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elk/libraries/Native/MJS.js
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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 */
29/*
30 * File: mjs
31 *
32 * Vector and Matrix math utilities for JavaScript, optimized for WebGL.
33 * Edited to work with Elm Programming Language
34 */
36Elm.Native.MJS = {};
37Elm.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;
43 /*
44 * Constant: MJS_VERSION
45 *
46 * mjs version number aa.bb.cc, encoded as an integer of the form:
47 * 0xaabbcc.
48 */
49 const MJS_VERSION = 0x000000;
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 const MJS_DO_ASSERT = true;
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 //const MJS_FLOAT_ARRAY_TYPE = WebGLFloatArray;
72 const MJS_FLOAT_ARRAY_TYPE = Float32Array;
73 //const MJS_FLOAT_ARRAY_TYPE = Float64Array;
74 //const MJS_FLOAT_ARRAY_TYPE = Array;
76 if (MJS_DO_ASSERT) {
77 function MathUtils_assert(cond, msg) {
78 if (!cond)
79 throw "Assertion failed: " + msg;
80 }
81 } else {
82 function MathUtils_assert() { }
83 }
85 /*
86 * Class: V3
87 *
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.
91 */
93 var V3 = { };
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_$(x, y, z) {
105 return [x, y, z];
106 };
108 V3.clone = function V3_clone(a) {
109 //MathUtils_assert(a.length == 3, "a.length == 3");
110 return [a[0], a[1], a[2]];
111 };
112 } else {
113 V3.x = new MJS_FLOAT_ARRAY_TYPE([1.0, 0.0, 0.0]);
114 V3.y = new MJS_FLOAT_ARRAY_TYPE([0.0, 1.0, 0.0]);
115 V3.z = new MJS_FLOAT_ARRAY_TYPE([0.0, 0.0, 1.0]);
117 /*
118 * Function: V3.$
119 *
120 * Creates a new 3-element vector with the given values.
121 *
122 * Parameters:
123 *
124 * x,y,z - the 3 elements of the new vector.
125 *
126 * Returns:
127 *
128 * A new vector containing with the given argument values.
129 */
131 V3.$ = function V3_$(x, y, z) {
132 return new MJS_FLOAT_ARRAY_TYPE([x, y, z]);
133 };
135 /*
136 * Function: V3.clone
137 *
138 * Clone the given 3-element vector.
139 *
140 * Parameters:
141 *
142 * a - the 3-element vector to clone
143 *
144 * Returns:
145 *
146 * A new vector with the same values as the passed-in one.
147 */
149 V3.clone = function V3_clone(a) {
150 //MathUtils_assert(a.length == 3, "a.length == 3");
151 return new MJS_FLOAT_ARRAY_TYPE(a);
152 };
153 }
155 V3.u = V3.x;
156 V3.v = V3.y;
158 /*
159 * Function: V3.add
160 *
161 * Perform r = a + b.
162 *
163 * Parameters:
164 *
165 * a - the first vector operand
166 * b - the second vector operand
167 * r - optional vector to store the result in
168 *
169 * Returns:
170 *
171 * If r is specified, returns r after performing the operation.
172 * Otherwise, returns a new 3-element vector with the result.
173 */
174 V3.add = function V3_add(a, b, r) {
175 //MathUtils_assert(a.length == 3, "a.length == 3");
176 //MathUtils_assert(b.length == 3, "b.length == 3");
177 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
179 if (r == undefined)
180 r = new MJS_FLOAT_ARRAY_TYPE(3);
181 r[0] = a[0] + b[0];
182 r[1] = a[1] + b[1];
183 r[2] = a[2] + b[2];
184 return r;
185 };
187 /*
188 * Function: V3.sub
189 *
190 * Perform
191 * r = a - b.
192 *
193 * Parameters:
194 *
195 * a - the first vector operand
196 * b - the second vector operand
197 * r - optional vector to store the result in
198 *
199 * Returns:
200 *
201 * If r is specified, returns r after performing the operation.
202 * Otherwise, returns a new 3-element vector with the result.
203 */
204 V3.sub = function V3_sub(a, b, r) {
205 //MathUtils_assert(a.length == 3, "a.length == 3");
206 //MathUtils_assert(b.length == 3, "b.length == 3");
207 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
209 if (r == undefined)
210 r = new MJS_FLOAT_ARRAY_TYPE(3);
211 r[0] = a[0] - b[0];
212 r[1] = a[1] - b[1];
213 r[2] = a[2] - b[2];
214 return r;
215 };
217 /*
218 * Function: V3.neg
219 *
220 * Perform
221 * r = - a.
222 *
223 * Parameters:
224 *
225 * a - the vector operand
226 * r - optional vector to store the result in
227 *
228 * Returns:
229 *
230 * If r is specified, returns r after performing the operation.
231 * Otherwise, returns a new 3-element vector with the result.
232 */
233 V3.neg = function V3_neg(a, r) {
234 //MathUtils_assert(a.length == 3, "a.length == 3");
235 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
237 if (r == undefined)
238 r = new MJS_FLOAT_ARRAY_TYPE(3);
239 r[0] = - a[0];
240 r[1] = - a[1];
241 r[2] = - a[2];
242 return r;
243 };
245 /*
246 * Function: V3.direction
247 *
248 * Perform
249 * r = (a - b) / |a - b|. The result is the normalized
250 * direction from a to b.
251 *
252 * Parameters:
253 *
254 * a - the first vector operand
255 * b - the second vector operand
256 * r - optional vector to store the result in
257 *
258 * Returns:
259 *
260 * If r is specified, returns r after performing the operation.
261 * Otherwise, returns a new 3-element vector with the result.
262 */
263 V3.direction = function V3_direction(a, b, r) {
264 //MathUtils_assert(a.length == 3, "a.length == 3");
265 //MathUtils_assert(b.length == 3, "b.length == 3");
266 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
268 if (r == undefined)
269 r = new MJS_FLOAT_ARRAY_TYPE(3);
270 return V3.normalize(V3.sub(a, b, r), r);
271 };
273 /*
274 * Function: V3.length
275 *
276 * Perform r = |a|.
277 *
278 * Parameters:
279 *
280 * a - the vector operand
281 *
282 * Returns:
283 *
284 * The length of the given vector.
285 */
286 V3.length = function V3_length(a) {
287 //MathUtils_assert(a.length == 3, "a.length == 3");
289 return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
290 };
292 /*
293 * Function: V3.lengthSquard
294 *
295 * Perform r = |a|*|a|.
296 *
297 * Parameters:
298 *
299 * a - the vector operand
300 *
301 * Returns:
302 *
303 * The square of the length of the given vector.
304 */
305 V3.lengthSquared = function V3_lengthSquared(a) {
306 //MathUtils_assert(a.length == 3, "a.length == 3");
308 return a[0]*a[0] + a[1]*a[1] + a[2]*a[2];
309 };
311 /*
312 * Function: V3.normalize
313 *
314 * Perform r = a / |a|.
315 *
316 * Parameters:
317 *
318 * a - the vector operand
319 * r - optional vector to store the result in
320 *
321 * Returns:
322 *
323 * If r is specified, returns r after performing the operation.
324 * Otherwise, returns a new 3-element vector with the result.
