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3− * Copyright (c) 2010 Mozilla Corporation
4− * Copyright (c) 2010 Vladimir Vukicevic
5− * Copyright (c) 2013 John Mayer
7− * Permission is hereby granted, free of charge, to any person
8− * obtaining a copy of this software and associated documentation
9− * files (the "Software"), to deal in the Software without
10− * restriction, including without limitation the rights to use,
11− * copy, modify, merge, publish, distribute, sublicense, and/or sell
12− * copies of the Software, and to permit persons to whom the
13− * Software is furnished to do so, subject to the following
16− * The above copyright notice and this permission notice shall be
17− * included in all copies or substantial portions of the Software.
19− * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
20− * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
21− * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
22− * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
23− * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
24− * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
25− * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
26− * OTHER DEALINGS IN THE SOFTWARE.
32− * Vector and Matrix math utilities for JavaScript, optimized for WebGL.
33− * Edited to work with Elm Programming Language
37−Elm.Native.MJS.make = function(elm) {
39− elm.Native = elm.Native || {};
40− elm.Native.MJS = elm.Native.MJS || {};
41− if (elm.Native.MJS.values) return elm.Native.MJS.values;
44− * Constant: MJS_VERSION
46− * mjs version number aa.bb.cc, encoded as an integer of the form:
49− var MJS_VERSION = 0x000000;
52− * Constant: MJS_DO_ASSERT
54− * Enables or disables runtime assertions.
56− * For potentially more performance, the assert methods can be
57− * commented out in each place where they are called.
59− //var MJS_DO_ASSERT = true;
62− * Constant: MJS_FLOAT_ARRAY_TYPE
64− * The base float array type. By default, WebGLFloatArray.
66− * mjs can work with any array-like elements, but if an array
67− * creation is requested, it will create an array of the type
68− * MJS_FLOAT_ARRAY_TYPE. Also, the builtin constants such as (M4x4.I)
69− * will be of this type.
71− //MJS_FLOAT_ARRAY_TYPE = WebGLFloatArray;
72− var MJS_FLOAT_ARRAY_TYPE = Float32Array;
73− //MJS_FLOAT_ARRAY_TYPE = Float64Array;
74− //MJS_FLOAT_ARRAY_TYPE = Array;
76− //if (MJS_DO_ASSERT) {
77− //function MathUtils_assert(cond, msg) {
79− //throw "Assertion failed: " + msg;
82− function MathUtils_assert() { }
88− * Methods for working with 3-element vectors. A vector is represented by a 3-element array.
89− * Any valid JavaScript array type may be used, but if new
90− * vectors are created they are created using the configured MJS_FLOAT_ARRAY_TYPE.
95− V3._temp1 = new MJS_FLOAT_ARRAY_TYPE(3);
96− V3._temp2 = new MJS_FLOAT_ARRAY_TYPE(3);
97− V3._temp3 = new MJS_FLOAT_ARRAY_TYPE(3);
99− if (MJS_FLOAT_ARRAY_TYPE == Array) {
100− V3.x = [1.0, 0.0, 0.0];
101− V3.y = [0.0, 1.0, 0.0];
102− V3.z = [0.0, 0.0, 1.0];
104− V3.$ = function V3_$(x, y, z) {
108− V3.clone = function V3_clone(a) {
109− //MathUtils_assert(a.length == 3, "a.length == 3");
110− return [a[0], a[1], a[2]];
113− V3.x = new MJS_FLOAT_ARRAY_TYPE([1.0, 0.0, 0.0]);
114− V3.y = new MJS_FLOAT_ARRAY_TYPE([0.0, 1.0, 0.0]);
115− V3.z = new MJS_FLOAT_ARRAY_TYPE([0.0, 0.0, 1.0]);
120− * Creates a new 3-element vector with the given values.
124− * x,y,z - the 3 elements of the new vector.
128− * A new vector containing with the given argument values.
131− V3.$ = function V3_$(x, y, z) {
132− return new MJS_FLOAT_ARRAY_TYPE([x, y, z]);
136− * Function: V3.clone
138− * Clone the given 3-element vector.
142− * a - the 3-element vector to clone
146− * A new vector with the same values as the passed-in one.
149− V3.clone = function V3_clone(a) {
150− //MathUtils_assert(a.length == 3, "a.length == 3");
151− return new MJS_FLOAT_ARRAY_TYPE(a);
158− /* Function: V3.toTuple3
160− * Turn into an Elm Tuple
162− V3.toTuple3 = function V3_toTuple3(a) {
174− * Perform r = a + b.
178− * a - the first vector operand
179− * b - the second vector operand
180− * r - optional vector to store the result in
184− * If r is specified, returns r after performing the operation.
185− * Otherwise, returns a new 3-element vector with the result.
187− V3.add = function V3_add(a, b, r) {
188− //MathUtils_assert(a.length == 3, "a.length == 3");
189− //MathUtils_assert(b.length == 3, "b.length == 3");
190− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
193− r = new MJS_FLOAT_ARRAY_TYPE(3);
208− * a - the first vector operand
209− * b - the second vector operand
210− * r - optional vector to store the result in
214− * If r is specified, returns r after performing the operation.
