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Updating trunk VERSION from 2139.0 to 2140.0
[chromium-blink-merge.git] / ui / gfx / transform_unittest.cc
blob77b28ca152c59ac128f0763a404f956aeaf0b0f1
1 // Copyright (c) 2011 The Chromium Authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style license that can be
3 // found in the LICENSE file.
4
5 // MSVC++ requires this to be set before any other includes to get M_PI.
6 #define _USE_MATH_DEFINES
7
8 #include "ui/gfx/transform.h"
9
10 #include <cmath>
11 #include <ostream>
12 #include <limits>
13
14 #include "base/basictypes.h"
15 #include "base/logging.h"
16 #include "testing/gtest/include/gtest/gtest.h"
17 #include "ui/gfx/box_f.h"
18 #include "ui/gfx/point.h"
19 #include "ui/gfx/point3_f.h"
20 #include "ui/gfx/quad_f.h"
21 #include "ui/gfx/transform_util.h"
22 #include "ui/gfx/vector3d_f.h"
23
24 namespace gfx {
25
26 namespace {
27
28 #define EXPECT_ROW1_EQ(a, b, c, d, transform) \
29 EXPECT_FLOAT_EQ((a), (transform).matrix().get(0, 0)); \
30 EXPECT_FLOAT_EQ((b), (transform).matrix().get(0, 1)); \
31 EXPECT_FLOAT_EQ((c), (transform).matrix().get(0, 2)); \
32 EXPECT_FLOAT_EQ((d), (transform).matrix().get(0, 3));
33
34 #define EXPECT_ROW2_EQ(a, b, c, d, transform) \
35 EXPECT_FLOAT_EQ((a), (transform).matrix().get(1, 0)); \
36 EXPECT_FLOAT_EQ((b), (transform).matrix().get(1, 1)); \
37 EXPECT_FLOAT_EQ((c), (transform).matrix().get(1, 2)); \
38 EXPECT_FLOAT_EQ((d), (transform).matrix().get(1, 3));
39
40 #define EXPECT_ROW3_EQ(a, b, c, d, transform) \
41 EXPECT_FLOAT_EQ((a), (transform).matrix().get(2, 0)); \
42 EXPECT_FLOAT_EQ((b), (transform).matrix().get(2, 1)); \
43 EXPECT_FLOAT_EQ((c), (transform).matrix().get(2, 2)); \
44 EXPECT_FLOAT_EQ((d), (transform).matrix().get(2, 3));
45
46 #define EXPECT_ROW4_EQ(a, b, c, d, transform) \
47 EXPECT_FLOAT_EQ((a), (transform).matrix().get(3, 0)); \
48 EXPECT_FLOAT_EQ((b), (transform).matrix().get(3, 1)); \
49 EXPECT_FLOAT_EQ((c), (transform).matrix().get(3, 2)); \
50 EXPECT_FLOAT_EQ((d), (transform).matrix().get(3, 3)); \
51
52 // Checking float values for equality close to zero is not robust using
53 // EXPECT_FLOAT_EQ (see gtest documentation). So, to verify rotation matrices,
54 // we must use a looser absolute error threshold in some places.
55 #define EXPECT_ROW1_NEAR(a, b, c, d, transform, errorThreshold) \
56 EXPECT_NEAR((a), (transform).matrix().get(0, 0), (errorThreshold)); \
57 EXPECT_NEAR((b), (transform).matrix().get(0, 1), (errorThreshold)); \
58 EXPECT_NEAR((c), (transform).matrix().get(0, 2), (errorThreshold)); \
59 EXPECT_NEAR((d), (transform).matrix().get(0, 3), (errorThreshold));
60
61 #define EXPECT_ROW2_NEAR(a, b, c, d, transform, errorThreshold) \
62 EXPECT_NEAR((a), (transform).matrix().get(1, 0), (errorThreshold)); \
63 EXPECT_NEAR((b), (transform).matrix().get(1, 1), (errorThreshold)); \
64 EXPECT_NEAR((c), (transform).matrix().get(1, 2), (errorThreshold)); \
65 EXPECT_NEAR((d), (transform).matrix().get(1, 3), (errorThreshold));
66
67 #define EXPECT_ROW3_NEAR(a, b, c, d, transform, errorThreshold) \
68 EXPECT_NEAR((a), (transform).matrix().get(2, 0), (errorThreshold)); \
69 EXPECT_NEAR((b), (transform).matrix().get(2, 1), (errorThreshold)); \
70 EXPECT_NEAR((c), (transform).matrix().get(2, 2), (errorThreshold)); \
71 EXPECT_NEAR((d), (transform).matrix().get(2, 3), (errorThreshold));
72
73 bool PointsAreNearlyEqual(const Point3F& lhs,
74 const Point3F& rhs) {
75 float epsilon = 0.0001f;
76 return lhs.SquaredDistanceTo(rhs) < epsilon;
77 }
78
79 bool MatricesAreNearlyEqual(const Transform& lhs,
80 const Transform& rhs) {
81 float epsilon = 0.0001f;
82 for (int row = 0; row < 4; ++row) {
83 for (int col = 0; col < 4; ++col) {
84 if (std::abs(lhs.matrix().get(row, col) -
85 rhs.matrix().get(row, col)) > epsilon)
86 return false;
87 }
88 }
89 return true;
90 }
91
92 void InitializeTestMatrix(Transform* transform) {
93 SkMatrix44& matrix = transform->matrix();
94 matrix.set(0, 0, 10.f);
95 matrix.set(1, 0, 11.f);
96 matrix.set(2, 0, 12.f);
97 matrix.set(3, 0, 13.f);
98 matrix.set(0, 1, 14.f);
99 matrix.set(1, 1, 15.f);
100 matrix.set(2, 1, 16.f);
101 matrix.set(3, 1, 17.f);
102 matrix.set(0, 2, 18.f);
103 matrix.set(1, 2, 19.f);
104 matrix.set(2, 2, 20.f);
105 matrix.set(3, 2, 21.f);
106 matrix.set(0, 3, 22.f);
107 matrix.set(1, 3, 23.f);
108 matrix.set(2, 3, 24.f);
