1 /*
2 * Copyright 2011 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8 #include "SkMatrix44.h"
9 #include "Test.h"
10
nearly_equal_double(double a,double b)11 static bool nearly_equal_double(double a, double b) {
12 const double tolerance = 1e-7;
13 double diff = a - b;
14 if (diff < 0)
15 diff = -diff;
16 return diff <= tolerance;
17 }
18
nearly_equal_mscalar(SkMScalar a,SkMScalar b)19 static bool nearly_equal_mscalar(SkMScalar a, SkMScalar b) {
20 const SkMScalar tolerance = SK_MScalar1 / 200000;
21
22 return SkTAbs<SkMScalar>(a - b) <= tolerance;
23 }
24
nearly_equal_scalar(SkScalar a,SkScalar b)25 static bool nearly_equal_scalar(SkScalar a, SkScalar b) {
26 const SkScalar tolerance = SK_Scalar1 / 200000;
27 return SkScalarAbs(a - b) <= tolerance;
28 }
29
assert16(skiatest::Reporter * reporter,const T data[],T m0,T m1,T m2,T m3,T m4,T m5,T m6,T m7,T m8,T m9,T m10,T m11,T m12,T m13,T m14,T m15)30 template <typename T> void assert16(skiatest::Reporter* reporter, const T data[],
31 T m0, T m1, T m2, T m3,
32 T m4, T m5, T m6, T m7,
33 T m8, T m9, T m10, T m11,
34 T m12, T m13, T m14, T m15) {
35 REPORTER_ASSERT(reporter, data[0] == m0);
36 REPORTER_ASSERT(reporter, data[1] == m1);
37 REPORTER_ASSERT(reporter, data[2] == m2);
38 REPORTER_ASSERT(reporter, data[3] == m3);
39
40 REPORTER_ASSERT(reporter, data[4] == m4);
41 REPORTER_ASSERT(reporter, data[5] == m5);
42 REPORTER_ASSERT(reporter, data[6] == m6);
43 REPORTER_ASSERT(reporter, data[7] == m7);
44
45 REPORTER_ASSERT(reporter, data[8] == m8);
46 REPORTER_ASSERT(reporter, data[9] == m9);
47 REPORTER_ASSERT(reporter, data[10] == m10);
48 REPORTER_ASSERT(reporter, data[11] == m11);
49
50 REPORTER_ASSERT(reporter, data[12] == m12);
51 REPORTER_ASSERT(reporter, data[13] == m13);
52 REPORTER_ASSERT(reporter, data[14] == m14);
53 REPORTER_ASSERT(reporter, data[15] == m15);
54 }
55
nearly_equal(const SkMatrix44 & a,const SkMatrix44 & b)56 static bool nearly_equal(const SkMatrix44& a, const SkMatrix44& b) {
57 for (int i = 0; i < 4; ++i) {
58 for (int j = 0; j < 4; ++j) {
59 if (!nearly_equal_mscalar(a.get(i, j), b.get(i, j))) {
60 SkDebugf("not equal %g %g\n", a.get(i, j), b.get(i, j));
61 return false;
62 }
63 }
64 }
65 return true;
66 }
67
is_identity(const SkMatrix44 & m)68 static bool is_identity(const SkMatrix44& m) {
69 SkMatrix44 identity(SkMatrix44::kIdentity_Constructor);
70 return nearly_equal(m, identity);
71 }
72
73 ///////////////////////////////////////////////////////////////////////////////
bits_isonly(int value,int mask)74 static bool bits_isonly(int value, int mask) {
75 return 0 == (value & ~mask);
76 }
77
test_constructor(skiatest::Reporter * reporter)78 static void test_constructor(skiatest::Reporter* reporter) {
79 // Allocate a matrix on the heap
80 SkMatrix44* placeholderMatrix = new SkMatrix44(SkMatrix44::kUninitialized_Constructor);
81 SkAutoTDelete<SkMatrix44> deleteMe(placeholderMatrix);
82
83 for (int row = 0; row < 4; ++row) {
84 for (int col = 0; col < 4; ++col) {
85 placeholderMatrix->setDouble(row, col, row * col);
86 }
87 }
88
89 // Use placement-new syntax to trigger the constructor on top of the heap
90 // address we already initialized. This allows us to check that the
91 // constructor did avoid initializing the matrix contents.
92 SkMatrix44* testMatrix = new(placeholderMatrix) SkMatrix44(SkMatrix44::kUninitialized_Constructor);
93 REPORTER_ASSERT(reporter, testMatrix == placeholderMatrix);
94 REPORTER_ASSERT(reporter, !testMatrix->isIdentity());
95 for (int row = 0; row < 4; ++row) {
96 for (int col = 0; col < 4; ++col) {
97 REPORTER_ASSERT(reporter, nearly_equal_double(row * col, testMatrix->getDouble(row, col)));
98 }
99 }
100
101 // Verify that kIdentity_Constructor really does initialize to an identity matrix.
102 testMatrix = 0;
103 testMatrix = new(placeholderMatrix) SkMatrix44(SkMatrix44::kIdentity_Constructor);
104 REPORTER_ASSERT(reporter, testMatrix == placeholderMatrix);
105 REPORTER_ASSERT(reporter, testMatrix->isIdentity());
106 REPORTER_ASSERT(reporter, *testMatrix == SkMatrix44::I());
107
108 // Verify that that constructing from an SkMatrix initializes everything.
