@@ -1,1789 +0,0 @@
1−
2−/*
3− * Copyright (c) 2010 Mozilla Corporation
4− * Copyright (c) 2010 Vladimir Vukicevic
5− * Copyright (c) 2013 John Mayer
6− *
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
14− * conditions:
15− *
16− * The above copyright notice and this permission notice shall be
17− * included in all copies or substantial portions of the Software.
18− *
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.
27− */
28−
29−/*
30− * File: mjs
31− *
32− * Vector and Matrix math utilities for JavaScript, optimized for WebGL.
33− * Edited to work with the Elm Programming Language
34− */
35−
36−Elm.Native.MJS = {};
37−Elm.Native.MJS.make = function(elm) {
38−
39− elm.Native = elm.Native || {};
40− elm.Native.MJS = elm.Native.MJS || {};
41− if (elm.Native.MJS.values) return elm.Native.MJS.values;
42−
43− /*
44− * Constant: MJS_VERSION
45− *
46− * mjs version number aa.bb.cc, encoded as an integer of the form:
47− * 0xaabbcc.
48− */
49− var MJS_VERSION = 0x000000;
50−
51− /*
52− * Constant: MJS_DO_ASSERT
53− *
54− * Enables or disables runtime assertions.
55− *
56− * For potentially more performance, the assert methods can be
57− * commented out in each place where they are called.
58− */
59− // var MJS_DO_ASSERT = false;
60−
61− /*
62− * Constant: MJS_FLOAT_ARRAY_TYPE
63− *
64− * The base float array type. By default, WebGLFloatArray.
65− *
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.
70− */
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;
75−
76− /*
77− if (MJS_DO_ASSERT) {
78− function MathUtils_assert(cond, msg) {
79− if (!cond) {
80− throw "Assertion failed: " + msg;
81− }
82− }
83− } else {
84− */
85− function MathUtils_assert() { }
86− //}
87−
88− /*
89− * Class: V3
90− *
91− * Methods for working with 3-element vectors. A vector is represented by a 3-element array.
92− * Any valid JavaScript array type may be used, but if new
93− * vectors are created they are created using the configured MJS_FLOAT_ARRAY_TYPE.
94− */
95−
96− var V3 = { };
97−
98− V3._temp1 = new MJS_FLOAT_ARRAY_TYPE(3);
99− V3._temp2 = new MJS_FLOAT_ARRAY_TYPE(3);
100− V3._temp3 = new MJS_FLOAT_ARRAY_TYPE(3);
101−
102− if (MJS_FLOAT_ARRAY_TYPE == Array) {
103− V3.x = [1.0, 0.0, 0.0];
104− V3.y = [0.0, 1.0, 0.0];
105− V3.z = [0.0, 0.0, 1.0];
106−
107− V3.$ = function V3_$(x, y, z) {
108− return [x, y, z];
109− };
110− } else {
111− V3.x = new MJS_FLOAT_ARRAY_TYPE([1.0, 0.0, 0.0]);
112− V3.y = new MJS_FLOAT_ARRAY_TYPE([0.0, 1.0, 0.0]);
113− V3.z = new MJS_FLOAT_ARRAY_TYPE([0.0, 0.0, 1.0]);
114−
115− /*
116− * Function: V3.$
117− *
118− * Creates a new 3-element vector with the given values.
119− *
120− * Parameters:
121− *
122− * x,y,z - the 3 elements of the new vector.
123− *
124− * Returns:
125− *
126− * A new vector containing with the given argument values.
127− */
128−
129− V3.$ = function V3_$(x, y, z) {
130− return new MJS_FLOAT_ARRAY_TYPE([x, y, z]);
131− };
132− }
133−
134− V3.u = V3.x;
135− V3.v = V3.y;
136−
137− V3.getX = function V3_getX(a) {
138− return a[0];
139− }
140− V3.getY = function V3_getY(a) {
141− return a[1];
142− }
143− V3.getZ = function V3_getZ(a) {
144− return a[2];
145− }
146− V3.setX = function V3_setX(x, a) {
147− return new MJS_FLOAT_ARRAY_TYPE(x, a[1], a[2]);
148− }
149− V3.setY = function V3_setY(y, a) {
150− return new MJS_FLOAT_ARRAY_TYPE(a[0], y, a[2]);
151− }
152− V3.setZ = function V3_setZ(z, a) {
153− return new MJS_FLOAT_ARRAY_TYPE(a[0], a[1], z);
154− }
155−
156− V3.toTuple3 = function V3_toTuple3(a) {
157− return {
158− ctor:"_Tuple3",
159− _0:a[0],
160− _1:a[1],
161− _2:a[2]
162− };
163− };
164− V3.fromTuple3 = function V3_fromTuple3(t) {
165− return new MJS_FLOAT_ARRAY_TYPE([t._0, t._1, t._2]);
166− };
167−
168− V3.toRecord3 = function V3_toRecord3(a) {
169− return {
170− _:{},
171− x:a[0],
172− y:a[1],
173− z:a[2]
174− };
175− };
176− V3.fromRecord3 = function V3_fromRecord3(r) {
177− return new MJS_FLOAT_ARRAY_TYPE([r.x, r.y, r.z]);
178− };
179−
180− /*
181− * Function: V3.add
182− *
183− * Perform r = a + b.
184− *
185− * Parameters:
186− *
187− * a - the first vector operand
188− * b - the second vector operand
189− * r - optional vector to store the result in
190− *
191− * Returns:
192− *
193− * If r is specified, returns r after performing the operation.
194− * Otherwise, returns a new 3-element vector with the result.
195− */
196− V3.add = function V3_add(a, b, r) {
197− //MathUtils_assert(a.length == 3, "a.length == 3");
198− //MathUtils_assert(b.length == 3, "b.length == 3");
199− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
200−
201− if (r == undefined)
202− r = new MJS_FLOAT_ARRAY_TYPE(3);
203− r[0] = a[0] + b[0];
204− r[1] = a[1] + b[1];
205− r[2] = a[2] + b[2];
206− return r;
207− };
208−
209− /*
210− * Function: V3.sub
211− *
212− * Perform
213− * r = a - b.
214− *
215− * Parameters:
216− *
217− * a - the first vector operand
218− * b - the second vector operand
219− * r - optional vector to store the result in
220− *
221− * Returns:
222− *
223− * If r is specified, returns r after performing the operation.
224− * Otherwise, returns a new 3-element vector with the result.
225− */
226− V3.sub = function V3_sub(a, b, r) {
227− //MathUtils_assert(a.length == 3, "a.length == 3");
228− //MathUtils_assert(b.length == 3, "b.length == 3");
229− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
230−
231− if (r == undefined)
232− r = new MJS_FLOAT_ARRAY_TYPE(3);
233− r[0] = a[0] - b[0];
234− r[1] = a[1] - b[1];
235− r[2] = a[2] - b[2];
236− return r;
237− };
238−
239− /*
240− * Function: V3.neg
241− *
242− * Perform
243− * r = - a.
244− *
245− * Parameters:
246− *
247− * a - the vector operand
248− * r - optional vector to store the result in
249− *
250− * Returns:
251− *
252− * If r is specified, returns r after performing the operation.
253− * Otherwise, returns a new 3-element vector with the result.
254− */
255− V3.neg = function V3_neg(a, r) {
256− //MathUtils_assert(a.length == 3, "a.length == 3");
257− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
258−
259− if (r == undefined)
260− r = new MJS_FLOAT_ARRAY_TYPE(3);
261− r[0] = - a[0];
262− r[1] = - a[1];
263− r[2] = - a[2];
264− return r;
265− };
266−
267− /*
268− * Function: V3.direction
269− *
270− * Perform
271− * r = (a - b) / |a - b|. The result is the normalized
272− * direction from a to b.