215− * Otherwise, returns a new 3-element vector with the result.
217− V3.sub = function V3_sub(a, b, r) {
218− //MathUtils_assert(a.length == 3, "a.length == 3");
219− //MathUtils_assert(b.length == 3, "b.length == 3");
220− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
223− r = new MJS_FLOAT_ARRAY_TYPE(3);
238− * a - the vector operand
239− * r - optional vector to store the result in
243− * If r is specified, returns r after performing the operation.
244− * Otherwise, returns a new 3-element vector with the result.
246− V3.neg = function V3_neg(a, r) {
247− //MathUtils_assert(a.length == 3, "a.length == 3");
248− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
251− r = new MJS_FLOAT_ARRAY_TYPE(3);
259− * Function: V3.direction
262− * r = (a - b) / |a - b|. The result is the normalized
263− * direction from a to b.
267− * a - the first vector operand
268− * b - the second vector operand
269− * r - optional vector to store the result in
273− * If r is specified, returns r after performing the operation.
274− * Otherwise, returns a new 3-element vector with the result.
276− V3.direction = function V3_direction(a, b, r) {
277− //MathUtils_assert(a.length == 3, "a.length == 3");
278− //MathUtils_assert(b.length == 3, "b.length == 3");
279− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
282− r = new MJS_FLOAT_ARRAY_TYPE(3);
283− return V3.normalize(V3.sub(a, b, r), r);
287− * Function: V3.length
293− * a - the vector operand
297− * The length of the given vector.
299− V3.length = function V3_length(a) {
300− //MathUtils_assert(a.length == 3, "a.length == 3");
302− return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
306− * Function: V3.lengthSquard
308− * Perform r = |a|*|a|.
312− * a - the vector operand
316− * The square of the length of the given vector.
318− V3.lengthSquared = function V3_lengthSquared(a) {
319− //MathUtils_assert(a.length == 3, "a.length == 3");
321− return a[0]*a[0] + a[1]*a[1] + a[2]*a[2];
325− * Function: V3.normalize
327− * Perform r = a / |a|.
331− * a - the vector operand
332− * r - optional vector to store the result in
336− * If r is specified, returns r after performing the operation.
337− * Otherwise, returns a new 3-element vector with the result.
339− V3.normalize = function V3_normalize(a, r) {
340− //MathUtils_assert(a.length == 3, "a.length == 3");
341− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
344− r = new MJS_FLOAT_ARRAY_TYPE(3);
345− var im = 1.0 / V3.length(a);
353− * Function: V3.scale
355− * Perform r = a * k.
359− * a - the vector operand
360− * k - a scalar value
361− * r - optional vector to store the result in
365− * If r is specified, returns r after performing the operation.
366− * Otherwise, returns a new 3-element vector with the result.
368− V3.scale = function V3_scale(a, k, r) {
369− //MathUtils_assert(a.length == 3, "a.length == 3");
370− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
373− r = new MJS_FLOAT_ARRAY_TYPE(3);
388− * a - the first vector operand
389− * b - the second vector operand
393− * The dot product of a and b.
395− V3.dot = function V3_dot(a, b) {
396− //MathUtils_assert(a.length == 3, "a.length == 3");
397− //MathUtils_assert(b.length == 3, "b.length == 3");
399− return a[0] * b[0] +
405− * Function: V3.cross
407− * Perform r = a x b.
411− * a - the first vector operand
412− * b - the second vector operand
413− * r - optional vector to store the result in
417− * If r is specified, returns r after performing the operation.
418− * Otherwise, returns a new 3-element vector with the result.
420− V3.cross = function V3_cross(a, b, r) {
421− //MathUtils_assert(a.length == 3, "a.length == 3");
422− //MathUtils_assert(b.length == 3, "b.length == 3");
423− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
426− r = new MJS_FLOAT_ARRAY_TYPE(3);
427− r[0] = a[1]*b[2] - a[2]*b[1];
428− r[1] = a[2]*b[0] - a[0]*b[2];
429− r[2] = a[0]*b[1] - a[1]*b[0];
434− * Function: V3.mul4x4
441− * m - the 4x4 matrix operand
442− * v - the 3-element vector operand
443− * r - optional vector to store the result in
447− * If r is specified, returns r after performing the operation.
448− * Otherwise, returns a new 3-element vector with the result.
449− * The 4-element result vector is divided by the w component
450− * and returned as a 3-element vector.
452− V3.mul4x4 = function V3_mul4x4(m, v, r) {
453− //MathUtils_assert(m.length == 16, "m.length == 16");
454− //MathUtils_assert(v.length == 3, "v.length == 3");
455− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
458− var tmp = V3._temp1;
460− r = new MJS_FLOAT_ARRAY_TYPE(3);
464− w = V3.dot(v, tmp) + m[15];
468− r[0] = (V3.dot(v, tmp) + m[12])/w;
472− r[1] = (V3.dot(v, tmp) + m[13])/w;
476− r[2] = (V3.dot(v, tmp) + m[14])/w;
483− * Methods for working with 4x4 matrices. A matrix is represented by a 16-element array
484− * in column-major order. Any valid JavaScript array type may be used, but if new
485− * matrices are created they are created using the configured MJS_FLOAT_ARRAY_TYPE.