109 SkMatrix44 scaleMatrix(SkMatrix44::kUninitialized_Constructor);
110 scaleMatrix.setScale(3, 4, 5);
111 REPORTER_ASSERT(reporter, scaleMatrix.isScale());
112 testMatrix = new(&scaleMatrix) SkMatrix44(SkMatrix::I());
113 REPORTER_ASSERT(reporter, testMatrix->isIdentity());
114 REPORTER_ASSERT(reporter, *testMatrix == SkMatrix44::I());
115 }
116
test_translate(skiatest::Reporter * reporter)117 static void test_translate(skiatest::Reporter* reporter) {
118 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
119 SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor);
120
121 mat.setTranslate(0, 0, 0);
122 REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kIdentity_Mask));
123 mat.setTranslate(1, 2, 3);
124 REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kTranslate_Mask));
125 REPORTER_ASSERT(reporter, mat.invert(&inverse));
126 REPORTER_ASSERT(reporter, bits_isonly(inverse.getType(), SkMatrix44::kTranslate_Mask));
127
128 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
129 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
130 SkMatrix44 c(SkMatrix44::kUninitialized_Constructor);
131 a.set3x3(1, 2, 3, 4, 5, 6, 7, 8, 9);
132 b.setTranslate(10, 11, 12);
133
134 c.setConcat(a, b);
135 mat = a;
136 mat.preTranslate(10, 11, 12);
137 REPORTER_ASSERT(reporter, mat == c);
138
139 c.setConcat(b, a);
140 mat = a;
141 mat.postTranslate(10, 11, 12);
142 REPORTER_ASSERT(reporter, mat == c);
143 }
144
test_scale(skiatest::Reporter * reporter)145 static void test_scale(skiatest::Reporter* reporter) {
146 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
147 SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor);
148
149 mat.setScale(1, 1, 1);
150 REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kIdentity_Mask));
151 mat.setScale(1, 2, 3);
152 REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kScale_Mask));
153 REPORTER_ASSERT(reporter, mat.invert(&inverse));
154 REPORTER_ASSERT(reporter, bits_isonly(inverse.getType(), SkMatrix44::kScale_Mask));
155
156 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
157 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
158 SkMatrix44 c(SkMatrix44::kUninitialized_Constructor);
159 a.set3x3(1, 2, 3, 4, 5, 6, 7, 8, 9);
160 b.setScale(10, 11, 12);
161
162 c.setConcat(a, b);
163 mat = a;
164 mat.preScale(10, 11, 12);
165 REPORTER_ASSERT(reporter, mat == c);
166
167 c.setConcat(b, a);
168 mat = a;
169 mat.postScale(10, 11, 12);
170 REPORTER_ASSERT(reporter, mat == c);
171 }
172
make_i(SkMatrix44 * mat)173 static void make_i(SkMatrix44* mat) { mat->setIdentity(); }
make_t(SkMatrix44 * mat)174 static void make_t(SkMatrix44* mat) { mat->setTranslate(1, 2, 3); }
make_s(SkMatrix44 * mat)175 static void make_s(SkMatrix44* mat) { mat->setScale(1, 2, 3); }
make_st(SkMatrix44 * mat)176 static void make_st(SkMatrix44* mat) {
177 mat->setScale(1, 2, 3);
178 mat->postTranslate(1, 2, 3);
179 }
make_a(SkMatrix44 * mat)180 static void make_a(SkMatrix44* mat) {
181 mat->setRotateDegreesAbout(1, 2, 3, 45);
182 }
make_p(SkMatrix44 * mat)183 static void make_p(SkMatrix44* mat) {
184 SkMScalar data[] = {
185 1, 2, 3, 4, 5, 6, 7, 8,
186 1, 2, 3, 4, 5, 6, 7, 8,
187 };
188 mat->setRowMajor(data);
189 }
190
191 typedef void (*Make44Proc)(SkMatrix44*);
192
193 static const Make44Proc gMakeProcs[] = {
194 make_i, make_t, make_s, make_st, make_a, make_p
195 };
196
test_map2(skiatest::Reporter * reporter,const SkMatrix44 & mat)197 static void test_map2(skiatest::Reporter* reporter, const SkMatrix44& mat) {
198 SkMScalar src2[] = { 1, 2 };
199 SkMScalar src4[] = { src2[0], src2[1], 0, 1 };
200 SkMScalar dstA[4], dstB[4];
201
202 for (int i = 0; i < 4; ++i) {
203 dstA[i] = SkDoubleToMScalar(123456789);
204 dstB[i] = SkDoubleToMScalar(987654321);
205 }
206
207 mat.map2(src2, 1, dstA);
208 mat.mapMScalars(src4, dstB);
209
210 for (int i = 0; i < 4; ++i) {
211 REPORTER_ASSERT(reporter, dstA[i] == dstB[i]);
212 }
213 }
214
test_map2(skiatest::Reporter * reporter)215 static void test_map2(skiatest::Reporter* reporter) {
216 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
217
218 for (size_t i = 0; i < SK_ARRAY_COUNT(gMakeProcs); ++i) {
219 gMakeProcs[i](&mat);
220 test_map2(reporter, mat);
221 }
222 }
223
