs.flat_math.Vector} a Operand vector. + * @param {!o3djs.flat_math.Vector} b Operand vector. + * @return {!o3djs.flat_math.Vector} The vector of products of entries of a and * b. */ -o3djs.math.mulVectorVector = function(a, b) { - var r = []; +o3djs.flat_math.mulVectorVector = function(a, b) { var aLength = a.length; + var r = new o3djs.flat_math.Vector(aLength); for (var i = 0; i < aLength; ++i) r[i] = a[i] * b[i]; return r; @@ -739,14 +1077,14 @@ o3djs.math.mulVectorVector = function(a, b) { /** * Divides a vector by another vector (component-wise); assumes a and * b have the same length. - * @param {!o3djs.math.Vector} a Operand vector. - * @param {!o3djs.math.Vector} b Operand vector. - * @return {!o3djs.math.Vector} The vector of quotients of entries of a and + * @param {!o3djs.flat_math.Vector} a Operand vector. + * @param {!o3djs.flat_math.Vector} b Operand vector. + * @return {!o3djs.flat_math.Vector} The vector of quotients of entries of a and * b. */ -o3djs.math.divVectorVector = function(a, b) { - var r = []; +o3djs.flat_math.divVectorVector = function(a, b) { var aLength = a.length; + var r = new o3djs.flat_math.Vector(aLength); for (var i = 0; i < aLength; ++i) r[i] = a[i] / b[i]; return r; @@ -754,398 +1092,490 @@ o3djs.math.divVectorVector = function(a, b) { /** * Multiplies a vector by a matrix; treats the vector as a row vector; assumes - * matrix entries are accessed in [row][column] fashion. - * @param {!o3djs.math.Vector} v The vector. - * @param {!o3djs.math.Matrix} m The matrix. - * @return {!o3djs.math.Vector} The product of v and m as a row vector. + * matrix entries are accessed in [row*4+column] fashion. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Vector} The product of v and m as a row vector. + */ +o3djs.flat_math.rowMajor.mulVectorMatrix4 = function(v, m) { + var r = new o3djs.flat_math.Vector(16); + for (var i = 0; i < 4; ++i) { + r[i] = 0.0; + for (var j = 0; j < 4; ++j) + r[i] += v[j] * m[j * 4 + i]; + } + return r; +}; + +/** + * Multiplies a vector by a matrix; treats the vector as a row vector; assumes + * matrix entries are accessed in [row*2+column] fashion. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @returns {!o3djs.flat_math.Vector} The product of v and m as a row vector. + */ +o3djs.flat_math.rowMajor.mulVectorMatrix2 = function(v, m) { + var r = new o3djs.flat_math.Vector(4); + for (var i = 0; i < 2; ++i) { + r[i] = 0.0; + for (var j = 0; j < 2; ++j) + r[i] += v[j] * m[j * 2 + i]; + } + return r; +}; + + +/** + * Multiplies a vector by a matrix; treats the vector as a row vector; assumes + * matrix entries are accessed in [row*3+column] fashion. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @returns {!o3djs.flat_math.Vector} The product of v and m as a row vector. + */ +o3djs.flat_math.rowMajor.mulVectorMatrix3 = function(v, m) { + var r = new o3djs.flat_math.Vector(9); + for (var i = 0; i < 3; ++i) { + r[i] = 0.0; + for (var j = 0; j < 3; ++j) + r[i] += v[j] * m[j * 3 + i]; + } + return r; +}; + + +/** + * Multiplies a vector by a matrix; treats the vector as a row vector; assumes + * matrix entries are accessed in [row*dimension+column] fashion. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Vector} The product of v and m as a row vector. + */ +o3djs.flat_math.rowMajor.mulVectorMatrix = function(v, m) { + switch(m.length) { + case 4: + return o3djs.flat_math.rowMajor.mulVectorMatrix2(v, m); + case 9: + return o3djs.flat_math.rowMajor.mulVectorMatrix3(v, m); + case 16: + return o3djs.flat_math.rowMajor.mulVectorMatrix4(v, m); + default: + throw "Cannot handle matrices of size other than 3x3 or 4x4"; + } +}; + + + +/** + * Multiplies a vector by a matrix; treats the vector as a row vector; assumes + * matrix entries are accessed in [column*4+row] fashion. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Vector} r The product of v and m as a row vector. + */ +o3djs.flat_math.rowMajor.mulMatrixVector4 = function(m, v) { + var r = new o3djs.flat_math.Vector(4); + var vLength = v.length; + for (var i = 0; i < 4; ++i) { + r[i] = 0.0; + for (var j = 0; j < 4; ++j) + r[i] += v[j] * m[i * 4 + j]; + } + return r; +}; + + +/** + * Multiplies a vector by a matrix; treats the vector as a row vector; assumes + * matrix entries are accessed in [column*3+row] fashion. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Vector} r The product of v and m as a row vector. */ -o3djs.math.rowMajor.mulVectorMatrix = function(v, m) { - var r = []; - var m0Length = m[0].length; +o3djs.flat_math.rowMajor.mulMatrixVector3 = function(m, v) { + var r = new o3djs.flat_math.Vector(3); var vLength = v.length; - for (var i = 0; i < m0Length; ++i) { + for (var i = 0; i < 3; ++i) { r[i] = 0.0; - for (var j = 0; j < vLength; ++j) - r[i] += v[j] * m[j][i]; + for (var j = 0; j < 3; ++j) + r[i] += v[j] * m[i * 3 + j]; } return r; }; /** * Multiplies a vector by a matrix; treats the vector as a row vector; assumes - * matrix entries are accessed in [column][row] fashion. - * @param {!o3djs.math.Vector} v The vector. - * @param {!o3djs.math.Matrix} m The matrix. - * @return {!o3djs.math.Vector} The product of v and m as a row vector. + * matrix entries are accessed in [column*2+row] fashion. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Vector} r The product of v and m as a row vector. */ -o3djs.math.columnMajor.mulVectorMatrix = function(v, m) { - var r = []; - var mLength = m.length; +o3djs.flat_math.rowMajor.mulMatrixVector2 = function(m, v) { + var r = new o3djs.flat_math.Vector(2); + var vLength = v.length; - for (var i = 0; i < mLength; ++i) { + for (var i = 0; i < 2; ++i) { r[i] = 0.0; - var column = m[i]; - for (var j = 0; j < vLength; ++j) - r[i] += v[j] * column[j]; + for (var j = 0; j < 2; ++j) + r[i] += v[j] * m[i * 2 + j]; } return r; }; + +/** + * Multiplies a vector by a matrix; treats the vector as a row vector; assumes + * matrix entries are accessed in [column*dimension+row] fashion. + * @param {!o3djs.flat_math.Vector} v The vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Vector} The product of v and m as a row vector. + */ +o3djs.flat_math.rowMajor.mulMatrixVector = function(m, v) { + switch(m.length) { + case 4: + return o3djs.flat_math.rowMajor.mulMatrixVector2(m, v); + case 9: + return o3djs.flat_math.rowMajor.mulMatrixVector3(m, v); + case 16: + return o3djs.flat_math.rowMajor.mulMatrixVector4(m, v); + default: + throw "Cannot handle matrices of size other than 3x3 or 4x4"; + } +}; + /** * Multiplies a vector by a matrix; treats the vector as a row vector. - * @param {!o3djs.math.Matrix} m The matrix. - * @param {!o3djs.math.Vector} v The vector. - * @return {!o3djs.math.Vector} The product of m and v as a row vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Vector} v The vector. + * @return {!o3djs.flat_math.Vector} The product of m and v as a row vector. */ -o3djs.math.mulVectorMatrix = null; +o3djs.flat_math.mulVectorMatrix = null; /** * Multiplies a matrix by a vector; treats the vector as a column vector. * assumes matrix entries are accessed in [row][column] fashion. - * @param {!o3djs.math.Matrix} m The matrix. - * @param {!o3djs.math.Vector} v The vector. - * @return {!o3djs.math.Vector} The product of m and v as a column vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Vector} v The vector. + * @return {!o3djs.flat_math.Vector} The product of m and v as a column vector. */ -o3djs.math.rowMajor.mulMatrixVector = function(m, v) { - var r = []; - var mLength = m.length; - var m0Length = m[0].length; - for (var i = 0; i < mLength; ++i) { - r[i] = 0.0; - var row = m[i]; - for (var j = 0; j < m0Length; ++j) - r[i] += row[j] * v[j]; - } - return r; +o3djs.flat_math.columnMajor.mulVectorMatrix = function (v, m) { + return o3djs.flat_math.rowMajor.mulMatrixVector(m, v); }; /** * Multiplies a matrix by a vector; treats the vector as a column vector; * assumes matrix entries are accessed in [column][row] fashion. - * @param {!o3djs.math.Matrix} m The matrix. - * @param {!o3djs.math.Vector} v The vector. - * @return {!o3djs.math.Vector} The product of m and v as a column vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Vector} v The vector. + * @return {!o3djs.flat_math.Vector} The product of m and v as a column vector. */ -o3djs.math.columnMajor.mulMatrixVector = function(m, v) { - var r = []; - var m0Length = m[0].length; - var vLength = v.length; - for (var i = 0; i < m0Length; ++i) { - r[i] = 0.0; - for (var j = 0; j < vLength; ++j) - r[i] += v[j] * m[j][i]; - } - return r; +o3djs.flat_math.columnMajor.mulMatrixVector = function(m, v) { + return o3djs.flat_math.rowMajor.mulVectorMatrix(v, m); }; /** * Multiplies a matrix by a vector; treats the vector as a column vector. - * @param {!o3djs.math.Matrix} m The matrix. - * @param {!o3djs.math.Vector} v The vector. - * @return {!o3djs.math.Vector} The product of m and v as a column vector. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Vector} v The vector. + * @return {!o3djs.flat_math.Vector} The product of m and v as a column vector. */ -o3djs.math.mulMatrixVector = null; +o3djs.flat_math.mulMatrixVector = null; /** * Multiplies two 2-by-2 matrices; assumes that the given matrices are 2-by-2; * assumes matrix entries are accessed in [row][column] fashion. - * @param {!o3djs.math.Matrix2} a The matrix on the left. - * @param {!o3djs.math.Matrix2} b The matrix on the right. - * @return {!o3djs.math.Matrix2} The matrix product of a and b. + * @param {!o3djs.flat_math.Matrix2} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix2} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix2} The matrix product of a and b. */ -o3djs.math.rowMajor.mulMatrixMatrix2 = function(a, b) { +o3djs.flat_math.rowMajor.mulMatrixMatrix2 = function(a, b) { var a0 = a[0]; var a1 = a[1]; var b0 = b[0]; var b1 = b[1]; - var a00 = a0[0]; - var a01 = a0[1]; - var a10 = a1[0]; - var a11 = a1[1]; - var b00 = b0[0]; - var b01 = b0[1]; - var b10 = b1[0]; - var b11 = b1[1]; - return [[a00 * b00 + a01 * b10, a00 * b01 + a01 * b11], - [a10 * b00 + a11 * b10, a10 * b01 + a11 * b11]]; + var a00 = a[0]; + var a01 = a[1]; + var a10 = a[2]; + var a11 = a[3]; + var b00 = b[0]; + var b01 = b[1]; + var b10 = b[2]; + var b11 = b[3]; + return o3djs.flat_math.makeMatrix2(a00 * b00 + a01 * b10, a00 * b01 + a01 * b11, + a10 * b00 + a11 * b10, a10 * b01 + a11 * b11); }; /** * Multiplies two 2-by-2 matrices; assumes that the given matrices are 2-by-2; * assumes matrix entries are accessed in [column][row] fashion. - * @param {!o3djs.math.Matrix2} a The matrix on the left. - * @param {!o3djs.math.Matrix2} b The matrix on the right. - * @return {!o3djs.math.Matrix2} The matrix product of a and b. + * @param {!o3djs.flat_math.Matrix2} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix2} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix2} The matrix product of a and b. */ -o3djs.math.columnMajor.mulMatrixMatrix2 = function(a, b) { +o3djs.flat_math.columnMajor.mulMatrixMatrix2 = function(a, b) { var a0 = a[0]; var a1 = a[1]; var b0 = b[0]; var b1 = b[1]; - var a00 = a0[0]; - var a01 = a0[1]; - var a10 = a1[0]; - var a11 = a1[1]; - var b00 = b0[0]; - var b01 = b0[1]; - var b10 = b1[0]; - var b11 = b1[1]; - return [[a00 * b00 + a10 * b01, a01 * b00 + a11 * b01], - [a00 * b10 + a10 * b11, a01 * b10 + a11 * b11]]; + var a00 = a[0]; + var a01 = a[1]; + var a10 = a[2]; + var a11 = a[3]; + var b00 = b[0]; + var b01 = b[1]; + var b10 = b[2]; + var b11 = b[3]; + return o3djs.flat_math.makeMatrix2(a00 * b00 + a10 * b01, a01 * b00 + a11 * b01, + a00 * b10 + a10 * b11, a01 * b10 + a11 * b11); }; /** * Multiplies two 2-by-2 matrices. - * @param {!o3djs.math.Matrix2} a The matrix on the left. - * @param {!o3djs.math.Matrix2} b