109 matrix.set(3, 3, 25.f);
110
111 // Sanity check
112 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, (*transform));
113 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, (*transform));
114 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, (*transform));
115 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, (*transform));
116 }
117
118 void InitializeTestMatrix2(Transform* transform) {
119 SkMatrix44& matrix = transform->matrix();
120 matrix.set(0, 0, 30.f);
121 matrix.set(1, 0, 31.f);
122 matrix.set(2, 0, 32.f);
123 matrix.set(3, 0, 33.f);
124 matrix.set(0, 1, 34.f);
125 matrix.set(1, 1, 35.f);
126 matrix.set(2, 1, 36.f);
127 matrix.set(3, 1, 37.f);
128 matrix.set(0, 2, 38.f);
129 matrix.set(1, 2, 39.f);
130 matrix.set(2, 2, 40.f);
131 matrix.set(3, 2, 41.f);
132 matrix.set(0, 3, 42.f);
133 matrix.set(1, 3, 43.f);
134 matrix.set(2, 3, 44.f);
135 matrix.set(3, 3, 45.f);
136
137 // Sanity check
138 EXPECT_ROW1_EQ(30.0f, 34.0f, 38.0f, 42.0f, (*transform));
139 EXPECT_ROW2_EQ(31.0f, 35.0f, 39.0f, 43.0f, (*transform));
140 EXPECT_ROW3_EQ(32.0f, 36.0f, 40.0f, 44.0f, (*transform));
141 EXPECT_ROW4_EQ(33.0f, 37.0f, 41.0f, 45.0f, (*transform));
142 }
143
144 const SkMScalar kApproxZero =
145 SkFloatToMScalar(std::numeric_limits<float>::epsilon());
146 const SkMScalar kApproxOne = 1 - kApproxZero;
147
148 void InitializeApproxIdentityMatrix(Transform* transform) {
149 SkMatrix44& matrix = transform->matrix();
150 matrix.set(0, 0, kApproxOne);
151 matrix.set(0, 1, kApproxZero);
152 matrix.set(0, 2, kApproxZero);
153 matrix.set(0, 3, kApproxZero);
154
155 matrix.set(1, 0, kApproxZero);
156 matrix.set(1, 1, kApproxOne);
157 matrix.set(1, 2, kApproxZero);
158 matrix.set(1, 3, kApproxZero);
159
160 matrix.set(2, 0, kApproxZero);
161 matrix.set(2, 1, kApproxZero);
162 matrix.set(2, 2, kApproxOne);
163 matrix.set(2, 3, kApproxZero);
164
165 matrix.set(3, 0, kApproxZero);
166 matrix.set(3, 1, kApproxZero);
167 matrix.set(3, 2, kApproxZero);
168 matrix.set(3, 3, kApproxOne);
169 }
170
171 #ifdef SK_MSCALAR_IS_DOUBLE
172 #define ERROR_THRESHOLD 1e-14
173 #else
174 #define ERROR_THRESHOLD 1e-7
175 #endif
176 #define LOOSE_ERROR_THRESHOLD 1e-7
177
178 TEST(XFormTest, Equality) {
179 Transform lhs, rhs, interpolated;
180 rhs.matrix().set3x3(1, 2, 3,
181 4, 5, 6,
182 7, 8, 9);
183 interpolated = lhs;
184 for (int i = 0; i <= 100; ++i) {
185 for (int row = 0; row < 4; ++row) {
186 for (int col = 0; col < 4; ++col) {
187 float a = lhs.matrix().get(row, col);
188 float b = rhs.matrix().get(row, col);
189 float t = i / 100.0f;
190 interpolated.matrix().set(row, col, a + (b - a) * t);
191 }
192 }
193 if (i == 100) {
194 EXPECT_TRUE(rhs == interpolated);
195 } else {
196 EXPECT_TRUE(rhs != interpolated);
197 }
198 }
199 lhs = Transform();
200 rhs = Transform();
201 for (int i = 1; i < 100; ++i) {
202 lhs.MakeIdentity();
203 rhs.MakeIdentity();
204 lhs.Translate(i, i);
205 rhs.Translate(-i, -i);
206 EXPECT_TRUE(lhs != rhs);
207 rhs.Translate(2*i, 2*i);
208 EXPECT_TRUE(lhs == rhs);
209 }
210 }
211
212 TEST(XFormTest, ConcatTranslate) {
213 static const struct TestCase {
214 int x1;
215 int y1;
216 float tx;
217 float ty;
218 int x2;
219 int y2;
220 } test_cases[] = {
221 { 0, 0, 10.0f, 20.0f, 10, 20 },
222 { 0, 0, -10.0f, -20.0f, 0, 0 },
223 { 0, 0, -10.0f, -20.0f, -10, -20 },
224 { 0, 0,
225 std::numeric_limits<float>::quiet_NaN(),
226 std::numeric_limits<float>::quiet_NaN(),
227 10, 20 },
228 };
229
230 Transform xform;
231 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
232 const TestCase& value = test_cases[i];
233 Transform translation;
234 translation.Translate(value.tx, value.ty);
235 xform = translation * xform;
236 Point3F p1(value.x1, value.y1, 0);
237 Point3F p2(value.x2, value.y2, 0);
238 xform.TransformPoint(&p1);
239 if (value.tx == value.tx &&
240 value.ty == value.ty) {
241 EXPECT_TRUE(PointsAreNearlyEqual(p1, p2));
242 }
243 }
244 }
245
246 TEST(XFormTest, ConcatScale) {
247 static const struct TestCase {
248 int before;
249 float scale;
250 int after;
251 } test_cases[] = {
252 { 1, 10.0f, 10 },
253 { 1, .1f, 1 },
254 { 1, 100.0f, 100 },
255 { 1, -1.0f, -100 },
256 { 1, std::numeric_limits<float>::quiet_NaN(), 1 }
257 };
258
259 Transform xform;
260 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
261 const TestCase& value = test_cases[i];