test_gettype(skiatest::Reporter * reporter)224 static void test_gettype(skiatest::Reporter* reporter) {
225 SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
226
227 REPORTER_ASSERT(reporter, matrix.isIdentity());
228 REPORTER_ASSERT(reporter, SkMatrix44::kIdentity_Mask == matrix.getType());
229
230 int expectedMask;
231
232 matrix.set(1, 1, 0);
233 expectedMask = SkMatrix44::kScale_Mask;
234 REPORTER_ASSERT(reporter, matrix.getType() == expectedMask);
235
236 matrix.set(0, 3, 1); // translate-x
237 expectedMask |= SkMatrix44::kTranslate_Mask;
238 REPORTER_ASSERT(reporter, matrix.getType() == expectedMask);
239
240 matrix.set(2, 0, 1);
241 expectedMask |= SkMatrix44::kAffine_Mask;
242 REPORTER_ASSERT(reporter, matrix.getType() == expectedMask);
243
244 matrix.set(3, 2, 1);
245 REPORTER_ASSERT(reporter, matrix.getType() & SkMatrix44::kPerspective_Mask);
246
247 // ensure that negative zero is treated as zero
248 SkMScalar dx = 0;
249 SkMScalar dy = 0;
250 SkMScalar dz = 0;
251 matrix.setTranslate(-dx, -dy, -dz);
252 REPORTER_ASSERT(reporter, matrix.isIdentity());
253 matrix.preTranslate(-dx, -dy, -dz);
254 REPORTER_ASSERT(reporter, matrix.isIdentity());
255 matrix.postTranslate(-dx, -dy, -dz);
256 REPORTER_ASSERT(reporter, matrix.isIdentity());
257 }
258
test_common_angles(skiatest::Reporter * reporter)259 static void test_common_angles(skiatest::Reporter* reporter) {
260 SkMatrix44 rot(SkMatrix44::kUninitialized_Constructor);
261 // Test precision of rotation in common cases
262 int common_angles[] = { 0, 90, -90, 180, -180, 270, -270, 360, -360 };
263 for (int i = 0; i < 9; ++i) {
264 rot.setRotateDegreesAbout(0, 0, -1, SkIntToScalar(common_angles[i]));
265
266 SkMatrix rot3x3 = rot;
267 REPORTER_ASSERT(reporter, rot3x3.rectStaysRect());
268 }
269 }
270
test_concat(skiatest::Reporter * reporter)271 static void test_concat(skiatest::Reporter* reporter) {
272 int i;
273 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
274 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
275 SkMatrix44 c(SkMatrix44::kUninitialized_Constructor);
276 SkMatrix44 d(SkMatrix44::kUninitialized_Constructor);
277
278 a.setTranslate(10, 10, 10);
279 b.setScale(2, 2, 2);
280
281 SkScalar src[8] = {
282 0, 0, 0, 1,
283 1, 1, 1, 1
284 };
285 SkScalar dst[8];
286
287 c.setConcat(a, b);
288
289 d = a;
290 d.preConcat(b);
291 REPORTER_ASSERT(reporter, d == c);
292
293 c.mapScalars(src, dst); c.mapScalars(src + 4, dst + 4);
294 for (i = 0; i < 3; ++i) {
295 REPORTER_ASSERT(reporter, 10 == dst[i]);
296 REPORTER_ASSERT(reporter, 12 == dst[i + 4]);
297 }
298
299 c.setConcat(b, a);
300
301 d = a;
302 d.postConcat(b);
303 REPORTER_ASSERT(reporter, d == c);
304
305 c.mapScalars(src, dst); c.mapScalars(src + 4, dst + 4);
306 for (i = 0; i < 3; ++i) {
307 REPORTER_ASSERT(reporter, 20 == dst[i]);
308 REPORTER_ASSERT(reporter, 22 == dst[i + 4]);
309 }
310 }
311
test_determinant(skiatest::Reporter * reporter)312 static void test_determinant(skiatest::Reporter* reporter) {
313 SkMatrix44 a(SkMatrix44::kIdentity_Constructor);
314 REPORTER_ASSERT(reporter, nearly_equal_double(1, a.determinant()));
315 a.set(1, 1, 2);
316 REPORTER_ASSERT(reporter, nearly_equal_double(2, a.determinant()));
317 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
318 REPORTER_ASSERT(reporter, a.invert(&b));
319 REPORTER_ASSERT(reporter, nearly_equal_double(0.5, b.determinant()));
320 SkMatrix44 c = b = a;
321 c.set(0, 1, 4);
322 b.set(1, 0, 4);
323 REPORTER_ASSERT(reporter,
324 nearly_equal_double(a.determinant(),
325 b.determinant()));
326 SkMatrix44 d = a;
327 d.set(0, 0, 8);
328 REPORTER_ASSERT(reporter, nearly_equal_double(16, d.determinant()));
329
330 SkMatrix44 e = a;
331 e.postConcat(d);
332 REPORTER_ASSERT(reporter, nearly_equal_double(32, e.determinant()));
333 e.set(0, 0, 0);
334 REPORTER_ASSERT(reporter, nearly_equal_double(0, e.determinant()));
335 }
336
test_invert(skiatest::Reporter * reporter)337 static void test_invert(skiatest::Reporter* reporter) {
338 SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor);
339 double inverseData[16];
340
341 SkMatrix44 identity(SkMatrix44::kIdentity_Constructor);
342 identity.invert(&inverse);
343 inverse.asRowMajord(inverseData);
344 assert16<double>(reporter, inverseData,
345 1, 0, 0, 0,
346 0, 1, 0, 0,
347 0, 0, 1, 0,
348 0, 0, 0, 1);