273− *
274− * Parameters:
275− *
276− * a - the first vector operand
277− * b - the second vector operand
278− * r - optional vector to store the result in
279− *
280− * Returns:
281− *
282− * If r is specified, returns r after performing the operation.
283− * Otherwise, returns a new 3-element vector with the result.
284− */
285− V3.direction = function V3_direction(a, b, r) {
286− //MathUtils_assert(a.length == 3, "a.length == 3");
287− //MathUtils_assert(b.length == 3, "b.length == 3");
288− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
289−
290− if (r == undefined)
291− r = new MJS_FLOAT_ARRAY_TYPE(3);
292− return V3.normalize(V3.sub(a, b, r), r);
293− };
294−
295− /*
296− * Function: V3.length
297− *
298− * Perform r = |a|.
299− *
300− * Parameters:
301− *
302− * a - the vector operand
303− *
304− * Returns:
305− *
306− * The length of the given vector.
307− */
308− V3.length = function V3_length(a) {
309− //MathUtils_assert(a.length == 3, "a.length == 3");
310−
311− return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
312− };
313−
314− /*
315− * Function: V3.lengthSquard
316− *
317− * Perform r = |a|*|a|.
318− *
319− * Parameters:
320− *
321− * a - the vector operand
322− *
323− * Returns:
324− *
325− * The square of the length of the given vector.
326− */
327− V3.lengthSquared = function V3_lengthSquared(a) {
328− //MathUtils_assert(a.length == 3, "a.length == 3");
329−
330− return a[0]*a[0] + a[1]*a[1] + a[2]*a[2];
331− };
332−
333− V3.distance = function V3_distance(a, b) {
334− var dx = a[0] - b[0];
335− var dy = a[1] - b[1];
336− var dz = a[2] - b[2];
337− return Math.sqrt(dx * dx + dy * dy + dz * dz);
338− };
339−
340− V3.distanceSquared = function V3_distanceSquared(a) {
341− var dx = a[0] - b[0];
342− var dy = a[1] - b[1];
343− var dz = a[2] - b[2];
344− return dx * dx + dy * dy + dz * dz;
345− };
346−
347− /*
348− * Function: V3.normalize
349− *
350− * Perform r = a / |a|.
351− *
352− * Parameters:
353− *
354− * a - the vector operand
355− * r - optional vector to store the result in
356− *
357− * Returns:
358− *
359− * If r is specified, returns r after performing the operation.
360− * Otherwise, returns a new 3-element vector with the result.
361− */
362− V3.normalize = function V3_normalize(a, r) {
363− //MathUtils_assert(a.length == 3, "a.length == 3");
364− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
365−
366− if (r == undefined)
367− r = new MJS_FLOAT_ARRAY_TYPE(3);
368− var im = 1.0 / V3.length(a);
369− r[0] = a[0] * im;
370− r[1] = a[1] * im;
371− r[2] = a[2] * im;
372− return r;
373− };
374−
375− /*
376− * Function: V3.scale
377− *
378− * Perform r = a * k.
379− *
380− * Parameters:
381− *
382− * a - the vector operand
383− * k - a scalar value
384− * r - optional vector to store the result in
385− *
386− * Returns:
387− *
388− * If r is specified, returns r after performing the operation.
389− * Otherwise, returns a new 3-element vector with the result.
390− */
391− V3.scale = function V3_scale(a, k, r) {
392− //MathUtils_assert(a.length == 3, "a.length == 3");
393− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
394−
395− if (r == undefined)
396− r = new MJS_FLOAT_ARRAY_TYPE(3);
397− r[0] = a[0] * k;
398− r[1] = a[1] * k;
399− r[2] = a[2] * k;
400− return r;
401− };
402−
403− /*
404− * Function: V3.dot
405− *
406− * Perform
407− * r = dot(a, b).
408− *
409− * Parameters:
410− *
411− * a - the first vector operand
412− * b - the second vector operand
413− *
414− * Returns:
415− *
416− * The dot product of a and b.
417− */
418− V3.dot = function V3_dot(a, b) {
419− //MathUtils_assert(a.length == 3, "a.length == 3");
420− //MathUtils_assert(b.length == 3, "b.length == 3");
421−
422− return a[0] * b[0] +
423− a[1] * b[1] +
424− a[2] * b[2];
425− };
426−
427− /*
428− * Function: V3.cross
429− *
430− * Perform r = a x b.
431− *
432− * Parameters:
433− *
434− * a - the first vector operand
435− * b - the second vector operand
436− * r - optional vector to store the result in
437− *
438− * Returns:
439− *
440− * If r is specified, returns r after performing the operation.
441− * Otherwise, returns a new 3-element vector with the result.
442− */
443− V3.cross = function V3_cross(a, b, r) {
444− //MathUtils_assert(a.length == 3, "a.length == 3");
445− //MathUtils_assert(b.length == 3, "b.length == 3");
446− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
447−
448− if (r == undefined)
449− r = new MJS_FLOAT_ARRAY_TYPE(3);
450− r[0] = a[1]*b[2] - a[2]*b[1];
451− r[1] = a[2]*b[0] - a[0]*b[2];
452− r[2] = a[0]*b[1] - a[1]*b[0];
453− return r;
454− };
455−
456− /*
457− * Function: V3.mul4x4
458− *
459− * Perform
460− * r = m * v.
461− *
462− * Parameters:
463− *
464− * m - the 4x4 matrix operand
465− * v - the 3-element vector operand
466− * r - optional vector to store the result in
467− *
468− * Returns:
469− *
470− * If r is specified, returns r after performing the operation.
471− * Otherwise, returns a new 3-element vector with the result.
472− * The 4-element result vector is divided by the w component
473− * and returned as a 3-element vector.
474− */
475− V3.mul4x4 = function V3_mul4x4(m, v, r) {
476− //MathUtils_assert(m.length == 16, "m.length == 16");
477− //MathUtils_assert(v.length == 3, "v.length == 3");
478− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
479−
480− var w;
481− var tmp = V3._temp1;
482− if (r == undefined)
483− r = new MJS_FLOAT_ARRAY_TYPE(3);
484− tmp[0] = m[ 3];
485− tmp[1] = m[ 7];
486− tmp[2] = m[11];
487− w = V3.dot(v, tmp) + m[15];
488− tmp[0] = m[ 0];
489− tmp[1] = m[ 4];
490− tmp[2] = m[ 8];
491− r[0] = (V3.dot(v, tmp) + m[12])/w;
492− tmp[0] = m[ 1];
493− tmp[1] = m[ 5];
494− tmp[2] = m[ 9];
495− r[1] = (V3.dot(v, tmp) + m[13])/w;
496− tmp[0] = m[ 2];
497− tmp[1] = m[ 6];
498− tmp[2] = m[10];
499− r[2] = (V3.dot(v, tmp) + m[14])/w;
500− return r;
501− };
502−
503− /*
504− * Class: M4x4
505− *
506− * Methods for working with 4x4 matrices. A matrix is represented by a 16-element array
507− * in column-major order. Any valid JavaScript array type may be used, but if new
508− * matrices are created they are created using the configured MJS_FLOAT_ARRAY_TYPE.