262 Transform scale;
263 scale.Scale(value.scale, value.scale);
264 xform = scale * xform;
265 Point3F p1(value.before, value.before, 0);
266 Point3F p2(value.after, value.after, 0);
267 xform.TransformPoint(&p1);
268 if (value.scale == value.scale) {
269 EXPECT_TRUE(PointsAreNearlyEqual(p1, p2));
270 }
271 }
272 }
273
274 TEST(XFormTest, ConcatRotate) {
275 static const struct TestCase {
276 int x1;
277 int y1;
278 float degrees;
279 int x2;
280 int y2;
281 } test_cases[] = {
282 { 1, 0, 90.0f, 0, 1 },
283 { 1, 0, -90.0f, 1, 0 },
284 { 1, 0, 90.0f, 0, 1 },
285 { 1, 0, 360.0f, 0, 1 },
286 { 1, 0, 0.0f, 0, 1 },
287 { 1, 0, std::numeric_limits<float>::quiet_NaN(), 1, 0 }
288 };
289
290 Transform xform;
291 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
292 const TestCase& value = test_cases[i];
293 Transform rotation;
294 rotation.Rotate(value.degrees);
295 xform = rotation * xform;
296 Point3F p1(value.x1, value.y1, 0);
297 Point3F p2(value.x2, value.y2, 0);
298 xform.TransformPoint(&p1);
299 if (value.degrees == value.degrees) {
300 EXPECT_TRUE(PointsAreNearlyEqual(p1, p2));
301 }
302 }
303 }
304
305 TEST(XFormTest, SetTranslate) {
306 static const struct TestCase {
307 int x1; int y1;
308 float tx; float ty;
309 int x2; int y2;
310 } test_cases[] = {
311 { 0, 0, 10.0f, 20.0f, 10, 20 },
312 { 10, 20, 10.0f, 20.0f, 20, 40 },
313 { 10, 20, 0.0f, 0.0f, 10, 20 },
314 { 0, 0,
315 std::numeric_limits<float>::quiet_NaN(),
316 std::numeric_limits<float>::quiet_NaN(),
317 0, 0 }
318 };
319
320 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
321 const TestCase& value = test_cases[i];
322 for (int k = 0; k < 3; ++k) {
323 Point3F p0, p1, p2;
324 Transform xform;
325 switch (k) {
326 case 0:
327 p1.SetPoint(value.x1, 0, 0);
328 p2.SetPoint(value.x2, 0, 0);
329 xform.Translate(value.tx, 0.0);
330 break;
331 case 1:
332 p1.SetPoint(0, value.y1, 0);
333 p2.SetPoint(0, value.y2, 0);
334 xform.Translate(0.0, value.ty);
335 break;
336 case 2:
337 p1.SetPoint(value.x1, value.y1, 0);
338 p2.SetPoint(value.x2, value.y2, 0);
339 xform.Translate(value.tx, value.ty);
340 break;
341 }
342 p0 = p1;
343 xform.TransformPoint(&p1);
344 if (value.tx == value.tx &&
345 value.ty == value.ty) {
346 EXPECT_TRUE(PointsAreNearlyEqual(p1, p2));
347 xform.TransformPointReverse(&p1);
348 EXPECT_TRUE(PointsAreNearlyEqual(p1, p0));
349 }
350 }
351 }
352 }
353
354 TEST(XFormTest, SetScale) {
355 static const struct TestCase {
356 int before;
357 float s;
358 int after;
359 } test_cases[] = {
360 { 1, 10.0f, 10 },
361 { 1, 1.0f, 1 },
362 { 1, 0.0f, 0 },
363 { 0, 10.0f, 0 },
364 { 1, std::numeric_limits<float>::quiet_NaN(), 0 },
365 };
366
367 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
368 const TestCase& value = test_cases[i];
369 for (int k = 0; k < 3; ++k) {
370 Point3F p0, p1, p2;
371 Transform xform;
372 switch (k) {
373 case 0:
374 p1.SetPoint(value.before, 0, 0);
375 p2.SetPoint(value.after, 0, 0);
376 xform.Scale(value.s, 1.0);
377 break;
378 case 1:
379 p1.SetPoint(0, value.before, 0);
380 p2.SetPoint(0, value.after, 0);
381 xform.Scale(1.0, value.s);
382 break;
383 case 2:
384 p1.SetPoint(value.before, value.before, 0);
385 p2.SetPoint(value.after, value.after, 0);
386 xform.Scale(value.s, value.s);
387 break;
388 }
389 p0 = p1;
390 xform.TransformPoint(&p1);
391 if (value.s == value.s) {
392 EXPECT_TRUE(PointsAreNearlyEqual(p1, p2));
393 if (value.s != 0.0f) {
394 xform.TransformPointReverse(&p1);
395 EXPECT_TRUE(PointsAreNearlyEqual(p1, p0));
396 }
397 }
398 }
399 }
400 }
401
402 TEST(XFormTest, SetRotate) {
403 static const struct SetRotateCase {
404 int x;
405 int y;
406 float degree;
407 int xprime;
408 int yprime;
409 } set_rotate_cases[] = {
410 { 100, 0, 90.0f, 0, 100 },
411 { 0, 0, 90.0f, 0, 0 },
412 { 0, 100, 90.0f, -100, 0 },
413 { 0, 1, -90.0f, 1, 0 },
414 { 100, 0, 0.0f, 100, 0 },
415 { 0, 0, 0.0f, 0, 0 },
416 { 0, 0, std::numeric_limits<float>::quiet_NaN(), 0, 0 },
417 { 100, 0, 360.0f, 100, 0 }
418 };
419
420 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(set_rotate_cases); ++i) {
421 const SetRotateCase& value = set_rotate_cases[i];
422 Point3F p0;
423 Point3F p1(value.x, value.y, 0);
424 Point3F p2(value.xprime, value.yprime, 0);
425 p0 = p1;
426 Transform xform;
427 xform.Rotate(value.degree);
428 // just want to make sure that we don't crash in the case of NaN.