349
350 SkMatrix44 translation(SkMatrix44::kUninitialized_Constructor);
351 translation.setTranslate(2, 3, 4);
352 translation.invert(&inverse);
353 inverse.asRowMajord(inverseData);
354 assert16<double>(reporter, inverseData,
355 1, 0, 0, -2,
356 0, 1, 0, -3,
357 0, 0, 1, -4,
358 0, 0, 0, 1);
359
360 SkMatrix44 scale(SkMatrix44::kUninitialized_Constructor);
361 scale.setScale(2, 4, 8);
362 scale.invert(&inverse);
363 inverse.asRowMajord(inverseData);
364 assert16<double>(reporter, inverseData,
365 0.5, 0, 0, 0,
366 0, 0.25, 0, 0,
367 0, 0, 0.125, 0,
368 0, 0, 0, 1);
369
370 SkMatrix44 scaleTranslation(SkMatrix44::kUninitialized_Constructor);
371 scaleTranslation.setScale(32, 128, 1024);
372 scaleTranslation.preTranslate(2, 3, 4);
373 scaleTranslation.invert(&inverse);
374 inverse.asRowMajord(inverseData);
375 assert16<double>(reporter, inverseData,
376 0.03125, 0, 0, -2,
377 0, 0.0078125, 0, -3,
378 0, 0, 0.0009765625, -4,
379 0, 0, 0, 1);
380
381 SkMatrix44 rotation(SkMatrix44::kUninitialized_Constructor);
382 rotation.setRotateDegreesAbout(0, 0, 1, 90);
383 rotation.invert(&inverse);
384 SkMatrix44 expected(SkMatrix44::kUninitialized_Constructor);
385 double expectedInverseRotation[16] =
386 {0, 1, 0, 0,
387 -1, 0, 0, 0,
388 0, 0, 1, 0,
389 0, 0, 0, 1};
390 expected.setRowMajord(expectedInverseRotation);
391 REPORTER_ASSERT(reporter, nearly_equal(expected, inverse));
392
393 SkMatrix44 affine(SkMatrix44::kUninitialized_Constructor);
394 affine.setRotateDegreesAbout(0, 0, 1, 90);
395 affine.preScale(10, 20, 100);
396 affine.preTranslate(2, 3, 4);
397 affine.invert(&inverse);
398 double expectedInverseAffine[16] =
399 {0, 0.1, 0, -2,
400 -0.05, 0, 0, -3,
401 0, 0, 0.01, -4,
402 0, 0, 0, 1};
403 expected.setRowMajord(expectedInverseAffine);
404 REPORTER_ASSERT(reporter, nearly_equal(expected, inverse));
405
406 SkMatrix44 perspective(SkMatrix44::kIdentity_Constructor);
407 perspective.setDouble(3, 2, 1.0);
408 perspective.invert(&inverse);
409 double expectedInversePerspective[16] =
410 {1, 0, 0, 0,
411 0, 1, 0, 0,
412 0, 0, 1, 0,
413 0, 0, -1, 1};
414 expected.setRowMajord(expectedInversePerspective);
415 REPORTER_ASSERT(reporter, nearly_equal(expected, inverse));
416
417 SkMatrix44 affineAndPerspective(SkMatrix44::kIdentity_Constructor);
418 affineAndPerspective.setDouble(3, 2, 1.0);
419 affineAndPerspective.preScale(10, 20, 100);
420 affineAndPerspective.preTranslate(2, 3, 4);
421 affineAndPerspective.invert(&inverse);
422 double expectedInverseAffineAndPerspective[16] =
423 {0.1, 0, 2, -2,
424 0, 0.05, 3, -3,
425 0, 0, 4.01, -4,
426 0, 0, -1, 1};
427 expected.setRowMajord(expectedInverseAffineAndPerspective);
428 REPORTER_ASSERT(reporter, nearly_equal(expected, inverse));
429
430 SkMatrix44 tinyScale(SkMatrix44::kIdentity_Constructor);
431 tinyScale.setDouble(0, 0, 1e-39);
432 REPORTER_ASSERT(reporter, tinyScale.getType() == SkMatrix44::kScale_Mask);
433 REPORTER_ASSERT(reporter, !tinyScale.invert(nullptr));
434 REPORTER_ASSERT(reporter, !tinyScale.invert(&inverse));
435
436 SkMatrix44 tinyScaleTranslate(SkMatrix44::kIdentity_Constructor);
437 tinyScaleTranslate.setDouble(0, 0, 1e-38);
438 REPORTER_ASSERT(reporter, tinyScaleTranslate.invert(nullptr));
439 tinyScaleTranslate.setDouble(0, 3, 10);
440 REPORTER_ASSERT(
441 reporter, tinyScaleTranslate.getType() ==
442 (SkMatrix44::kScale_Mask | SkMatrix44::kTranslate_Mask));
443 REPORTER_ASSERT(reporter, !tinyScaleTranslate.invert(nullptr));
444 REPORTER_ASSERT(reporter, !tinyScaleTranslate.invert(&inverse));
445
446 SkMatrix44 tinyScalePerspective(SkMatrix44::kIdentity_Constructor);
447 tinyScalePerspective.setDouble(0, 0, 1e-39);
448 tinyScalePerspective.setDouble(3, 2, -1);
449 REPORTER_ASSERT(reporter, (tinyScalePerspective.getType() &
450 SkMatrix44::kPerspective_Mask) ==
451 SkMatrix44::kPerspective_Mask);
452 REPORTER_ASSERT(reporter, !tinyScalePerspective.invert(nullptr));
453 REPORTER_ASSERT(reporter, !tinyScalePerspective.invert(&inverse));
454 }
455
test_transpose(skiatest::Reporter * reporter)456 static void test_transpose(skiatest::Reporter* reporter) {
457 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
458 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
459
460 int i = 0;
461 for (int row = 0; row < 4; ++row) {