509− */
510−
511− var M4x4 = { };
512−
513− M4x4._temp1 = new MJS_FLOAT_ARRAY_TYPE(16);
514− M4x4._temp2 = new MJS_FLOAT_ARRAY_TYPE(16);
515−
516− if (MJS_FLOAT_ARRAY_TYPE == Array) {
517− M4x4.I = [1.0, 0.0, 0.0, 0.0,
518− 0.0, 1.0, 0.0, 0.0,
519− 0.0, 0.0, 1.0, 0.0,
520− 0.0, 0.0, 0.0, 1.0];
521−
522− M4x4.$ = function M4x4_$(m00, m01, m02, m03,
523− m04, m05, m06, m07,
524− m08, m09, m10, m11,
525− m12, m13, m14, m15)
526− {
527− return [m00, m01, m02, m03,
528− m04, m05, m06, m07,
529− m08, m09, m10, m11,
530− m12, m13, m14, m15];
531− };
532− } else {
533− M4x4.I = new MJS_FLOAT_ARRAY_TYPE([1.0, 0.0, 0.0, 0.0,
534− 0.0, 1.0, 0.0, 0.0,
535− 0.0, 0.0, 1.0, 0.0,
536− 0.0, 0.0, 0.0, 1.0]);
537−
538− /*
539− * Function: M4x4.$
540− *
541− * Creates a new 4x4 matrix with the given values.
542− *
543− * Parameters:
544− *
545− * m00..m15 - the 16 elements of the new matrix.
546− *
547− * Returns:
548− *
549− * A new matrix filled with the given argument values.
550− */
551− M4x4.$ = function M4x4_$(m00, m01, m02, m03,
552− m04, m05, m06, m07,
553− m08, m09, m10, m11,
554− m12, m13, m14, m15)
555− {
556− return new MJS_FLOAT_ARRAY_TYPE([m00, m01, m02, m03,
557− m04, m05, m06, m07,
558− m08, m09, m10, m11,
559− m12, m13, m14, m15]);
560− };
561− }
562−
563− M4x4.identity = M4x4.I;
564−
565− /*
566− * Function: M4x4.topLeft3x3
567− *
568− * Return the top left 3x3 matrix from the given 4x4 matrix m.
569− *
570− * Parameters:
571− *
572− * m - the matrix
573− * r - optional 3x3 matrix to store the result in
574− *
575− * Returns:
576− *
577− * If r is specified, returns r after performing the operation.
578− * Otherwise, returns a new 3x3 matrix with the result.
579− */
580− M4x4.topLeft3x3 = function M4x4_topLeft3x3(m, r) {
581− //MathUtils_assert(m.length == 16, "m.length == 16");
582− //MathUtils_assert(r == undefined || r.length == 9, "r == undefined || r.length == 9");
583−
584− if (r == undefined)
585− r = new MJS_FLOAT_ARRAY_TYPE(9);
586− r[0] = m[0]; r[1] = m[1]; r[2] = m[2];
587− r[3] = m[4]; r[4] = m[5]; r[5] = m[6];
588− r[6] = m[8]; r[7] = m[9]; r[8] = m[10];
589− return r;
590− };
591−
592− /*
593− * Function: M4x4.inverseOrthonormal
594− *
595− * Computes the inverse of the given matrix m, assuming that
596− * the matrix is orthonormal.
597− *
598− * Parameters:
599− *
600− * m - the matrix
601− * r - optional 4x4 matrix to store the result in
602− *
603− * Returns:
604− *
605− * If r is specified, returns r after performing the operation.
606− * Otherwise, returns a new 4x4 matrix with the result.
607− */
608− M4x4.inverseOrthonormal = function M4x4_inverseOrthonormal(m, r) {
609− //MathUtils_assert(m.length == 16, "m.length == 16");
610− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
611− //MathUtils_assert(m != r, "m != r");
612−
613− if (r == undefined)
614− r = new MJS_FLOAT_ARRAY_TYPE(16);
615− M4x4.transpose(m, r);
616− var t = [m[12], m[13], m[14]];
617− r[3] = r[7] = r[11] = 0;
618− r[12] = -V3.dot([r[0], r[4], r[8]], t);
619− r[13] = -V3.dot([r[1], r[5], r[9]], t);
620− r[14] = -V3.dot([r[2], r[6], r[10]], t);
621− return r;
622− };
623−
624− /*
625− * Function: M4x4.inverseTo3x3
626− *
627− * Computes the inverse of the given matrix m, but calculates
628− * only the top left 3x3 values of the result.
629− *
630− * Parameters:
631− *
632− * m - the matrix
633− * r - optional 3x3 matrix to store the result in
634− *
635− * Returns:
636− *
637− * If r is specified, returns r after performing the operation.
638− * Otherwise, returns a new 3x3 matrix with the result.
639− */
640− M4x4.inverseTo3x3 = function M4x4_inverseTo3x3(m, r) {
641− //MathUtils_assert(m.length == 16, "m.length == 16");
642− //MathUtils_assert(r == undefined || r.length == 9, "r == undefined || r.length == 9");
643−
644− if (r == undefined)
645− r = new MJS_FLOAT_ARRAY_TYPE(9);
646−
647− var a11 = m[10]*m[5]-m[6]*m[9],
648− a21 = -m[10]*m[1]+m[2]*m[9],
649− a31 = m[6]*m[1]-m[2]*m[5],
650− a12 = -m[10]*m[4]+m[6]*m[8],
651− a22 = m[10]*m[0]-m[2]*m[8],
652− a32 = -m[6]*m[0]+m[2]*m[4],
653− a13 = m[9]*m[4]-m[5]*m[8],
654− a23 = -m[9]*m[0]+m[1]*m[8],
655− a33 = m[5]*m[0]-m[1]*m[4];
656− var det = m[0]*(a11) + m[1]*(a12) + m[2]*(a13);
657− if (det == 0) // no inverse
658− throw "matrix not invertible";
659− var idet = 1.0 / det;
660−
661− r[0] = idet*a11;
662− r[1] = idet*a21;
663− r[2] = idet*a31;
664− r[3] = idet*a12;
665− r[4] = idet*a22;
666− r[5] = idet*a32;
667− r[6] = idet*a13;
668− r[7] = idet*a23;
669− r[8] = idet*a33;
670−
671− return r;
672− };
673−
674− /*
675− * Function: M4x4.makeFrustum
676− *
677− * Creates a matrix for a projection frustum with the given parameters.
678− *
679− * Parameters:
680− *
681− * left - the left coordinate of the frustum
682− * right- the right coordinate of the frustum
683− * bottom - the bottom coordinate of the frustum
684− * top - the top coordinate of the frustum
685− * znear - the near z distance of the frustum
686− * zfar - the far z distance of the frustum
687− * r - optional 4x4 matrix to store the result in
688− *
689− * Returns:
690− *
691− * If r is specified, returns r after creating the projection matrix.
692− * Otherwise, returns a new 4x4 matrix.
693− */
694− M4x4.makeFrustum = function M4x4_makeFrustum(left, right, bottom, top, znear, zfar, r) {
695− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
696−
697− if (r == undefined)
698− r = new MJS_FLOAT_ARRAY_TYPE(16);
699−
700− var X = 2*znear/(right-left);
701− var Y = 2*znear/(top-bottom);
702− var A = (right+left)/(right-left);
703− var B = (top+bottom)/(top-bottom);
704− var C = -(zfar+znear)/(zfar-znear);
705− var D = -2*zfar*znear/(zfar-znear);
706−
707− r[0] = 2*znear/(right-left);
708− r[1] = 0;
709− r[2] = 0;
710− r[3] = 0;
711− r[4] = 0;
712− r[5] = 2*znear/(top-bottom);
713− r[6] = 0;
714− r[7] = 0;
715− r[8] = (right+left)/(right-left);
716− r[9] = (top+bottom)/(top-bottom);
717− r[10] = -(zfar+znear)/(zfar-znear);
718− r[11] = -1;
719− r[12] = 0;
720− r[13] = 0;
721− r[14] = -2*zfar*znear/(zfar-znear);
722− r[15] = 0;
723−
724− return r;
725− };
726−
727− /*
728− * Function: M4x4.makePerspective
729− *
730− * Creates a matrix for a perspective projection with the given parameters.