The matrix on the right. - * @return {!o3djs.math.Matrix2} The matrix product of a and b. + * @param {!o3djs.flat_math.Matrix2} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix2} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix2} The matrix product of a and b. */ -o3djs.math.mulMatrixMatrix2 = null; +o3djs.flat_math.mulMatrixMatrix2 = null; /** * Multiplies two 3-by-3 matrices; assumes that the given matrices are 3-by-3; * assumes matrix entries are accessed in [row][column] fashion. - * @param {!o3djs.math.Matrix3} a The matrix on the left. - * @param {!o3djs.math.Matrix3} b The matrix on the right. - * @return {!o3djs.math.Matrix3} The matrix product of a and b. + * @param {!o3djs.flat_math.Matrix3} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix3} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix3} The matrix product of a and b. */ -o3djs.math.rowMajor.mulMatrixMatrix3 = function(a, b) { +o3djs.flat_math.rowMajor.mulMatrixMatrix3 = function(a, b) { var a0 = a[0]; var a1 = a[1]; var a2 = a[2]; var b0 = b[0]; var b1 = b[1]; var b2 = b[2]; - var a00 = a0[0]; - var a01 = a0[1]; - var a02 = a0[2]; - var a10 = a1[0]; - var a11 = a1[1]; - var a12 = a1[2]; - var a20 = a2[0]; - var a21 = a2[1]; - var a22 = a2[2]; - var b00 = b0[0]; - var b01 = b0[1]; - var b02 = b0[2]; - var b10 = b1[0]; - var b11 = b1[1]; - var b12 = b1[2]; - var b20 = b2[0]; - var b21 = b2[1]; - var b22 = b2[2]; - return [[a00 * b00 + a01 * b10 + a02 * b20, + var a00 = a[0]; + var a01 = a[1]; + var a02 = a[2]; + var a10 = a[3]; + var a11 = a[4]; + var a12 = a[5]; + var a20 = a[6]; + var a21 = a[7]; + var a22 = a[8]; + var b00 = b[0]; + var b01 = b[1]; + var b02 = b[2]; + var b10 = b[3]; + var b11 = b[4]; + var b12 = b[5]; + var b20 = b[6]; + var b21 = b[7]; + var b22 = b[8]; + return o3djs.flat_math.makeMatrix3(a00 * b00 + a01 * b10 + a02 * b20, a00 * b01 + a01 * b11 + a02 * b21, - a00 * b02 + a01 * b12 + a02 * b22], - [a10 * b00 + a11 * b10 + a12 * b20, + a00 * b02 + a01 * b12 + a02 * b22, + a10 * b00 + a11 * b10 + a12 * b20, a10 * b01 + a11 * b11 + a12 * b21, - a10 * b02 + a11 * b12 + a12 * b22], - [a20 * b00 + a21 * b10 + a22 * b20, + a10 * b02 + a11 * b12 + a12 * b22, + a20 * b00 + a21 * b10 + a22 * b20, a20 * b01 + a21 * b11 + a22 * b21, - a20 * b02 + a21 * b12 + a22 * b22]]; + a20 * b02 + a21 * b12 + a22 * b22); }; /** * Multiplies two 3-by-3 matrices; assumes that the given matrices are 3-by-3; * assumes matrix entries are accessed in [column][row] fashion. - * @param {!o3djs.math.Matrix3} a The matrix on the left. - * @param {!o3djs.math.Matrix3} b The matrix on the right. - * @return {!o3djs.math.Matrix3} The matrix product of a and b. - */ -o3djs.math.columnMajor.mulMatrixMatrix3 = function(a, b) { - var a0 = a[0]; - var a1 = a[1]; - var a2 = a[2]; - var b0 = b[0]; - var b1 = b[1]; - var b2 = b[2]; - var a00 = a0[0]; - var a01 = a0[1]; - var a02 = a0[2]; - var a10 = a1[0]; - var a11 = a1[1]; - var a12 = a1[2]; - var a20 = a2[0]; - var a21 = a2[1]; - var a22 = a2[2]; - var b00 = b0[0]; - var b01 = b0[1]; - var b02 = b0[2]; - var b10 = b1[0]; - var b11 = b1[1]; - var b12 = b1[2]; - var b20 = b2[0]; - var b21 = b2[1]; - var b22 = b2[2]; - return [[a00 * b00 + a10 * b01 + a20 * b02, + * @param {!o3djs.flat_math.Matrix3} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix3} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix3} The matrix product of a and b. + */ +o3djs.flat_math.columnMajor.mulMatrixMatrix3 = function(a, b) { + + var a00 = a[0]; + var a01 = a[1]; + var a02 = a[2]; + var a10 = a[3]; + var a11 = a[4]; + var a12 = a[5]; + var a20 = a[6]; + var a21 = a[7]; + var a22 = a[8]; + var b00 = b[0]; + var b01 = b[1]; + var b02 = b[2]; + var b10 = b[3]; + var b11 = b[4]; + var b12 = b[5]; + var b20 = b[6]; + var b21 = b[7]; + var b22 = b[8]; + + return o3djs.flat_math.makeMatrix4(a00 * b00 + a10 * b01 + a20 * b02, a01 * b00 + a11 * b01 + a21 * b02, - a02 * b00 + a12 * b01 + a22 * b02], - [a00 * b10 + a10 * b11 + a20 * b12, + a02 * b00 + a12 * b01 + a22 * b02, + a00 * b10 + a10 * b11 + a20 * b12, a01 * b10 + a11 * b11 + a21 * b12, - a02 * b10 + a12 * b11 + a22 * b12], - [a00 * b20 + a10 * b21 + a20 * b22, + a02 * b10 + a12 * b11 + a22 * b12, + a00 * b20 + a10 * b21 + a20 * b22, a01 * b20 + a11 * b21 + a21 * b22, - a02 * b20 + a12 * b21 + a22 * b22]]; + a02 * b20 + a12 * b21 + a22 * b22); }; /** * Multiplies two 3-by-3 matrices; assumes that the given matrices are 3-by-3. - * @param {!o3djs.math.Matrix3} a The matrix on the left. - * @param {!o3djs.math.Matrix3} b The matrix on the right. - * @return {!o3djs.math.Matrix3} The matrix product of a and b. + * @param {!o3djs.flat_math.Matrix3} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix3} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix3} The matrix product of a and b. */ -o3djs.math.mulMatrixMatrix3 = null; +o3djs.flat_math.mulMatrixMatrix3 = null; /** * Multiplies two 4-by-4 matrices; assumes that the given matrices are 4-by-4; * assumes matrix entries are accessed in [row][column] fashion. - * @param {!o3djs.math.Matrix4} a The matrix on the left. - * @param {!o3djs.math.Matrix4} b The matrix on the right. - * @return {!o3djs.math.Matrix4} The matrix product of a and b. - */ -o3djs.math.rowMajor.mulMatrixMatrix4 = function(a, b) { - var a0 = a[0]; - var a1 = a[1]; - var a2 = a[2]; - var a3 = a[3]; - var b0 = b[0]; - var b1 = b[1]; - var b2 = b[2]; - var b3 = b[3]; - var a00 = a0[0]; - var a01 = a0[1]; - var a02 = a0[2]; - var a03 = a0[3]; - var a10 = a1[0]; - var a11 = a1[1]; - var a12 = a1[2]; - var a13 = a1[3]; - var a20 = a2[0]; - var a21 = a2[1]; - var a22 = a2[2]; - var a23 = a2[3]; - var a30 = a3[0]; - var a31 = a3[1]; - var a32 = a3[2]; - var a33 = a3[3]; - var b00 = b0[0]; - var b01 = b0[1]; - var b02 = b0[2]; - var b03 = b0[3]; - var b10 = b1[0]; - var b11 = b1[1]; - var b12 = b1[2]; - var b13 = b1[3]; - var b20 = b2[0]; - var b21 = b2[1]; - var b22 = b2[2]; - var b23 = b2[3]; - var b30 = b3[0]; - var b31 = b3[1]; - var b32 = b3[2]; - var b33 = b3[3]; - return [[a00 * b00 + a01 * b10 + a02 * b20 + a03 * b30, + * @param {!o3djs.flat_math.Matrix4} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix4} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix4} The matrix product of a and b. + */ +o3djs.flat_math.rowMajor.mulMatrixMatrix4 = function(a, b) { + + var a00 = a[0]; + var a01 = a[1]; + var a02 = a[2]; + var a03 = a[3]; + var a10 = a[4]; + var a11 = a[5]; + var a12 = a[6]; + var a13 = a[7]; + var a20 = a[8]; + var a21 = a[9]; + var a22 = a[10]; + var a23 = a[11]; + var a30 = a[12]; + var a31 = a[13]; + var a32 = a[14]; + var a33 = a[15]; + var b00 = b[0]; + var b01 = b[1]; + var b02 = b[2]; + var b03 = b[3]; + var b10 = b[4]; + var b11 = b[5]; + var b12 = b[6]; + var b13 = b[7]; + var b20 = b[8]; + var b21 = b[9]; + var b22 = b[10]; + var b23 = b[11]; + var b30 = b[12]; + var b31 = b[13]; + var b32 = b[14]; + var b33 = b[15]; + return o3djs.flat_math.makeMatrix4(a00 * b00 + a01 * b10 + a02 * b20 + a03 * b30, a00 * b01 + a01 * b11 + a02 * b21 + a03 * b31, a00 * b02 + a01 * b12 + a02 * b22 + a03 * b32, - a00 * b03 + a01 * b13 + a02 * b23 + a03 * b33], - [a10 * b00 + a11 * b10 + a12 * b20 + a13 * b30, + a00 * b03 + a01 * b13 + a02 * b23 + a03 * b33, + a10 * b00 + a11 * b10 + a12 * b20 + a13 * b30, a10 * b01 + a11 * b11 + a12 * b21 + a13 * b31, a10 * b02 + a11 * b12 + a12 * b22 + a13 * b32, - a10 * b03 + a11 * b13 + a12 * b23 + a13 * b33], - [a20 * b00 + a21 * b10 + a22 * b20 + a23 * b30, + a10 * b03 + a11 * b13 + a12 * b23 + a13 * b33, + a20 * b00 + a21 * b10 + a22 * b20 + a23 * b30, a20 * b01 + a21 * b11 + a22 * b21 + a23 * b31, a20 * b02 + a21 * b12 + a22 * b22 + a23 * b32, - a20 * b03 + a21 * b13 + a22 * b23 + a23 * b33], - [a30 * b00 + a31 * b10 + a32 * b20 + a33 * b30, + a20 * b03 + a21 * b13 + a22 * b23 + a23 * b33, + a30 * b00 + a31 * b10 + a32 * b20 + a33 * b30, a30 * b01 + a31 * b11 + a32 * b21 + a33 * b31, a30 * b02 + a31 * b12 + a32 * b22 + a33 * b32, - a30 * b03 + a31 * b13 + a32 * b23 + a33 * b33]]; + a30 * b03 + a31 * b13 + a32 * b23 + a33 * b33); }; /** * Multiplies two 4-by-4 matrices; assumes that the given matrices are 4-by-4; * assumes matrix entries are accessed in [column][row] fashion. - * @param {!o3djs.math.Matrix4} a The matrix on the left. - * @param {!o3djs.math.Matrix4} b The matrix on the right. - * @return {!o3djs.math.Matrix4} The matrix product of a and b. - */ -o3djs.math.columnMajor.mulMatrixMatrix4 = function(a, b) { - var a0 = a[0]; - var a1 = a[1]; - var a2 = a[2]; - var a3 = a[3]; - var b0 = b[0]; - var b1 = b[1]; - var b2 = b[2]; - var b3 = b[3]; - var a00 = a0[0]; - var a01 = a0[1]; - var a02 = a0[2]; - var a03 = a0[3]; - var a10 = a1[0]; - var a11 = a1[1]; - var a12 = a1[2]; - var a13 = a1[3]; - var a20 = a2[0]; - var a21 = a2[1]; - var a22 = a2[2]; - var a23 = a2[3]; - var a30 = a3[0]; - var a31 = a3[1]; - var a32 = a3[2]; - var a33 = a3[3]; - var b00 = b0[0]; - var b01 = b0[1]; - var b02 = b0[2]; - var b03 = b0[3]; - var b10 = b1[0]; - var b11 = b1[1]; - var b12 = b1[2]; - var b13 = b1[3]; - var b20 = b2[0]; - var b21 = b2[1]; - var b22 = b2[2]; - var b23 = b2[3]; - var b30 = b3[0]; - var b31 = b3[1]; - var b32 = b3[2]; - var b33 = b3[3]; - return [[a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03, - a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03, - a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03, - a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03], - [a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13, - a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13, - a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13, - a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13], - [a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23, - a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23, - a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23, - a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23], - [a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33, - a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33, - a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33, - a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33]]; + * @param {!o3djs.flat_math.Matrix4} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix4} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix4} The matrix product of a and b. + */ +o3djs.flat_math.columnMajor.mulMatrixMatrix4 = function(a, b) { + + var a00 = a[0]; + var a01 = a[1]; + var a02 = a[2]; + var a03 = a[3]; + var a10 = a[4]; + var a11 = a[5]; + var a12 = a[6]; + var a13 = a[7]; + var a20 = a[8]; + var a21 = a[9]; + var a22 = a[10]; + var a23 = a[11]; + var a30 = a[12]; + var a31 = a[13]; + var a32 = a[14]; + var a33 = a[15]; + var b00 = b[0]; + var b01 = b[1]; + var b02 = b[2]; + var b03 = b[3]; + var b10 = b[4]; + var b11 = b[5]; + var b12 = b[6]; + var b13 = b[7]; + var b20 = b[8]; + var b21 = b[9]; + var b22 = b[10]; + var b23 = b[11]; + var b30 = b[12]; + var b31 = b[13]; + var b32 = b[14]; + var b33 = b[15]; + return o3djs.flat_math.makeMatrix4( + a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03, + a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03, + a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03, + a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03, + a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13, + a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13, + a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13, + a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13, + a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23, + a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23, + a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23, + a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23, + a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33, + a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33, + a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33, + a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33); }; /** * Multiplies