462 for (int col = 0; col < 4; ++col) {
463 a.setDouble(row, col, i);
464 b.setDouble(col, row, i++);
465 }
466 }
467
468 a.transpose();
469 REPORTER_ASSERT(reporter, nearly_equal(a, b));
470 }
471
test_get_set_double(skiatest::Reporter * reporter)472 static void test_get_set_double(skiatest::Reporter* reporter) {
473 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
474 for (int row = 0; row < 4; ++row) {
475 for (int col = 0; col < 4; ++col) {
476 a.setDouble(row, col, 3.141592653589793);
477 REPORTER_ASSERT(reporter,
478 nearly_equal_double(3.141592653589793,
479 a.getDouble(row, col)));
480 a.setDouble(row, col, 0);
481 REPORTER_ASSERT(reporter,
482 nearly_equal_double(0, a.getDouble(row, col)));
483 }
484 }
485 }
486
test_set_row_col_major(skiatest::Reporter * reporter)487 static void test_set_row_col_major(skiatest::Reporter* reporter) {
488 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
489 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
490
491 for (int row = 0; row < 4; ++row) {
492 for (int col = 0; col < 4; ++col) {
493 a.setDouble(row, col, row * 4 + col);
494 }
495 }
496
497 double bufferd[16];
498 float bufferf[16];
499 a.asColMajord(bufferd);
500 b.setColMajord(bufferd);
501 REPORTER_ASSERT(reporter, nearly_equal(a, b));
502 b.setRowMajord(bufferd);
503 b.transpose();
504 REPORTER_ASSERT(reporter, nearly_equal(a, b));
505 a.asColMajorf(bufferf);
506 b.setColMajorf(bufferf);
507 REPORTER_ASSERT(reporter, nearly_equal(a, b));
508 b.setRowMajorf(bufferf);
509 b.transpose();
510 REPORTER_ASSERT(reporter, nearly_equal(a, b));
511 }
512
test_3x3_conversion(skiatest::Reporter * reporter)513 static void test_3x3_conversion(skiatest::Reporter* reporter) {
514 SkMScalar values4x4[16] = { 1, 2, 3, 4,
515 5, 6, 7, 8,
516 9, 10, 11, 12,
517 13, 14, 15, 16 };
518 SkScalar values3x3[9] = { 1, 2, 4,
519 5, 6, 8,
520 13, 14, 16 };
521 SkMScalar values4x4flattened[16] = { 1, 2, 0, 4,
522 5, 6, 0, 8,
523 0, 0, 1, 0,
524 13, 14, 0, 16 };
525 SkMatrix44 a44(SkMatrix44::kUninitialized_Constructor);
526 a44.setRowMajor(values4x4);
527
528 SkMatrix a33 = a44;
529 SkMatrix expected33;
530 for (int i = 0; i < 9; i++) expected33[i] = values3x3[i];
531 REPORTER_ASSERT(reporter, expected33 == a33);
532
533 SkMatrix44 a44flattened = a33;
534 SkMatrix44 expected44flattened(SkMatrix44::kUninitialized_Constructor);
535 expected44flattened.setRowMajor(values4x4flattened);
536 REPORTER_ASSERT(reporter, nearly_equal(a44flattened, expected44flattened));
537
538 // Test that a point with a Z value of 0 is transformed the same way.
539 SkScalar vec4[4] = { 2, 4, 0, 8 };
540 SkScalar vec3[3] = { 2, 4, 8 };
541
542 SkScalar vec4transformed[4];
543 SkScalar vec3transformed[3];
544 SkScalar vec4transformed2[4];
545 a44.mapScalars(vec4, vec4transformed);
546 a33.mapHomogeneousPoints(vec3transformed, vec3, 1);
547 a44flattened.mapScalars(vec4, vec4transformed2);
548 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[0], vec3transformed[0]));
549 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[1], vec3transformed[1]));
550 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[3], vec3transformed[2]));
551 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[0], vec4transformed2[0]));
552 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[1], vec4transformed2[1]));
553 REPORTER_ASSERT(reporter, !nearly_equal_scalar(vec4transformed[2], vec4transformed2[2]));
554 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[3], vec4transformed2[3]));
555 }
556
test_has_perspective(skiatest::Reporter * reporter)557 static void test_has_perspective(skiatest::Reporter* reporter) {
558 SkMatrix44 transform(SkMatrix44::kIdentity_Constructor);
559
560 transform.setDouble(3, 2, -0.1);
561 REPORTER_ASSERT(reporter, transform.hasPerspective());
562
563 transform.reset();
564 REPORTER_ASSERT(reporter, !transform.hasPerspective());
565
566 transform.setDouble(3, 0, -1.0);
567 REPORTER_ASSERT(reporter, transform.hasPerspective());
568
569 transform.reset();
570 transform.setDouble(3, 1, -1.0);
571 REPORTER_ASSERT(reporter, transform.hasPerspective());
572
573 transform.reset();
574 transform.setDouble(3, 2, -0.3);
575 REPORTER_ASSERT(reporter, transform.hasPerspective());
576
577 transform.reset();