731− *
732− * Parameters:
733− *
734− * fovy - field of view in the y axis, in degrees
735− * aspect - aspect ratio
736− * znear - the near z distance of the projection
737− * zfar - the far z distance of the projection
738− * r - optional 4x4 matrix to store the result in
739− *
740− * Returns:
741− *
742− * If r is specified, returns r after creating the projection matrix.
743− * Otherwise, returns a new 4x4 matrix.
744− */
745− M4x4.makePerspective = function M4x4_makePerspective (fovy, aspect, znear, zfar, r) {
746− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
747−
748− var ymax = znear * Math.tan(fovy * Math.PI / 360.0);
749− var ymin = -ymax;
750− var xmin = ymin * aspect;
751− var xmax = ymax * aspect;
752−
753− return M4x4.makeFrustum(xmin, xmax, ymin, ymax, znear, zfar, r);
754− };
755−
756− /*
757− * Function: M4x4.makeOrtho
758− *
759− * Creates a matrix for an orthogonal frustum projection with the given parameters.
760− *
761− * Parameters:
762− *
763− * left - the left coordinate of the frustum
764− * right- the right coordinate of the frustum
765− * bottom - the bottom coordinate of the frustum
766− * top - the top coordinate of the frustum
767− * znear - the near z distance of the frustum
768− * zfar - the far z distance of the frustum
769− * r - optional 4x4 matrix to store the result in
770− *
771− * Returns:
772− *
773− * If r is specified, returns r after creating the projection matrix.
774− * Otherwise, returns a new 4x4 matrix.
775− */
776− M4x4.makeOrtho = function M4x4_makeOrtho (left, right, bottom, top, znear, zfar, r) {
777− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
778−
779− if (r == undefined)
780− r = new MJS_FLOAT_ARRAY_TYPE(16);
781−
782− var tX = -(right+left)/(right-left);
783− var tY = -(top+bottom)/(top-bottom);
784− var tZ = -(zfar+znear)/(zfar-znear);
785− var X = 2 / (right-left);
786− var Y = 2 / (top-bottom);
787− var Z = -2 / (zfar-znear);
788−
789− r[0] = 2 / (right-left);
790− r[1] = 0;
791− r[2] = 0;
792− r[3] = 0;
793− r[4] = 0;
794− r[5] = 2 / (top-bottom);
795− r[6] = 0;
796− r[7] = 0;
797− r[8] = 0;
798− r[9] = 0;
799− r[10] = -2 / (zfar-znear);
800− r[11] = 0;
801− r[12] = -(right+left)/(right-left);
802− r[13] = -(top+bottom)/(top-bottom);
803− r[14] = -(zfar+znear)/(zfar-znear);
804− r[15] = 1;
805−
806− return r;
807− };
808−
809− /*
810− * Function: M4x4.makeOrtho2D
811− *
812− * Creates a matrix for a 2D orthogonal frustum projection with the given parameters.
813− * znear and zfar are assumed to be -1 and 1, respectively.
814− *
815− * Parameters:
816− *
817− * left - the left coordinate of the frustum
818− * right- the right coordinate of the frustum
819− * bottom - the bottom coordinate of the frustum
820− * top - the top coordinate of the frustum
821− * r - optional 4x4 matrix to store the result in
822− *
823− * Returns:
824− *
825− * If r is specified, returns r after creating the projection matrix.
826− * Otherwise, returns a new 4x4 matrix.
827− */
828− M4x4.makeOrtho2D = function M4x4_makeOrtho2D (left, right, bottom, top, r) {
829− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
830−
831− return M4x4.makeOrtho(left, right, bottom, top, -1, 1, r);
832− };
833−
834− /*
835− * Function: M4x4.mul
836− *
837− * Performs r = a * b.
838− *
839− * Parameters:
840− *
841− * a - the first matrix operand
842− * b - the second matrix operand
843− * r - optional 4x4 matrix to store the result in
844− *
845− * Returns:
846− *
847− * If r is specified, returns r after performing the operation.
848− * Otherwise, returns a new 4x4 matrix with the result.
849− */
850− M4x4.mul = function M4x4_mul(a, b, r) {
851− //MathUtils_assert(a.length == 16, "a.length == 16");
852− //MathUtils_assert(b.length == 16, "b.length == 16");
853− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
854− //MathUtils_assert(a != r && b != r, "a != r && b != r");
855−
856− if (r == undefined)
857− r = new MJS_FLOAT_ARRAY_TYPE(16);
858−
859− var a11 = a[0];
860− var a21 = a[1];
861− var a31 = a[2];
862− var a41 = a[3];
863− var a12 = a[4];
864− var a22 = a[5];
865− var a32 = a[6];
866− var a42 = a[7];
867− var a13 = a[8];
868− var a23 = a[9];
869− var a33 = a[10];
870− var a43 = a[11];
871− var a14 = a[12];
872− var a24 = a[13];
873− var a34 = a[14];
874− var a44 = a[15];
875−
876− var b11 = b[0];
877− var b21 = b[1];
878− var b31 = b[2];
879− var b41 = b[3];
880− var b12 = b[4];
881− var b22 = b[5];
882− var b32 = b[6];
883− var b42 = b[7];
884− var b13 = b[8];
885− var b23 = b[9];
886− var b33 = b[10];
887− var b43 = b[11];
888− var b14 = b[12];
889− var b24 = b[13];
890− var b34 = b[14];
891− var b44 = b[15];
892−
893− r[0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
894− r[1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
895− r[2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
896− r[3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
897− r[4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
898− r[5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
899− r[6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
900− r[7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
901− r[8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
902− r[9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
903− r[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
904− r[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
905− r[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
906− r[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
907− r[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
908− r[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
909−
910− return r;
911− };
912−
913− /*
914− * Function: M4x4.mulAffine
915− *
916− * Performs r = a * b, assuming a and b are affine (elements 3,7,11,15 = 0,0,0,1)
917− *
918− * Parameters:
919− *
920− * a - the first matrix operand
921− * b - the second matrix operand
922− * r - optional 4x4 matrix to store the result in
923− *
924− * Returns:
925− *
926− * If r is specified, returns r after performing the operation.
927− * Otherwise, returns a new 4x4 matrix with the result.
928− */
929− M4x4.mulAffine = function M4x4_mulAffine(a, b, r) {
930− //MathUtils_assert(a.length == 16, "a.length == 16");
931− //MathUtils_assert(b.length == 16, "b.length == 16");
932− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
933− //MathUtils_assert(a != r && b != r, "a != r && b != r");
934−
935− if (r == undefined)
936− r = new MJS_FLOAT_ARRAY_TYPE(16);
937− var a11 = a[0];
938− var a21 = a[1];
939− var a31 = a[2];
940− var a12 = a[4];
941− var a22 = a[5];
942− var a32 = a[6];
943− var a13 = a[8];
944− var a23 = a[9];
945− var a33 = a[10];
946− var a14 = a[12];
947− var a24 = a[13];
948− var a34 = a[14];
949−
950− var b11 = b[0];
951− var b21 = b[1];
952− var b31 = b[2];
953− var b12 = b[4];
954− var b22 = b[5];
955− var b32 = b[6];
956− var b13 = b[8];
957− var b23 = b[9];
958− var b33 = b[10];
959− var b14 = b[12];
960− var b24 = b[13];
961− var b34 = b[14];
962−
963− r[0] = a11 * b11 + a12 * b21 + a13 * b31;
964− r[1] = a21 * b11 + a22 * b21 + a23 * b31;
965− r[2] = a31 * b11 + a32 * b21 + a33 * b31;
966− r[3] = 0;
967− r[4] = a11 * b12 + a12 * b22 + a13 * b32;
968− r[5] = a21 * b12 + a22 * b22 + a23 * b32;
969− r[6] = a31 * b12 + a32 * b22 + a33 * b32;
970− r[7] = 0;
971− r[8] = a11 * b13 + a12 * b23 + a13 * b33;
972− r[9] = a21 * b13 + a22 * b23 + a23 * b33;
973− r[10] = a31 * b13 + a32 * b23 + a33 * b33;
974− r[11] = 0;
975− r[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14;
976− r[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24;
977− r[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34;
978− r[15] = 1;
979−
980− return r;
981− };
982−
983− /*
984− * Function: M4x4.makeRotate
985− *
986− * Creates a transformation matrix for rotation by angle radians about the 3-element vector axis.