490− M4x4._temp1 = new MJS_FLOAT_ARRAY_TYPE(16);
491− M4x4._temp2 = new MJS_FLOAT_ARRAY_TYPE(16);
493− if (MJS_FLOAT_ARRAY_TYPE == Array) {
494− M4x4.I = [1.0, 0.0, 0.0, 0.0,
497− 0.0, 0.0, 0.0, 1.0];
499− M4x4.$ = function M4x4_$(m00, m01, m02, m03,
504− return [m00, m01, m02, m03,
507− m12, m13, m14, m15];
510− M4x4.clone = function M4x4_clone(m) {
511− //MathUtils_assert(m.length == 16, "m.length == 16");
512− return new [m[0], m[1], m[2], m[3],
513− m[4], m[5], m[6], m[7],
514− m[8], m[9], m[10], m[11],
515− m[12], m[13], m[14], m[15]];
518− M4x4.I = new MJS_FLOAT_ARRAY_TYPE([1.0, 0.0, 0.0, 0.0,
521− 0.0, 0.0, 0.0, 1.0]);
526− * Creates a new 4x4 matrix with the given values.
530− * m00..m15 - the 16 elements of the new matrix.
534− * A new matrix filled with the given argument values.
536− M4x4.$ = function M4x4_$(m00, m01, m02, m03,
541− return new MJS_FLOAT_ARRAY_TYPE([m00, m01, m02, m03,
544− m12, m13, m14, m15]);
548− * Function: M4x4.clone
550− * Clone the given 4x4 matrix.
554− * m - the 4x4 matrix to clone
558− * A new matrix with the same values as the passed-in one.
560− M4x4.clone = function M4x4_clone(m) {
561− //MathUtils_assert(m.length == 16, "m.length == 16");
562− return new MJS_FLOAT_ARRAY_TYPE(m);
566− M4x4.identity = M4x4.I;
569− * Function: M4x4.topLeft3x3
571− * Return the top left 3x3 matrix from the given 4x4 matrix m.
576− * r - optional 3x3 matrix to store the result in
580− * If r is specified, returns r after performing the operation.
581− * Otherwise, returns a new 3x3 matrix with the result.
583− M4x4.topLeft3x3 = function M4x4_topLeft3x3(m, r) {
584− //MathUtils_assert(m.length == 16, "m.length == 16");
585− //MathUtils_assert(r == undefined || r.length == 9, "r == undefined || r.length == 9");
588− r = new MJS_FLOAT_ARRAY_TYPE(9);
589− r[0] = m[0]; r[1] = m[1]; r[2] = m[2];
590− r[3] = m[4]; r[4] = m[5]; r[5] = m[6];
591− r[6] = m[8]; r[7] = m[9]; r[8] = m[10];
596− * Function: M4x4.inverseOrthonormal
598− * Computes the inverse of the given matrix m, assuming that
599− * the matrix is orthonormal.
604− * r - optional 4x4 matrix to store the result in
608− * If r is specified, returns r after performing the operation.
609− * Otherwise, returns a new 4x4 matrix with the result.
611− M4x4.inverseOrthonormal = function M4x4_inverseOrthonormal(m, r) {
612− //MathUtils_assert(m.length == 16, "m.length == 16");
613− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
614− //MathUtils_assert(m != r, "m != r");
617− r = new MJS_FLOAT_ARRAY_TYPE(16);
618− M4x4.transpose(m, r);
619− var t = [m[12], m[13], m[14]];
620− r[3] = r[7] = r[11] = 0;
621− r[12] = -V3.dot([r[0], r[4], r[8]], t);
622− r[13] = -V3.dot([r[1], r[5], r[9]], t);
623− r[14] = -V3.dot([r[2], r[6], r[10]], t);
628− * Function: M4x4.inverseTo3x3
630− * Computes the inverse of the given matrix m, but calculates
631− * only the top left 3x3 values of the result.
636− * r - optional 3x3 matrix to store the result in
640− * If r is specified, returns r after performing the operation.
641− * Otherwise, returns a new 3x3 matrix with the result.
643− M4x4.inverseTo3x3 = function M4x4_inverseTo3x3(m, r) {
644− //MathUtils_assert(m.length == 16, "m.length == 16");
645− //MathUtils_assert(r == undefined || r.length == 9, "r == undefined || r.length == 9");
648− r = new MJS_FLOAT_ARRAY_TYPE(9);
650− var a11 = m[10]*m[5]-m[6]*m[9],
651− a21 = -m[10]*m[1]+m[2]*m[9],
652− a31 = m[6]*m[1]-m[2]*m[5],
653− a12 = -m[10]*m[4]+m[6]*m[8],
654− a22 = m[10]*m[0]-m[2]*m[8],
655− a32 = -m[6]*m[0]+m[2]*m[4],
656− a13 = m[9]*m[4]-m[5]*m[8],
657− a23 = -m[9]*m[0]+m[1]*m[8],
658− a33 = m[5]*m[0]-m[1]*m[4];
659− var det = m[0]*(a11) + m[1]*(a12) + m[2]*(a13);
660− if (det == 0) // no inverse
661− throw "matrix not invertible";
662− var idet = 1.0 / det;
678− * Function: M4x4.makeFrustum
680− * Creates a matrix for a projection frustum with the given parameters.