578 transform.setDouble(3, 3, 0.5);
579 REPORTER_ASSERT(reporter, transform.hasPerspective());
580
581 transform.reset();
582 transform.setDouble(3, 3, 0.0);
583 REPORTER_ASSERT(reporter, transform.hasPerspective());
584 }
585
is_rectilinear(SkVector4 & p1,SkVector4 & p2,SkVector4 & p3,SkVector4 & p4)586 static bool is_rectilinear (SkVector4& p1, SkVector4& p2, SkVector4& p3, SkVector4& p4) {
587 return (SkScalarNearlyEqual(p1.fData[0], p2.fData[0]) &&
588 SkScalarNearlyEqual(p2.fData[1], p3.fData[1]) &&
589 SkScalarNearlyEqual(p3.fData[0], p4.fData[0]) &&
590 SkScalarNearlyEqual(p4.fData[1], p1.fData[1])) ||
591 (SkScalarNearlyEqual(p1.fData[1], p2.fData[1]) &&
592 SkScalarNearlyEqual(p2.fData[0], p3.fData[0]) &&
593 SkScalarNearlyEqual(p3.fData[1], p4.fData[1]) &&
594 SkScalarNearlyEqual(p4.fData[0], p1.fData[0]));
595 }
596
mul_with_persp_divide(const SkMatrix44 & transform,const SkVector4 & target)597 static SkVector4 mul_with_persp_divide(const SkMatrix44& transform, const SkVector4& target) {
598 SkVector4 result = transform * target;
599 if (result.fData[3] != 0.0f && result.fData[3] != SK_Scalar1) {
600 float wInverse = SK_Scalar1 / result.fData[3];
601 result.set(result.fData[0] * wInverse,
602 result.fData[1] * wInverse,
603 result.fData[2] * wInverse,
604 SK_Scalar1);
605 }
606 return result;
607 }
608
empirically_preserves_2d_axis_alignment(skiatest::Reporter * reporter,const SkMatrix44 & transform)609 static bool empirically_preserves_2d_axis_alignment(skiatest::Reporter* reporter,
610 const SkMatrix44& transform) {
611 SkVector4 p1(5.0f, 5.0f, 0.0f);
612 SkVector4 p2(10.0f, 5.0f, 0.0f);
613 SkVector4 p3(10.0f, 20.0f, 0.0f);
614 SkVector4 p4(5.0f, 20.0f, 0.0f);
615
616 REPORTER_ASSERT(reporter, is_rectilinear(p1, p2, p3, p4));
617
618 p1 = mul_with_persp_divide(transform, p1);
619 p2 = mul_with_persp_divide(transform, p2);
620 p3 = mul_with_persp_divide(transform, p3);
621 p4 = mul_with_persp_divide(transform, p4);
622
623 return is_rectilinear(p1, p2, p3, p4);
624 }
625
test(bool expected,skiatest::Reporter * reporter,const SkMatrix44 & transform)626 static void test(bool expected, skiatest::Reporter* reporter, const SkMatrix44& transform) {
627 if (expected) {
628 REPORTER_ASSERT(reporter, empirically_preserves_2d_axis_alignment(reporter, transform));
629 REPORTER_ASSERT(reporter, transform.preserves2dAxisAlignment());
630 } else {
631 REPORTER_ASSERT(reporter, !empirically_preserves_2d_axis_alignment(reporter, transform));
632 REPORTER_ASSERT(reporter, !transform.preserves2dAxisAlignment());
633 }
634 }
635
test_preserves_2d_axis_alignment(skiatest::Reporter * reporter)636 static void test_preserves_2d_axis_alignment(skiatest::Reporter* reporter) {
637 SkMatrix44 transform(SkMatrix44::kUninitialized_Constructor);
638 SkMatrix44 transform2(SkMatrix44::kUninitialized_Constructor);
639
640 static const struct TestCase {
641 SkMScalar a; // row 1, column 1
642 SkMScalar b; // row 1, column 2
643 SkMScalar c; // row 2, column 1
644 SkMScalar d; // row 2, column 2
645 bool expected;
646 } test_cases[] = {
647 { 3.f, 0.f,
648 0.f, 4.f, true }, // basic case
649 { 0.f, 4.f,
650 3.f, 0.f, true }, // rotate by 90
651 { 0.f, 0.f,
652 0.f, 4.f, true }, // degenerate x
653 { 3.f, 0.f,
654 0.f, 0.f, true }, // degenerate y
655 { 0.f, 0.f,
656 3.f, 0.f, true }, // degenerate x + rotate by 90
657 { 0.f, 4.f,
658 0.f, 0.f, true }, // degenerate y + rotate by 90
659 { 3.f, 4.f,
660 0.f, 0.f, false },
661 { 0.f, 0.f,
662 3.f, 4.f, false },
663 { 0.f, 3.f,
664 0.f, 4.f, false },
665 { 3.f, 0.f,
666 4.f, 0.f, false },
667 { 3.f, 4.f,
668 5.f, 0.f, false },
669 { 3.f, 4.f,
670 0.f, 5.f, false },
671 { 3.f, 0.f,
672 4.f, 5.f, false },
673 { 0.f, 3.f,
674 4.f, 5.f, false },
675 { 2.f, 3.f,
676 4.f, 5.f, false },
677 };
678
679 for (size_t i = 0; i < sizeof(test_cases)/sizeof(TestCase); ++i) {
680 const TestCase& value = test_cases[i];
681 transform.setIdentity();
682 transform.set(0, 0, value.a);
683 transform.set(0, 1, value.b);
684 transform.set(1, 0, value.c);
685 transform.set(1, 1, value.d);
686
687 test(value.expected, reporter, transform);
688 }
689
690 // Try the same test cases again, but this time make sure that other matrix
691 // elements (except perspective) have entries, to test that they are ignored.