325 */
326 V3.normalize = function V3_normalize(a, r) {
327 //MathUtils_assert(a.length == 3, "a.length == 3");
328 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
330 if (r == undefined)
331 r = new MJS_FLOAT_ARRAY_TYPE(3);
332 var im = 1.0 / V3.length(a);
333 r[0] = a[0] * im;
334 r[1] = a[1] * im;
335 r[2] = a[2] * im;
336 return r;
337 };
339 /*
340 * Function: V3.scale
341 *
342 * Perform r = a * k.
343 *
344 * Parameters:
345 *
346 * a - the vector operand
347 * k - a scalar value
348 * r - optional vector to store the result in
349 *
350 * Returns:
351 *
352 * If r is specified, returns r after performing the operation.
353 * Otherwise, returns a new 3-element vector with the result.
354 */
355 V3.scale = function V3_scale(a, k, r) {
356 //MathUtils_assert(a.length == 3, "a.length == 3");
357 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
359 if (r == undefined)
360 r = new MJS_FLOAT_ARRAY_TYPE(3);
361 r[0] = a[0] * k;
362 r[1] = a[1] * k;
363 r[2] = a[2] * k;
364 return r;
365 };
367 /*
368 * Function: V3.dot
369 *
370 * Perform
371 * r = dot(a, b).
372 *
373 * Parameters:
374 *
375 * a - the first vector operand
376 * b - the second vector operand
377 *
378 * Returns:
379 *
380 * The dot product of a and b.
381 */
382 V3.dot = function V3_dot(a, b) {
383 //MathUtils_assert(a.length == 3, "a.length == 3");
384 //MathUtils_assert(b.length == 3, "b.length == 3");
386 return a[0] * b[0] +
387 a[1] * b[1] +
388 a[2] * b[2];
389 };
391 /*
392 * Function: V3.cross
393 *
394 * Perform r = a x b.
395 *
396 * Parameters:
397 *
398 * a - the first vector operand
399 * b - the second vector operand
400 * r - optional vector to store the result in
401 *
402 * Returns:
403 *
404 * If r is specified, returns r after performing the operation.
405 * Otherwise, returns a new 3-element vector with the result.
406 */
407 V3.cross = function V3_cross(a, b, r) {
408 //MathUtils_assert(a.length == 3, "a.length == 3");
409 //MathUtils_assert(b.length == 3, "b.length == 3");
410 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
412 if (r == undefined)
413 r = new MJS_FLOAT_ARRAY_TYPE(3);
414 r[0] = a[1]*b[2] - a[2]*b[1];
415 r[1] = a[2]*b[0] - a[0]*b[2];
416 r[2] = a[0]*b[1] - a[1]*b[0];
417 return r;
418 };
420 /*
421 * Function: V3.mul4x4
422 *
423 * Perform
424 * r = m * v.
425 *
426 * Parameters:
427 *
428 * m - the 4x4 matrix operand
429 * v - the 3-element vector operand
430 * r - optional vector to store the result in
431 *
432 * Returns:
433 *
434 * If r is specified, returns r after performing the operation.
435 * Otherwise, returns a new 3-element vector with the result.
436 * The 4-element result vector is divided by the w component
437 * and returned as a 3-element vector.
438 */
439 V3.mul4x4 = function V3_mul4x4(m, v, r) {
440 //MathUtils_assert(m.length == 16, "m.length == 16");
441 //MathUtils_assert(v.length == 3, "v.length == 3");
442 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
444 var w;
445 var tmp = V3._temp1;
446 if (r == undefined)
447 r = new MJS_FLOAT_ARRAY_TYPE(3);
448 tmp[0] = m[ 3];
449 tmp[1] = m[ 7];
450 tmp[2] = m[11];
451 w = V3.dot(v, tmp) + m[15];
452 tmp[0] = m[ 0];
453 tmp[1] = m[ 4];
454 tmp[2] = m[ 8];
455 r[0] = (V3.dot(v, tmp) + m[12])/w;
456 tmp[0] = m[ 1];
457 tmp[1] = m[ 5];
458 tmp[2] = m[ 9];
459 r[1] = (V3.dot(v, tmp) + m[13])/w;
460 tmp[0] = m[ 2];
461 tmp[1] = m[ 6];
462 tmp[2] = m[10];
463 r[2] = (V3.dot(v, tmp) + m[14])/w;
464 return r;
465 };
467 /*
468 * Class: M4x4
469 *
470 * Methods for working with 4x4 matrices. A matrix is represented by a 16-element array
471 * in column-major order. Any valid JavaScript array type may be used, but if new
472 * matrices are created they are created using the configured MJS_FLOAT_ARRAY_TYPE.
473 */
475 var M4x4 = { };
477 M4x4._temp1 = new MJS_FLOAT_ARRAY_TYPE(16);
478 M4x4._temp2 = new MJS_FLOAT_ARRAY_TYPE(16);
480 if (MJS_FLOAT_ARRAY_TYPE == Array) {
481 M4x4.I = [1.0, 0.0, 0.0, 0.0,
482 0.0, 1.0, 0.0, 0.0,
483 0.0, 0.0, 1.0, 0.0,
484 0.0, 0.0, 0.0, 1.0];
486 M4x4.$ = function M4x4_$(m00, m01, m02, m03,
487 m04, m05, m06, m07,
488 m08, m09, m10, m11,
489 m12, m13, m14, m15)
490 {
491 return [m00, m01, m02, m03,
492 m04, m05, m06, m07,
493 m08, m09, m10, m11,
494 m12, m13, m14, m15];
495 };
497 M4x4.clone = function M4x4_clone(m) {
498 //MathUtils_assert(m.length == 16, "m.length == 16");
499 return new [m[0], m[1], m[2], m[3],
500 m[4], m[5], m[6], m[7],
501 m[8], m[9], m[10], m[11],
502 m[12], m[13], m[14], m[15]];
503 };
504 } else {
505 M4x4.I = new MJS_FLOAT_ARRAY_TYPE([1.0, 0.0, 0.0, 0.0,
506 0.0, 1.0, 0.0, 0.0,
507 0.0, 0.0, 1.0, 0.0,
508 0.0, 0.0, 0.0, 1.0]);
510 /*
511 * Function: M4x4.$
512 *
513 * Creates a new 4x4 matrix with the given values.
514 *
515 * Parameters:
516 *
517 * m00..m15 - the 16 elements of the new matrix.
518 *
519 * Returns:
520 *
521 * A new matrix filled with the given argument values.
522 */
523 M4x4.$ = function M4x4_$(m00, m01, m02, m03,
524 m04, m05, m06, m07,
525 m08, m09, m10, m11,
526 m12, m13, m14, m15)
527 {
528 return new MJS_FLOAT_ARRAY_TYPE([m00, m01, m02, m03,
529 m04, m05, m06, m07,
530 m08, m09, m10, m11,
531 m12, m13, m14, m15]);
532 };
534 /*
535 * Function: M4x4.clone
536 *
537 * Clone the given 4x4 matrix.
538 *
539 * Parameters:
540 *
541 * m - the 4x4 matrix to clone
542 *
543 * Returns:
544 *
545 * A new matrix with the same values as the passed-in one.