684− * left - the left coordinate of the frustum
685− * right- the right coordinate of the frustum
686− * bottom - the bottom coordinate of the frustum
687− * top - the top coordinate of the frustum
688− * znear - the near z distance of the frustum
689− * zfar - the far z distance of the frustum
690− * r - optional 4x4 matrix to store the result in
694− * If r is specified, returns r after creating the projection matrix.
695− * Otherwise, returns a new 4x4 matrix.
697− M4x4.makeFrustum = function M4x4_makeFrustum(left, right, bottom, top, znear, zfar, r) {
698− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
701− r = new MJS_FLOAT_ARRAY_TYPE(16);
703− var X = 2*znear/(right-left);
704− var Y = 2*znear/(top-bottom);
705− var A = (right+left)/(right-left);
706− var B = (top+bottom)/(top-bottom);
707− var C = -(zfar+znear)/(zfar-znear);
708− var D = -2*zfar*znear/(zfar-znear);
710− r[0] = 2*znear/(right-left);
715− r[5] = 2*znear/(top-bottom);
718− r[8] = (right+left)/(right-left);
719− r[9] = (top+bottom)/(top-bottom);
720− r[10] = -(zfar+znear)/(zfar-znear);
724− r[14] = -2*zfar*znear/(zfar-znear);
731− * Function: M4x4.makePerspective
733− * Creates a matrix for a perspective projection with the given parameters.
737− * fovy - field of view in the y axis, in degrees
738− * aspect - aspect ratio
739− * znear - the near z distance of the projection
740− * zfar - the far z distance of the projection
741− * r - optional 4x4 matrix to store the result in
745− * If r is specified, returns r after creating the projection matrix.
746− * Otherwise, returns a new 4x4 matrix.
748− M4x4.makePerspective = function M4x4_makePerspective (fovy, aspect, znear, zfar, r) {
749− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
751− var ymax = znear * Math.tan(fovy * Math.PI / 360.0);
753− var xmin = ymin * aspect;
754− var xmax = ymax * aspect;
756− return M4x4.makeFrustum(xmin, xmax, ymin, ymax, znear, zfar, r);
760− * Function: M4x4.makeOrtho
762− * Creates a matrix for an orthogonal frustum projection with the given parameters.
766− * left - the left coordinate of the frustum
767− * right- the right coordinate of the frustum
768− * bottom - the bottom coordinate of the frustum
769− * top - the top coordinate of the frustum
770− * znear - the near z distance of the frustum
771− * zfar - the far z distance of the frustum
772− * r - optional 4x4 matrix to store the result in
776− * If r is specified, returns r after creating the projection matrix.
777− * Otherwise, returns a new 4x4 matrix.
779− M4x4.makeOrtho = function M4x4_makeOrtho (left, right, bottom, top, znear, zfar, r) {
780− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
783− r = new MJS_FLOAT_ARRAY_TYPE(16);
785− var tX = -(right+left)/(right-left);
786− var tY = -(top+bottom)/(top-bottom);
787− var tZ = -(zfar+znear)/(zfar-znear);
788− var X = 2 / (right-left);
789− var Y = 2 / (top-bottom);
790− var Z = -2 / (zfar-znear);
792− r[0] = 2 / (right-left);
797− r[5] = 2 / (top-bottom);
802− r[10] = -2 / (zfar-znear);
804− r[12] = -(right+left)/(right-left);
805− r[13] = -(top+bottom)/(top-bottom);
806− r[14] = -(zfar+znear)/(zfar-znear);
813− * Function: M4x4.makeOrtho2D
815− * Creates a matrix for a 2D orthogonal frustum projection with the given parameters.
816− * znear and zfar are assumed to be -1 and 1, respectively.
820− * left - the left coordinate of the frustum
821− * right- the right coordinate of the frustum
822− * bottom - the bottom coordinate of the frustum
823− * top - the top coordinate of the frustum
824− * r - optional 4x4 matrix to store the result in
828− * If r is specified, returns r after creating the projection matrix.
829− * Otherwise, returns a new 4x4 matrix.
831− M4x4.makeOrtho2D = function M4x4_makeOrtho2D (left, right, bottom, top, r) {
832− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
834− return M4x4.makeOrtho(left, right, bottom, top, -1, 1, r);
838− * Function: M4x4.mul
840− * Performs r = a * b.
844− * a - the first matrix operand
845− * b - the second matrix operand
846− * r - optional 4x4 matrix to store the result in
850− * If r is specified, returns r after performing the operation.
851− * Otherwise, returns a new 4x4 matrix with the result.