two 4-by-4 matrices; assumes that the given matrices are 4-by-4. - * @param {!o3djs.math.Matrix4} a The matrix on the left. - * @param {!o3djs.math.Matrix4} b The matrix on the right. - * @return {!o3djs.math.Matrix4} The matrix product of a and b. + * @param {!o3djs.flat_math.Matrix4} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix4} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix4} The matrix product of a and b. */ -o3djs.math.mulMatrixMatrix4 = null; +o3djs.flat_math.mulMatrixMatrix4 = null; /** * Multiplies two matrices; assumes that the sizes of the matrices are * appropriately compatible; assumes matrix entries are accessed in * [row][column] fashion. - * @param {!o3djs.math.Matrix} a The matrix on the left. - * @param {!o3djs.math.Matrix} b The matrix on the right. - * @return {!o3djs.math.Matrix} The matrix product of a and b. - */ -o3djs.math.rowMajor.mulMatrixMatrix = function(a, b) { + * @param {!o3djs.flat_math.Matrix} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix} The matrix product of a and b. + */ +o3djs.flat_math.rowMajor.mulMatrixMatrix = function(a, b) { + switch(a.length) { + case 4: + return o3djs.flat_math.rowMajor.mulMatrixMatrix2(a,b); + case 9: + return o3djs.flat_math.rowMajor.mulMatrixMatrix3(a,b); + case 16: + return o3djs.flat_math.rowMajor.mulMatrixMatrix4(a,b); + default: + throw "Unable to handle irregular matrices or matrices of dim > 4 or < 2"; + } + }; + +o3djs.flat_math.rowMajor.generalizedMulMatrixMatrix= function(a, b) { var r = []; var aRows = a.length; var bColumns = b[0].length; @@ -1167,49 +1597,56 @@ o3djs.math.rowMajor.mulMatrixMatrix = function(a, b) { * Multiplies two matrices; assumes that the sizes of the matrices are * appropriately compatible; assumes matrix entries are accessed in * [row][column] fashion. - * @param {!o3djs.math.Matrix} a The matrix on the left. - * @param {!o3djs.math.Matrix} b The matrix on the right. - * @return {!o3djs.math.Matrix} The matrix product of a and b. - */ -o3djs.math.columnMajor.mulMatrixMatrix = function(a, b) { - var r = []; - var bColumns = b.length; - var aRows = a[0].length; - var aColumns = a.length; - for (var i = 0; i < bColumns; ++i) { - var v = []; // v becomes a column of the answer. - var bi = b[i]; // ith column of b. - for (var j = 0; j < aRows; ++j) { - v[j] = 0.0; - for (var k = 0; k < aColumns; ++k) - v[j] += bi[k] * a[k][j]; // kth column, jth row. - } - r[i] = v; + * @param {!o3djs.flat_math.Matrix} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix} The matrix product of a and b. + */ +o3djs.flat_math.columnMajor.mulMatrixMatrix = function(a, b) { + switch(a.length) { + case 4: + return o3djs.flat_math.columnMajor.mulMatrixMatrix2(a,b); + case 9: + return o3djs.flat_math.columnMajor.mulMatrixMatrix3(a,b); + case 16: + return o3djs.flat_math.columnMajor.mulMatrixMatrix4(a,b); + default: + throw "Unable to handle irregular matrices or matrices of dim > 4 or < 2"; } - return r; }; /** * Multiplies two matrices; assumes that the sizes of the matrices are * appropriately compatible. - * @param {!o3djs.math.Matrix} a The matrix on the left. - * @param {!o3djs.math.Matrix} b The matrix on the right. - * @return {!o3djs.math.Matrix} The matrix product of a and b. + * @param {!o3djs.flat_math.Matrix} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix} The matrix product of a and b. */ -o3djs.math.mulMatrixMatrix = null; +o3djs.flat_math.mulMatrixMatrix = null; /** * Gets the jth column of the given matrix m; assumes matrix entries are - * accessed in [row][column] fashion. - * @param {!o3djs.math.Matrix} m The matrix. + * accessed in [row*dimension+column] fashion. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @param {number} j The index of the desired column. - * @return {!o3djs.math.Vector} The jth column of m as a vector. + * @return {!o3djs.flat_math.Vector} The jth column of m as a vector. */ -o3djs.math.rowMajor.column = function(m, j) { - var r = []; +o3djs.flat_math.rowMajor.column = function(m, j) { var mLength = m.length; - for (var i = 0; i < mLength; ++i) { - r[i] = m[i][j]; + var dimension; + switch (mLength){ + case 4: + dimension = 2; + break; + case 9: + dimension = 3; + break; + case 16: + dimension = 4; + break; + } + var r = new o3djs.flat_math.Vector(dimension); + for (var i = 0; i < dimension; ++i) { + r[i] = m[i * dimension + j]; } return r; }; @@ -1217,85 +1654,110 @@ o3djs.math.rowMajor.column = function(m, j) { /** * Gets the jth column of the given matrix m; assumes matrix entries are * accessed in [column][row] fashion. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @param {number} j The index of the desired column. - * @return {!o3djs.math.Vector} The jth column of m as a vector. + * @return {!o3djs.flat_math.Vector} The jth column of m as a vector. */ -o3djs.math.columnMajor.column = function(m, j) { - return m[j].slice(); +o3djs.flat_math.columnMajor.column = function(m, j) { + var dimension; + var mLength = m.length; + switch (mLength){ + case 4: + dimension = 2; + break; + case 9: + dimension = 3; + break; + case 16: + dimension = 4; + break; + default: + dimension = Math.sqrt(dimension); + if (Math.round(dimension) * Math.round(dimension) != mLength) { + throw "Calling column on nonsquare matrix"; + } + } + return m.slice(j * dimension, j * dimension + dimension); }; /** * Gets the jth column of the given matrix m. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @param {number} j The index of the desired column. - * @return {!o3djs.math.Vector} The jth column of m as a vector. + * @return {!o3djs.flat_math.Vector} The jth column of m as a vector. */ -o3djs.math.column = null; +o3djs.flat_math.column = null; /** * Gets the ith row of the given matrix m; assumes matrix entries are * accessed in [row][column] fashion. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @param {number} i The index of the desired row. - * @return {!o3djs.math.Vector} The ith row of m. + * @return {!o3djs.flat_math.Vector} The ith row of m. */ -o3djs.math.rowMajor.row = function(m, i) { - return m[i].slice(); -}; +o3djs.flat_math.rowMajor.row = o3djs.flat_math.columnMajor.column; /** * Gets the ith row of the given matrix m; assumes matrix entries are * accessed in [column][row] fashion. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @param {number} i The index of the desired row. - * @return {!o3djs.math.Vector} The ith row of m. + * @return {!o3djs.flat_math.Vector} The ith row of m. */ -o3djs.math.columnMajor.row = function(m, i) { - var r = []; - var mLength = m.length; - for (var j = 0; j < mLength; ++j) { - r[j] = m[j][i]; - } - return r; -}; +o3djs.flat_math.columnMajor.row = o3djs.flat_math.rowMajor.column; /** * Gets the ith row of the given matrix m. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @param {number} i The index of the desired row. - * @return {!o3djs.math.Vector} The ith row of m. + * @return {!o3djs.flat_math.Vector} The ith row of m. */ -o3djs.math.row = null; +o3djs.flat_math.row = null; /** * Creates an n-by-n identity matrix. * @param {number} n The dimension of the identity matrix required. - * @return {!o3djs.math.Matrix} An n-by-n identity matrix. + * @return {!o3djs.flat_math.Matrix} An n-by-n identity matrix. */ -o3djs.math.identity = function(n) { - var r = []; +o3djs.flat_math.identity = function(n) { + var r = new o3djs.flat_math.Matrix(n*n); + for (var j = 0; j < n; ++j) { - r[j] = []; for (var i = 0; i < n; ++i) - r[j][i] = (i == j) ? 1 : 0; + r[j * n + i] = (i == j) ? 1 : 0; } return r; }; /** * Takes the transpose of a matrix. - * @param {!o3djs.math.Matrix} m The matrix. - * @return {!o3djs.math.Matrix} The transpose of m. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Matrix} The transpose of m. */ -o3djs.math.transpose = function(m) { - var r = []; - var m0Length = m[0].length; +o3djs.flat_math.transpose = function(m) { var mLength = m.length; - for (var j = 0; j < m0Length; ++j) { - r[j] = []; - for (var i = 0; i < mLength; ++i) - r[j][i] = m[i][j]; + var r = new o3djs.flat_math.Matrix(mLength); + var dimension; + switch (mLength){ + case 4: + dimension = 2; + break; + case 9: + dimension = 3; + break; + case 16: + dimension = 4; + break; + default: + dimension = Math.sqrt(dimension); + if (Math.round(dimension) * Math.round(dimension) != mLength) { + throw "Calling transpose on nonsquare matrix"; + } + } + + for (var j = 0; j < dimension; ++j) { + for (var i = 0; i < dimension; ++i) + r[j * dimension + i] = m[i * dimension + j]; } return r; }; @@ -1303,218 +1765,259 @@ o3djs.math.transpose = function(m) { /** * Computes the trace (sum of the diagonal entries) of a square matrix; * assumes m is square. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @return {number} The trace of m. */ -o3djs.math.trace = function(m) { +o3djs.flat_math.trace = function(m) { var r = 0.0; - var mLength = m.length; + var dimension; + switch (mLength){ + case 4: + dimension = 2; + break; + case 9: + dimension = 3; + break; + case 16: + dimension = 4; + break; + } + var mLength = dimension; for (var i = 0; i < mLength; ++i) - r += m[i][i]; + r += m[i * dimension + i]; return r; }; /** * Computes the determinant of a 1-by-1 matrix. - * @param {!o3djs.math.Matrix1} m The matrix. + * @param {!o3djs.flat_math.Matrix1} m The matrix. * @return {number} The determinant of m. */ -o3djs.math.det1 = function(m) { - return m[0][0]; +o3djs.flat_math.det1 = function(m) { + return m[0]; }; /** * Computes the determinant of a 2-by-2 matrix. - * @param {!o3djs.math.Matrix2} m The matrix. + * @param {!o3djs.flat_math.Matrix2} m The matrix. * @return {number} The determinant of m. */ -o3djs.math.det2 = function(m) { - return m[0][0] * m[1][1] - m[0][1] * m[1][0]; +o3djs.flat_math.det2 = function(m) { + return m[0] * m[3] - m[1] * m[2]; }; /** * Computes the determinant of a 3-by-3 matrix. - * @param {!o3djs.math.Matrix3} m The matrix. + * @param {!o3djs.flat_math.Matrix3} m The matrix. * @return {number} The determinant of m. */ -o3djs.math.det3 = function(m) { - return m[2][2] * (m[0][0] * m[1][1] - m[0][1] * m[1][0]) - - m[2][1] * (m[0][0] * m[1][2] - m[0][2] * m[1][0]) + - m[2][0] * (m[0][1] * m[1][2] - m[0][2] * m[1][1]); +o3djs.flat_math.det3 = function(m) { + return m[8] * (m[0 * 3] * m[4] - m[1] * m[1 * 3]) - + m[7] * (m[0 * 3] * m[5] - m[2] * m[1 * 3]) + + m[2 * 3] * (m[1] * m[5] - m[2] * m[4]); }; /** * Computes the determinant of a 4-by-4 matrix. - * @param {!o3djs.math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Matrix4} m The matrix. * @return {number} The determinant of m. */ -o3djs.math.det4 = function(m) { - var t01 = m[0][0] * m[1][1] - m[0][1] * m[1][0]; - var t02 = m[0][0] * m[1][2] - m[0][2] * m[1][0]; - var t03 = m[0][0] * m[1][3] - m[0][3] * m[1][0]; - var t12 = m[0][1] * m[1][2] - m[0][2] * m[1][1]; - var t13 = m[0][1] * m[1][3] - m[0][3] * m[1][1]; - var t23 = m[0][2] * m[1][3] - m[0][3] * m[1][2]; - return m[3][3] * (m[2][2] * t01 - m[2][1] * t02 + m[2][0] * t12) - - m[3][2] * (m[2][3] * t01 - m[2][1] * t03 + m[2][0] * t13) + - m[3][1] * (m[2][3] * t02 - m[2][2] * t03 + m[2][0] * t23) - - m[3][0] * (m[2][3] * t12 - m[2][2] * t13 + m[2][1] * t23); +o3djs.flat_math.det4 = function(m) { + var t01 = m[0] * m[5] - m[1] * m[4]; + var t02 = m[0] * m[6] - m[2] * m[4]; + var t03 = m[0] * m[7] - m[3] * m[4]; + var t12 = m[1] * m[6] - m[2] * m[5]; + var t13 = m[1] * m[7] - m[3] * m[5]; + var t23 = m[2] * m[7] - m[3] * m[6]; + return m[15] * (m[10] * t01 - m[9] * t02 + m[8] * t12) - + m[14] * (m[11] * t01 - m[9] * t03 + m[8] * t13) + + m[13] * (m[11] * t02 - m[10] * t03 + m[8] * t23) - + m[12] * (m[11] * t12 - m[10] * t13 + m[9] * t23); }; /** * Computes the inverse of a 1-by-1 matrix. - * @param {!o3djs.math.Matrix1} m The matrix. - * @return {!o3djs.math.Matrix1} The inverse of m. + * @param {!o3djs.flat_math.Matrix1} m The matrix. + * @return {!o3djs.flat_math.Matrix1} The inverse of m. */ -o3djs.math.inverse1 = function(m) { - return [[1.0 / m[0][0]]]; +o3djs.flat_math.inverse1 = function(m) { + var retval = new o3djs.flat_math.Matrix(1); + retval[0] = 1.0 / m[0]; + return retval; }; /** * Computes the inverse of a 2-by-2 matrix. - * @param {!o3djs.math.Matrix2} m The matrix. - * @return {!o3djs.math.Matrix2} The inverse of m. + * @param {!o3djs.flat_math.Matrix2} m The matrix. + * @return {!o3djs.flat_math.Matrix2} The inverse of m. */ -o3djs.math.inverse2 = function(m) { - var d = 1.0 / (m[0][0] * m[1][1] - m[0][1] * m[1][0]); - return [[d * m[1][1], -d * m[0][1]], [-d * m[1][0], d * m[0][0]]]; +o3djs.flat_math.inverse2 = function(m) { + var d = 1.0 / (m[0] * m[3] - m[1] * m[2]); + return o3djs.flat_math.makeMatrix2(d * m[3], -d * m[1], + -d * m[2], d * m[0]); }; /** * Computes the inverse of a 3-by-3 matrix. - * @param {!o3djs.math.Matrix3} m The matrix. - * @return {!o3djs.math.Matrix3} The inverse of m. + * @param {!o3djs.flat_math.Matrix3} m The matrix. + * @return {!o3djs.flat_math.Matrix3} The inverse of m. */ -o3djs.math.inverse3 = function(m) { - var t00 = m[1][1] * m[2][2] - m[1][2] * m[2][1]; - var t10 = m[0][1] * m[2][2] - m[0][2] * m[2][1]; - var t20 = m[0][1] * m[1][2] - m[0][2] * m[1][1]; - var d = 1.0 / (m[0][0] * t00 - m[1][0] * t10 + m[2][0] * t20); - return [[d * t00, -d * t10, d * t20], - [-d * (m[1][0] * m[2][2] - m[1][2] * m[2][0]), - d * (m[0][0] * m[2][2] - m[0][2] * m[2][0]), - -d * (m[0][0] * m[1][2] - m[0][2] * m[1][0])], - [d * (m[1][0] * m[2][1] - m[1][1] * m[2][0]), - -d * (m[0][0] * m[2][1] - m[0][1] * m[2][0]), - d * (m[0][0] * m[1][1] - m[0][1] * m[1][0])]]; +o3djs.flat_math.inverse3 = function(m) { + var t00 = m[4] * m[8] - m[5] * m[7]; + var t10 = m[1] * m[8] - m[2] * m[7]; + var t20 = m[1] * m[5] - m[2] * m[4]; + var d = 1.0 / (m[0] * t00 - m[3] * t10 + m[6] * t20); + return o3djs.flat_math.makeMatrix3(d * t00, -d * t10, d * t20, + -d * (m[3] * m[8] - m[5] * m[6]), + d * (m[0] * m[8] - m[2] * m[6]), + -d * (m[0] * m[5] - m[2] * m[3]), + d * (m[3] * m[7] - m[4] * m[6]), + -d * (m[0] * m[7] - m[1] * m[6]), + d * (m[0] * m[4] - m[1] * m[3])); }; /** * Computes the inverse of a 4-by-4 matrix. - * @param {!o3djs.math.Matrix4} m The matrix. - * @return {!o3djs.math.Matrix4} The inverse of m. - */ -o3djs.math.inverse4 = function(m) { - var tmp_0 = m[2][2] * m[3][3]; - var tmp_1 = m[3][2] * m[2][3]; - var tmp_2 = m[1][2] * m[3][3]; - var tmp_3 = m[3][2] * m[1][3]; - var tmp_4 = m[1][2] * m[2][3]; - var tmp_5 = m[2][2] * m[1][3]; - var tmp_6 = m[0][2] * m[3][3]; - var tmp_7 = m[3][2] * m[0][3]; - var tmp_8 = m[0][2] * m[2][3]; - var tmp_9 = m[2][2] * m[0][3]; - var tmp_10 = m[0][2] * m[1][3]; - var tmp_11 = m[1][2] * m[0][3]; - var tmp_12 = m[2][0] * m[3][1]; - var tmp_13 = m[3][0] * m[2][1]; - var tmp_14 = m[1][0] * m[3][1]; - var tmp_15 = m[3][0] * m[1][1]; - var tmp_16 = m[1][0] * m[2][1]; - var tmp_17 = m[2][0] * m[1][1]; - var tmp_18 = m[0][0] * m[3][1]; - var tmp_19 = m[3][0] * m[0][1]; - var tmp_20 = m[0][0] * m[2][1]; - var tmp_21 = m[2][0] * m[0][1]; - var tmp_22 = m[0][0] * m[1][1]; - var tmp_23 = m[1][0] * m[0][1]; - - var t0 = (tmp_0 * m[1][1] + tmp_3 * m[2][1] + tmp_4 * m[3][1]) - - (tmp_1 * m[1][1] + tmp_2 * m[2][1] + tmp_5 * m[3][1]); - var t1 = (tmp_1 * m[0][1] + tmp_6 * m[2][1] + tmp_9 * m[3][1]) - - (tmp_0 * m[0][1] + tmp_7 * m[2][1] + tmp_8 * m[3][1]); - var t2 = (tmp_2 * m[0][1] + tmp_7 * m[1][1] + tmp_10 * m[3][1]) - - (tmp_3 * m[0][1] + tmp_6 * m[1][1] + tmp_11 * m[3][1]); - var t3 = (tmp_5 * m[0][1] + tmp_8 * m[1][1] + tmp_11 * m[2][1]) - - (tmp_4 * m[0][1] + tmp_9 * m[1][1] + tmp_10 * m[2][1]); - - var d = 1.0 / (m[0][0] * t0 + m[1][0] * t1 + m[2][0] * t2 + m[3][0] * t3); - - var row0 = [d * t0, d * t1, d * t2, d * t3]; - var row1 = [d * ((tmp_1 * m[1][0] + tmp_2 * m[2][0] + tmp_5 * m[3][0]) - - (tmp_0 * m[1][0] + tmp_3 * m[2][0] + tmp_4 * m[3][0])), - d * ((tmp_0 * m[0][0] + tmp_7 * m[2][0] + tmp_8 * m[3][0]) - - (tmp_1 * m[0][0] + tmp_6 * m[2][0] + tmp_9 * m[3][0])), - d * ((tmp_3 * m[0][0] + tmp_6 * m[1][0] + tmp_11 * m[3][0]) - - (tmp_2 * m[0][0] + tmp_7 * m[1][0] + tmp_10 * m[3][0])), - d * ((tmp_4 * m[0][0] + tmp_9 * m[1][0] + tmp_10 * m[2][0]) - - (tmp_5 * m[0][0] + tmp_8 * m[1][0] + tmp_11 * m[2][0]))]; - var row2 =[d * ((tmp_12 * m[1][3] + tmp_15 * m[2][3] + tmp_16 * m[3][3]) - - (tmp_13 * m[1][3] + tmp_14 * m[2][3] + tmp_17 * m[3][3])), - d * ((tmp_13 * m[0][3] + tmp_18 * m[2][3] + tmp_21 * m[3][3]) - - (tmp_12 * m[0][3] + tmp_19 * m[2][3] + tmp_20 * m[3][3])), - d * ((tmp_14 * m[0][3] + tmp_19 * m[1][3] + tmp_22 * m[3][3]) - - (tmp_15 * m[0][3] + tmp_18 * m[1][3] + tmp_23 * m[3][3])), - d * ((tmp_17 * m[0][3] + tmp_20 * m[1][3] + tmp_23 * m[2][3]) - - (tmp_16 * m[0][3] + tmp_21 * m[1][3] + tmp_22 * m[2][3]))]; - var row3 = [d * ((tmp_14 * m[2][2] + tmp_17 * m[3][2] + tmp_13 * m[1][2]) - - (tmp_16 * m[3][2] + tmp_12 * m[1][2] + tmp_15 * m[2][2])), - d * ((tmp_20 * m[3][2] + tmp_12 * m[0][2] + tmp_19 * m[2][2]) - - (tmp_18 * m[2][2] + tmp_21 * m[3][2] + tmp_13 * m[0][2])), - d * ((tmp_18 * m[1][2] + tmp_23 * m[3][2] + tmp_15 * m[0][2]) - - (tmp_22 * m[3][2] + tmp_14 * m[0][2] + tmp_19 * m[1][2])), - d * ((tmp_22 * m[2][2] + tmp_16 * m[0][2] + tmp_21 * m[1][2]) - - (tmp_20 * m[1][2] + tmp_23 * m[2][2] + tmp_17 * m[0][2]))]; - return [row0, row1, row2, row3]; + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @return {!o3djs.flat_math.Matrix4} The inverse of m. + */ +o3djs.flat_math.inverse4 = function(m) { + var tmp_0 = m[10] * m[15]; + var tmp_1 = m[14] * m[11]; + var tmp_2 = m[6] * m[15]; + var tmp_3 = m[14] * m[7]; + var tmp_4 = m[6] * m[11]; + var tmp_5 = m[10] * m[7]; + var tmp_6 = m[2] * m[15]; + var tmp_7 = m[14] * m[3]; + var tmp_8 = m[2] * m[11]; + var tmp_9 = m[10] * m[3]; + var tmp_10 = m[2] * m[7]; + var tmp_11 = m[6] * m[3]; + var tmp_12 = m[8] * m[13]; + var tmp_13 = m[12] * m[9]; + var tmp_14 = m[4] * m[13]; + var tmp_15 = m[12] * m[5]; + var tmp_16 = m[4] * m[9]; + var tmp_17 = m[8] * m[5]; + var tmp_18 = m[0] * m[13]; + var tmp_19 = m[12] * m[1]; + var tmp_20 = m[0] * m[9]; + var tmp_21 = m[8] * m[1]; + var tmp_22 = m[0] * m[5]; + var tmp_23 = m[4] * m[1]; + + var t0 = tmp_0 * m[5] + tmp_3 * m[9] + tmp_4 * m[13] - + (tmp_1 * m[5] + tmp_2 * m[9] + tmp_5 * m[13]); + var t1 = tmp_1 * m[1] + tmp_6 * m[9] + tmp_9 * m[13] - + (tmp_0 * m[1] + tmp_7 * m[9] + tmp_8 * m[13]); + var t2 = tmp_2 * m[1] + tmp_7 * m[5] + tmp_10 * m[13] - + (tmp_3 * m[1] + tmp_6 * m[5] + tmp_11 * m[13]); + var t3 = (tmp_5 * m[1] + tmp_8 * m[5] + tmp_11 * m[9]) - + (tmp_4 * m[1] + tmp_9 * m[5] + tmp_10 * m[9]); + + var d = 1.0 / (m[0] * t0 + m[1 * 4] * t1 + m[8] * t2 + m[12] * t3); + + return o3djs.flat_math.makeMatrix4(d * t0, d * t1, d * t2, d * t3, + d * ((tmp_1 * m[1 * 4] + tmp_2 * m[8] + tmp_5 * m[12]) - + (tmp_0 * m[1 * 4] + tmp_3 * m[8] + tmp_4 * m[12])), + d * ((tmp_0 * m[0 * 4] + tmp_7 * m[8] + tmp_8 * m[12]) - + (tmp_1 * m[0 * 4] + tmp_6 * m[8] + tmp_9 * m[12])), + d * ((tmp_3 * m[0 * 4] + tmp_6 * m[1 * 4] + tmp_11 * m[12]) - + (tmp_2 * m[0 * 4] + tmp_7 * m[1 * 4] + tmp_10 * m[12])), + d * ((tmp_4 * m[0 * 4] + tmp_9 * m[1 * 4] + tmp_10 * m[8]) - + (tmp_5 * m[0 * 4] + tmp_8 * m[1 * 4] + tmp_11 * m[8])), + d * ((tmp_12 * m[4 + 3] + tmp_15 * m[11] + tmp_16 * m[15]) - + (tmp_13 * m[4 + 3] + tmp_14 * m[11] + tmp_17 * m[15])), + d * ((tmp_13 * m[3] + tmp_18 * m[11] + tmp_21 * m[15]) - + (tmp_12 * m[3] + tmp_19 * m[11] + tmp_20 * m[15])), + d * ((tmp_14 * m[3] + tmp_19 * m[7] + tmp_22 * m[15]) - + (tmp_15 * m[3] + tmp_18 * m[7] + tmp_23 * m[15])), + d * ((tmp_17 * m[3] + tmp_20 * m[7] + tmp_23 * m[11]) - + (tmp_16 * m[3] + tmp_21 * m[7] + tmp_22 * m[11])), + d * ((tmp_14 * m[10] + tmp_17 * m[14] + tmp_13 * m[4 + 2]) - + (tmp_16 * m[14] + tmp_12 * m[4 + 2] + tmp_15 * m[10])), + d * ((tmp_20 * m[14] + tmp_12 * m[2] + tmp_19 * m[10]) - + (tmp_18 * m[10] + tmp_21 * m[14] + tmp_13 * m[2])), + d * ((tmp_18 * m[6] + tmp_23 * m[14] + tmp_15 * m[2]) - + (tmp_22 * m[14] + tmp_14 * m[2] + tmp_19 * m[6])), + d * ((tmp_22 * m[10] + tmp_16 * m[2] + tmp_21 * m[6]) - + (tmp_20 * m[6] + tmp_23 * m[10] + tmp_17 * m[2]))); }; /** * Computes the determinant of the cofactor matrix obtained by removal * of a specified row and column. This is a helper function for the general * determinant and matrix inversion functions. - * @param {!o3djs.math.Matrix} a The original matrix. + * @param {!o3djs.flat_math.Matrix} a The original matrix. * @param {number} x The row to be removed. * @param {number} y The column to be removed. * @return {number} The determinant of the matrix obtained by removing * row x and column y from a. */ -o3djs.math.codet = function(a, x, y) { - var size = a.length; - var b = []; +o3djs.flat_math.codet = function(a, x, y) { + var aLength = a.length; + var size; + switch (aLength) { + case 4: + size = 2; + break; + case 9: + size = 3; + break; + case 16: + size = 4; + break; + default: + size=Math.sqrt(aLength); + if (Math.round(size) * Math.round(size) != aLength) { + throw "Calling codet on nonsquare matrix"; + } + } + var b = new o3djs.flat_math.Matrix(aLength); var ai = 0; for (var bi = 0; bi < size - 1; ++bi) { if (ai == x) ai++; - b[bi] = []; var aj = 0; for (var bj = 0; bj < size - 1; ++bj) { if (aj == y) aj++; - b[bi][bj] = a[ai][aj]; + b[bi*size+bj] = a[ai*size+aj]; aj++; } ai++; } - return o3djs.math.det(b); + return o3djs.flat_math.det(b); }; /** * Computes the determinant of an arbitrary square matrix. - * @param {!o3djs.math.Matrix} m The matrix. + * @param {!o3djs.flat_math.Matrix} m The matrix. * @return {number} the determinant of m. */ -o3djs.math.det = function(m) { +o3djs.flat_math.det = function(m) { var d = m.length; - if (d <= 4) { - return o3djs.math['det' + d](m); + switch (d) { + case 4: + return o3djs.flat_math.det2(m); + case 9: + return o3djs.flat_math.det3(m); + case 16: + return o3djs.flat_math.det4(m); + default: + d = Math.sqrt(d); + if (Math.round(d) * Math.round(d) != m.length) { + throw "Calling det on nonsquare matrix"; + } + break; } var r = 0.0; var sign = 1; - var row = m[0]; + var row = m; var mLength = m.length; for (var y = 0; y < mLength; y++) { - r += sign * row[y] * o3djs.math.codet(m, 0, y); + r += sign * m[0] * o3djs.flat_math.codet(m, 0, y); sign *= -1; } return r; @@ -1522,22 +2025,34 @@ o3djs.math.det = function(m) { /** * Computes the inverse of an arbitrary square matrix. - * @param {!o3djs.math.Matrix} m The matrix. - * @return {!o3djs.math.Matrix} The inverse of m. + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Matrix} The inverse of m. */ -o3djs.math.inverse = function(m) { +o3djs.flat_math.inverse = function(m) { var d = m.length; - if (d <= 4) { - return o3djs.math['inverse' + d](m); + switch (d) { + case 4: + return o3djs.flat_math.inverse2(m); + case 9: + return o3djs.flat_math.inverse3(m); + case 16: + return o3djs.flat_math.inverse4(m); + default: + d = Math.sqrt(d); + if (Math.round(d) * Math.round(d) != m.length) { + throw "Calling inverse on nonsquare matrix"; + } + break; } - var r = []; + var r = new o3djs.flat_math.Matrix(m.length); var size = m.length; + var det = o3djs.flat_math.det(m); for (var j = 0; j < size; ++j) { - r[j] = []; for (var i = 0; i < size; ++i) - r[j][i] = ((i + j) % 2 ? -1 : 1) * o3djs.math.codet(m, i, j); + r[j * d + i] = + ((i + j) % 2 ? -1 : 1) * o3djs.flat_math.codet(m, i, j) / det; } - return o3djs.math.divMatrixScalar(r, o3djs.math.det(m)); + return r; }; /** @@ -1546,80 +2061,99 @@ o3djs.math.inverse = function(m) { * multiplying many orthogonal matrices together, errors can accumulate causing * the product to fail to be orthogonal. This function can be used to correct * that. - * @param {!o3djs.math.Matrix} m The matrix. - * @return {!o3djs.math.Matrix} A matrix whose rows are obtained from the + * @param {!o3djs.flat_math.Matrix} m The matrix. + * @return {!o3djs.flat_math.Matrix} A matrix whose rows are obtained from the * rows of m by the Graham-Schmidt process. */ -o3djs.math.orthonormalize = function(m) { - var r = []; - var mLength = m.length; - for (var i = 0; i < mLength; ++i) { - var v = m[i]; +o3djs.flat_math.orthonormalize = function(m) { + var d = m.length; + var r = new o3djs.flat_math.Matrix(d); + switch (d) { + case 4: + d = 2; break; + case 9: + d = 3; break; + case 16: + d = 4; break; + default: + d = Math.sqrt(d); + if (Math.round(d) * Math.round(d) != m.length) { + throw "Calling orthonormalize on nonsquare matrix"; + } + break; + } + for (var i = 0; i < d; ++i) { + var v = m.slice(i*d,i*d+d); for (var j = 0; j < i; ++j) { - v = o3djs.math.subVector(v, o3djs.math.mulScalarVector( - o3djs.math.dot(r[j], m[i]), r[j])); + v = o3djs.flat_math.subVector(v, o3djs.flat_math.mulScalarVector( + o3djs.flat_math.dot(r[j], v), r[j])); + } + var ri = o3djs.flat_math.normalize(v); + for (var k = 0; k < d; ++ k) { + r[i * d +k ] = ri[k]; } - r[i] = o3djs.math.normalize(v); } return r; }; /** * Computes the inverse of a 4-by-4 matrix. - * Note: It is faster to call this than o3djs.math.inverse. - * @param {!o3djs.math.Matrix4} m The matrix. - * @return {!o3djs.math.Matrix4} The inverse of m. + * Note: It is faster to call this than o3djs.flat_math.inverse. + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @return {!o3djs.flat_math.Matrix4} The inverse of m. */ -o3djs.math.matrix4.inverse = function(m) { - return o3djs.math.inverse4(m); +o3djs.flat_math.matrix4.inverse = function(m) { + return o3djs.flat_math.inverse4(m); }; /** * Multiplies two 4-by-4 matrices; assumes that the given matrices are 4-by-4. - * Note: It is faster to call this than o3djs.math.mul. - * @param {!o3djs.math.Matrix4} a The matrix on the left. - * @param {!o3djs.math.Matrix4} b The matrix on the right. - * @return {!o3djs.math.Matrix4} The matrix product of a and b. + * Note: It is faster to call this than o3djs.flat_math.mul. + * @param {!o3djs.flat_math.Matrix4} a The matrix on the left. + * @param {!o3djs.flat_math.Matrix4} b The matrix on the right. + * @return {!o3djs.flat_math.Matrix4} The matrix product of a and b. */ -o3djs.math.matrix4.mul = function(a, b) { - return o3djs.math.mulMatrixMatrix4(a, b); +o3djs.flat_math.matrix4.mul = function(a, b) { + return o3djs.flat_math.mulMatrixMatrix4(a, b); }; /** * Computes the determinant of a 4-by-4 matrix. - * Note: It is faster to call this than o3djs.math.det. - * @param {!o3djs.math.Matrix4} m The matrix. + * Note: It is faster to call this than o3djs.flat_math.det. + * @param {!o3djs.flat_math.Matrix4} m The matrix. * @return {number} The determinant of m. */ -o3djs.math.matrix4.det = function(m) { - return o3djs.math.det4(m); +o3djs.flat_math.matrix4.det = function(m) { + return o3djs.flat_math.det4(m); }; /** * Copies a Matrix4. - * Note: It is faster to call this than o3djs.math.copy. - * @param {!o3djs.math.Matrix4} m The matrix. - * @return {!o3djs.math.Matrix4} A copy of m. + * Note: It is faster to call this than o3djs.flat_math.copy. + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @return {!o3djs.flat_math.Matrix4} A copy of m. */ -o3djs.math.matrix4.copy = function(m) { - return o3djs.math.copyMatrix(m); +o3djs.flat_math.matrix4.copy = function(m) { + return o3djs.flat_math.copyMatrix(m); }; /** * Sets the upper 3-by-3 block of matrix a to the upper 3-by-3 block of matrix * b; assumes that a and b are big enough to contain an upper 3-by-3 block. - * @param {!o3djs.math.Matrix4} a A matrix. - * @param {!o3djs.math.Matrix3} b A 3-by-3 matrix. - * @return {!o3djs.math.Matrix4} a once modified. - */ -o3djs.math.matrix4.setUpper3x3 = function(a, b) { - var b0 = b[0]; - var b1 = b[1]; - var b2 = b[2]; - - a[0].splice(0, 3, b0[0], b0[1], b0[2]); - a[1].splice(0, 3, b1[0], b1[1], b1[2]); - a[2].splice(0, 3, b2[0], b2[1], b2[2]); + * @param {!o3djs.flat_math.Matrix4} a A matrix. + * @param {!o3djs.flat_math.Matrix3} b A 3-by-3 matrix. + * @return {!o3djs.flat_math.Matrix4} a once modified. + */ +o3djs.flat_math.matrix4.setUpper3x3 = function(a, b) { + a[0] = b[0]; + a[1] = b[1]; + a[2] = b[2]; + a[4] = b[4]; + a[5] = b[5]; + a[6] = b[6]; + a[8] = b[8]; + a[9] = b[9]; + a[10] = b[10]; return a; }; @@ -1627,80 +2161,107 @@ o3djs.math.matrix4.setUpper3x3 = function(a, b) { /** * Returns a 3-by-3 matrix mimicking the upper 3-by-3 block of m; assumes m * is big enough to contain an upper 3-by-3 block. - * @param {!o3djs.math.Matrix4} m The matrix. - * @return {!o3djs.math.Matrix3} The upper 3-by-3 block of m. + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @return {!o3djs.flat_math.Matrix3} The upper 3-by-3 block of m. */ -o3djs.math.matrix4.getUpper3x3 = function(m) { - return [m[0].slice(0, 3), m[1].slice(0, 3), m[2].slice(0, 3)]; +o3djs.flat_math.matrix4.getUpper3x3 = function(m) { + return o3djs.flat_math.makeMatrix3( + m[0], m[1], m[2], + m[4], m[5], m[6], + m[8], m[9], m[10]); }; /** * Sets the translation component of a 4-by-4 matrix to the given * vector. - * @param {!o3djs.math.Matrix4} a The matrix. - * @param {(!o3djs.math.Vector3|!o3djs.math.Vector4)} v The vector. - * @return {!o3djs.math.Matrix4} a once modified. - */ -o3djs.math.matrix4.setTranslation = function(a, v) { - a[3].splice(0, 4, v[0], v[1], v[2], 1); + * @param {!o3djs.flat_math.Matrix4} a The matrix. + * @param {(!o3djs.flat_math.Vector3|!o3djs.flat_math.Vector4)} v The vector. + * @return {!o3djs.flat_math.Matrix4} a once modified. + */ +o3djs.flat_math.matrix4.setTranslation = function(a, v) { + a[12] = v[0]; + a[13] = v[1]; + a[14] = v[2]; return a; }; /** * Returns the translation component of a 4-by-4 matrix as a vector with 3 * entries. - * @param {!o3djs.math.Matrix4} m The matrix. - * @return {!o3djs.math.Vector3} The translation component of m. + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @return {!o3djs.flat_math.Vector3} The translation component of m. */ -o3djs.math.matrix4.getTranslation = function(m) { - return m[3].slice(0, 3); +o3djs.flat_math.matrix4.getTranslation = function(m) { + var retval =new o3djs.flat_math.Vector(3); + retval[0] = m[12]; + retval[1] = m[13]; + retval[2] = m[14]; + return retval; }; /** * Takes a 4-by-4 matrix and a vector with 3 entries, * interprets the vector as a point, transforms that point by the matrix, and * returns the result as a vector with 3 entries. - * @param {!o3djs.math.Matrix4} m The matrix. - * @param {!o3djs.math.Vector3} v The point. - * @return {!o3djs.math.Vector3} The transformed point. + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Vector3} v The point. + * @return {!o3djs.flat_math.Vector3} The transformed point. */ -o3djs.math.matrix4.transformPoint = function(m, v) { +o3djs.flat_math.matrix4.transformPoint = function(m, v) { var v0 = v[0]; var v1 = v[1]; var v2 = v[2]; - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - var d = v0 * m0[3] + v1 * m1[3] + v2 * m2[3] + m3[3]; - return [(v0 * m0[0] + v1 * m1[0] + v2 * m2[0] + m3[0]) / d, - (v0 * m0[1] + v1 * m1[1] + v2 * m2[1] + m3[1]) / d, - (v0 * m0[2] + v1 * m1[2] + v2 * m2[2] + m3[2]) / d]; + var d = v0 * m[3] + + v1 * m[7] + + v2 * m[11] + + m[15]; + var retval = new o3djs.flat_math.Vector(3); + retval[0] = (v0 * m[0] + + v1 * m[4] + + v2 * m[8] + + m[12]) / d; + retval[1] = (v0 * m[1] + + v1 * m[5] + + v2 * m[9] + + m[13]) / d; + retval[2] = (v0 * m[2] + + v1 * m[6] + + v2 * m[10] + + m[14]) / d; + return retval; }; /** * Takes a 4-by-4 matrix and a vector with 4 entries, transforms that vector by * the matrix, and returns the result as a vector with 4 entries. - * @param {!o3djs.math.Matrix4} m The matrix. - * @param {!o3djs.math.Vector4} v The point in homogenous coordinates. - * @return {!o3djs.math.Vector4} The transformed point in homogenous + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Vector4} v The point in homogenous coordinates. + * @return {!o3djs.flat_math.Vector4} The transformed point in homogenous * coordinates. */ -o3djs.math.matrix4.transformVector4 = function(m, v) { +o3djs.flat_math.matrix4.transformVector4 = function(m, v) { var v0 = v[0]; var v1 = v[1]; var v2 = v[2]; var v3 = v[3]; - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - return [v0 * m0[0] + v1 * m1[0] + v2 * m2[0] + v3 * m3[0], - v0 * m0[1] + v1 * m1[1] + v2 * m2[1] + v3 * m3[1], - v0 * m0[2] + v1 * m1[2] + v2 * m2[2] + v3 * m3[2], - v0 * m0[3] + v1 * m1[3] + v2 * m2[3] + v3 * m3[3]]; + return [v0 * m[0] + + v1 * m[4] + + v2 * m[8] + + v3 * m[12], + v0 * m[1] + + v1 * m[5] + + v2 * m[9] + + v3 * m[13], + v0 * m[2] + + v1 * m[6] + + v2 * m[10] + + v3 * m[14], + v0 * m[3] + + v1 * m[7] + + v2 * m[11] + + v3 * m[15]]; }; /** @@ -1710,22 +2271,24 @@ o3djs.math.matrix4.transformVector4 = function(m, v) { * is parallel-preserving, i.e. any combination of rotation, scaling and * translation, but not a perspective distortion. Returns a vector with 3 * entries. - * @param {!o3djs.math.Matrix4} m The matrix. - * @param {!o3djs.math.Vector3} v The direction. - * @return {!o3djs.math.Vector3} The transformed direction. + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Vector3} v The direction. + * @return {!o3djs.flat_math.Vector3} The transformed direction. */ -o3djs.math.matrix4.transformDirection = function(m, v) { +o3djs.flat_math.matrix4.transformDirection = function(m, v) { var v0 = v[0]; var v1 = v[1]; var v2 = v[2]; - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - return [v0 * m0[0] + v1 * m1[0] + v2 * m2[0], - v0 * m0[1] + v1 * m1[1] + v2 * m2[1], - v0 * m0[2] + v1 * m1[2] + v2 * m2[2]]; + return [v0 * m[0] + + v1 * m[4] + + v2 * m[8], + v0 * m[1] + + v1 * m[5] + + v2 * m[9], + v0 * m[2] + + v1 * m[6] + + v2 * m[10]]; }; /** @@ -1737,50 +2300,49 @@ o3djs.math.matrix4.transformDirection = function(m, v) { * matrix is parallel-preserving, i.e. any combination of rotation, scaling and * translation, but not a perspective distortion. Returns a vector with 3 * entries. - * @param {!o3djs.math.Matrix4} m The matrix. - * @param {!o3djs.math.Vector3} v The normal. - * @return {!o3djs.math.Vector3} The transformed normal. + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Vector3} v The normal. + * @return {!o3djs.flat_math.Vector3} The transformed normal. */ -o3djs.math.matrix4.transformNormal = function(m, v) { - var mInverse = o3djs.math.inverse4(m); +o3djs.flat_math.matrix4.transformNormal = function(m, v) { + var mInverse = o3djs.flat_math.inverse4(m); var v0 = v[0]; var v1 = v[1]; var v2 = v[2]; - var mi0 = mInverse[0]; - var mi1 = mInverse[1]; - var mi2 = mInverse[2]; - var mi3 = mInverse[3]; - return [v0 * mi0[0] + v1 * mi0[1] + v2 * mi0[2], - v0 * mi1[0] + v1 * mi1[1] + v2 * mi1[2], - v0 * mi2[0] + v1 * mi2[1] + v2 * mi2[2]]; + return [v0 * mInverse[0] + v1 * mInverse[1] + v2 * mInverse[2], + v0 * mInverse[4] + + v1 * mInverse[5] + + v2 * mInverse[6], + v0 * mInverse[8] + + v1 * mInverse[9] + + v2 * mInverse[10]]; }; /** * Creates a 4-by-4 identity matrix. - * @return {!o3djs.math.Matrix4} The 4-by-4 identity. + * @return {!o3djs.flat_math.Matrix4} The 