546 */
547 M4x4.clone = function M4x4_clone(m) {
548 //MathUtils_assert(m.length == 16, "m.length == 16");
549 return new MJS_FLOAT_ARRAY_TYPE(m);
550 };
551 }
553 M4x4.identity = M4x4.I;
555 /*
556 * Function: M4x4.topLeft3x3
557 *
558 * Return the top left 3x3 matrix from the given 4x4 matrix m.
559 *
560 * Parameters:
561 *
562 * m - the matrix
563 * r - optional 3x3 matrix to store the result in
564 *
565 * Returns:
566 *
567 * If r is specified, returns r after performing the operation.
568 * Otherwise, returns a new 3x3 matrix with the result.
569 */
570 M4x4.topLeft3x3 = function M4x4_topLeft3x3(m, r) {
571 //MathUtils_assert(m.length == 16, "m.length == 16");
572 //MathUtils_assert(r == undefined || r.length == 9, "r == undefined || r.length == 9");
574 if (r == undefined)
575 r = new MJS_FLOAT_ARRAY_TYPE(9);
576 r[0] = m[0]; r[1] = m[1]; r[2] = m[2];
577 r[3] = m[4]; r[4] = m[5]; r[5] = m[6];
578 r[6] = m[8]; r[7] = m[9]; r[8] = m[10];
579 return r;
580 };
582 /*
583 * Function: M4x4.inverseOrthonormal
584 *
585 * Computes the inverse of the given matrix m, assuming that
586 * the matrix is orthonormal.
587 *
588 * Parameters:
589 *
590 * m - the matrix
591 * r - optional 4x4 matrix to store the result in
592 *
593 * Returns:
594 *
595 * If r is specified, returns r after performing the operation.
596 * Otherwise, returns a new 4x4 matrix with the result.
597 */
598 M4x4.inverseOrthonormal = function M4x4_inverseOrthonormal(m, r) {
599 //MathUtils_assert(m.length == 16, "m.length == 16");
600 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
601 //MathUtils_assert(m != r, "m != r");
603 if (r == undefined)
604 r = new MJS_FLOAT_ARRAY_TYPE(16);
605 M4x4.transpose(m, r);
606 var t = [m[12], m[13], m[14]];
607 r[3] = r[7] = r[11] = 0;
608 r[12] = -V3.dot([r[0], r[4], r[8]], t);
609 r[13] = -V3.dot([r[1], r[5], r[9]], t);
610 r[14] = -V3.dot([r[2], r[6], r[10]], t);
611 return r;
612 };
614 /*
615 * Function: M4x4.inverseTo3x3
616 *
617 * Computes the inverse of the given matrix m, but calculates
618 * only the top left 3x3 values of the result.
619 *
620 * Parameters:
621 *
622 * m - the matrix
623 * r - optional 3x3 matrix to store the result in
624 *
625 * Returns:
626 *
627 * If r is specified, returns r after performing the operation.
628 * Otherwise, returns a new 3x3 matrix with the result.
629 */
630 M4x4.inverseTo3x3 = function M4x4_inverseTo3x3(m, r) {
631 //MathUtils_assert(m.length == 16, "m.length == 16");
632 //MathUtils_assert(r == undefined || r.length == 9, "r == undefined || r.length == 9");
634 if (r == undefined)
635 r = new MJS_FLOAT_ARRAY_TYPE(9);
637 var a11 = m[10]*m[5]-m[6]*m[9],
638 a21 = -m[10]*m[1]+m[2]*m[9],
639 a31 = m[6]*m[1]-m[2]*m[5],
640 a12 = -m[10]*m[4]+m[6]*m[8],
641 a22 = m[10]*m[0]-m[2]*m[8],
642 a32 = -m[6]*m[0]+m[2]*m[4],
643 a13 = m[9]*m[4]-m[5]*m[8],
644 a23 = -m[9]*m[0]+m[1]*m[8],
645 a33 = m[5]*m[0]-m[1]*m[4];
646 var det = m[0]*(a11) + m[1]*(a12) + m[2]*(a13);
647 if (det == 0) // no inverse
648 throw "matrix not invertible";
649 var idet = 1.0 / det;
651 r[0] = idet*a11;
652 r[1] = idet*a21;
653 r[2] = idet*a31;
654 r[3] = idet*a12;
655 r[4] = idet*a22;
656 r[5] = idet*a32;
657 r[6] = idet*a13;
658 r[7] = idet*a23;
659 r[8] = idet*a33;
661 return r;
662 };
664 /*
665 * Function: M4x4.makeFrustum
666 *
667 * Creates a matrix for a projection frustum with the given parameters.
668 *
669 * Parameters:
670 *
671 * left - the left coordinate of the frustum
672 * right- the right coordinate of the frustum
673 * bottom - the bottom coordinate of the frustum
674 * top - the top coordinate of the frustum
675 * znear - the near z distance of the frustum
676 * zfar - the far z distance of the frustum
677 * r - optional 4x4 matrix to store the result in
678 *
679 * Returns:
680 *
681 * If r is specified, returns r after creating the projection matrix.
682 * Otherwise, returns a new 4x4 matrix.
683 */
684 M4x4.makeFrustum = function M4x4_makeFrustum(left, right, bottom, top, znear, zfar, r) {
685 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
687 if (r == undefined)
688 r = new MJS_FLOAT_ARRAY_TYPE(16);
690 var X = 2*znear/(right-left);
691 var Y = 2*znear/(top-bottom);
692 var A = (right+left)/(right-left);
693 var B = (top+bottom)/(top-bottom);
694 var C = -(zfar+znear)/(zfar-znear);
695 var D = -2*zfar*znear/(zfar-znear);
697 r[0] = 2*znear/(right-left);
698 r[1] = 0;
699 r[2] = 0;
700 r[3] = 0;
701 r[4] = 0;
702 r[5] = 2*znear/(top-bottom);
703 r[6] = 0;
704 r[7] = 0;
705 r[8] = (right+left)/(right-left);
706 r[9] = (top+bottom)/(top-bottom);
707 r[10] = -(zfar+znear)/(zfar-znear);
708 r[11] = -1;
709 r[12] = 0;
710 r[13] = 0;
711 r[14] = -2*zfar*znear/(zfar-znear);
712 r[15] = 0;
714 return r;
715 };
717 /*
718 * Function: M4x4.makePerspective
719 *
720 * Creates a matrix for a perspective projection with the given parameters.
721 *
722 * Parameters:
723 *
724 * fovy - field of view in the y axis, in degrees
725 * aspect - aspect ratio
726 * znear - the near z distance of the projection
727 * zfar - the far z distance of the projection
728 * r - optional 4x4 matrix to store the result in
729 *
730 * Returns:
731 *
732 * If r is specified, returns r after creating the projection matrix.
733 * Otherwise, returns a new 4x4 matrix.
734 */
735 M4x4.makePerspective = function M4x4_makePerspective (fovy, aspect, znear, zfar, r) {
736 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
738 var ymax = znear * Math.tan(fovy * Math.PI / 360.0);
739 var ymin = -ymax;
740 var xmin = ymin * aspect;
741 var xmax = ymax * aspect;
743 return M4x4.makeFrustum(xmin, xmax, ymin, ymax, znear, zfar, r);
744 };
746 /*
747 * Function: M4x4.makeOrtho
748 *
749 * Creates a matrix for an orthogonal frustum projection with the given parameters.