853− M4x4.mul = function M4x4_mul(a, b, r) {
854− //MathUtils_assert(a.length == 16, "a.length == 16");
855− //MathUtils_assert(b.length == 16, "b.length == 16");
856− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
857− //MathUtils_assert(a != r && b != r, "a != r && b != r");
860− r = new MJS_FLOAT_ARRAY_TYPE(16);
896− r[0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
897− r[1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
898− r[2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
899− r[3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
900− r[4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
901− r[5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
902− r[6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
903− r[7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
904− r[8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
905− r[9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
906− r[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
907− r[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
908− r[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
909− r[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
910− r[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
911− r[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
917− * Function: M4x4.mulAffine
919− * Performs r = a * b, assuming a and b are affine (elements 3,7,11,15 = 0,0,0,1)
923− * a - the first matrix operand
924− * b - the second matrix operand
925− * r - optional 4x4 matrix to store the result in
929− * If r is specified, returns r after performing the operation.
930− * Otherwise, returns a new 4x4 matrix with the result.
932− M4x4.mulAffine = function M4x4_mulAffine(a, b, r) {
933− //MathUtils_assert(a.length == 16, "a.length == 16");
934− //MathUtils_assert(b.length == 16, "b.length == 16");
935− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
936− //MathUtils_assert(a != r && b != r, "a != r && b != r");
939− r = new MJS_FLOAT_ARRAY_TYPE(16);
966− r[0] = a11 * b11 + a12 * b21 + a13 * b31;
967− r[1] = a21 * b11 + a22 * b21 + a23 * b31;
968− r[2] = a31 * b11 + a32 * b21 + a33 * b31;
970− r[4] = a11 * b12 + a12 * b22 + a13 * b32;
971− r[5] = a21 * b12 + a22 * b22 + a23 * b32;
972− r[6] = a31 * b12 + a32 * b22 + a33 * b32;
974− r[8] = a11 * b13 + a12 * b23 + a13 * b33;
975− r[9] = a21 * b13 + a22 * b23 + a23 * b33;
976− r[10] = a31 * b13 + a32 * b23 + a33 * b33;
978− r[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14;
979− r[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24;
980− r[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34;
987− * Function: M4x4.makeRotate
989− * Creates a transformation matrix for rotation by angle radians about the 3-element vector axis.
993− * angle - the angle of rotation, in radians
994− * axis - the axis around which the rotation is performed, a 3-element vector
995− * r - optional 4x4 matrix to store the result in
999− * If r is specified, returns r after creating the matrix.
1000− * Otherwise, returns a new 4x4 matrix with the result.
1002− M4x4.makeRotate = function M4x4_makeRotate(angle, axis, r) {
1003− //MathUtils_assert(angle.length == 3, "angle.length == 3");
1004− //MathUtils_assert(axis.length == 3, "axis.length == 3");
1005− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1007− if (r == undefined)
1008− r = new MJS_FLOAT_ARRAY_TYPE(16);
1010− axis = V3.normalize(axis, V3._temp1);
1011− var x = axis[0], y = axis[1], z = axis[2];
1012− var c = Math.cos(angle);
1014− var s = Math.sin(angle);
1037− * Function: M4x4.rotate
1039− * Concatenates a rotation of angle radians about the axis to the give matrix m.
1043− * angle - the angle of rotation, in radians
1044− * axis - the axis around which the rotation is performed, a 3-element vector
1045− * m - the matrix to concatenate the rotation to
1046− * r - optional 4x4 matrix to store the result in
1050− * If r is specified, returns r after performing the operation.
1051− * Otherwise, returns a new 4x4 matrix with the result.
1053− M4x4.rotate = function M4x4_rotate(angle, axis, m, r) {
1054− //MathUtils_assert(angle.length == 3, "angle.length == 3");
1055− //MathUtils_assert(axis.length == 3, "axis.length == 3");
1056− //MathUtils_assert(m.length == 16, "m.length == 16");
1057− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1059− if (r == undefined)
1060− r = new MJS_FLOAT_ARRAY_TYPE(16);
1061− var a0=axis [0], a1=axis [1], a2=axis [2];
1062− var l = Math.sqrt(a0*a0 + a1*a1 + a2*a2);
1063− var x = a0, y = a1, z = a2;
1070− var c = Math.cos(angle);
1072− var s = Math.sin(angle);
1076− var xyc1 = x * y * c1;
1077− var xzc1 = x * z * c1;
1078− var yzc1 = y * z * c1;
1093− var t11 = x * x * c1 + c;
1094− var t21 = xyc1 + zs;
1095− var t31 = xzc1 - ys;
1096− var t12 = xyc1 - zs;
1097− var t22 = y * y * c1 + c;
1098− var t32 = yzc1 + xs;
1099− var t13 = xzc1 + ys;
1100− var t23 = yzc1 - xs;
1101− var t33 = z * z * c1 + c;
1103− r[0] = m11 * t11 + m12 * t21 + m13 * t31;
1104− r[1] = m21 * t11 + m22 * t21 + m23 * t31;
1105− r[2] = m31 * t11 + m32 * t21 + m33 * t31;
1106− r[3] = m41 * t11 + m42 * t21 + m43 * t31;
1107− r[4] = m11 * t12 + m12 * t22 + m13 * t32;
1108− r[5] = m21 * t12 + m22 * t22 + m23 * t32;
1109− r[6] = m31 * t12 + m32 * t22 + m33 * t32;
1110− r[7] = m41 * t12 + m42 * t22 + m43 * t32;
1111− r[8] = m11 * t13 + m12 * t23 + m13 * t33;
1112− r[9] = m21 * t13 + m22 * t23 + m23 * t33;
1113− r[10] = m31 * t13 + m32 * t23 + m33 * t33;
1114− r[11] = m41 * t13 + m42 * t23 + m43 * t33;
1125− * Function: M4x4.makeScale3
1127− * Creates a transformation matrix for scaling by 3 scalar values, one for
1128− * each of the x, y, and z directions.