987− *
988− * Parameters:
989− *
990− * angle - the angle of rotation, in radians
991− * axis - the axis around which the rotation is performed, a 3-element vector
992− * r - optional 4x4 matrix to store the result in
993− *
994− * Returns:
995− *
996− * If r is specified, returns r after creating the matrix.
997− * Otherwise, returns a new 4x4 matrix with the result.
998− */
999− M4x4.makeRotate = function M4x4_makeRotate(angle, axis, r) {
1000− //MathUtils_assert(angle.length == 3, "angle.length == 3");
1001− //MathUtils_assert(axis.length == 3, "axis.length == 3");
1002− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1003−
1004− if (r == undefined)
1005− r = new MJS_FLOAT_ARRAY_TYPE(16);
1006−
1007− axis = V3.normalize(axis, V3._temp1);
1008− var x = axis[0], y = axis[1], z = axis[2];
1009− var c = Math.cos(angle);
1010− var c1 = 1-c;
1011− var s = Math.sin(angle);
1012−
1013− r[0] = x*x*c1+c;
1014− r[1] = y*x*c1+z*s;
1015− r[2] = z*x*c1-y*s;
1016− r[3] = 0;
1017− r[4] = x*y*c1-z*s;
1018− r[5] = y*y*c1+c;
1019− r[6] = y*z*c1+x*s;
1020− r[7] = 0;
1021− r[8] = x*z*c1+y*s;
1022− r[9] = y*z*c1-x*s;
1023− r[10] = z*z*c1+c;
1024− r[11] = 0;
1025− r[12] = 0;
1026− r[13] = 0;
1027− r[14] = 0;
1028− r[15] = 1;
1029−
1030− return r;
1031− };
1032−
1033− /*
1034− * Function: M4x4.rotate
1035− *
1036− * Concatenates a rotation of angle radians about the axis to the give matrix m.
1037− *
1038− * Parameters:
1039− *
1040− * angle - the angle of rotation, in radians
1041− * axis - the axis around which the rotation is performed, a 3-element vector
1042− * m - the matrix to concatenate the rotation to
1043− * r - optional 4x4 matrix to store the result in
1044− *
1045− * Returns:
1046− *
1047− * If r is specified, returns r after performing the operation.
1048− * Otherwise, returns a new 4x4 matrix with the result.
1049− */
1050− M4x4.rotate = function M4x4_rotate(angle, axis, m, r) {
1051− //MathUtils_assert(angle.length == 3, "angle.length == 3");
1052− //MathUtils_assert(axis.length == 3, "axis.length == 3");
1053− //MathUtils_assert(m.length == 16, "m.length == 16");
1054− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1055−
1056− if (r == undefined)
1057− r = new MJS_FLOAT_ARRAY_TYPE(16);
1058− var a0=axis [0], a1=axis [1], a2=axis [2];
1059− var l = Math.sqrt(a0*a0 + a1*a1 + a2*a2);
1060− var x = a0, y = a1, z = a2;
1061− if (l != 1.0) {
1062− var im = 1.0 / l;
1063− x *= im;
1064− y *= im;
1065− z *= im;
1066− }
1067− var c = Math.cos(angle);
1068− var c1 = 1-c;
1069− var s = Math.sin(angle);
1070− var xs = x*s;
1071− var ys = y*s;
1072− var zs = z*s;
1073− var xyc1 = x * y * c1;
1074− var xzc1 = x * z * c1;
1075− var yzc1 = y * z * c1;
1076−
1077− var m11 = m[0];
1078− var m21 = m[1];
1079− var m31 = m[2];
1080− var m41 = m[3];
1081− var m12 = m[4];
1082− var m22 = m[5];
1083− var m32 = m[6];
1084− var m42 = m[7];
1085− var m13 = m[8];
1086− var m23 = m[9];
1087− var m33 = m[10];
1088− var m43 = m[11];
1089−
1090− var t11 = x * x * c1 + c;
1091− var t21 = xyc1 + zs;
1092− var t31 = xzc1 - ys;
1093− var t12 = xyc1 - zs;
1094− var t22 = y * y * c1 + c;
1095− var t32 = yzc1 + xs;
1096− var t13 = xzc1 + ys;
1097− var t23 = yzc1 - xs;
1098− var t33 = z * z * c1 + c;
1099−
1100− r[0] = m11 * t11 + m12 * t21 + m13 * t31;
1101− r[1] = m21 * t11 + m22 * t21 + m23 * t31;
1102− r[2] = m31 * t11 + m32 * t21 + m33 * t31;
1103− r[3] = m41 * t11 + m42 * t21 + m43 * t31;
1104− r[4] = m11 * t12 + m12 * t22 + m13 * t32;
1105− r[5] = m21 * t12 + m22 * t22 + m23 * t32;
1106− r[6] = m31 * t12 + m32 * t22 + m33 * t32;
1107− r[7] = m41 * t12 + m42 * t22 + m43 * t32;
1108− r[8] = m11 * t13 + m12 * t23 + m13 * t33;
1109− r[9] = m21 * t13 + m22 * t23 + m23 * t33;
1110− r[10] = m31 * t13 + m32 * t23 + m33 * t33;
1111− r[11] = m41 * t13 + m42 * t23 + m43 * t33;
1112− if (r != m) {
1113− r[12] = m[12];
1114− r[13] = m[13];
1115− r[14] = m[14];
1116− r[15] = m[15];
1117− }
1118− return r;
1119− };
1120−
1121− /*
1122− * Function: M4x4.makeScale3
1123− *
1124− * Creates a transformation matrix for scaling by 3 scalar values, one for
1125− * each of the x, y, and z directions.
1126− *
1127− * Parameters:
1128− *
1129− * x - the scale for the x axis
1130− * y - the scale for the y axis
1131− * z - the scale for the z axis
1132− * r - optional 4x4 matrix to store the result in
1133− *
1134− * Returns:
1135− *
1136− * If r is specified, returns r after creating the matrix.
1137− * Otherwise, returns a new 4x4 matrix with the result.
1138− */
1139− M4x4.makeScale3 = function M4x4_makeScale3(x, y, z, r) {
1140− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1141−
1142− if (r == undefined)
1143− r = new MJS_FLOAT_ARRAY_TYPE(16);
1144−
1145− r[0] = x;
1146− r[1] = 0;
1147− r[2] = 0;
1148− r[3] = 0;
1149− r[4] = 0;
1150− r[5] = y;
1151− r[6] = 0;
1152− r[7] = 0;
1153− r[8] = 0;
1154− r[9] = 0;
1155− r[10] = z;
1156− r[11] = 0;
1157− r[12] = 0;
1158− r[13] = 0;
1159− r[14] = 0;
1160− r[15] = 1;
1161−
1162− return r;
1163− };
1164−
1165− /*
1166− * Function: M4x4.makeScale1
1167− *
1168− * Creates a transformation matrix for a uniform scale by a single scalar value.
1169− *
1170− * Parameters:
1171− *
1172− * k - the scale factor
1173− * r - optional 4x4 matrix to store the result in
1174− *
1175− * Returns:
1176− *
1177− * If r is specified, returns r after creating the matrix.