750 *
751 * Parameters:
752 *
753 * left - the left coordinate of the frustum
754 * right- the right coordinate of the frustum
755 * bottom - the bottom coordinate of the frustum
756 * top - the top coordinate of the frustum
757 * znear - the near z distance of the frustum
758 * zfar - the far z distance of the frustum
759 * r - optional 4x4 matrix to store the result in
760 *
761 * Returns:
762 *
763 * If r is specified, returns r after creating the projection matrix.
764 * Otherwise, returns a new 4x4 matrix.
765 */
766 M4x4.makeOrtho = function M4x4_makeOrtho (left, right, bottom, top, znear, zfar, r) {
767 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
769 if (r == undefined)
770 r = new MJS_FLOAT_ARRAY_TYPE(16);
772 var tX = -(right+left)/(right-left);
773 var tY = -(top+bottom)/(top-bottom);
774 var tZ = -(zfar+znear)/(zfar-znear);
775 var X = 2 / (right-left);
776 var Y = 2 / (top-bottom);
777 var Z = -2 / (zfar-znear);
779 r[0] = 2 / (right-left);
780 r[1] = 0;
781 r[2] = 0;
782 r[3] = 0;
783 r[4] = 0;
784 r[5] = 2 / (top-bottom);
785 r[6] = 0;
786 r[7] = 0;
787 r[8] = 0;
788 r[9] = 0;
789 r[10] = -2 / (zfar-znear);
790 r[11] = 0;
791 r[12] = -(right+left)/(right-left);
792 r[13] = -(top+bottom)/(top-bottom);
793 r[14] = -(zfar+znear)/(zfar-znear);
794 r[15] = 1;
796 return r;
797 };
799 /*
800 * Function: M4x4.makeOrtho2D
801 *
802 * Creates a matrix for a 2D orthogonal frustum projection with the given parameters.
803 * znear and zfar are assumed to be -1 and 1, respectively.
804 *
805 * Parameters:
806 *
807 * left - the left coordinate of the frustum
808 * right- the right coordinate of the frustum
809 * bottom - the bottom coordinate of the frustum
810 * top - the top coordinate of the frustum
811 * r - optional 4x4 matrix to store the result in
812 *
813 * Returns:
814 *
815 * If r is specified, returns r after creating the projection matrix.
816 * Otherwise, returns a new 4x4 matrix.
817 */
818 M4x4.makeOrtho2D = function M4x4_makeOrtho2D (left, right, bottom, top, r) {
819 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
821 return M4x4.makeOrtho(left, right, bottom, top, -1, 1, r);
822 };
824 /*
825 * Function: M4x4.mul
826 *
827 * Performs r = a * b.
828 *
829 * Parameters:
830 *
831 * a - the first matrix operand
832 * b - the second matrix operand
833 * r - optional 4x4 matrix to store the result in
834 *
835 * Returns:
836 *
837 * If r is specified, returns r after performing the operation.
838 * Otherwise, returns a new 4x4 matrix with the result.
839 */
840 M4x4.mul = function M4x4_mul(a, b, r) {
841 //MathUtils_assert(a.length == 16, "a.length == 16");
842 //MathUtils_assert(b.length == 16, "b.length == 16");
843 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
844 //MathUtils_assert(a != r && b != r, "a != r && b != r");
846 if (r == undefined)
847 r = new MJS_FLOAT_ARRAY_TYPE(16);
849 var a11 = a[0];
850 var a21 = a[1];
851 var a31 = a[2];
852 var a41 = a[3];
853 var a12 = a[4];
854 var a22 = a[5];
855 var a32 = a[6];
856 var a42 = a[7];
857 var a13 = a[8];
858 var a23 = a[9];
859 var a33 = a[10];
860 var a43 = a[11];
861 var a14 = a[12];
862 var a24 = a[13];
863 var a34 = a[14];
864 var a44 = a[15];
866 var b11 = b[0];
867 var b21 = b[1];
868 var b31 = b[2];
869 var b41 = b[3];
870 var b12 = b[4];
871 var b22 = b[5];
872 var b32 = b[6];
873 var b42 = b[7];
874 var b13 = b[8];
875 var b23 = b[9];
876 var b33 = b[10];
877 var b43 = b[11];
878 var b14 = b[12];
879 var b24 = b[13];
880 var b34 = b[14];
881 var b44 = b[15];
883 r[0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
884 r[1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
885 r[2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
886 r[3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
887 r[4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
888 r[5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
889 r[6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
890 r[7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
891 r[8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
892 r[9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
893 r[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
894 r[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
895 r[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
896 r[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
897 r[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
898 r[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
900 return r;
901 };
903 /*
904 * Function: M4x4.mulAffine
905 *
906 * Performs r = a * b, assuming a and b are affine (elements 3,7,11,15 = 0,0,0,1)
907 *
908 * Parameters:
909 *
910 * a - the first matrix operand
911 * b - the second matrix operand
912 * r - optional 4x4 matrix to store the result in
913 *
914 * Returns:
915 *
916 * If r is specified, returns r after performing the operation.
917 * Otherwise, returns a new 4x4 matrix with the result.
918 */
919 M4x4.mulAffine = function M4x4_mulAffine(a, b, r) {
920 //MathUtils_assert(a.length == 16, "a.length == 16");
921 //MathUtils_assert(b.length == 16, "b.length == 16");
922 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
923 //MathUtils_assert(a != r && b != r, "a != r && b != r");
925 if (r == undefined)
926 r = new MJS_FLOAT_ARRAY_TYPE(16);
927 var a11 = a[0];
928 var a21 = a[1];
929 var a31 = a[2];
930 var a12 = a[4];
931 var a22 = a[5];
932 var a32 = a[6];
933 var a13 = a[8];
934 var a23 = a[9];
935 var a33 = a[10];
936 var a14 = a[12];
937 var a24 = a[13];
938 var a34 = a[14];
940 var b11 = b[0];
941 var b21 = b[1];
942 var b31 = b[2];
943 var b12 = b[4];
944 var b22 = b[5];
945 var b32 = b[6];
946 var b13 = b[8];
947 var b23 = b[9];
948 var b33 = b[10];
949 var b14 = b[12];
950 var b24 = b[13];
951 var b34 = b[14];
953 r[0] = a11 * b11 + a12 * b21 + a13 * b31;
954 r[1] = a21 * b11 + a22 * b21 + a23 * b31;
955 r[2] = a31 * b11 + a32 * b21 + a33 * b31;
956 r[3] = 0;
957 r[4] = a11 * b12 + a12 * b22 + a13 * b32;
958 r[5] = a21 * b12 + a22 * b22 + a23 * b32;
959 r[6] = a31 * b12 + a32 * b22 + a33 * b32;
960 r[7] = 0;
961 r[8] = a11 * b13 + a12 * b23 + a13 * b33;
962 r[9] = a21 * b13 + a22 * b23 + a23 * b33;
963 r[10] = a31 * b13 + a32 * b23 + a33 * b33;
964 r[11] = 0;
965 r[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14;
966 r[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24;
967 r[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34;
968 r[15] = 1;
970 return r;
971 };
973 /*
974 * Function: M4x4.makeRotate
975 *
976 * Creates a transformation matrix for rotation by angle radians about the 3-element vector axis.