1132− * x - the scale for the x axis
1133− * y - the scale for the y axis
1134− * z - the scale for the z axis
1135− * r - optional 4x4 matrix to store the result in
1139− * If r is specified, returns r after creating the matrix.
1140− * Otherwise, returns a new 4x4 matrix with the result.
1142− M4x4.makeScale3 = function M4x4_makeScale3(x, y, z, r) {
1143− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1145− if (r == undefined)
1146− r = new MJS_FLOAT_ARRAY_TYPE(16);
1169− * Function: M4x4.makeScale1
1171− * Creates a transformation matrix for a uniform scale by a single scalar value.
1175− * k - the scale factor
1176− * r - optional 4x4 matrix to store the result in
1180− * If r is specified, returns r after creating the matrix.
1181− * Otherwise, returns a new 4x4 matrix with the result.
1183− M4x4.makeScale1 = function M4x4_makeScale1(k, r) {
1184− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1186− return M4x4.makeScale3(k, k, k, r);
1190− * Function: M4x4.makeScale
1192− * Creates a transformation matrix for scaling each of the x, y, and z axes by the amount
1193− * given in the corresponding element of the 3-element vector.
1197− * v - the 3-element vector containing the scale factors
1198− * r - optional 4x4 matrix to store the result in
1202− * If r is specified, returns r after creating the matrix.
1203− * Otherwise, returns a new 4x4 matrix with the result.
1205− M4x4.makeScale = function M4x4_makeScale(v, r) {
1206− //MathUtils_assert(v.length == 3, "v.length == 3");
1207− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1209− return M4x4.makeScale3(v[0], v[1], v[2], r);
1213− * Function: M4x4.scale3
1215− M4x4.scale3 = function M4x4_scale3(x, y, z, m, r) {
1216− //MathUtils_assert(m.length == 16, "m.length == 16");
1217− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1235− if (r == undefined)
1236− r = new MJS_FLOAT_ARRAY_TYPE(16);
1259− * Function: M4x4.scale1
1261− M4x4.scale1 = function M4x4_scale1(k, m, r) {
1262− //MathUtils_assert(m.length == 16, "m.length == 16");
1263− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1281− if (r == undefined)
1282− r = new MJS_FLOAT_ARRAY_TYPE(16);
1305− * Function: M4x4.scale1
1307− M4x4.scale = function M4x4_scale(v, m, r) {
1308− //MathUtils_assert(v.length == 3, "v.length == 3");
1309− //MathUtils_assert(m.length == 16, "m.length == 16");
1310− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1311− var x = v[0], y = v[1], z = v[2];
1329− if (r == undefined)
1330− r = new MJS_FLOAT_ARRAY_TYPE(16);
1354− * Function: M4x4.makeTranslate3
1356− M4x4.makeTranslate3 = function M4x4_makeTranslate3(x, y, z, r) {
1357− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1359− if (r == undefined)
1360− r = new MJS_FLOAT_ARRAY_TYPE(16);
1383− * Function: M4x4.makeTranslate1
1385− M4x4.makeTranslate1 = function M4x4_makeTranslate1 (k, r) {
1386− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1388− return M4x4.makeTranslate3(k, k, k, r);
1392− * Function: M4x4.makeTranslate
1394− M4x4.makeTranslate = function M4x4_makeTranslate (v, r) {
1395− //MathUtils_assert(v.length == 3, "v.length == 3");
1396− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1398− return M4x4.makeTranslate3(v[0], v[1], v[2], r);
1402− * Function: M4x4.translate3Self
1404− M4x4.translate3Self = function M4x4_translate3Self (x, y, z, m) {
1405− //MathUtils_assert(m.length == 16, "m.length == 16");
1406− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1407− m[12] += m[0] * x + m[4] * y + m[8] * z;
1408− m[13] += m[1] * x + m[5] * y + m[9] * z;
1409− m[14] += m[2] * x + m[6] * y + m[10] * z;
1410− m[15] += m[3] * x + m[7] * y + m[11] * z;
1415− * Function: M4x4.translate3
1417− M4x4.translate3 = function M4x4_translate3 (x, y, z, m, r) {
1418− //MathUtils_assert(m.length == 16, "m.length == 16");
1419− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1422− m[12] += m[0] * x + m[4] * y + m[8] * z;
1423− m[13] += m[1] * x + m[5] * y + m[9] * z;