4-by-4 identity. */ -o3djs.math.matrix4.identity = function() { - return [ - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0], - [0, 0, 0, 1] - ]; +o3djs.flat_math.matrix4.identity = function() { + return o3djs.flat_math.makeMatrix4( + 1, 0, 0, 0, + 0, 1, 0, 0, + 0, 0, 1, 0, + 0, 0, 0, 1); }; /** * Sets the given 4-by-4 matrix to the identity matrix. - * @param {!o3djs.math.Matrix4} m The matrix to set to identity. - * @return {!o3djs.math.Matrix4} m once modified. + * @param {!o3djs.flat_math.Matrix4} m The matrix to set to identity. + * @return {!o3djs.flat_math.Matrix4} m once modified. */ -o3djs.math.matrix4.setIdentity = function(m) { +o3djs.flat_math.matrix4.setIdentity = function(m) { for (var i = 0; i < 4; i++) { for (var j = 0; j < 4; j++) { if (i == j) { - m[i][j] = 1; + m[i * 4 + j] = 1; } else { - m[i][j] = 0; + m[i * 4 + j] = 0; } } } @@ -1804,18 +2366,18 @@ o3djs.math.matrix4.setIdentity = function(m) { * of the near clipping plane. * @param {number} far The depth (negative z coordinate) * of the far clipping plane. - * @return {!o3djs.math.Matrix4} The perspective matrix. + * @return {!o3djs.flat_math.Matrix4} The perspective matrix. */ -o3djs.math.matrix4.perspective = function(angle, aspect, near, far) { +o3djs.flat_math.matrix4.perspective = function(angle, aspect, near, far) { var f = Math.tan(0.5 * (Math.PI - angle)); var range = near - far; - return [ - [f / aspect, 0, 0, 0], - [0, f, 0, 0], - [0, 0, far / range, -1], - [0, 0, near * far / range, 0] - ]; + return o3djs.flat_math.makeMatrix4 ( + f / aspect, 0, 0, 0, + 0, f, 0, 0, + 0, 0, 2 * far / range + 1, -1, + 0, 0, 2 * near * far / range, 0 + ); }; /** @@ -1832,18 +2394,17 @@ o3djs.math.matrix4.perspective = function(angle, aspect, near, far) { * @param {number} top The y coordinate of the right plane of the box. * @param {number} near The negative z coordinate of the near plane of the box. * @param {number} far The negative z coordinate of the far plane of the box. - * @return {!o3djs.math.Matrix4} The orthographic projection matrix. + * @return {!o3djs.flat_math.Matrix4} The orthographic projection matrix. */ -o3djs.math.matrix4.orthographic = +o3djs.flat_math.matrix4.orthographic = function(left, right, bottom, top, near, far) { - return [ - [2 / (right - left), 0, 0, 0], - [0, 2 / (top - bottom), 0, 0], - [0, 0, 1 / (near - far), 0], - [(left + right) / (left - right), - (bottom + top) / (bottom - top), - near / (near - far), 1] - ]; + return o3djs.flat_math.makeMatrix4 ( + 2 / (right - left), 0, 0, 0, + 0, 2 / (top - bottom), 0, 0, + 0, 0, 2 / (near - far), 0, + (left + right) / (left - right), + (bottom + top) / (bottom - top), + (near + far) / (near - far), 1); }; /** @@ -1861,17 +2422,17 @@ o3djs.math.matrix4.orthographic = * @param {number} top The y coordinate of the right plane of the box. * @param {number} near The negative z coordinate of the near plane of the box. * @param {number} far The negative z coordinate of the far plane of the box. - * @return {!o3djs.math.Matrix4} The perspective projection matrix. + * @return {!o3djs.flat_math.Matrix4} The perspective projection matrix. */ -o3djs.math.matrix4.frustum = function(left, right, bottom, top, near, far) { +o3djs.flat_math.matrix4.frustum = function(left, right, bottom, top, near, far) { var dx = (right - left); var dy = (top - bottom); var dz = (near - far); - return [ - [2 * near / dx, 0, 0, 0], - [0, 2 * near / dy, 0, 0], - [(left + right) / dx, (top + bottom) / dy, far / dz, -1], - [0, 0, near * far / dz, 0]]; + return o3djs.flat_math.makeMatrix4( + 2 * near / dx, 0, 0, 0, + 0, 2 * near / dy, 0, 0, + (left + right) / dx, (top + bottom) / dy, far / dz, -1, + 0, 0, near * far / dz, 0); }; /** @@ -1881,22 +2442,25 @@ o3djs.math.matrix4.frustum = function(left, right, bottom, top, near, far) { * vector pointing from the eye to the target to a vector pointing in the * negative z direction, and also sends the up vector into the upper half of * the yz plane. - * @param {(!o3djs.math.Vector3|!o3djs.math.Vector4)} eye The position + * @param {(!o3djs.flat_math.Vector3|!o3djs.flat_math.Vector4)} eye The position * of the eye. - * @param {(!o3djs.math.Vector3|!o3djs.math.Vector4)} target The + * @param {(!o3djs.flat_math.Vector3|!o3djs.flat_math.Vector4)} target The * position meant to be viewed. - * @param {(!o3djs.math.Vector3|!o3djs.math.Vector4)} up A vector + * @param {(!o3djs.flat_math.Vector3|!o3djs.flat_math.Vector4)} up A vector * pointing up. - * @return {!o3djs.math.Matrix4} The look-at matrix. + * @return {!o3djs.flat_math.Matrix4} The look-at matrix. */ -o3djs.math.matrix4.lookAt = function(eye, target, up) { - var vz = o3djs.math.normalize( - o3djs.math.subVector(eye, target).slice(0, 3)).concat(0); - var vx = o3djs.math.normalize( - o3djs.math.cross(up, vz)).concat(0); - var vy = o3djs.math.cross(vz, vx).concat(0); - - return o3djs.math.inverse([vx, vy, vz, eye.concat(1)]); +o3djs.flat_math.matrix4.lookAt = function(eye, target, up) { + var vz = o3djs.flat_math.normalize( + o3djs.flat_math.subVector(eye, target).slice(0, 3)); + var vx = o3djs.flat_math.normalize( + o3djs.flat_math.cross(up, vz)); + var vy = o3djs.flat_math.cross(vz, vx); + return o3djs.flat_math.inverse4(o3djs.flat_math.makeMatrix4( + vx[0], vx[1], vx[2], 0, + vy[0], vy[1], vy[2], 0, + vz[0], vz[1], vz[2], 0, + eye[0], eye[1], eye[2], 1)); }; /** @@ -1905,67 +2469,60 @@ o3djs.math.matrix4.lookAt = function(eye, target, up) { * transform by b first and then a. Note this is subtly different from just * multiplying the matrices together. For given a and b, this function returns * the same object in both row-major and column-major mode. - * @param {!o3djs.math.Matrix4} a A 4-by-4 matrix. - * @param {!o3djs.math.Matrix4} b A 4-by-4 matrix. - * @return {!o3djs.math.Matrix4} the composition of a and b, b first then a. - */ -o3djs.math.matrix4.composition = function(a, b) { - var a0 = a[0]; - var a1 = a[1]; - var a2 = a[2]; - var a3 = a[3]; - var b0 = b[0]; - var b1 = b[1]; - var b2 = b[2]; - var b3 = b[3]; - var a00 = a0[0]; - var a01 = a0[1]; - var a02 = a0[2]; - var a03 = a0[3]; - var a10 = a1[0]; - var a11 = a1[1]; - var a12 = a1[2]; - var a13 = a1[3]; - var a20 = a2[0]; - var a21 = a2[1]; - var a22 = a2[2]; - var a23 = a2[3]; - var a30 = a3[0]; - var a31 = a3[1]; - var a32 = a3[2]; - var a33 = a3[3]; - var b00 = b0[0]; - var b01 = b0[1]; - var b02 = b0[2]; - var b03 = b0[3]; - var b10 = b1[0]; - var b11 = b1[1]; - var b12 = b1[2]; - var b13 = b1[3]; - var b20 = b2[0]; - var b21 = b2[1]; - var b22 = b2[2]; - var b23 = b2[3]; - var b30 = b3[0]; - var b31 = b3[1]; - var b32 = b3[2]; - var b33 = b3[3]; - return [[a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03, - a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03, - a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03, - a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03], - [a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13, - a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13, - a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13, - a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13], - [a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23, - a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23, - a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23, - a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23], - [a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33, - a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33, - a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33, - a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33]]; + * @param {!o3djs.flat_math.Matrix4} a A 4-by-4 matrix. + * @param {!o3djs.flat_math.Matrix4} b A 4-by-4 matrix. + * @return {!o3djs.flat_math.Matrix4} the composition of a and b, b first then a. + */ +o3djs.flat_math.matrix4.composition = function(a, b) { + var a00 = a[0]; + var a01 = a[1]; + var a02 = a[2]; + var a03 = a[3]; + var a10 = a[4]; + var a11 = a[5]; + var a12 = a[6]; + var a13 = a[7]; + var a20 = a[8]; + var a21 = a[9]; + var a22 = a[10]; + var a23 = a[11]; + var a30 = a[12]; + var a31 = a[13]; + var a32 = a[14]; + var a33 = a[15]; + var b00 = b[0]; + var b01 = b[1]; + var b02 = b[2]; + var b03 = b[3]; + var b10 = b[4]; + var b11 = b[5]; + var b12 = b[6]; + var b13 = b[7]; + var b20 = b[8]; + var b21 = b[9]; + var b22 = b[10]; + var b23 = b[11]; + var b30 = b[12]; + var b31 = b[13]; + var b32 = b[14]; + var b33 = b[15]; + return o3djs.flat_math.makeMatrix( + a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03, + a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03, + a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03, + a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03, + a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13, + a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13, + a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13, + a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13, + a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23, + a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23, + a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23, + a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23, + a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33, + a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33, + a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33, + a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33); }; /** @@ -1974,121 +2531,105 @@ o3djs.math.matrix4.composition = function(a, b) { * transform by b first and then a. Note this is subtly different from just * multiplying the matrices together. For given a and b, a, upon modification, * will be the same object in both row-major and column-major mode. - * @param {!o3djs.math.Matrix4} a A 4-by-4 matrix. - * @param {!o3djs.math.Matrix4} b A 4-by-4 matrix. - * @return {!o3djs.math.Matrix4} a once modified. - */ -o3djs.math.matrix4.compose = function(a, b) { - var a0 = a[0]; - var a1 = a[1]; - var a2 = a[2]; - var a3 = a[3]; - var b0 = b[0]; - var b1 = b[1]; - var b2 = b[2]; - var b3 = b[3]; - var a00 = a0[0]; - var a01 = a0[1]; - var a02 = a0[2]; - var a03 = a0[3]; - var a10 = a1[0]; - var a11 = a1[1]; - var a12 = a1[2]; - var a13 = a1[3]; - var a20 = a2[0]; - var a21 = a2[1]; - var a22 = a2[2]; - var a23 = a2[3]; - var a30 = a3[0]; - var a31 = a3[1]; - var a32 = a3[2]; - var a33 = a3[3]; - var b00 = b0[0]; - var b01 = b0[1]; - var b02 = b0[2]; - var b03 = b0[3]; - var b10 = b1[0]; - var b11 = b1[1]; - var b12 = b1[2]; - var b13 = b1[3]; - var b20 = b2[0]; - var b21 = b2[1]; - var b22 = b2[2]; - var b23 = b2[3]; - var b30 = b3[0]; - var b31 = b3[1]; - var b32 = b3[2]; - var b33 = b3[3]; - a[0].splice(0, 4, a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03, - a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03, - a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03, - a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03); - a[1].splice(0, 4, a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13, - a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13, - a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13, - a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13); - a[2].splice(0, 4, a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23, - a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23, - a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23, - a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23), - a[3].splice(0, 4, a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33, - a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33, - a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33, - a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33); + * @param {!o3djs.flat_math.Matrix4} a A 4-by-4 matrix. + * @param {!o3djs.flat_math.Matrix4} b A 4-by-4 matrix. + * @return {!o3djs.flat_math.Matrix4} a once modified. + */ +o3djs.flat_math.matrix4.compose = function(a, b) { + var a00 = a[0]; + var a01 = a[1]; + var a02 = a[2]; + var a03 = a[3]; + var a10 = a[4]; + var a11 = a[5]; + var a12 = a[6]; + var a13 = a[7]; + var a20 = a[8]; + var a21 = a[9]; + var a22 = a[10]; + var a23 = a[11]; + var a30 = a[12]; + var a31 = a[13]; + var a32 = a[14]; + var a33 = a[15]; + var b00 = b[0]; + var b01 = b[1]; + var b02 = b[2]; + var b03 = b[3]; + var b10 = b[4]; + var b11 = b[5]; + var b12 = b[6]; + var b13 = b[7]; + var b20 = b[8]; + var b21 = b[9]; + var b22 = b[10]; + var b23 = b[11]; + var b30 = b[12]; + var b31 = b[13]; + var b32 = b[14]; + var b33 = b[15]; + a[0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03; + a[1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03; + a[2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03; + a[3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03; + a[4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13; + a[5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13; + a[6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13; + a[7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13; + a[8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23; + a[9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23; + a[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23; + a[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23; + a[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33; + a[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33; + a[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33; + a[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33; return a; }; /** * Creates a 4-by-4 matrix which translates by the given vector v. - * @param {(!o3djs.math.Vector3|!o3djs.math.Vector4)} v The vector by + * @param {(!o3djs.flat_math.Vector3|!o3djs.flat_math.Vector4)} v The vector by * which to translate. - * @return {!o3djs.math.Matrix4} The translation matrix. + * @return {!o3djs.flat_math.Matrix4} The translation matrix. */ -o3djs.math.matrix4.translation = function(v) { - return [ - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0], - [v[0], v[1], v[2], 1] - ]; +o3djs.flat_math.matrix4.translation = function(v) { + return o3djs.flat_math.makeMatrix4( + 1, 0, 0, 0, + 0, 1, 0, 0, + 0, 0, 1, 0, + v[0], v[1], v[2], 1); }; /** * Modifies the given 4-by-4 matrix by translation by the given vector v. - * @param {!o3djs.math.Matrix4} m The matrix. - * @param {(!o3djs.math.Vector3|!o3djs.math.Vector4)} v The vector by + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @param {(!o3djs.flat_math.Vector3|!o3djs.flat_math.Vector4)} v The vector by * which to translate. - * @return {!o3djs.math.Matrix4} m once modified. - */ -o3djs.math.matrix4.translate = function(m, v) { - var v0 = v[0]; - var v1 = v[1]; - var v2 = v[2]; - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - var m00 = m0[0]; - var m01 = m0[1]; - var m02 = m0[2]; - var m03 = m0[3]; - var m10 = m1[0]; - var m11 = m1[1]; - var m12 = m1[2]; - var m13 = m1[3]; - var m20 = m2[0]; - var m21 = m2[1]; - var m22 = m2[2]; - var m23 = m2[3]; - var m30 = m3[0]; - var m31 = m3[1]; - var m32 = m3[2]; - var m33 = m3[3]; - - m3.splice(0, 4, m00 * v0 + m10 * v1 + m20 * v2 + m30, - m01 * v0 + m11 * v1 + m21 * v2 + m31, - m02 * v0 + m12 * v1 + m22 * v2 + m32, - m03 * v0 + m13 * v1 + m23 * v2 + m33); + * @return {!o3djs.flat_math.Matrix4} m once modified. + */ +o3djs.flat_math.matrix4.translate = function(m, v) { + var m00 = m[0]; + var m01 = m[1]; + var m02 = m[2]; + var m03 = m[3]; + var m10 = m[4]; + var m11 = m[5]; + var m12 = m[6]; + var m13 = m[7]; + var m20 = m[8]; + var m21 = m[9]; + var m22 = m[10]; + var m23 = m[11]; + var m30 = m[12]; + var m31 = m[13]; + var m32 = m[14]; + var m33 = m[15]; + + m[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30; + m[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31; + m[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32; + m[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33; return m; }; @@ -2097,41 +2638,38 @@ o3djs.math.matrix4.translate = function(m, v) { * Creates a 4-by-4 matrix which scales in each dimension by an amount given by * the corresponding entry in the given vector; assumes the vector has three * entries. - * @param {!o3djs.math.Vector3} v A vector of + * @param {!o3djs.flat_math.Vector3} v A vector of * three entries specifying the factor by which to scale in each dimension. - * @return {!o3djs.math.Matrix4} The scaling matrix. + * @return {!o3djs.flat_math.Matrix4} The scaling matrix. */ -o3djs.math.matrix4.scaling = function(v) { - return [ - [v[0], 0, 0, 0], - [0, v[1], 0, 0], - [0, 0, v[2], 0], - [0, 0, 0, 1] - ]; +o3djs.flat_math.matrix4.scaling = function(v) { + return o3djs.flat_math.makeMatrix( + v[0], 0, 0, 0, + 0, v[1], 0, 0, + 0, 0, v[2], 0, + 0, 0, 0, 1 + ); }; /** * Modifies the given 4-by-4 matrix, scaling in each dimension by an amount * given by the corresponding entry in the given vector; assumes the vector has * three entries. - * @param {!o3djs.math.Matrix4} m The matrix to be modified. - * @param {!o3djs.math.Vector3} v A vector of three entries specifying the + * @param {!o3djs.flat_math.Matrix4} m The matrix to be modified. + * @param {!o3djs.flat_math.Vector3} v A vector of three entries specifying the * factor by which to scale in each dimension. - * @return {!o3djs.math.Matrix4} m once modified. + * @return {!o3djs.flat_math.Matrix4} m once modified. */ -o3djs.math.matrix4.scale = function(m, v) { +o3djs.flat_math.matrix4.scale = function(m, v) { var v0 = v[0]; var v1 = v[1]; var v2 = v[2]; - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - - m0.splice(0, 4, v0 * m0[0], v0 * m0[1], v0 * m0[2], v0 * m0[3]); - m1.splice(0, 4, v1 * m1[0], v1 * m1[1], v1 * m1[2], v1 * m1[3]); - m2.splice(0, 4, v2 * m2[0], v2 * m2[1], v2 * m2[2], v2 * m2[3]); + for (var i = 0; i < 4; ++i) { + m[i] *= v0; + m[4 + i] *= v1; + m[8 + i] *= v2; + } return m; }; @@ -2139,51 +2677,46 @@ o3djs.math.matrix4.scale = function(m, v) { /** * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle. * @param {number} angle The angle by which to rotate (in radians). - * @return {!o3djs.math.Matrix4} The rotation matrix. + * @return {!o3djs.flat_math.Matrix4} The rotation matrix. */ -o3djs.math.matrix4.rotationX = function(angle) { +o3djs.flat_math.matrix4.rotationX = function(angle) { var c = Math.cos(angle); var s = Math.sin(angle); - return [ - [1, 0, 0, 0], - [0, c, s, 0], - [0, -s, c, 0], - [0, 0, 0, 1] - ]; + return o3djs.flat_math.makeMatrix( + 1, 0, 0, 0, + 0, c, s, 0, + 0, -s, c, 0, + 0, 0, 0, 1); }; /** * Modifies the given 4-by-4 matrix by a rotation around the x-axis by the given * angle. - * @param {!o3djs.math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Matrix4} m The matrix. * @param {number} angle The angle by which to rotate (in radians). - * @return {!o3djs.math.Matrix4} m once modified. - */ -o3djs.math.matrix4.rotateX = function(m, angle) { - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - var m10 = m1[0]; - var m11 = m1[1]; - var m12 = m1[2]; - var m13 = m1[3]; - var m20 = m2[0]; - var m21 = m2[1]; - var m22 = m2[2]; - var m23 = m2[3]; + * @return {!o3djs.flat_math.Matrix4} m once modified. + */ +o3djs.flat_math.matrix4.rotateX = function(m, angle) { + var m10 = m[4]; + var m11 = m[5]; + var m12 = m[6]; + var m13 = m[7]; + var m20 = m[8]; + var m21 = m[9]; + var m22 = m[10]; + var m23 = m[11]; var c = Math.cos(angle); var s = Math.sin(angle); - m1.splice(0, 4, c * m10 + s * m20, - c * m11 + s * m21, - c * m12 + s * m22, - c * m13 + s * m23); - m2.splice(0, 4, c * m20 - s * m10, - c * m21 - s * m11, - c * m22 - s * m12, - c * m23 - s * m13); + m[4] = c * m10 + s * m20; + m[5] = c * m11 + s * m21; + m[6] = c * m12 + s * m22; + m[7] = c * m13 + s * m23; + m[8] = c * m20 - s * m10; + m[9] = c * m21 - s * m11; + m[10] = c * m22 - s * m12; + m[11] = c * m23 - s * m13; return m; }; @@ -2191,51 +2724,46 @@ o3djs.math.matrix4.rotateX = function(m, angle) { /** * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle. * @param {number} angle The angle by which to rotate (in radians). - * @return {!o3djs.math.Matrix4} The rotation matrix. + * @return {!o3djs.flat_math.Matrix4} The rotation matrix. */ -o3djs.math.matrix4.rotationY = function(angle) { +o3djs.flat_math.matrix4.rotationY = function(angle) { var c = Math.cos(angle); var s = Math.sin(angle); - return [ - [c, 0, -s, 0], - [0, 1, 0, 0], - [s, 0, c, 0], - [0, 0, 0, 1] - ]; + return o3djs.flat_math.makeMatrix( + c, 0, -s, 0, + 0, 1, 0, 0, + s, 0, c, 0, + 0, 0, 0, 1); }; /** * Modifies the given 4-by-4 matrix by a rotation around the y-axis by the given * angle. - * @param {!o3djs.math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Matrix4} m The matrix. * @param {number} angle The angle by which to rotate (in radians). - * @return {!o3djs.math.Matrix4} m once modified. - */ -o3djs.math.matrix4.rotateY = function(m, angle) { - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - var m00 = m0[0]; - var m01 = m0[1]; - var m02 = m0[2]; - var m03 = m0[3]; - var m20 = m2[0]; - var m21 = m2[1]; - var m22 = m2[2]; - var m23 = m2[3]; + * @return {!o3djs.flat_math.Matrix4} m once modified. + */ +o3djs.flat_math.matrix4.rotateY = function(m, angle) { + var m00 = m[0]; + var m01 = m[1]; + var m02 = m[2]; + var m03 = m[3]; + var m20 = m[8]; + var m21 = m[9]; + var m22 = m[10]; + var m23 = m[11]; var c = Math.cos(angle); var s = Math.sin(angle); - m0.splice(0, 4, c * m00 - s * m20, - c * m01 - s * m21, - c * m02 - s * m22, - c * m03 - s * m23); - m2.splice(0, 4, c * m20 + s * m00, - c * m21 + s * m01, - c * m22 + s * m02, - c * m23 + s * m03); + m[0] = c * m00 - s * m20; + m[1] = c * m01 - s * m21; + m[2] = c * m02 - s * m22; + m[3] = c * m03 - s * m23; + m[8] = c * m20 + s * m00; + m[9] = c * m21 + s * m01; + m[10] = c * m22 + s * m02; + m[11] = c * m23 + s * m03; return m; }; @@ -2243,51 +2771,46 @@ o3djs.math.matrix4.rotateY = function(m, angle) { /** * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle. * @param {number} angle The angle by which to rotate (in radians). - * @return {!o3djs.math.Matrix4} The rotation matrix. + * @return {!o3djs.flat_math.Matrix4} The rotation matrix. */ -o3djs.math.matrix4.rotationZ = function(angle) { +o3djs.flat_math.matrix4.rotationZ = function(angle) { var c = Math.cos(angle); var s = Math.sin(angle); - return [ - [c, s, 0, 0], - [-s, c, 0, 0], - [0, 0, 1, 0], - [0, 0, 0, 1] - ]; + return o3djs.flat_math.makeMatrix( + c, s, 0, 0, + -s, c, 0, 0, + 0, 0, 1, 0, + 0, 0, 0, 1); }; /** * Modifies the given 4-by-4 matrix by a rotation around the z-axis by the given * angle. - * @param {!o3djs.math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Matrix4} m The matrix. * @param {number} angle The angle by which to rotate (in radians). - * @return {!o3djs.math.Matrix4} m once modified. - */ -o3djs.math.matrix4.rotateZ = function(m, angle) { - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - var m00 = m0[0]; - var m01 = m0[1]; - var m02 = m0[2]; - var m03 = m0[3]; - var m10 = m1[0]; - var m11 = m1[1]; - var m12 = m1[2]; - var m13 = m1[3]; + * @return {!o3djs.flat_math.Matrix4} m once modified. + */ +o3djs.flat_math.matrix4.rotateZ = function(m, angle) { + var m00 = m[0]; + var m01 = m[1]; + var m02 = m[2]; + var m03 = m[3]; + var m10 = m[4]; + var m11 = m[5]; + var m12 = m[6]; + var m13 = m[7]; var c = Math.cos(angle); var s = Math.sin(angle); - m0.splice(0, 4, c * m00 + s * m10, - c * m01 + s * m11, - c * m02 + s * m12, - c * m03 + s * m13); - m1.splice(0, 4, c * m10 - s * m00, - c * m11 - s * m01, - c * m12 - s * m02, - c * m13 - s * m03); + m[0] = c * m00 + s * m10; + m[1] = c * m01 + s * m11; + m[2] = c * m02 + s * m12; + m[3] = c * m03 + s * m13; + m[4] = c * m10 - s * m00; + m[5] = c * m11 - s * m01; + m[6] = c * m12 - s * m02; + m[7] = c * m13 - s * m03; return m; }; @@ -2297,10 +2820,10 @@ o3djs.math.matrix4.rotateZ = function(m, angle) { * vector as angles by which to rotate around the x, y and z axes, returns a * a matrix which rotates around the x-axis first, then the y-axis, then the * z-axis. - * @param {!o3djs.math.Vector3} v A vector of angles (in radians). - * @return {!o3djs.math.Matrix4} The rotation matrix. + * @param {!o3djs.flat_math.Vector3} v A vector of angles (in radians). + * @return {!o3djs.flat_math.Matrix4} The rotation matrix. */ -o3djs.math.matrix4.rotationZYX = function(v) { +o3djs.flat_math.matrix4.rotationZYX = function(v) { var sinx = Math.sin(v[0]); var cosx = Math.cos(v[0]); var siny = Math.sin(v[1]); @@ -2311,29 +2834,22 @@ o3djs.math.matrix4.rotationZYX = function(v) { var coszsiny = cosz * siny; var sinzsiny = sinz * siny; - return [ - [cosz * cosy, sinz * cosy, -siny, 0], - [coszsiny * sinx - sinz * cosx, - sinzsiny * sinx + cosz * cosx, - cosy * sinx, - 0], - [coszsiny * cosx + sinz * sinx, - sinzsiny * cosx - cosz * sinx, - cosy * cosx, - 0], - [0, 0, 0, 1] - ]; + return o3djs.flat_math.makeMatrix( + cosz * cosy, sinz * cosy, -siny, 0, coszsiny * sinx - sinz * cosx, + sinzsiny * sinx + cosz * cosx, cosy * sinx, 0, + coszsiny * cosx + sinz * sinx, sinzsiny * cosx - cosz * sinx, cosy * cosx, + 0, 0, 0, 0, 1); }; /** * Modifies a 4-by-4 matrix by a rotation. Interprets the coordinates of the * given vector as angles by which to rotate around the x, y and z axes, rotates * around the x-axis first, then the y-axis, then the z-axis. - * @param {!o3djs.math.Matrix4} m The matrix. - * @param {!o3djs.math.Vector3} v A vector of angles (in radians). - * @return {!o3djs.math.Matrix4} m once modified. + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @param {!o3djs.flat_math.Vector3} v A vector of angles (in radians). + * @return {!o3djs.flat_math.Matrix4} m once modified. */ -o3djs.math.matrix4.rotateZYX = function(m, v) { +o3djs.flat_math.matrix4.rotateZYX = function(m, v) { var sinX = Math.sin(v[0]); var cosX = Math.cos(v[0]); var sinY = Math.sin(v[1]); @@ -2354,45 +2870,37 @@ o3djs.math.matrix4.rotateZYX = function(m, v) { var r21 = sinZSinY * cosX - cosZ * sinX; var r22 = cosY * cosX; - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - - var m00 = m0[0]; - var m01 = m0[1]; - var m02 = m0[2]; - var m03 = m0[3]; - var m10 = m1[0]; - var m11 = m1[1]; - var m12 = m1[2]; - var m13 = m1[3]; - var m20 = m2[0]; - var m21 = m2[1]; - var m22 = m2[2]; - var m23 = m2[3]; - var m30 = m3[0]; - var m31 = m3[1]; - var m32 = m3[2]; - var m33 = m3[3]; - - m0.splice(0, 4, - r00 * m00 + r01 * m10 + r02 * m20, - r00 * m01 + r01 * m11 + r02 * m21, - r00 * m02 + r01 * m12 + r02 * m22, - r00 * m03 + r01 * m13 + r02 * m23); - - m1.splice(0, 4, - r10 * m00 + r11 * m10 + r12 * m20, - r10 * m01 + r11 * m11 + r12 * m21, - r10 * m02 + r11 * m12 + r12 * m22, - r10 * m03 + r11 * m13 + r12 * m23); - - m2.splice(0, 4, - r20 * m00 + r21 * m10 + r22 * m20, - r20 * m01 + r21 * m11 + r22 * m21, - r20 * m02 + r21 * m12 + r22 * m22, - r20 * m03 + r21 * m13 + r22 * m23); + var m00 = m[0]; + var m01 = m[1]; + var m02 = m[2]; + var m03 = m[3]; + var m10 = m[4]; + var m11 = m[5]; + var m12 = m[6]; + var m13 = m[7]; + var m20 = m[8]; + var m21 = m[9]; + var m22 = m[10]; + var m23 = m[11]; + var m30 = m[12]; + var m31 = m[13]; + var m32 = m[14]; + var m33 = m[15]; + + m[0] = r00 * m00 + r01 * m10 + r02 * m20; + m[1] = r00 * m01 + r01 * m11 + r02 * m21; + m[2] = r00 * m02 + r01 * m12 + r02 * m22; + m[3] = r00 * m03 + r01 * m13 + r02 * m23; + + m[4] = r10 * m00 + r11 * m10 + r12 * m20; + m[5] = r10 * m01 + r11 * m11 + r12 * m21; + m[6] = r10 * m02 + r11 * m12 + r12 * m22; + m[7] = r10 * m03 + r11 * m13 + r12 * m23; + + m[8] = r20 * m00 + r21 * m10 + r22 * m20; + m[9] = r20 * m01 + r21 * m11 + r22 * m21; + m[10] = r20 * m02 + r21 * m12 + r22 * m22; + m[11] = r20 * m03 + r21 * m13 + r22 * m23; return m; }; @@ -2400,13 +2908,13 @@ o3djs.math.matrix4.rotateZYX = function(m, v) { /** * Creates a 4-by-4 matrix which rotates around the given axis by the given * angle. - * @param {(!o3djs.math.Vector3|!o3djs.math.Vector4)} axis The axis + * @param {(!o3djs.flat_math.Vector3|!o3djs.flat_math.Vector4)} axis The axis * about which to rotate. * @param {number} angle The angle by which to rotate (in radians). - * @return {!o3djs.math.Matrix4} A matrix which rotates angle radians + * @return {!o3djs.flat_math.Matrix4} A matrix which rotates angle radians * around the axis. */ -o3djs.math.matrix4.axisRotation = function(axis, angle) { +o3djs.flat_math.matrix4.axisRotation = function(axis, angle) { var x = axis[0]; var y = axis[1]; var z = axis[2]; @@ -2421,33 +2929,33 @@ o3djs.math.matrix4.axisRotation = function(axis, angle) { var s = Math.sin(angle); var oneMinusCosine = 1 - c; - return [ - [xx + (1 - xx) * c, + return o3djs.flat_math.makeMatrix( + xx + (1 - xx) * c, x * y * oneMinusCosine + z * s, x * z * oneMinusCosine - y * s, - 0], - [x * y * oneMinusCosine - z * s, + 0, + x * y * oneMinusCosine - z * s, yy + (1 - yy) * c, y * z * oneMinusCosine + x * s, - 0], - [x * z * oneMinusCosine + y * s, + 0, + x * z * oneMinusCosine + y * s, y * z * oneMinusCosine - x * s, zz + (1 - zz) * c, - 0], - [0, 0, 0, 1] - ]; + 0, + 0, 0, 0, 1 + ); }; /** * Modifies the given 4-by-4 matrix by rotation around the given axis by the * given angle. - * @param {!o3djs.math.Matrix4} m The matrix. - * @param {(!o3djs.math.Vector3|!o3djs.math.Vector4)} axis The axis + * @param {!o3djs.flat_math.Matrix4} m The matrix. + * @param {(!o3djs.flat_math.Vector3|!o3djs.flat_math.Vector4)} axis The axis * about which to rotate. * @param {number} angle The angle by which to rotate (in radians). - * @return {!o3djs.math.Matrix4} m once modified. + * @return {!o3djs.flat_math.Matrix4} m once modified. */ -o3djs.math.matrix4.axisRotate = function(m, axis, angle) { +o3djs.flat_math.matrix4.axisRotate = function(m, axis, angle) { var x = axis[0]; var y = axis[1]; var z = axis[2]; @@ -2472,97 +2980,105 @@ o3djs.math.matrix4.axisRotate = function(m, axis, angle) { var r21 = y * z * oneMinusCosine - x * s; var r22 = zz + (1 - zz) * c; - var m0 = m[0]; - var m1 = m[1]; - var m2 = m[2]; - var m3 = m[3]; - - var m00 = m0[0]; - var m01 = m0[1]; - var m02 = m0[2]; - var m03 = m0[3]; - var m10 = m1[0]; - var m11 = m1[1]; - var m12 = m1[2]; - var m13 = m1[3]; - var m20 = m2[0]; - var m21 = m2[1]; - var m22 = m2[2]; - var m23 = m2[3]; - var m30 = m3[0]; - var m31 = m3[1]; - var m32 = m3[2]; - var m33 = m3[3]; - - m0.splice(0, 4, - r00 * m00 + r01 * m10 + r02 * m20, - r00 * m01 + r01 * m11 + r02 * m21, - r00 * m02 + r01 * m12 + r02 * m22, - r00 * m03 + r01 * m13 + r02 * m23); - - m1.splice(0, 4, - r10 * m00 + r11 * m10 + r12 * m20, - r10 * m01 + r11 * m11 + r12 * m21, - r10 * m02 + r11 * m12 + r12 * m22, - r10 * m03 + r11 * m13 + r12 * m23); - - m2.splice(0, 4, - r20 * m00 + r21 * m10 + r22 * m20, - r20 * m01 + r21 * m11 + r22 * m21, - r20 * m02 + r21 * m12 + r22 * m22, - r20 * m03 + r21 * m13 + r22 * m23); + var m00 = m[0]; + var m01 = m[1]; + var m02 = m[2]; + var m03 = m[3]; + var m10 = m[4]; + var m11 = m[5]; + var m12 = m[6]; + var m13 = m[7]; + var m20 = m[8]; + var m21 = m[9]; + var m22 = m[10]; + var m23 = m[11]; + var m30 = m[12]; + var m31 = m[13]; + var m32 = m[14]; + var m33 = m[15]; + + m[0] = r00 * m00 + r01 * m10 + r02 * m20; + m[1] = r00 * m01 + r01 * m11 + r02 * m21; + m[2] = r00 * m02 + r01 * m12 + r02 * m22; + m[3] = r00 * m03 + r01 * m13 + r02 * m23; + + m[4] = r10 * m00 + r11 * m10 + r12 * m20; + m[5] = r10 * m01 + r11 * m11 + r12 * m21; + m[6] = r10 * m02 + r11 * m12 + r12 * m22; + m[7] = r10 * m03 + r11 * m13 + r12 * m23; + + m[8] = r20 * m00 + r21 * m10 + r22 * m20; + m[9] = r20 * m01 + r21 * m11 + r22 * m21; + m[10] = r20 * m02 + r21 * m12 + r22 * m22; + m[11] = r20 * m03 + r21 * m13 + r22 * m23; return m; }; /** - * Sets each function in the namespace o3djs.math to the row major - * version in o3djs.math.rowMajor (provided such a function exists in - * o3djs.math.rowMajor). Call this function to establish the row major + * Sets each function in the namespace o3djs.flat_math to the row major + * version in o3djs.flat_math.rowMajor (provided such a function exists in + * o3djs.flat_math.rowMajor). Call this function to establish the row major * convention. */ -o3djs.math.installRowMajorFunctions = function() { - for (var f in o3djs.math.rowMajor) { - o3djs.math[f] = o3djs.math.rowMajor[f]; +o3djs.flat_math.installRowMajorFunctions = function() { + for (var f in o3djs.flat_math.rowMajor) { + o3djs.flat_math[f] = o3djs.flat_math.rowMajor[f]; } }; /** - * Sets each function in the namespace o3djs.math to the column major - * version in o3djs.math.columnMajor (provided such a function exists in - * o3djs.math.columnMajor). Call this function to establish the column + * Sets each function in the namespace o3djs.flat_math to the column major + * version in o3djs.flat_math.columnMajor (provided such a function exists in + * o3djs.flat_math.columnMajor). Call this function to establish the column * major convention. */ -o3djs.math.installColumnMajorFunctions = function() { - for (var f in o3djs.math.columnMajor) { - o3djs.math[f] = o3djs.math.columnMajor[f]; +o3djs.flat_math.installColumnMajorFunctions = function() { + for (var f in o3djs.flat_math.columnMajor) { + o3djs.flat_math[f] = o3djs.flat_math.columnMajor[f]; } }; /** - * Sets each function in the namespace o3djs.math to the error checking - * version in o3djs.math.errorCheck (provided such a function exists in - * o3djs.math.errorCheck). + * Sets each function in the namespace o3djs.flat_math to the error checking + * version in o3djs.flat_math.errorCheck (provided such a function exists in + * o3djs.flat_math.errorCheck). */ -o3djs.math.installErrorCheckFunctions = function() { - for (var f in o3djs.math.errorCheck) { - o3djs.math[f] = o3djs.math.errorCheck[f]; +o3djs.flat_math.installErrorCheckFunctions = function() { + for (var f in o3djs.flat_math.errorCheck) { + o3djs.flat_math[f] = o3djs.flat_math.errorCheck[f]; } }; /** - * Sets each function in the namespace o3djs.math to the error checking free - * version in o3djs.math.errorCheckFree (provided such a function exists in - * o3djs.math.errorCheckFree). + * Sets each function in the namespace o3djs.flat_math to the error checking free + * version in o3djs.flat_math.errorCheckFree (provided such a function exists in + * o3djs.flat_math.errorCheckFree). */ -o3djs.math.installErrorCheckFreeFunctions = function() { - for (var f in o3djs.math.errorCheckFree) { - o3djs.math[f] = o3djs.math.errorCheckFree[f]; +o3djs.flat_math.installErrorCheckFreeFunctions = function() { + for (var f in o3djs.flat_math.errorCheckFree) { + o3djs.flat_math[f] = o3djs.flat_math.errorCheckFree[f]; } -} +}; // By default, install the row-major functions. -o3djs.math.installRowMajorFunctions(); +o3djs.flat_math.installRowMajorFunctions(); // By default, install prechecking. -o3djs.math.installErrorCheckFunctions(); +o3djs.flat_math.installErrorCheckFunctions(); + +if (!use_plugin_math) { + for (var i in o3djs.flat_math) { + o3djs.math[i] = o3djs.flat_math[i]; + } +} + + +/** + * True if we are using the plugin math library in which matrices are + * represented by 2-dimensional arrays. + * @type {boolean} + * @private + */ +o3djs.math.usePluginMath_ = true; + |