692 for (size_t i = 0; i < sizeof(test_cases)/sizeof(TestCase); ++i) {
693 const TestCase& value = test_cases[i];
694 transform.setIdentity();
695 transform.set(0, 0, value.a);
696 transform.set(0, 1, value.b);
697 transform.set(1, 0, value.c);
698 transform.set(1, 1, value.d);
699
700 transform.set(0, 2, 1.f);
701 transform.set(0, 3, 2.f);
702 transform.set(1, 2, 3.f);
703 transform.set(1, 3, 4.f);
704 transform.set(2, 0, 5.f);
705 transform.set(2, 1, 6.f);
706 transform.set(2, 2, 7.f);
707 transform.set(2, 3, 8.f);
708
709 test(value.expected, reporter, transform);
710 }
711
712 // Try the same test cases again, but this time add perspective which is
713 // always assumed to not-preserve axis alignment.
714 for (size_t i = 0; i < sizeof(test_cases)/sizeof(TestCase); ++i) {
715 const TestCase& value = test_cases[i];
716 transform.setIdentity();
717 transform.set(0, 0, value.a);
718 transform.set(0, 1, value.b);
719 transform.set(1, 0, value.c);
720 transform.set(1, 1, value.d);
721
722 transform.set(0, 2, 1.f);
723 transform.set(0, 3, 2.f);
724 transform.set(1, 2, 3.f);
725 transform.set(1, 3, 4.f);
726 transform.set(2, 0, 5.f);
727 transform.set(2, 1, 6.f);
728 transform.set(2, 2, 7.f);
729 transform.set(2, 3, 8.f);
730 transform.set(3, 0, 9.f);
731 transform.set(3, 1, 10.f);
732 transform.set(3, 2, 11.f);
733 transform.set(3, 3, 12.f);
734
735 test(false, reporter, transform);
736 }
737
738 // Try a few more practical situations to check precision
739 // Reuse TestCase (a, b, c, d) as (x, y, z, degrees) axis to rotate about.
740 TestCase rotation_tests[] = {
741 { 0.0, 0.0, 1.0, 90.0, true },
742 { 0.0, 0.0, 1.0, 180.0, true },
743 { 0.0, 0.0, 1.0, 270.0, true },
744 { 0.0, 1.0, 0.0, 90.0, true },
745 { 1.0, 0.0, 0.0, 90.0, true },
746 { 0.0, 0.0, 1.0, 45.0, false },
747 // In 3d these next two are non-preserving, but we're testing in 2d after
748 // orthographic projection, where they are.
749 { 0.0, 1.0, 0.0, 45.0, true },
750 { 1.0, 0.0, 0.0, 45.0, true },
751 };
752
753 for (size_t i = 0; i < sizeof(rotation_tests)/sizeof(TestCase); ++i) {
754 const TestCase& value = rotation_tests[i];
755 transform.setRotateDegreesAbout(value.a, value.b, value.c, value.d);
756 test(value.expected, reporter, transform);
757 }
758
759 static const struct DoubleRotationCase {
760 SkMScalar x1;
761 SkMScalar y1;
762 SkMScalar z1;
763 SkMScalar degrees1;
764 SkMScalar x2;
765 SkMScalar y2;
766 SkMScalar z2;
767 SkMScalar degrees2;
768 bool expected;
769 } double_rotation_tests[] = {
770 { 0.0, 0.0, 1.0, 90.0, 0.0, 1.0, 0.0, 90.0, true },
771 { 0.0, 0.0, 1.0, 90.0, 1.0, 0.0, 0.0, 90.0, true },
772 { 0.0, 1.0, 0.0, 90.0, 0.0, 0.0, 1.0, 90.0, true },
773 };
774
775 for (size_t i = 0; i < sizeof(double_rotation_tests)/sizeof(DoubleRotationCase); ++i) {
776 const DoubleRotationCase& value = double_rotation_tests[i];
777 transform.setRotateDegreesAbout(value.x1, value.y1, value.z1, value.degrees1);
778 transform2.setRotateDegreesAbout(value.x2, value.y2, value.z2, value.degrees2);
779 transform.postConcat(transform2);
780 test(value.expected, reporter, transform);
781 }
782
783 // Perspective cases.