1424− m[14] += m[2] * x + m[6] * y + m[10] * z;
1425− m[15] += m[3] * x + m[7] * y + m[11] * z;
1429− if (r == undefined)
1430− r = new MJS_FLOAT_ARRAY_TYPE(16);
1458− r[12] = m11 * x + m12 * y + m13 * z + m[12];
1459− r[13] = m21 * x + m22 * y + m23 * z + m[13];
1460− r[14] = m31 * x + m32 * y + m33 * z + m[14];
1461− r[15] = m41 * x + m42 * y + m43 * z + m[15];
1467− * Function: M4x4.translate1
1469− M4x4.translate1 = function M4x4_translate1 (k, m, r) {
1470− //MathUtils_assert(m.length == 16, "m.length == 16");
1471− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1473− return M4x4.translate3(k, k, k, m, r);
1476− * Function: M4x4.translateSelf
1478− M4x4.translateSelf = function M4x4_translateSelf (v, m) {
1479− //MathUtils_assert(v.length == 3, "v.length == 3");
1480− //MathUtils_assert(m.length == 16, "m.length == 16");
1481− var x=v[0], y=v[1], z=v[2];
1482− m[12] += m[0] * x + m[4] * y + m[8] * z;
1483− m[13] += m[1] * x + m[5] * y + m[9] * z;
1484− m[14] += m[2] * x + m[6] * y + m[10] * z;
1485− m[15] += m[3] * x + m[7] * y + m[11] * z;
1489− * Function: M4x4.translate
1491− M4x4.translate = function M4x4_translate (v, m, r) {
1492− //MathUtils_assert(v.length == 3, "v.length == 3");
1493− //MathUtils_assert(m.length == 16, "m.length == 16");
1494− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1495− var x=v[0], y=v[1], z=v[2];
1497− m[12] += m[0] * x + m[4] * y + m[8] * z;
1498− m[13] += m[1] * x + m[5] * y + m[9] * z;
1499− m[14] += m[2] * x + m[6] * y + m[10] * z;
1500− m[15] += m[3] * x + m[7] * y + m[11] * z;
1504− if (r == undefined)
1505− r = new MJS_FLOAT_ARRAY_TYPE(16);
1532− r[12] = m11 * x + m12 * y + m13 * z + m[12];
1533− r[13] = m21 * x + m22 * y + m23 * z + m[13];
1534− r[14] = m31 * x + m32 * y + m33 * z + m[14];
1535− r[15] = m41 * x + m42 * y + m43 * z + m[15];
1541− * Function: M4x4.makeLookAt
1543− M4x4.makeLookAt = function M4x4_makeLookAt (eye, center, up, r) {
1544− //MathUtils_assert(eye.length == 3, "eye.length == 3");
1545− //MathUtils_assert(center.length == 3, "center.length == 3");
1546− //MathUtils_assert(up.length == 3, "up.length == 3");
1547− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1549− var z = V3.direction(eye, center, V3._temp1);
1550− var x = V3.normalize(V3.cross(up, z, V3._temp2), V3._temp2);
1551− var y = V3.normalize(V3.cross(z, x, V3._temp3), V3._temp3);
1553− var tm1 = M4x4._temp1;
1554− var tm2 = M4x4._temp2;
1573− tm2[0] = 1; tm2[1] = 0; tm2[2] = 0; tm2[3] = 0;
1574− tm2[4] = 0; tm2[5] = 1; tm2[6] = 0; tm2[7] = 0;
1575− tm2[8] = 0; tm2[9] = 0; tm2[10] = 1; tm2[11] = 0;
1576− tm2[12] = -eye[0]; tm2[13] = -eye[1]; tm2[14] = -eye[2]; tm2[15] = 1;
1578− if (r == undefined)
1579− r = new MJS_FLOAT_ARRAY_TYPE(16);
1580− return M4x4.mul(tm1, tm2, r);
1584− * Function: M4x4.transposeSelf
1586− M4x4.transposeSelf = function M4x4_transposeSelf (m) {
1587− //MathUtils_assert(m.length == 16, "m.length == 16");
1588− var tmp = m[1]; m[1] = m[4]; m[4] = tmp;
1589− tmp = m[2]; m[2] = m[8]; m[8] = tmp;
1590− tmp = m[3]; m[3] = m[12]; m[12] = tmp;
1591− tmp = m[6]; m[6] = m[9]; m[9] = tmp;
1592− tmp = m[7]; m[7] = m[13]; m[13] = tmp;
1593− tmp = m[11]; m[11] = m[14]; m[14] = tmp;
1597− * Function: M4x4.transpose
1599− M4x4.transpose = function M4x4_transpose (m, r) {
1600− //MathUtils_assert(m.length == 16, "m.length == 16");
1601− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1605− tmp = m[1]; m[1] = m[4]; m[4] = tmp;
1606− tmp = m[2]; m[2] = m[8]; m[8] = tmp;
1607− tmp = m[3]; m[3] = m[12]; m[12] = tmp;
1608− tmp = m[6]; m[6] = m[9]; m[9] = tmp;
1609− tmp = m[7]; m[7] = m[13]; m[13] = tmp;
1610− tmp = m[11]; m[11] = m[14]; m[14] = tmp;
1614− if (r == undefined)
1615− r = new MJS_FLOAT_ARRAY_TYPE(16);
1617− r[0] = m[0]; r[1] = m[4]; r[2] = m[8]; r[3] = m[12];
1618− r[4] = m[1]; r[5] = m[5]; r[6] = m[9]; r[7] = m[13];
1619− r[8] = m[2]; r[9] = m[6]; r[10] = m[10]; r[11] = m[14];