977 *
978 * Parameters:
979 *
980 * angle - the angle of rotation, in radians
981 * axis - the axis around which the rotation is performed, a 3-element vector
982 * r - optional 4x4 matrix to store the result in
983 *
984 * Returns:
985 *
986 * If r is specified, returns r after creating the matrix.
987 * Otherwise, returns a new 4x4 matrix with the result.
988 */
989 M4x4.makeRotate = function M4x4_makeRotate(angle, axis, r) {
990 //MathUtils_assert(angle.length == 3, "angle.length == 3");
991 //MathUtils_assert(axis.length == 3, "axis.length == 3");
992 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
994 if (r == undefined)
995 r = new MJS_FLOAT_ARRAY_TYPE(16);
997 axis = V3.normalize(axis, V3._temp1);
998 var x = axis[0], y = axis[1], z = axis[2];
999 var c = Math.cos(angle);
1000 var c1 = 1-c;
1001 var s = Math.sin(angle);
1003 r[0] = x*x*c1+c;
1004 r[1] = y*x*c1+z*s;
1005 r[2] = z*x*c1-y*s;
1006 r[3] = 0;
1007 r[4] = x*y*c1-z*s;
1008 r[5] = y*y*c1+c;
1009 r[6] = y*z*c1+x*s;
1010 r[7] = 0;
1011 r[8] = x*z*c1+y*s;
1012 r[9] = y*z*c1-x*s;
1013 r[10] = z*z*c1+c;
1014 r[11] = 0;
1015 r[12] = 0;
1016 r[13] = 0;
1017 r[14] = 0;
1018 r[15] = 1;
1020 return r;
1021 };
1023 /*
1024 * Function: M4x4.rotate
1026 * Concatenates a rotation of angle radians about the axis to the give matrix m.
1028 * Parameters:
1030 * angle - the angle of rotation, in radians
1031 * axis - the axis around which the rotation is performed, a 3-element vector
1032 * m - the matrix to concatenate the rotation to
1033 * r - optional 4x4 matrix to store the result in
1035 * Returns:
1037 * If r is specified, returns r after performing the operation.
1038 * Otherwise, returns a new 4x4 matrix with the result.
1039 */
1040 M4x4.rotate = function M4x4_rotate(angle, axis, m, r) {
1041 //MathUtils_assert(angle.length == 3, "angle.length == 3");
1042 //MathUtils_assert(axis.length == 3, "axis.length == 3");
1043 //MathUtils_assert(m.length == 16, "m.length == 16");
1044 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1046 if (r == undefined)
1047 r = new MJS_FLOAT_ARRAY_TYPE(16);
1048 var a0=axis [0], a1=axis [1], a2=axis [2];
1049 var l = Math.sqrt(a0*a0 + a1*a1 + a2*a2);
1050 var x = a0, y = a1, z = a2;
1051 if (l != 1.0) {
1052 var im = 1.0 / l;
1053 x *= im;
1054 y *= im;
1055 z *= im;
1057 var c = Math.cos(angle);
1058 var c1 = 1-c;
1059 var s = Math.sin(angle);
1060 var xs = x*s;
1061 var ys = y*s;
1062 var zs = z*s;
1063 var xyc1 = x * y * c1;
1064 var xzc1 = x * z * c1;
1065 var yzc1 = y * z * c1;
1067 var m11 = m[0];
1068 var m21 = m[1];
1069 var m31 = m[2];
1070 var m41 = m[3];
1071 var m12 = m[4];
1072 var m22 = m[5];
1073 var m32 = m[6];
1074 var m42 = m[7];
1075 var m13 = m[8];
1076 var m23 = m[9];
1077 var m33 = m[10];
1078 var m43 = m[11];
1080 var t11 = x * x * c1 + c;
1081 var t21 = xyc1 + zs;
1082 var t31 = xzc1 - ys;
1083 var t12 = xyc1 - zs;
1084 var t22 = y * y * c1 + c;
1085 var t32 = yzc1 + xs;
1086 var t13 = xzc1 + ys;
1087 var t23 = yzc1 - xs;
1088 var t33 = z * z * c1 + c;
1090 r[0] = m11 * t11 + m12 * t21 + m13 * t31;
1091 r[1] = m21 * t11 + m22 * t21 + m23 * t31;
1092 r[2] = m31 * t11 + m32 * t21 + m33 * t31;
1093 r[3] = m41 * t11 + m42 * t21 + m43 * t31;
1094 r[4] = m11 * t12 + m12 * t22 + m13 * t32;
1095 r[5] = m21 * t12 + m22 * t22 + m23 * t32;
1096 r[6] = m31 * t12 + m32 * t22 + m33 * t32;
1097 r[7] = m41 * t12 + m42 * t22 + m43 * t32;
1098 r[8] = m11 * t13 + m12 * t23 + m13 * t33;
1099 r[9] = m21 * t13 + m22 * t23 + m23 * t33;
1100 r[10] = m31 * t13 + m32 * t23 + m33 * t33;
1101 r[11] = m41 * t13 + m42 * t23 + m43 * t33;
1102 if (r != m) {
1103 r[12] = m[12];
1104 r[13] = m[13];
1105 r[14] = m[14];
1106 r[15] = m[15];
1108 return r;
1109 };
1111 /*
1112 * Function: M4x4.makeScale3
1114 * Creates a transformation matrix for scaling by 3 scalar values, one for
1115 * each of the x, y, and z directions.
1117 * Parameters:
1119 * x - the scale for the x axis
1120 * y - the scale for the y axis
1121 * z - the scale for the z axis
1122 * r - optional 4x4 matrix to store the result in
1124 * Returns:
1126 * If r is specified, returns r after creating the matrix.
1127 * Otherwise, returns a new 4x4 matrix with the result.
1128 */
1129 M4x4.makeScale3 = function M4x4_makeScale3(x, y, z, r) {
1130 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1132 if (r == undefined)
1133 r = new MJS_FLOAT_ARRAY_TYPE(16);
1135 r[0] = x;
1136 r[1] = 0;
1137 r[2] = 0;
1138 r[3] = 0;
1139 r[4] = 0;
1140 r[5] = y;
1141 r[6] = 0;
1142 r[7] = 0;
1143 r[8] = 0;
1144 r[9] = 0;
1145 r[10] = z;
1146 r[11] = 0;
1147 r[12] = 0;
1148 r[13] = 0;
1149 r[14] = 0;
1150 r[15] = 1;
1152 return r;
1153 };
1155 /*
1156 * Function: M4x4.makeScale1
1158 * Creates a transformation matrix for a uniform scale by a single scalar value.
1160 * Parameters:
1162 * k - the scale factor
1163 * r - optional 4x4 matrix to store the result in
1165 * Returns:
1167 * If r is specified, returns r after creating the matrix.
1168 * Otherwise, returns a new 4x4 matrix with the result.
1169 */
1170 M4x4.makeScale1 = function M4x4_makeScale1(k, r) {
1171 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1173 return M4x4.makeScale3(k, k, k, r);
1174 };
1176 /*
1177 * Function: M4x4.makeScale
1179 * Creates a transformation matrix for scaling each of the x, y, and z axes by the amount
1180 * given in the corresponding element of the 3-element vector.