1178− * Otherwise, returns a new 4x4 matrix with the result.
1179− */
1180− M4x4.makeScale1 = function M4x4_makeScale1(k, r) {
1181− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1182−
1183− return M4x4.makeScale3(k, k, k, r);
1184− };
1185−
1186− /*
1187− * Function: M4x4.makeScale
1188− *
1189− * Creates a transformation matrix for scaling each of the x, y, and z axes by the amount
1190− * given in the corresponding element of the 3-element vector.
1191− *
1192− * Parameters:
1193− *
1194− * v - the 3-element vector containing the scale factors
1195− * r - optional 4x4 matrix to store the result in
1196− *
1197− * Returns:
1198− *
1199− * If r is specified, returns r after creating the matrix.
1200− * Otherwise, returns a new 4x4 matrix with the result.
1201− */
1202− M4x4.makeScale = function M4x4_makeScale(v, r) {
1203− //MathUtils_assert(v.length == 3, "v.length == 3");
1204− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1205−
1206− return M4x4.makeScale3(v[0], v[1], v[2], r);
1207− };
1208−
1209− /*
1210− * Function: M4x4.scale3
1211− */
1212− M4x4.scale3 = function M4x4_scale3(x, y, z, m, r) {
1213− //MathUtils_assert(m.length == 16, "m.length == 16");
1214− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1215−
1216− if (r == m) {
1217− m[0] *= x;
1218− m[1] *= x;
1219− m[2] *= x;
1220− m[3] *= x;
1221− m[4] *= y;
1222− m[5] *= y;
1223− m[6] *= y;
1224− m[7] *= y;
1225− m[8] *= z;
1226− m[9] *= z;
1227− m[10] *= z;
1228− m[11] *= z;
1229− return m;
1230− }
1231−
1232− if (r == undefined)
1233− r = new MJS_FLOAT_ARRAY_TYPE(16);
1234−
1235− r[0] = m[0] * x;
1236− r[1] = m[1] * x;
1237− r[2] = m[2] * x;
1238− r[3] = m[3] * x;
1239− r[4] = m[4] * y;
1240− r[5] = m[5] * y;
1241− r[6] = m[6] * y;
1242− r[7] = m[7] * y;
1243− r[8] = m[8] * z;
1244− r[9] = m[9] * z;
1245− r[10] = m[10] * z;
1246− r[11] = m[11] * z;
1247− r[12] = m[12];
1248− r[13] = m[13];
1249− r[14] = m[14];
1250− r[15] = m[15];
1251−
1252− return r;
1253− };
1254−
1255− /*
1256− * Function: M4x4.scale1
1257− */
1258− M4x4.scale1 = function M4x4_scale1(k, m, r) {
1259− //MathUtils_assert(m.length == 16, "m.length == 16");
1260− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1261− if (r == m) {
1262− m[0] *= k;
1263− m[1] *= k;
1264− m[2] *= k;
1265− m[3] *= k;
1266− m[4] *= k;
1267− m[5] *= k;
1268− m[6] *= k;
1269− m[7] *= k;
1270− m[8] *= k;
1271− m[9] *= k;
1272− m[10] *= k;
1273− m[11] *= k;
1274− return m;
1275− }
1276−
1277−
1278− if (r == undefined)
1279− r = new MJS_FLOAT_ARRAY_TYPE(16);
1280−
1281− r[0] = m[0] * k;
1282− r[1] = m[1] * k;
1283− r[2] = m[2] * k;
1284− r[3] = m[3] * k;
1285− r[4] = m[4] * k;
1286− r[5] = m[5] * k;
1287− r[6] = m[6] * k;
1288− r[7] = m[7] * k;
1289− r[8] = m[8] * k;
1290− r[9] = m[9] * k;
1291− r[10] = m[10] * k;
1292− r[11] = m[11] * k;
1293− r[12] = m[12];
1294− r[13] = m[13];
1295− r[14] = m[14];
1296− r[15] = m[15];
1297−
1298− return r;
1299− };
1300−
1301− /*
1302− * Function: M4x4.scale1
1303− */
1304− M4x4.scale = function M4x4_scale(v, m, r) {
1305− //MathUtils_assert(v.length == 3, "v.length == 3");
1306− //MathUtils_assert(m.length == 16, "m.length == 16");
1307− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1308− var x = v[0], y = v[1], z = v[2];
1309−
1310− if (r == m) {
1311− m[0] *= x;
1312− m[1] *= x;
1313− m[2] *= x;
1314− m[3] *= x;
1315− m[4] *= y;
1316− m[5] *= y;
1317− m[6] *= y;
1318− m[7] *= y;
1319− m[8] *= z;
1320− m[9] *= z;
1321− m[10] *= z;
1322− m[11] *= z;
1323− return m;
1324− }
1325−
1326− if (r == undefined)
1327− r = new MJS_FLOAT_ARRAY_TYPE(16);
1328−
1329−
1330− r[0] = m[0] * x;
1331− r[1] = m[1] * x;
1332− r[2] = m[2] * x;
1333− r[3] = m[3] * x;
1334− r[4] = m[4] * y;
1335− r[5] = m[5] * y;
1336− r[6] = m[6] * y;
1337− r[7] = m[7] * y;
1338− r[8] = m[8] * z;
1339− r[9] = m[9] * z;
1340− r[10] = m[10] * z;
1341− r[11] = m[11] * z;
1342− r[12] = m[12];
1343− r[13] = m[13];
1344− r[14] = m[14];
1345− r[15] = m[15];
1346−
1347− return r;
1348− };
1349−
1350− /*
1351− * Function: M4x4.makeTranslate3
1352− */
1353− M4x4.makeTranslate3 = function M4x4_makeTranslate3(x, y, z, r) {
1354− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1355−
1356− if (r == undefined)
1357− r = new MJS_FLOAT_ARRAY_TYPE(16);
1358−
1359− r[0] = 1;
1360− r[1] = 0;
1361− r[2] = 0;
1362− r[3] = 0;
1363− r[4] = 0;
1364− r[5] = 1;
1365− r[6] = 0;
1366− r[7] = 0;
1367− r[8] = 0;
1368− r[9] = 0;
1369− r[10] = 1;
1370− r[11] = 0;
1371− r[12] = x;
1372− r[13] = y;
1373− r[14] = z;
1374− r[15] = 1;
1375−
1376− return r;
1377− };
1378−
1379− /*
1380− * Function: M4x4.makeTranslate1
1381− */
1382− M4x4.makeTranslate1 = function M4x4_makeTranslate1 (k, r) {
1383− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1384−
1385− return M4x4.makeTranslate3(k, k, k, r);
1386− };
1387−
1388− /*
1389− * Function: M4x4.makeTranslate
1390− */
1391− M4x4.makeTranslate = function M4x4_makeTranslate (v, r) {
1392− //MathUtils_assert(v.length == 3, "v.length == 3");
1393− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1394−
1395− return M4x4.makeTranslate3(v[0], v[1], v[2], r);
1396− };
1397−
1398− /*
1399− * Function: M4x4.translate3Self
1400− */
1401− M4x4.translate3Self = function M4x4_translate3Self (x, y, z, m) {
1402− //MathUtils_assert(m.length == 16, "m.length == 16");
1403− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1404− m[12] += m[0] * x + m[4] * y + m[8] * z;
1405− m[13] += m[1] * x + m[5] * y + m[9] * z;
1406− m[14] += m[2] * x + m[6] * y + m[10] * z;
1407− m[15] += m[3] * x + m[7] * y + m[11] * z;
1408− return m;
1409− };
1410−
1411− /*
1412− * Function: M4x4.translate3
1413− */