429 if (value.degree == value.degree) {
430 xform.TransformPoint(&p1);
431 EXPECT_TRUE(PointsAreNearlyEqual(p1, p2));
432 xform.TransformPointReverse(&p1);
433 EXPECT_TRUE(PointsAreNearlyEqual(p1, p0));
434 }
435 }
436 }
437
438 // 2D tests
439 TEST(XFormTest, ConcatTranslate2D) {
440 static const struct TestCase {
441 int x1;
442 int y1;
443 float tx;
444 float ty;
445 int x2;
446 int y2;
447 } test_cases[] = {
448 { 0, 0, 10.0f, 20.0f, 10, 20},
449 { 0, 0, -10.0f, -20.0f, 0, 0},
450 { 0, 0, -10.0f, -20.0f, -10, -20},
451 { 0, 0,
452 std::numeric_limits<float>::quiet_NaN(),
453 std::numeric_limits<float>::quiet_NaN(),
454 10, 20},
455 };
456
457 Transform xform;
458 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
459 const TestCase& value = test_cases[i];
460 Transform translation;
461 translation.Translate(value.tx, value.ty);
462 xform = translation * xform;
463 Point p1(value.x1, value.y1);
464 Point p2(value.x2, value.y2);
465 xform.TransformPoint(&p1);
466 if (value.tx == value.tx &&
467 value.ty == value.ty) {
468 EXPECT_EQ(p1.x(), p2.x());
469 EXPECT_EQ(p1.y(), p2.y());
470 }
471 }
472 }
473
474 TEST(XFormTest, ConcatScale2D) {
475 static const struct TestCase {
476 int before;
477 float scale;
478 int after;
479 } test_cases[] = {
480 { 1, 10.0f, 10},
481 { 1, .1f, 1},
482 { 1, 100.0f, 100},
483 { 1, -1.0f, -100},
484 { 1, std::numeric_limits<float>::quiet_NaN(), 1}
485 };
486
487 Transform xform;
488 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
489 const TestCase& value = test_cases[i];
490 Transform scale;
491 scale.Scale(value.scale, value.scale);
492 xform = scale * xform;
493 Point p1(value.before, value.before);
494 Point p2(value.after, value.after);
495 xform.TransformPoint(&p1);
496 if (value.scale == value.scale) {
497 EXPECT_EQ(p1.x(), p2.x());
498 EXPECT_EQ(p1.y(), p2.y());
499 }
500 }
501 }
502
503 TEST(XFormTest, ConcatRotate2D) {
504 static const struct TestCase {
505 int x1;
506 int y1;
507 float degrees;
508 int x2;
509 int y2;
510 } test_cases[] = {
511 { 1, 0, 90.0f, 0, 1},
512 { 1, 0, -90.0f, 1, 0},
513 { 1, 0, 90.0f, 0, 1},
514 { 1, 0, 360.0f, 0, 1},
515 { 1, 0, 0.0f, 0, 1},
516 { 1, 0, std::numeric_limits<float>::quiet_NaN(), 1, 0}
517 };
518
519 Transform xform;
520 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
521 const TestCase& value = test_cases[i];
522 Transform rotation;
523 rotation.Rotate(value.degrees);
524 xform = rotation * xform;
525 Point p1(value.x1, value.y1);
526 Point p2(value.x2, value.y2);
527 xform.TransformPoint(&p1);
528 if (value.degrees == value.degrees) {
529 EXPECT_EQ(p1.x(), p2.x());
530 EXPECT_EQ(p1.y(), p2.y());
531 }
532 }
533 }
534
535 TEST(XFormTest, SetTranslate2D) {
536 static const struct TestCase {
537 int x1; int y1;
538 float tx; float ty;
539 int x2; int y2;
540 } test_cases[] = {
541 { 0, 0, 10.0f, 20.0f, 10, 20},
542 { 10, 20, 10.0f, 20.0f, 20, 40},
543 { 10, 20, 0.0f, 0.0f, 10, 20},
544 { 0, 0,
545 std::numeric_limits<float>::quiet_NaN(),
546 std::numeric_limits<float>::quiet_NaN(),
547 0, 0}
548 };
549
550 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
551 const TestCase& value = test_cases[i];
552 for (int j = -1; j < 2; ++j) {
553 for (int k = 0; k < 3; ++k) {
554 float epsilon = 0.0001f;
555 Point p0, p1, p2;
556 Transform xform;
557 switch (k) {
558 case 0:
559 p1.SetPoint(value.x1, 0);
560 p2.SetPoint(value.x2, 0);
561 xform.Translate(value.tx + j * epsilon, 0.0);
562 break;
563 case 1:
564 p1.SetPoint(0, value.y1);
565 p2.SetPoint(0, value.y2);
566 xform.Translate(0.0, value.ty + j * epsilon);
567 break;
568 case 2:
569 p1.SetPoint(value.x1, value.y1);
570 p2.SetPoint(value.x2, value.y2);
571 xform.Translate(value.tx + j * epsilon,
572 value.ty + j * epsilon);
573 break;
574 }
575 p0 = p1;
576 xform.TransformPoint(&p1);
577 if (value.tx == value.tx &&
578 value.ty == value.ty) {
579 EXPECT_EQ(p1.x(), p2.x());
580 EXPECT_EQ(p1.y(), p2.y());
581 xform.TransformPointReverse(&p1);
582 EXPECT_EQ(p1.x(), p0.x());
583 EXPECT_EQ(p1.y(), p0.y());
584 }
585 }
586 }
587 }
588 }
589
590 TEST(XFormTest, SetScale2D) {
591 static const struct TestCase {
592 int before;
593 float s;
594 int after;
595 } test_cases[] = {
596 { 1, 10.0f, 10},
597 { 1, 1.0f, 1},
598 { 1, 0.0f, 0},
599 { 0, 10.0f, 0},
600 { 1, std::numeric_limits<float>::quiet_NaN(), 0},
601 };
602
603 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
604 const TestCase& value = test_cases[i];
605 for (int j = -1; j < 2; ++j) {
606 for (int k = 0; k < 3; ++k) {
607 float epsilon = 0.0001f;
608 Point p0, p1, p2;
609 Transform xform;
610 switch (k) {
611 case 0:
612 p1.SetPoint(value.before, 0);
613 p2.SetPoint(value.after, 0);
614 xform.Scale(value.s + j * epsilon, 1.0);
615 break;
616 case 1:
617 p1.SetPoint(0, value.before);
618 p2.SetPoint(0, value.after);
619 xform.Scale(1.0, value.s + j * epsilon);
620 break;
621 case 2:
622 p1.SetPoint(value.before,
623 value.before);
624 p2.SetPoint(value.after,
625 value.after);
626 xform.Scale(value.s + j * epsilon,
627 value.s + j * epsilon);
628 break;
629 }
630 p0 = p1;
631 xform.TransformPoint(&p1);
632 if (value.s == value.s) {
633 EXPECT_EQ(p1.x(), p2.x());
634 EXPECT_EQ(p1.y(), p2.y());
635 if (value.s != 0.0f) {
636 xform.TransformPointReverse(&p1);
637 EXPECT_EQ(p1.x(), p0.x());
638 EXPECT_EQ(p1.y(), p0.y());
639 }
640 }
641 }
642 }
643 }
644 }
645
646 TEST(XFormTest, SetRotate2D) {
647 static const struct SetRotateCase {
648 int x;
649 int y;
650 float degree;
651 int xprime;
652 int yprime;
653 } set_rotate_cases[] = {
654 { 100, 0, 90.0f, 0, 100},
655 { 0, 0, 90.0f, 0, 0},
656 { 0, 100, 90.0f, -100, 0},
657 { 0, 1, -90.0f, 1, 0},
658 { 100, 0, 0.0f, 100, 0},
659 { 0, 0, 0.0f, 0, 0},
660 { 0, 0, std::numeric_limits<float>::quiet_NaN(), 0, 0},
661 { 100, 0, 360.0f, 100, 0}
662 };
663
664 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(set_rotate_cases); ++i) {
665 const SetRotateCase& value = set_rotate_cases[i];
666 for (int j = 1; j >= -1; --j) {
667 float epsilon = 0.1f;
668 Point pt(value.x, value.y);
669 Transform xform;
670 // should be invariant to small floating point errors.