1182 * Parameters:
1184 * v - the 3-element vector containing the scale factors
1185 * r - optional 4x4 matrix to store the result in
1187 * Returns:
1189 * If r is specified, returns r after creating the matrix.
1190 * Otherwise, returns a new 4x4 matrix with the result.
1191 */
1192 M4x4.makeScale = function M4x4_makeScale(v, r) {
1193 //MathUtils_assert(v.length == 3, "v.length == 3");
1194 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1196 return M4x4.makeScale3(v[0], v[1], v[2], r);
1197 };
1199 /*
1200 * Function: M4x4.scale3
1201 */
1202 M4x4.scale3 = function M4x4_scale3(x, y, z, m, r) {
1203 //MathUtils_assert(m.length == 16, "m.length == 16");
1204 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1206 if (r == m) {
1207 m[0] *= x;
1208 m[1] *= x;
1209 m[2] *= x;
1210 m[3] *= x;
1211 m[4] *= y;
1212 m[5] *= y;
1213 m[6] *= y;
1214 m[7] *= y;
1215 m[8] *= z;
1216 m[9] *= z;
1217 m[10] *= z;
1218 m[11] *= z;
1219 return m;
1222 if (r == undefined)
1223 r = new MJS_FLOAT_ARRAY_TYPE(16);
1225 r[0] = m[0] * x;
1226 r[1] = m[1] * x;
1227 r[2] = m[2] * x;
1228 r[3] = m[3] * x;
1229 r[4] = m[4] * y;
1230 r[5] = m[5] * y;
1231 r[6] = m[6] * y;
1232 r[7] = m[7] * y;
1233 r[8] = m[8] * z;
1234 r[9] = m[9] * z;
1235 r[10] = m[10] * z;
1236 r[11] = m[11] * z;
1237 r[12] = m[12];
1238 r[13] = m[13];
1239 r[14] = m[14];
1240 r[15] = m[15];
1242 return r;
1243 };
1245 /*
1246 * Function: M4x4.scale1
1247 */
1248 M4x4.scale1 = function M4x4_scale1(k, m, r) {
1249 //MathUtils_assert(m.length == 16, "m.length == 16");
1250 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1251 if (r == m) {
1252 m[0] *= k;
1253 m[1] *= k;
1254 m[2] *= k;
1255 m[3] *= k;
1256 m[4] *= k;
1257 m[5] *= k;
1258 m[6] *= k;
1259 m[7] *= k;
1260 m[8] *= k;
1261 m[9] *= k;
1262 m[10] *= k;
1263 m[11] *= k;
1264 return m;
1268 if (r == undefined)
1269 r = new MJS_FLOAT_ARRAY_TYPE(16);
1271 r[0] = m[0] * k;
1272 r[1] = m[1] * k;
1273 r[2] = m[2] * k;
1274 r[3] = m[3] * k;
1275 r[4] = m[4] * k;
1276 r[5] = m[5] * k;
1277 r[6] = m[6] * k;
1278 r[7] = m[7] * k;
1279 r[8] = m[8] * k;
1280 r[9] = m[9] * k;
1281 r[10] = m[10] * k;
1282 r[11] = m[11] * k;
1283 r[12] = m[12];
1284 r[13] = m[13];
1285 r[14] = m[14];
1286 r[15] = m[15];
1288 return r;
1289 };
1291 /*
1292 * Function: M4x4.scale1
1293 */
1294 M4x4.scale = function M4x4_scale(v, m, r) {
1295 //MathUtils_assert(v.length == 3, "v.length == 3");
1296 //MathUtils_assert(m.length == 16, "m.length == 16");
1297 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1298 var x = v[0], y = v[1], z = v[2];
1300 if (r == m) {
1301 m[0] *= x;
1302 m[1] *= x;
1303 m[2] *= x;
1304 m[3] *= x;
1305 m[4] *= y;
1306 m[5] *= y;
1307 m[6] *= y;
1308 m[7] *= y;
1309 m[8] *= z;
1310 m[9] *= z;
1311 m[10] *= z;
1312 m[11] *= z;
1313 return m;
1316 if (r == undefined)
1317 r = new MJS_FLOAT_ARRAY_TYPE(16);
1320 r[0] = m[0] * x;
1321 r[1] = m[1] * x;
1322 r[2] = m[2] * x;
1323 r[3] = m[3] * x;
1324 r[4] = m[4] * y;
1325 r[5] = m[5] * y;
1326 r[6] = m[6] * y;
1327 r[7] = m[7] * y;
1328 r[8] = m[8] * z;
1329 r[9] = m[9] * z;
1330 r[10] = m[10] * z;
1331 r[11] = m[11] * z;
1332 r[12] = m[12];
1333 r[13] = m[13];
1334 r[14] = m[14];
1335 r[15] = m[15];
1337 return r;
1338 };
1340 /*
1341 * Function: M4x4.makeTranslate3
1342 */
1343 M4x4.makeTranslate3 = function M4x4_makeTranslate3(x, y, z, r) {
1344 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1346 if (r == undefined)
1347 r = new MJS_FLOAT_ARRAY_TYPE(16);
1349 r[0] = 1;
1350 r[1] = 0;
1351 r[2] = 0;
1352 r[3] = 0;
1353 r[4] = 0;
1354 r[5] = 1;
1355 r[6] = 0;
1356 r[7] = 0;
1357 r[8] = 0;
1358 r[9] = 0;
1359 r[10] = 1;
1360 r[11] = 0;
1361 r[12] = x;
1362 r[13] = y;
1363 r[14] = z;
1364 r[15] = 1;
1366 return r;
1367 };
1369 /*
1370 * Function: M4x4.makeTranslate1
1371 */
1372 M4x4.makeTranslate1 = function M4x4_makeTranslate1 (k, r) {
1373 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1375 return M4x4.makeTranslate3(k, k, k, r);
1376 };
1378 /*
1379 * Function: M4x4.makeTranslate
1380 */
1381 M4x4.makeTranslate = function M4x4_makeTranslate (v, r) {
1382 //MathUtils_assert(v.length == 3, "v.length == 3");
1383 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1385 return M4x4.makeTranslate3(v[0], v[1], v[2], r);
1386 };
1388 /*
1389 * Function: M4x4.translate3Self
1390 */
1391 M4x4.translate3Self = function M4x4_translate3Self (x, y, z, m) {
1392 //MathUtils_assert(m.length == 16, "m.length == 16");
1393 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1394 m[12] += m[0] * x + m[4] * y + m[8] * z;
1395 m[13] += m[1] * x + m[5] * y + m[9] * z;
1396 m[14] += m[2] * x + m[6] * y + m[10] * z;
1397 m[15] += m[3] * x + m[7] * y + m[11] * z;
1398 return m;
1399 };
1401 /*
1402 * Function: M4x4.translate3
1403 */
1404 M4x4.translate3 = function M4x4_translate3 (x, y, z, m, r) {
1405 //MathUtils_assert(m.length == 16, "m.length == 16");
1406 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1408 if (r == m) {
1409 m[12] += m[0] * x + m[4] * y + m[8] * z;