1414− M4x4.translate3 = function M4x4_translate3 (x, y, z, m, r) {
1415− //MathUtils_assert(m.length == 16, "m.length == 16");
1416− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1417−
1418− if (r == m) {
1419− m[12] += m[0] * x + m[4] * y + m[8] * z;
1420− m[13] += m[1] * x + m[5] * y + m[9] * z;
1421− m[14] += m[2] * x + m[6] * y + m[10] * z;
1422− m[15] += m[3] * x + m[7] * y + m[11] * z;
1423− return m;
1424− }
1425−
1426− if (r == undefined)
1427− r = new MJS_FLOAT_ARRAY_TYPE(16);
1428−
1429− var m11 = m[0];
1430− var m21 = m[1];
1431− var m31 = m[2];
1432− var m41 = m[3];
1433− var m12 = m[4];
1434− var m22 = m[5];
1435− var m32 = m[6];
1436− var m42 = m[7];
1437− var m13 = m[8];
1438− var m23 = m[9];
1439− var m33 = m[10];
1440− var m43 = m[11];
1441−
1442−
1443− r[0] = m11;
1444− r[1] = m21;
1445− r[2] = m31;
1446− r[3] = m41;
1447− r[4] = m12;
1448− r[5] = m22;
1449− r[6] = m32;
1450− r[7] = m42;
1451− r[8] = m13;
1452− r[9] = m23;
1453− r[10] = m33;
1454− r[11] = m43;
1455− r[12] = m11 * x + m12 * y + m13 * z + m[12];
1456− r[13] = m21 * x + m22 * y + m23 * z + m[13];
1457− r[14] = m31 * x + m32 * y + m33 * z + m[14];
1458− r[15] = m41 * x + m42 * y + m43 * z + m[15];
1459−
1460− return r;
1461− };
1462−
1463− /*
1464− * Function: M4x4.translate1
1465− */
1466− M4x4.translate1 = function M4x4_translate1 (k, m, r) {
1467− //MathUtils_assert(m.length == 16, "m.length == 16");
1468− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1469−
1470− return M4x4.translate3(k, k, k, m, r);
1471− };
1472− /*
1473− * Function: M4x4.translateSelf
1474− */
1475− M4x4.translateSelf = function M4x4_translateSelf (v, m) {
1476− //MathUtils_assert(v.length == 3, "v.length == 3");
1477− //MathUtils_assert(m.length == 16, "m.length == 16");
1478− var x=v[0], y=v[1], z=v[2];
1479− m[12] += m[0] * x + m[4] * y + m[8] * z;
1480− m[13] += m[1] * x + m[5] * y + m[9] * z;
1481− m[14] += m[2] * x + m[6] * y + m[10] * z;
1482− m[15] += m[3] * x + m[7] * y + m[11] * z;
1483− return m;
1484− };
1485− /*
1486− * Function: M4x4.translate
1487− */
1488− M4x4.translate = function M4x4_translate (v, m, r) {
1489− //MathUtils_assert(v.length == 3, "v.length == 3");
1490− //MathUtils_assert(m.length == 16, "m.length == 16");
1491− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1492− var x=v[0], y=v[1], z=v[2];
1493− if (r == m) {
1494− m[12] += m[0] * x + m[4] * y + m[8] * z;
1495− m[13] += m[1] * x + m[5] * y + m[9] * z;
1496− m[14] += m[2] * x + m[6] * y + m[10] * z;
1497− m[15] += m[3] * x + m[7] * y + m[11] * z;
1498− return m;
1499− }
1500−
1501− if (r == undefined)
1502− r = new MJS_FLOAT_ARRAY_TYPE(16);
1503−
1504− var m11 = m[0];
1505− var m21 = m[1];
1506− var m31 = m[2];
1507− var m41 = m[3];
1508− var m12 = m[4];
1509− var m22 = m[5];
1510− var m32 = m[6];
1511− var m42 = m[7];
1512− var m13 = m[8];
1513− var m23 = m[9];
1514− var m33 = m[10];
1515− var m43 = m[11];
1516−
1517− r[0] = m11;
1518− r[1] = m21;
1519− r[2] = m31;
1520− r[3] = m41;
1521− r[4] = m12;
1522− r[5] = m22;
1523− r[6] = m32;
1524− r[7] = m42;
1525− r[8] = m13;
1526− r[9] = m23;
1527− r[10] = m33;
1528− r[11] = m43;
1529− r[12] = m11 * x + m12 * y + m13 * z + m[12];
1530− r[13] = m21 * x + m22 * y + m23 * z + m[13];
1531− r[14] = m31 * x + m32 * y + m33 * z + m[14];
1532− r[15] = m41 * x + m42 * y + m43 * z + m[15];
1533−
1534− return r;
1535− };
1536−
1537− /*
1538− * Function: M4x4.makeLookAt
1539− */
1540− M4x4.makeLookAt = function M4x4_makeLookAt (eye, center, up, r) {
1541− //MathUtils_assert(eye.length == 3, "eye.length == 3");
1542− //MathUtils_assert(center.length == 3, "center.length == 3");
1543− //MathUtils_assert(up.length == 3, "up.length == 3");
1544− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1545−
1546− var z = V3.direction(eye, center, V3._temp1);
1547− var x = V3.normalize(V3.cross(up, z, V3._temp2), V3._temp2);
1548− var y = V3.normalize(V3.cross(z, x, V3._temp3), V3._temp3);
1549−
1550− var tm1 = M4x4._temp1;
1551− var tm2 = M4x4._temp2;
1552−
1553− tm1[0] = x[0];
1554− tm1[1] = y[0];
1555− tm1[2] = z[0];
1556− tm1[3] = 0;
1557− tm1[4] = x[1];
1558− tm1[5] = y[1];
1559− tm1[6] = z[1];
1560− tm1[7] = 0;
1561− tm1[8] = x[2];
1562− tm1[9] = y[2];
1563− tm1[10] = z[2];
1564− tm1[11] = 0;
1565− tm1[12] = 0;
1566− tm1[13] = 0;
1567− tm1[14] = 0;
1568− tm1[15] = 1;
1569−
1570− tm2[0] = 1; tm2[1] = 0; tm2[2] = 0; tm2[3] = 0;
1571− tm2[4] = 0; tm2[5] = 1; tm2[6] = 0; tm2[7] = 0;
1572− tm2[8] = 0; tm2[9] = 0; tm2[10] = 1; tm2[11] = 0;
1573− tm2[12] = -eye[0]; tm2[13] = -eye[1]; tm2[14] = -eye[2]; tm2[15] = 1;
1574−
1575− if (r == undefined)
1576− r = new MJS_FLOAT_ARRAY_TYPE(16);
1577− return M4x4.mul(tm1, tm2, r);
1578− };
1579−
1580− /*
1581− * Function: M4x4.transposeSelf
1582− */
1583− M4x4.transposeSelf = function M4x4_transposeSelf (m) {
1584− //MathUtils_assert(m.length == 16, "m.length == 16");
1585− var tmp = m[1]; m[1] = m[4]; m[4] = tmp;
1586− tmp = m[2]; m[2] = m[8]; m[8] = tmp;
1587− tmp = m[3]; m[3] = m[12]; m[12] = tmp;
1588− tmp = m[6]; m[6] = m[9]; m[9] = tmp;
1589− tmp = m[7]; m[7] = m[13]; m[13] = tmp;
1590− tmp = m[11]; m[11] = m[14]; m[14] = tmp;
1591− return m;
1592− };
1593− /*
1594− * Function: M4x4.transpose
1595− */
1596− M4x4.transpose = function M4x4_transpose (m, r) {
1597− //MathUtils_assert(m.length == 16, "m.length == 16");
1598− //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1599−
1600− if (m == r) {
1601− var tmp = 0.0;
1602− tmp = m[1]; m[1] = m[4]; m[4] = tmp;
1603− tmp = m[2]; m[2] = m[8]; m[8] = tmp;
1604− tmp = m[3]; m[3] = m[12]; m[12] = tmp;
1605− tmp = m[6]; m[6] = m[9]; m[9] = tmp;