671 xform.Rotate(value.degree + j * epsilon);
672 // just want to make sure that we don't crash in the case of NaN.
673 if (value.degree == value.degree) {
674 xform.TransformPoint(&pt);
675 EXPECT_EQ(value.xprime, pt.x());
676 EXPECT_EQ(value.yprime, pt.y());
677 xform.TransformPointReverse(&pt);
678 EXPECT_EQ(pt.x(), value.x);
679 EXPECT_EQ(pt.y(), value.y);
680 }
681 }
682 }
683 }
684
685 TEST(XFormTest, TransformPointWithExtremePerspective) {
686 Point3F point(1.f, 1.f, 1.f);
687 Transform perspective;
688 perspective.ApplyPerspectiveDepth(1.f);
689 Point3F transformed = point;
690 perspective.TransformPoint(&transformed);
691 EXPECT_EQ(point.ToString(), transformed.ToString());
692
693 transformed = point;
694 perspective.MakeIdentity();
695 perspective.ApplyPerspectiveDepth(1.1f);
696 perspective.TransformPoint(&transformed);
697 EXPECT_FLOAT_EQ(11.f, transformed.x());
698 EXPECT_FLOAT_EQ(11.f, transformed.y());
699 EXPECT_FLOAT_EQ(11.f, transformed.z());
700 }
701
702 TEST(XFormTest, BlendTranslate) {
703 Transform from;
704 for (int i = -5; i < 15; ++i) {
705 Transform to;
706 to.Translate3d(1, 1, 1);
707 double t = i / 9.0;
708 EXPECT_TRUE(to.Blend(from, t));
709 EXPECT_FLOAT_EQ(t, to.matrix().get(0, 3));
710 EXPECT_FLOAT_EQ(t, to.matrix().get(1, 3));
711 EXPECT_FLOAT_EQ(t, to.matrix().get(2, 3));
712 }
713 }
714
715 TEST(XFormTest, BlendRotate) {
716 Vector3dF axes[] = {
717 Vector3dF(1, 0, 0),
718 Vector3dF(0, 1, 0),
719 Vector3dF(0, 0, 1),
720 Vector3dF(1, 1, 1)
721 };
722 Transform from;
723 for (size_t index = 0; index < ARRAYSIZE_UNSAFE(axes); ++index) {
724 for (int i = -5; i < 15; ++i) {
725 Transform to;
726 to.RotateAbout(axes[index], 90);
727 double t = i / 9.0;
728 EXPECT_TRUE(to.Blend(from, t));
729
730 Transform expected;
731 expected.RotateAbout(axes[index], 90 * t);
732
733 EXPECT_TRUE(MatricesAreNearlyEqual(expected, to));
734 }
735 }
736 }
737
738 #if defined(_WIN64)
739 // http://crbug.com/406574
740 #define MAYBE_BlendRotateFollowsShortestPath DISABLED_BlendRotateFollowsShortestPath
741 #else
742 #define MAYBE_BlendRotateFollowsShortestPath BlendRotateFollowsShortestPath
743 #endif
744 TEST(XFormTest, MAYBE_BlendRotateFollowsShortestPath) {
745 // Verify that we interpolate along the shortest path regardless of whether
746 // this path crosses the 180-degree point.
747 Vector3dF axes[] = {
748 Vector3dF(1, 0, 0),
749 Vector3dF(0, 1, 0),
750 Vector3dF(0, 0, 1),
751 Vector3dF(1, 1, 1)
752 };
753 for (size_t index = 0; index < ARRAYSIZE_UNSAFE(axes); ++index) {
754 for (int i = -5; i < 15; ++i) {
755 Transform from1;
756 from1.RotateAbout(axes[index], 130.0);
757 Transform to1;
758 to1.RotateAbout(axes[index], 175.0);
759
760 Transform from2;
761 from2.RotateAbout(axes[index], 140.0);
762 Transform to2;
763 to2.RotateAbout(axes[index], 185.0);
764
765 double t = i / 9.0;
766 EXPECT_TRUE(to1.Blend(from1, t));
767 EXPECT_TRUE(to2.Blend(from2, t));
768
769 Transform expected1;
770 expected1.RotateAbout(axes[index], 130.0 + 45.0 * t);
771
772 Transform expected2;
773 expected2.RotateAbout(axes[index], 140.0 + 45.0 * t);
774
775 EXPECT_TRUE(MatricesAreNearlyEqual(expected1, to1));
776 EXPECT_TRUE(MatricesAreNearlyEqual(expected2, to2));
777 }
778 }
779 }
780
781 TEST(XFormTest, CanBlend180DegreeRotation) {
782 Vector3dF axes[] = {
783 Vector3dF(1, 0, 0),
784 Vector3dF(0, 1, 0),
785 Vector3dF(0, 0, 1),
786 Vector3dF(1, 1, 1)
787 };
788 Transform from;
789 for (size_t index = 0; index < ARRAYSIZE_UNSAFE(axes); ++index) {
790 for (int i = -5; i < 15; ++i) {
791 Transform to;
792 to.RotateAbout(axes[index], 180.0);
793 double t = i / 9.0;
794 EXPECT_TRUE(to.Blend(from, t));
795
796 // A 180 degree rotation is exactly opposite on the sphere, therefore
797 // either great circle arc to it is equivalent (and numerical precision
798 // will determine which is closer). Test both directions.