1410 m[13] += m[1] * x + m[5] * y + m[9] * z;
1411 m[14] += m[2] * x + m[6] * y + m[10] * z;
1412 m[15] += m[3] * x + m[7] * y + m[11] * z;
1413 return m;
1416 if (r == undefined)
1417 r = new MJS_FLOAT_ARRAY_TYPE(16);
1419 var m11 = m[0];
1420 var m21 = m[1];
1421 var m31 = m[2];
1422 var m41 = m[3];
1423 var m12 = m[4];
1424 var m22 = m[5];
1425 var m32 = m[6];
1426 var m42 = m[7];
1427 var m13 = m[8];
1428 var m23 = m[9];
1429 var m33 = m[10];
1430 var m43 = m[11];
1433 r[0] = m11;
1434 r[1] = m21;
1435 r[2] = m31;
1436 r[3] = m41;
1437 r[4] = m12;
1438 r[5] = m22;
1439 r[6] = m32;
1440 r[7] = m42;
1441 r[8] = m13;
1442 r[9] = m23;
1443 r[10] = m33;
1444 r[11] = m43;
1445 r[12] = m11 * x + m12 * y + m13 * z + m[12];
1446 r[13] = m21 * x + m22 * y + m23 * z + m[13];
1447 r[14] = m31 * x + m32 * y + m33 * z + m[14];
1448 r[15] = m41 * x + m42 * y + m43 * z + m[15];
1450 return r;
1451 };
1453 /*
1454 * Function: M4x4.translate1
1455 */
1456 M4x4.translate1 = function M4x4_translate1 (k, m, r) {
1457 //MathUtils_assert(m.length == 16, "m.length == 16");
1458 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1460 return M4x4.translate3(k, k, k, m, r);
1461 };
1462 /*
1463 * Function: M4x4.translateSelf
1464 */
1465 M4x4.translateSelf = function M4x4_translateSelf (v, m) {
1466 //MathUtils_assert(v.length == 3, "v.length == 3");
1467 //MathUtils_assert(m.length == 16, "m.length == 16");
1468 var x=v[0], y=v[1], z=v[2];
1469 m[12] += m[0] * x + m[4] * y + m[8] * z;
1470 m[13] += m[1] * x + m[5] * y + m[9] * z;
1471 m[14] += m[2] * x + m[6] * y + m[10] * z;
1472 m[15] += m[3] * x + m[7] * y + m[11] * z;
1473 return m;
1474 };
1475 /*
1476 * Function: M4x4.translate
1477 */
1478 M4x4.translate = function M4x4_translate (v, m, r) {
1479 //MathUtils_assert(v.length == 3, "v.length == 3");
1480 //MathUtils_assert(m.length == 16, "m.length == 16");
1481 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1482 var x=v[0], y=v[1], z=v[2];
1483 if (r == m) {
1484 m[12] += m[0] * x + m[4] * y + m[8] * z;
1485 m[13] += m[1] * x + m[5] * y + m[9] * z;
1486 m[14] += m[2] * x + m[6] * y + m[10] * z;
1487 m[15] += m[3] * x + m[7] * y + m[11] * z;
1488 return m;
1491 if (r == undefined)
1492 r = new MJS_FLOAT_ARRAY_TYPE(16);
1494 var m11 = m[0];
1495 var m21 = m[1];
1496 var m31 = m[2];
1497 var m41 = m[3];
1498 var m12 = m[4];
1499 var m22 = m[5];
1500 var m32 = m[6];
1501 var m42 = m[7];
1502 var m13 = m[8];
1503 var m23 = m[9];
1504 var m33 = m[10];
1505 var m43 = m[11];
1507 r[0] = m11;
1508 r[1] = m21;
1509 r[2] = m31;
1510 r[3] = m41;
1511 r[4] = m12;
1512 r[5] = m22;
1513 r[6] = m32;
1514 r[7] = m42;
1515 r[8] = m13;
1516 r[9] = m23;
1517 r[10] = m33;
1518 r[11] = m43;
1519 r[12] = m11 * x + m12 * y + m13 * z + m[12];
1520 r[13] = m21 * x + m22 * y + m23 * z + m[13];
1521 r[14] = m31 * x + m32 * y + m33 * z + m[14];
1522 r[15] = m41 * x + m42 * y + m43 * z + m[15];
1524 return r;
1525 };
1527 /*
1528 * Function: M4x4.makeLookAt
1529 */
1530 M4x4.makeLookAt = function M4x4_makeLookAt (eye, center, up, r) {
1531 //MathUtils_assert(eye.length == 3, "eye.length == 3");
1532 //MathUtils_assert(center.length == 3, "center.length == 3");
1533 //MathUtils_assert(up.length == 3, "up.length == 3");
1534 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1536 var z = V3.direction(eye, center, V3._temp1);
1537 var x = V3.normalize(V3.cross(up, z, V3._temp2), V3._temp2);
1538 var y = V3.normalize(V3.cross(z, x, V3._temp3), V3._temp3);
1540 var tm1 = M4x4._temp1;
1541 var tm2 = M4x4._temp2;
1543 tm1[0] = x[0];
1544 tm1[1] = y[0];
1545 tm1[2] = z[0];
1546 tm1[3] = 0;
1547 tm1[4] = x[1];
1548 tm1[5] = y[1];
1549 tm1[6] = z[1];
1550 tm1[7] = 0;
1551 tm1[8] = x[2];
1552 tm1[9] = y[2];
1553 tm1[10] = z[2];
1554 tm1[11] = 0;
1555 tm1[12] = 0;
1556 tm1[13] = 0;
1557 tm1[14] = 0;
1558 tm1[15] = 1;
1560 tm2[0] = 1; tm2[1] = 0; tm2[2] = 0; tm2[3] = 0;
1561 tm2[4] = 0; tm2[5] = 1; tm2[6] = 0; tm2[7] = 0;
1562 tm2[8] = 0; tm2[9] = 0; tm2[10] = 1; tm2[11] = 0;
1563 tm2[12] = -eye[0]; tm2[13] = -eye[1]; tm2[14] = -eye[2]; tm2[15] = 1;
1565 if (r == undefined)
1566 r = new MJS_FLOAT_ARRAY_TYPE(16);
1567 return M4x4.mul(tm1, tm2, r);
1568 };
1570 /*
1571 * Function: M4x4.transposeSelf
1572 */
1573 M4x4.transposeSelf = function M4x4_transposeSelf (m) {
1574 //MathUtils_assert(m.length == 16, "m.length == 16");
1575 var tmp = m[1]; m[1] = m[4]; m[4] = tmp;
1576 tmp = m[2]; m[2] = m[8]; m[8] = tmp;
1577 tmp = m[3]; m[3] = m[12]; m[12] = tmp;
1578 tmp = m[6]; m[6] = m[9]; m[9] = tmp;
1579 tmp = m[7]; m[7] = m[13]; m[13] = tmp;
1580 tmp = m[11]; m[11] = m[14]; m[14] = tmp;
1581 return m;
1582 };
1583 /*
1584 * Function: M4x4.transpose
1585 */
1586 M4x4.transpose = function M4x4_transpose (m, r) {
1587 //MathUtils_assert(m.length == 16, "m.length == 16");
1588 //MathUtils_assert(r == undefined || r.length == 16, "r == undefined || r.length == 16");
1590 if (m == r) {
1591 var tmp = 0.0;
1592 tmp = m[1]; m[1] = m[4]; m[4] = tmp;
1593 tmp = m[2]; m[2] = m[8]; m[8] = tmp;
1594 tmp = m[3]; m[3] = m[12]; m[12] = tmp;