784 transform.setIdentity();
785 transform.setDouble(3, 2, -0.1); // Perspective depth 10
786 transform2.setRotateDegreesAbout(0.0, 1.0, 0.0, 45.0);
787 transform.preConcat(transform2);
788 test(false, reporter, transform);
789
790 transform.setIdentity();
791 transform.setDouble(3, 2, -0.1); // Perspective depth 10
792 transform2.setRotateDegreesAbout(0.0, 0.0, 1.0, 90.0);
793 transform.preConcat(transform2);
794 test(true, reporter, transform);
795 }
796
797 // just want to exercise the various converters for MScalar
test_toint(skiatest::Reporter * reporter)798 static void test_toint(skiatest::Reporter* reporter) {
799 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
800 mat.setScale(3, 3, 3);
801
802 SkMScalar sum = SkMScalarFloor(mat.get(0, 0)) +
803 SkMScalarRound(mat.get(1, 0)) +
804 SkMScalarCeil(mat.get(2, 0));
805 int isum = SkMScalarFloorToInt(mat.get(0, 1)) +
806 SkMScalarRoundToInt(mat.get(1, 2)) +
807 SkMScalarCeilToInt(mat.get(2, 3));
808 REPORTER_ASSERT(reporter, sum >= 0);
809 REPORTER_ASSERT(reporter, isum >= 0);
810 REPORTER_ASSERT(reporter, static_cast<SkMScalar>(isum) == SkIntToMScalar(isum));
811 }
812
DEF_TEST(Matrix44,reporter)813 DEF_TEST(Matrix44, reporter) {
814 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
815 SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor);
816 SkMatrix44 iden1(SkMatrix44::kUninitialized_Constructor);
817 SkMatrix44 iden2(SkMatrix44::kUninitialized_Constructor);
818 SkMatrix44 rot(SkMatrix44::kUninitialized_Constructor);
819
820 mat.setTranslate(1, 1, 1);
821 mat.invert(&inverse);
822 iden1.setConcat(mat, inverse);
823 REPORTER_ASSERT(reporter, is_identity(iden1));
824
825 mat.setScale(2, 2, 2);
826 mat.invert(&inverse);
827 iden1.setConcat(mat, inverse);
828 REPORTER_ASSERT(reporter, is_identity(iden1));
829
830 mat.setScale(SK_MScalar1/2, SK_MScalar1/2, SK_MScalar1/2);
831 mat.invert(&inverse);
832 iden1.setConcat(mat, inverse);
833 REPORTER_ASSERT(reporter, is_identity(iden1));
834
835 mat.setScale(3, 3, 3);
836 rot.setRotateDegreesAbout(0, 0, -1, 90);
837 mat.postConcat(rot);
838 REPORTER_ASSERT(reporter, mat.invert(nullptr));
839 mat.invert(&inverse);
840 iden1.setConcat(mat, inverse);
841 REPORTER_ASSERT(reporter, is_identity(iden1));
842 iden2.setConcat(inverse, mat);
843 REPORTER_ASSERT(reporter, is_identity(iden2));
844
845 // test tiny-valued matrix inverse
846 mat.reset();
847 auto v = SkDoubleToMScalar(1.0e-12);
848 mat.setScale(v,v,v);
849 rot.setRotateDegreesAbout(0, 0, -1, 90);
850 mat.postConcat(rot);
851 mat.postTranslate(v,v,v);
852 REPORTER_ASSERT(reporter, mat.invert(nullptr));
853 mat.invert(&inverse);
854 iden1.setConcat(mat, inverse);
855 REPORTER_ASSERT(reporter, is_identity(iden1));
856
857 // test mixed-valued matrix inverse
858 mat.reset();
859 mat.setScale(SkDoubleToMScalar(1.0e-2),
860 SkDoubleToMScalar(3.0),
861 SkDoubleToMScalar(1.0e+2));
862 rot.setRotateDegreesAbout(0, 0, -1, 90);
863 mat.postConcat(rot);
864 mat.postTranslate(SkDoubleToMScalar(1.0e+2),
865 SkDoubleToMScalar(3.0),
866 SkDoubleToMScalar(1.0e-2));
867 REPORTER_ASSERT(reporter, mat.invert(nullptr));
868 mat.invert(&inverse);
869 iden1.setConcat(mat, inverse);
870 REPORTER_ASSERT(reporter, is_identity(iden1));
871
872 // test degenerate matrix
873 mat.reset();
874 mat.set3x3(1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0);
875 REPORTER_ASSERT(reporter, !mat.invert(nullptr));
876
877 // test rol/col Major getters
878 {
879 mat.setTranslate(2, 3, 4);
880 float dataf[16];
881 double datad[16];
882
883 mat.asColMajorf(dataf);
884 assert16<float>(reporter, dataf,
885 1, 0, 0, 0,
886 0, 1, 0, 0,
887 0, 0, 1, 0,
888 2, 3, 4, 1);
889 mat.asColMajord(datad);
890 assert16<double>(reporter, datad, 1, 0, 0, 0,
891 0, 1, 0, 0,
892 0, 0, 1, 0,
893 2, 3, 4, 1);
894 mat.asRowMajorf(dataf);
895 assert16<float>(reporter, dataf, 1, 0, 0, 2,
896 0, 1, 0, 3,
897 0, 0, 1, 4,
898 0, 0, 0, 1);
899 mat.asRowMajord(datad);
900 assert16<double>(reporter, datad, 1, 0, 0, 2,
901 0, 1, 0, 3,
902 0, 0, 1, 4,
903 0, 0, 0, 1);
904 }
905
906 test_concat(reporter);
907
908 if (false) { // avoid bit rot, suppress warning (working on making this pass)
909 test_common_angles(reporter);
910 }
911
912 test_constructor(reporter);
913 test_gettype(reporter);
914 test_determinant(reporter);
915 test_invert(reporter);
916 test_transpose(reporter);
917 test_get_set_double(reporter);
918 test_set_row_col_major(reporter);
919 test_translate(reporter);
920 test_scale(reporter);
921 test_map2(reporter);
922 test_3x3_conversion(reporter);
923 test_has_perspective(reporter);
924 test_preserves_2d_axis_alignment(reporter);
925 test_toint(reporter);
926 }
927