799 Transform expected1;
800 expected1.RotateAbout(axes[index], 180.0 * t);
801 Transform expected2;
802 expected2.RotateAbout(axes[index], -180.0 * t);
803
804 EXPECT_TRUE(MatricesAreNearlyEqual(expected1, to) ||
805 MatricesAreNearlyEqual(expected2, to))
806 << "axis: " << index << ", i: " << i;
807 }
808 }
809 }
810
811 #if defined(_WIN64)
812 // http://crbug.com/406574
813 #define MAYBE_BlendScale DISABLED_BlendScale
814 #else
815 #define MAYBE_BlendScale BlendScale
816 #endif
817 TEST(XFormTest, MAYBE_BlendScale) {
818 Transform from;
819 for (int i = -5; i < 15; ++i) {
820 Transform to;
821 to.Scale3d(5, 4, 3);
822 double t = i / 9.0;
823 EXPECT_TRUE(to.Blend(from, t));
824 EXPECT_FLOAT_EQ(t * 4 + 1, to.matrix().get(0, 0)) << "i: " << i;
825 EXPECT_FLOAT_EQ(t * 3 + 1, to.matrix().get(1, 1)) << "i: " << i;
826 EXPECT_FLOAT_EQ(t * 2 + 1, to.matrix().get(2, 2)) << "i: " << i;
827 }
828 }
829
830 TEST(XFormTest, BlendSkew) {
831 Transform from;
832 for (int i = 0; i < 2; ++i) {
833 Transform to;
834 to.SkewX(10);
835 to.SkewY(5);
836 double t = i;
837 Transform expected;
838 expected.SkewX(t * 10);
839 expected.SkewY(t * 5);
840 EXPECT_TRUE(to.Blend(from, t));
841 EXPECT_TRUE(MatricesAreNearlyEqual(expected, to));
842 }
843 }
844
845 TEST(XFormTest, ExtrapolateSkew) {
846 Transform from;
847 for (int i = -1; i < 2; ++i) {
848 Transform to;
849 to.SkewX(20);
850 double t = i;
851 Transform expected;
852 expected.SkewX(t * 20);
853 EXPECT_TRUE(to.Blend(from, t));
854 EXPECT_TRUE(MatricesAreNearlyEqual(expected, to));
855 }
856 }
857
858 #if defined(_WIN64)
859 // http://crbug.com/406574
860 #define MAYBE_BlendPerspective DISABLED_BlendPerspective
861 #else
862 #define MAYBE_BlendPerspective BlendPerspective
863 #endif
864 TEST(XFormTest, MAYBE_BlendPerspective) {
865 Transform from;
866 from.ApplyPerspectiveDepth(200);
867 for (int i = -1; i < 3; ++i) {
868 Transform to;
869 to.ApplyPerspectiveDepth(800);
870 double t = i;
871 double depth = 1.0 / ((1.0 / 200) * (1.0 - t) + (1.0 / 800) * t);
872 Transform expected;
873 expected.ApplyPerspectiveDepth(depth);
874 EXPECT_TRUE(to.Blend(from, t));
875 EXPECT_TRUE(MatricesAreNearlyEqual(expected, to));
876 }
877 }
878
879 TEST(XFormTest, BlendIdentity) {
880 Transform from;
881 Transform to;
882 EXPECT_TRUE(to.Blend(from, 0.5));
883 EXPECT_EQ(to, from);
884 }
885
886 TEST(XFormTest, CannotBlendSingularMatrix) {
887 Transform from;
888 Transform to;
889 to.matrix().set(1, 1, SkDoubleToMScalar(0));
890 EXPECT_FALSE(to.Blend(from, 0.5));
891 }
892
893 TEST(XFormTest, VerifyBlendForTranslation) {
894 Transform from;
895 from.Translate3d(100.0, 200.0, 100.0);
896
897 Transform to;
898
899 to.Translate3d(200.0, 100.0, 300.0);
900 to.Blend(from, 0.0);
901 EXPECT_EQ(from, to);
902
903 to = Transform();
904 to.Translate3d(200.0, 100.0, 300.0);
905 to.Blend(from, 0.25);
906 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 125.0f, to);
907 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 175.0f, to);
908 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 150.0f, to);
909 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
910
911 to = Transform();
912 to.Translate3d(200.0, 100.0, 300.0);
913 to.Blend(from, 0.5);
914 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 150.0f, to);
915 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 150.0f, to);
916 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 200.0f, to);
917 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
918
919 to = Transform();
920 to.Translate3d(200.0, 100.0, 300.0);
921 to.Blend(from, 1.0);
922 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 200.0f, to);
923 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 100.0f, to);
924 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 300.0f, to);
925 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
926 }
927
928 TEST(XFormTest, VerifyBlendForScale) {
929 Transform from;
930 from.Scale3d(100.0, 200.0, 100.0);
931
932 Transform to;
933
934 to.Scale3d(200.0, 100.0, 300.0);
935 to.Blend(from, 0.0);
936 EXPECT_EQ(from, to);
937
938 to = Transform();
939 to.Scale3d(200.0, 100.0, 300.0);
940 to.Blend(from, 0.25);
941 EXPECT_ROW1_EQ(125.0f, 0.0f, 0.0f, 0.0f, to);
942 EXPECT_ROW2_EQ(0.0f, 175.0f, 0.0f, 0.0f, to);
943 EXPECT_ROW3_EQ(0.0f, 0.0f, 150.0f, 0.0f, to);
944 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
945
946 to = Transform();
947 to.Scale3d(200.0, 100.0, 300.0);
948 to.Blend(from, 0.5);
949 EXPECT_ROW1_EQ(150.0f, 0.0f, 0.0f, 0.0f, to);
950 EXPECT_ROW2_EQ(0.0f, 150.0f, 0.0f, 0.0f, to);
951 EXPECT_ROW3_EQ(0.0f, 0.0f, 200.0f, 0.0f, to);
952 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
953
954 to = Transform();
955 to.Scale3d(200.0, 100.0, 300.0);
956 to.Blend(from, 1.0);
957 EXPECT_ROW1_EQ(200.0f, 0.0f, 0.0f, 0.0f, to);
958 EXPECT_ROW2_EQ(0.0f, 100.0f, 0.0f, 0.0f, to);
959 EXPECT_ROW3_EQ(0.0f, 0.0f, 300.0f, 0.0f, to);
960 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
961 }
962
963 TEST(XFormTest, VerifyBlendForSkewX) {
964 Transform from;
965 from.SkewX(0.0);
966
967 Transform to;
968
969 to.SkewX(45.0);
970 to.Blend(from, 0.0);
971 EXPECT_EQ(from, to);
972
973 to = Transform();
974 to.SkewX(45.0);
975 to.Blend(from, 0.5);
976 EXPECT_ROW1_EQ(1.0f, 0.5f, 0.0f, 0.0f, to);
977 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, to);
978 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
979 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
980
981 to = Transform();
982 to.SkewX(45.0);
983 to.Blend(from, 0.25);
984 EXPECT_ROW1_EQ(1.0f, 0.25f, 0.0f, 0.0f, to);
985 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, to);
986 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
987 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
988
989 to = Transform();
990 to.SkewX(45.0);
991 to.Blend(from, 1.0);
992 EXPECT_ROW1_EQ(1.0f, 1.0f, 0.0f, 0.0f, to);
993 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, to);
994 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
995 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
996 }
997
998 TEST(XFormTest, VerifyBlendForSkewY) {
999 // NOTE CAREFULLY: Decomposition of skew and rotation terms of the matrix
1000 // is inherently underconstrained, and so it does not always compute the
1001 // originally intended skew parameters. The current implementation uses QR
1002 // decomposition, which decomposes the shear into a rotation + non-uniform
1003 // scale.