1595 tmp = m[6]; m[6] = m[9]; m[9] = tmp;
1596 tmp = m[7]; m[7] = m[13]; m[13] = tmp;
1597 tmp = m[11]; m[11] = m[14]; m[14] = tmp;
1598 return m;
1601 if (r == undefined)
1602 r = new MJS_FLOAT_ARRAY_TYPE(16);
1604 r[0] = m[0]; r[1] = m[4]; r[2] = m[8]; r[3] = m[12];
1605 r[4] = m[1]; r[5] = m[5]; r[6] = m[9]; r[7] = m[13];
1606 r[8] = m[2]; r[9] = m[6]; r[10] = m[10]; r[11] = m[14];
1607 r[12] = m[3]; r[13] = m[7]; r[14] = m[11]; r[15] = m[15];
1609 return r;
1610 };
1613 /*
1614 * Function: M4x4.transformPoint
1615 */
1616 M4x4.transformPoint = function M4x4_transformPoint (m, v, r) {
1617 //MathUtils_assert(m.length == 16, "m.length == 16");
1618 //MathUtils_assert(v.length == 3, "v.length == 3");
1619 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1620 if (r == undefined)
1621 r = new MJS_FLOAT_ARRAY_TYPE(3);
1623 var v0 = v[0], v1 = v[1], v2 = v[2];
1625 r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2 + m[12];
1626 r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2 + m[13];
1627 r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2 + m[14];
1628 var w = m[3] * v0 + m[7] * v1 + m[11] * v2 + m[15];
1630 if (w != 1.0) {
1631 r[0] /= w;
1632 r[1] /= w;
1633 r[2] /= w;
1636 return r;
1637 };
1639 /*
1640 * Function: M4x4.transformLine
1641 */
1642 M4x4.transformLine = function M4x4_transformLine(m, v, r) {
1643 //MathUtils_assert(m.length == 16, "m.length == 16");
1644 //MathUtils_assert(v.length == 3, "v.length == 3");
1645 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1646 if (r == undefined)
1647 r = new MJS_FLOAT_ARRAY_TYPE(3);
1649 var v0 = v[0], v1 = v[1], v2 = v[2];
1650 r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2;
1651 r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2;
1652 r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2;
1653 var w = m[3] * v0 + m[7] * v1 + m[11] * v2;
1655 if (w != 1.0) {
1656 r[0] /= w;
1657 r[1] /= w;
1658 r[2] /= w;
1661 return r;
1662 };
1665 /*
1666 * Function: M4x4.transformPointAffine
1667 */
1668 M4x4.transformPointAffine = function M4x4_transformPointAffine (m, v, r) {
1669 //MathUtils_assert(m.length == 16, "m.length == 16");
1670 //MathUtils_assert(v.length == 3, "v.length == 3");
1671 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1672 if (r == undefined)
1673 r = new MJS_FLOAT_ARRAY_TYPE(3);
1675 var v0 = v[0], v1 = v[1], v2 = v[2];
1677 r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2 + m[12];
1678 r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2 + m[13];
1679 r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2 + m[14];
1681 return r;
1682 };
1684 /*
1685 * Function: M4x4.transformLineAffine
1686 */
1687 M4x4.transformLineAffine = function M4x4_transformLineAffine(m, v, r) {
1688 //MathUtils_assert(m.length == 16, "m.length == 16");
1689 //MathUtils_assert(v.length == 3, "v.length == 3");
1690 //MathUtils_assert(r == undefined || r.length == 3, "r == undefined || r.length == 3");
1691 if (r == undefined)
1692 r = new MJS_FLOAT_ARRAY_TYPE(3);
1694 var v0 = v[0], v1 = v[1], v2 = v[2];
1695 r[0] = m[0] * v0 + m[4] * v1 + m[8] * v2;
1696 r[1] = m[1] * v0 + m[5] * v1 + m[9] * v2;
1697 r[2] = m[2] * v0 + m[6] * v1 + m[10] * v2;
1699 return r;
1700 };
1702 M4x4.makeBasis = function M4x4_makeBasis(vx,vy,vz) {
1704 var r = new MJS_FLOAT_ARRAY_TYPE(16);
1706 r[0] = vx[0];
1707 r[1] = vx[1];
1708 r[2] = vx[2];
1709 r[3] = 0;
1710 r[4] = vy[0];
1711 r[5] = vy[1];
1712 r[6] = vy[2];
1713 r[7] = 0;
1714 r[8] = vz[0];
1715 r[9] = vz[1];
1716 r[10] = vz[2];
1717 r[11] = 0;
1718 r[12] = 0;
1719 r[13] = 0;
1720 r[14] = 0;
1721 r[15] = 1;
1723 return r;
1725 };
1727 return {
1728 V3: V3,
1729 v3: F3(V3.$),
1730 v3add: F2(V3.add),
1731 v3sub: F2(V3.sub),
1732 v3neg: V3.neg,
1733 v3direction: F2(V3.direction),
1734 v3length: V3.length,
1735 v3lengthSquared: V3.lengthSquared,
1736 v3normalize: V3.normalize,
1737 v3scale: F2(V3.scale),
1738 v3dot: F2(V3.dot),
1739 v3cross: F2(V3.cross),
1740 v3mul4x4: F2(V3.mul4x4),
1741 M4x4:M4x4,
1742 m4x4identity: M4x4.identity,
1743 m4x4topLeft3x3: M4x4.topLeft3x3,
1744 m4x4inverseOrthonormal: M4x4.inverseOrthonormal,
1745 m4x4inverseTo3x3: M4x4.inverseTo3x3,
1746 m4x4makeFrustum: F6(M4x4.makeFrustum),
1747 m4x4makePerspective: F4(M4x4.makePerspective),
1748 m4x4makeOrtho: F6(M4x4.makeOrtho),
1749 m4x4makeOrtho2D: F4(M4x4.makeOrtho2D),
1750 m4x4mul: F2(M4x4.mul),
1751 m4x4Affine: F2(M4x4.mulAffine),
1752 m4x4makeRotate: F2(M4x4.makeRotate),
1753 m4x4rotate: F3(M4x4.rotate),
1754 m4x4makeScale3: F3(M4x4.makeScale3),
1755 m4x4makeScale1: M4x4.makeScale1,
1756 m4x4makeScale: M4x4.makeScale,
1757 m4x4scale3: F4(M4x4.scale3),
1758 m4x4scale: F2(M4x4.scale),
1759 m4x4makeTranslate3: F3(M4x4.makeTranslate3),
1760 m4x4makeTranslate: M4x4.makeTranslate,
1761 m4x4translate3: F4(M4x4.translate3),
1762 m4x4translate: F2(M4x4.translate),
1763 m4x4makeLookAt: F3(M4x4.makeLookAt),
1764 m4x4transpose: M4x4.transpose,
1765 m4x4transformPoint: F2(M4x4.transformPoint),
1766 m4x4makeBasis: F3(M4x4.makeBasis),
1767 };