1606− tmp = m[7]; m[7] = m[13]; m[13] = tmp;
1607− tmp = m[11]; m[11] = m[14]; m[14] = tmp;
1608− return m;
1609− }
1610−
1611− if (r == undefined)
1612− r = new MJS_FLOAT_ARRAY_TYPE(16);
1613−
1614− r[0] = m[0]; r[1] = m[4]; r[2] = m[8]; r[3] = m[12];
1615− r[4] = m[1]; r[5] = m[5]; r[6] = m[9]; r[7] = m[13];
1616− r[8] = m[2]; r[9] = m[6]; r[10] = m[10]; r[11] = m[14];
1617− r[12] = m[3]; r[13] = m[7]; r[14] = m[11]; r[15] = m[15];
1618−
1619− return r;
1620− };
1621−
1622−
1623− /*
1624− * Function: M4x4.transformPoint
1625− */
1626− M4x4.transformPoint = function M4x4_transformPoint (m, v, r) {
1627− //MathUtils_assert(m.length == 16, "m.length == 16");
1628− //MathUtils_assert(v.length == 3, "v.length == 3");
1629− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1630− if (r == undefined)
1631− r = new MJS_FLOAT_ARRAY_TYPE(3);
1632−
1633− var v0 = v[0], v1 = v[1], v2 = v[2];
1634−
1635− r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2 + m[12];
1636− r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2 + m[13];
1637− r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2 + m[14];
1638− var w = m[3] * v0 + m[7] * v1 + m[11] * v2 + m[15];
1639−
1640− if (w != 1.0) {
1641− r[0] /= w;
1642− r[1] /= w;
1643− r[2] /= w;
1644− }
1645−
1646− return r;
1647− };
1648−
1649− /*
1650− * Function: M4x4.transformLine
1651− */
1652− M4x4.transformLine = function M4x4_transformLine(m, v, r) {
1653− //MathUtils_assert(m.length == 16, "m.length == 16");
1654− //MathUtils_assert(v.length == 3, "v.length == 3");
1655− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1656− if (r == undefined)
1657− r = new MJS_FLOAT_ARRAY_TYPE(3);
1658−
1659− var v0 = v[0], v1 = v[1], v2 = v[2];
1660− r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2;
1661− r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2;
1662− r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2;
1663− var w = m[3] * v0 + m[7] * v1 + m[11] * v2;
1664−
1665− if (w != 1.0) {
1666− r[0] /= w;
1667− r[1] /= w;
1668− r[2] /= w;
1669− }
1670−
1671− return r;
1672− };
1673−
1674−
1675− /*
1676− * Function: M4x4.transformPointAffine
1677− */
1678− M4x4.transformPointAffine = function M4x4_transformPointAffine (m, v, r) {
1679− //MathUtils_assert(m.length == 16, "m.length == 16");
1680− //MathUtils_assert(v.length == 3, "v.length == 3");
1681− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1682− if (r == undefined)
1683− r = new MJS_FLOAT_ARRAY_TYPE(3);
1684−
1685− var v0 = v[0], v1 = v[1], v2 = v[2];
1686−
1687− r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2 + m[12];
1688− r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2 + m[13];
1689− r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2 + m[14];
1690−
1691− return r;
1692− };
1693−
1694− /*
1695− * Function: M4x4.transformLineAffine
1696− */
1697− M4x4.transformLineAffine = function M4x4_transformLineAffine(m, v, r) {
1698− //MathUtils_assert(m.length == 16, "m.length == 16");
1699− //MathUtils_assert(v.length == 3, "v.length == 3");
1700− //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1701− if (r == undefined)
1702− r = new MJS_FLOAT_ARRAY_TYPE(3);
1703−
1704− var v0 = v[0], v1 = v[1], v2 = v[2];
1705− r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2;
1706− r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2;
1707− r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2;
1708−
1709− return r;
1710− };
1711−
1712− M4x4.makeBasis = function M4x4_makeBasis(vx,vy,vz) {
1713−
1714− var r = new MJS_FLOAT_ARRAY_TYPE(16);
1715−
1716− r[0] = vx[0];
1717− r[1] = vx[1];
1718− r[2] = vx[2];
1719− r[3] = 0;
1720− r[4] = vy[0];
1721− r[5] = vy[1];
1722− r[6] = vy[2];
1723− r[7] = 0;
1724− r[8] = vz[0];
1725− r[9] = vz[1];
1726− r[10] = vz[2];
1727− r[11] = 0;
1728− r[12] = 0;
1729− r[13] = 0;
1730− r[14] = 0;
1731− r[15] = 1;
1732−
1733− return r;
1734−
1735− };
1736−
1737− return {
1738− v3: F3(V3.$),
1739− v3getX: V3.getX,
1740− v3getY: V3.getY,
1741− v3getZ: V3.getZ,
1742− v3setX: F2(V3.setX),
1743− v3setY: F2(V3.setY),
1744− v3setZ: F2(V3.setZ),
1745− toTuple3: V3.toTuple3,
1746− toRecord3: V3.toRecord3,
1747− fromTuple3: V3.fromTuple3,
1748− fromRecord3: V3.fromRecord3,
1749− v3add: F2(V3.add),
1750− v3sub: F2(V3.sub),
1751− v3neg: V3.neg,
1752− v3direction: F2(V3.direction),
1753− v3length: V3.length,
1754− v3lengthSquared: V3.lengthSquared,
1755− v3distance: F2(V3.distance),
1756− v3distanceSquared: F2(V3.distanceSquared),
1757− v3normalize: V3.normalize,
1758− v3scale: F2(V3.scale),
1759− v3dot: F2(V3.dot),
1760− v3cross: F2(V3.cross),
1761− v3mul4x4: F2(V3.mul4x4),
1762− m4x4identity: M4x4.identity,
1763− m4x4topLeft3x3: M4x4.topLeft3x3,
1764− m4x4inverseOrthonormal: M4x4.inverseOrthonormal,
1765− m4x4inverseTo3x3: M4x4.inverseTo3x3,
1766− m4x4makeFrustum: F6(M4x4.makeFrustum),
1767− m4x4makePerspective: F4(M4x4.makePerspective),
1768− m4x4makeOrtho: F6(M4x4.makeOrtho),
1769− m4x4makeOrtho2D: F4(M4x4.makeOrtho2D),
1770− m4x4mul: F2(M4x4.mul),
1771− m4x4Affine: F2(M4x4.mulAffine),
1772− m4x4makeRotate: F2(M4x4.makeRotate),
1773− m4x4rotate: F3(M4x4.rotate),
1774− m4x4makeScale3: F3(M4x4.makeScale3),
1775− m4x4makeScale1: M4x4.makeScale1,
1776− m4x4makeScale: M4x4.makeScale,
1777− m4x4scale3: F4(M4x4.scale3),
1778− m4x4scale: F2(M4x4.scale),
1779− m4x4makeTranslate3: F3(M4x4.makeTranslate3),
1780− m4x4makeTranslate: M4x4.makeTranslate,
1781− m4x4translate3: F4(M4x4.translate3),
1782− m4x4translate: F2(M4x4.translate),
1783− m4x4makeLookAt: F3(M4x4.makeLookAt),
1784− m4x4transpose: M4x4.transpose,
1785− m4x4transformPoint: F2(M4x4.transformPoint),
1786− m4x4makeBasis: F3(M4x4.makeBasis)
1787− };
1788−
1789−}