1620− r[12] = m[3]; r[13] = m[7]; r[14] = m[11]; r[15] = m[15];
1627− * Function: M4x4.transformPoint
1629− M4x4.transformPoint = function M4x4_transformPoint (m, v, r) {
1630− //MathUtils_assert(m.length == 16, "m.length == 16");
1631− //MathUtils_assert(v.length == 3, "v.length == 3");
1632− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1633− if (r == undefined)
1634− r = new MJS_FLOAT_ARRAY_TYPE(3);
1636− var v0 = v[0], v1 = v[1], v2 = v[2];
1638− r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2 + m[12];
1639− r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2 + m[13];
1640− r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2 + m[14];
1641− var w = m[3] * v0 + m[7] * v1 + m[11] * v2 + m[15];
1653− * Function: M4x4.transformLine
1655− M4x4.transformLine = function M4x4_transformLine(m, v, r) {
1656− //MathUtils_assert(m.length == 16, "m.length == 16");
1657− //MathUtils_assert(v.length == 3, "v.length == 3");
1658− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1659− if (r == undefined)
1660− r = new MJS_FLOAT_ARRAY_TYPE(3);
1662− var v0 = v[0], v1 = v[1], v2 = v[2];
1663− r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2;
1664− r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2;
1665− r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2;
1666− var w = m[3] * v0 + m[7] * v1 + m[11] * v2;
1679− * Function: M4x4.transformPointAffine
1681− M4x4.transformPointAffine = function M4x4_transformPointAffine (m, v, r) {
1682− //MathUtils_assert(m.length == 16, "m.length == 16");
1683− //MathUtils_assert(v.length == 3, "v.length == 3");
1684− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1685− if (r == undefined)
1686− r = new MJS_FLOAT_ARRAY_TYPE(3);
1688− var v0 = v[0], v1 = v[1], v2 = v[2];
1690− r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2 + m[12];
1691− r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2 + m[13];
1692− r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2 + m[14];
1698− * Function: M4x4.transformLineAffine
1700− M4x4.transformLineAffine = function M4x4_transformLineAffine(m, v, r) {
1701− //MathUtils_assert(m.length == 16, "m.length == 16");
1702− //MathUtils_assert(v.length == 3, "v.length == 3");
1703− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1704− if (r == undefined)
1705− r = new MJS_FLOAT_ARRAY_TYPE(3);
1707− var v0 = v[0], v1 = v[1], v2 = v[2];
1708− r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2;
1709− r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2;
1710− r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2;
1715− M4x4.makeBasis = function M4x4_makeBasis(vx,vy,vz) {
1717− var r = new MJS_FLOAT_ARRAY_TYPE(16);
1743− toTuple3: V3.toTuple3,
1747− v3direction: F2(V3.direction),
1748− v3length: V3.length,
1749− v3lengthSquared: V3.lengthSquared,
1750− v3normalize: V3.normalize,
1751− v3scale: F2(V3.scale),
1753− v3cross: F2(V3.cross),
1754− v3mul4x4: F2(V3.mul4x4),
1756− m4x4identity: M4x4.identity,
1757− m4x4topLeft3x3: M4x4.topLeft3x3,
1758− m4x4inverseOrthonormal: M4x4.inverseOrthonormal,
1759− m4x4inverseTo3x3: M4x4.inverseTo3x3,
1760− m4x4makeFrustum: F6(M4x4.makeFrustum),
1761− m4x4makePerspective: F4(M4x4.makePerspective),
1762− m4x4makeOrtho: F6(M4x4.makeOrtho),
1763− m4x4makeOrtho2D: F4(M4x4.makeOrtho2D),
1764− m4x4mul: F2(M4x4.mul),
1765− m4x4Affine: F2(M4x4.mulAffine),
1766− m4x4makeRotate: F2(M4x4.makeRotate),
1767− m4x4rotate: F3(M4x4.rotate),
1768− m4x4makeScale3: F3(M4x4.makeScale3),
1769− m4x4makeScale1: M4x4.makeScale1,
1770− m4x4makeScale: M4x4.makeScale,
1771− m4x4scale3: F4(M4x4.scale3),
1772− m4x4scale: F2(M4x4.scale),
1773− m4x4makeTranslate3: F3(M4x4.makeTranslate3),
1774− m4x4makeTranslate: M4x4.makeTranslate,
1775− m4x4translate3: F4(M4x4.translate3),
1776− m4x4translate: F2(M4x4.translate),
1777− m4x4makeLookAt: F3(M4x4.makeLookAt),
1778− m4x4transpose: M4x4.transpose,
1779− m4x4transformPoint: F2(M4x4.transformPoint),
1780− m4x4makeBasis: F3(M4x4.makeBasis),