1004 //
1005 // It is unlikely that the decomposition implementation will need to change
1006 // very often, so to get any test coverage, the compromise is to verify the
1007 // exact matrix that the.Blend() operation produces.
1008 //
1009 // This problem also potentially exists for skewX, but the current QR
1010 // decomposition implementation just happens to decompose those test
1011 // matrices intuitively.
1012 //
1013 // Unfortunately, this case suffers from uncomfortably large precision
1014 // error.
1015
1016 Transform from;
1017 from.SkewY(0.0);
1018
1019 Transform to;
1020
1021 to.SkewY(45.0);
1022 to.Blend(from, 0.0);
1023 EXPECT_EQ(from, to);
1024
1025 to = Transform();
1026 to.SkewY(45.0);
1027 to.Blend(from, 0.25);
1028 EXPECT_ROW1_NEAR(1.0823489449280947471976333,
1029 0.0464370719145053845178239,
1030 0.0,
1031 0.0,
1032 to,
1033 LOOSE_ERROR_THRESHOLD);
1034 EXPECT_ROW2_NEAR(0.2152925909665224513123150,
1035 0.9541702441750861130032035,
1036 0.0,
1037 0.0,
1038 to,
1039 LOOSE_ERROR_THRESHOLD);
1040 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
1041 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1042
1043 to = Transform();
1044 to.SkewY(45.0);
1045 to.Blend(from, 0.5);
1046 EXPECT_ROW1_NEAR(1.1152212925809066312865525,
1047 0.0676495144007326631996335,
1048 0.0,
1049 0.0,
1050 to,
1051 LOOSE_ERROR_THRESHOLD);
1052 EXPECT_ROW2_NEAR(0.4619397844342648662419037,
1053 0.9519009045724774464858342,
1054 0.0,
1055 0.0,
1056 to,
1057 LOOSE_ERROR_THRESHOLD);
1058 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
1059 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1060
1061 to = Transform();
1062 to.SkewY(45.0);
1063 to.Blend(from, 1.0);
1064 EXPECT_ROW1_NEAR(1.0, 0.0, 0.0, 0.0, to, LOOSE_ERROR_THRESHOLD);
1065 EXPECT_ROW2_NEAR(1.0, 1.0, 0.0, 0.0, to, LOOSE_ERROR_THRESHOLD);
1066 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
1067 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1068 }
1069
1070 #if defined(_WIN64)
1071 // http://crbug.com/406574
1072 #define MAYBE_VerifyBlendForRotationAboutX DISABLED_VerifyBlendForRotationAboutX
1073 #else
1074 #define MAYBE_VerifyBlendForRotationAboutX VerifyBlendForRotationAboutX
1075 #endif
1076 TEST(XFormTest, MAYBE_VerifyBlendForRotationAboutX) {
1077 // Even though.Blending uses quaternions, axis-aligned rotations should.
1078 // Blend the same with quaternions or Euler angles. So we can test
1079 // rotation.Blending by comparing against manually specified matrices from
1080 // Euler angles.
1081
1082 Transform from;
1083 from.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 0.0);
1084
1085 Transform to;
1086
1087 to.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1088 to.Blend(from, 0.0);
1089 EXPECT_EQ(from, to);
1090
1091 double expectedRotationAngle = 22.5 * M_PI / 180.0;
1092 to = Transform();
1093 to.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1094 to.Blend(from, 0.25);
1095 EXPECT_ROW1_NEAR(1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1096 EXPECT_ROW2_NEAR(0.0,
1097 std::cos(expectedRotationAngle),
1098 -std::sin(expectedRotationAngle),
1099 0.0,
1100 to,
1101 ERROR_THRESHOLD);
1102 EXPECT_ROW3_NEAR(0.0,
1103 std::sin(expectedRotationAngle),
1104 std::cos(expectedRotationAngle),
1105 0.0,
1106 to,
1107 ERROR_THRESHOLD);
1108 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1109
1110 expectedRotationAngle = 45.0 * M_PI / 180.0;
1111 to = Transform();
1112 to.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1113 to.Blend(from, 0.5);
1114 EXPECT_ROW1_NEAR(1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1115 EXPECT_ROW2_NEAR(0.0,
1116 std::cos(expectedRotationAngle),
1117 -std::sin(expectedRotationAngle),
1118 0.0,
1119 to,
1120 ERROR_THRESHOLD);
1121 EXPECT_ROW3_NEAR(0.0,
1122 std::sin(expectedRotationAngle),
1123 std::cos(expectedRotationAngle),
1124 0.0,
1125 to,
1126 ERROR_THRESHOLD);
1127 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1128
1129 to = Transform();
1130 to.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1131 to.Blend(from, 1.0);
1132 EXPECT_ROW1_NEAR(1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1133 EXPECT_ROW2_NEAR(0.0, 0.0, -1.0, 0.0, to, ERROR_THRESHOLD);
1134 EXPECT_ROW3_NEAR(0.0, 1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1135 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1136 }
1137
1138 #if defined(_WIN64)
1139 // http://crbug.com/406574
1140 #define MAYBE_VerifyBlendForRotationAboutY DISABLED_VerifyBlendForRotationAboutY
1141 #else
1142 #define MAYBE_VerifyBlendForRotationAboutY VerifyBlendForRotationAboutY
1143 #endif
1144 TEST(XFormTest, MAYBE_VerifyBlendForRotationAboutY) {
1145 Transform from;
1146 from.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 0.0);
1147
1148 Transform to;
1149
1150 to.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1151 to.Blend(from, 0.0);
1152 EXPECT_EQ(from, to);
1153
1154 double expectedRotationAngle = 22.5 * M_PI / 180.0;
1155 to = Transform();
1156 to.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1157 to.Blend(from, 0.25);
1158 EXPECT_ROW1_NEAR(std::cos(expectedRotationAngle),
1159 0.0,
1160 std::sin(expectedRotationAngle),
1161 0.0,
1162 to,
1163 ERROR_THRESHOLD);
1164 EXPECT_ROW2_NEAR(0.0, 1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1165 EXPECT_ROW3_NEAR(-std::sin(expectedRotationAngle),
1166 0.0,
1167 std::cos(expectedRotationAngle),
1168 0.0,
1169 to,
1170 ERROR_THRESHOLD);
1171 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1172
1173 expectedRotationAngle = 45.0 * M_PI / 180.0;
1174 to = Transform();
1175 to.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1176 to.Blend(from, 0.5);
1177 EXPECT_ROW1_NEAR(std::cos(expectedRotationAngle),
1178 0.0,
1179 std::sin(expectedRotationAngle),
1180 0.0,
1181 to,
1182 ERROR_THRESHOLD);
1183 EXPECT_ROW2_NEAR(0.0, 1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1184 EXPECT_ROW3_NEAR(-std::sin(expectedRotationAngle),
1185 0.0,
1186 std::cos(expectedRotationAngle),
1187 0.0,
1188 to,
1189 ERROR_THRESHOLD);
1190 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1191
1192 to = Transform();
1193 to.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1194 to.Blend(from, 1.0);
1195 EXPECT_ROW1_NEAR(0.0, 0.0, 1.0, 0.0, to, ERROR_THRESHOLD);
1196 EXPECT_ROW2_NEAR(0.0, 1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1197 EXPECT_ROW3_NEAR(-1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1198 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1199 }
1200
1201 #if defined(_WIN64)
1202 // http://crbug.com/406574
1203 #define MAYBE_VerifyBlendForRotationAboutZ DISABLED_VerifyBlendForRotationAboutZ
1204 #else
1205 #define MAYBE_VerifyBlendForRotationAboutZ VerifyBlendForRotationAboutZ
1206 #endif
1207 TEST(XFormTest, MAYBE_VerifyBlendForRotationAboutZ) {
1208 Transform from;
1209 from.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 0.0);
1210
1211 Transform to;
1212
1213 to.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1214 to.Blend(from, 0.0);
1215 EXPECT_EQ(from, to);
1216
1217 double expectedRotationAngle = 22.5 * M_PI / 180.0;
1218 to = Transform();
1219 to.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1220 to.Blend(from, 0.25);
1221 EXPECT_ROW1_NEAR(std::cos(expectedRotationAngle),
1222 -std::sin(expectedRotationAngle),
1223 0.0,
1224 0.0,
1225 to,
1226 ERROR_THRESHOLD);
1227 EXPECT_ROW2_NEAR(std::sin(expectedRotationAngle),
1228 std::cos(expectedRotationAngle),
1229 0.0,
1230 0.0,
1231 to,
1232 ERROR_THRESHOLD);
1233 EXPECT_ROW3_NEAR(0.0, 0.0, 1.0, 0.0, to, ERROR_THRESHOLD);
1234 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1235
1236 expectedRotationAngle = 45.0 * M_PI / 180.0;
1237 to = Transform();
1238 to.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1239 to.Blend(from, 0.5);
1240 EXPECT_ROW1_NEAR(std::cos(expectedRotationAngle),
1241 -std::sin(expectedRotationAngle),
1242 0.0,
1243 0.0,
1244 to,
1245 ERROR_THRESHOLD);
1246 EXPECT_ROW2_NEAR(std::sin(expectedRotationAngle),
1247 std::cos(expectedRotationAngle),
1248 0.0,
1249 0.0,
1250 to,
1251 ERROR_THRESHOLD);
1252 EXPECT_ROW3_NEAR(0.0, 0.0, 1.0, 0.0, to, ERROR_THRESHOLD);
1253 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1254
1255 to = Transform();
1256 to.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1257 to.Blend(from, 1.0);
1258 EXPECT_ROW1_NEAR(0.0, -1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1259 EXPECT_ROW2_NEAR(1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1260 EXPECT_ROW3_NEAR(0.0, 0.0, 1.0, 0.0, to, ERROR_THRESHOLD);
1261 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1262 }
1263
1264 TEST(XFormTest, VerifyBlendForCompositeTransform) {
1265 // Verify that the.Blending was done with a decomposition in correct order
1266 // by blending a composite transform. Using matrix x vector notation
1267 // (Ax = b, where x is column vector), the ordering should be:
1268 // perspective * translation * rotation * skew * scale
1269 //
1270 // It is not as important (or meaningful) to check intermediate
1271 // interpolations; order of operations will be tested well enough by the
1272 // end cases that are easier to specify.
1273
1274 Transform from;
1275 Transform to;
1276
1277 Transform expectedEndOfAnimation;
1278 expectedEndOfAnimation.ApplyPerspectiveDepth(1.0);
1279 expectedEndOfAnimation.Translate3d(10.0, 20.0, 30.0);
1280 expectedEndOfAnimation.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 25.0);
1281 expectedEndOfAnimation.SkewY(45.0);
1282 expectedEndOfAnimation.Scale3d(6.0, 7.0, 8.0);
1283
1284 to = expectedEndOfAnimation;
1285 to.Blend(from, 0.0);
1286 EXPECT_EQ(from, to);
1287
1288 to = expectedEndOfAnimation;
1289 // We short circuit if blend is >= 1, so to check the numerics, we will
1290 // check that we get close to what we expect when we're nearly done
1291 // interpolating.
1292 to.Blend(from, .99999f);
1293
1294 // Recomposing the matrix results in a normalized matrix, so to verify we
1295 // need to normalize the expectedEndOfAnimation before comparing elements.
1296 // Normalizing means dividing everything by expectedEndOfAnimation.m44().
1297 Transform normalizedExpectedEndOfAnimation = expectedEndOfAnimation;
1298 Transform normalizationMatrix;
1299 normalizationMatrix.matrix().set(
1300 0.0,
1301 0.0,
1302 SkDoubleToMScalar(1 / expectedEndOfAnimation.matrix().get(3.0, 3.0)));
1303 normalizationMatrix.matrix().set(
1304 1.0,
1305 1.0,
1306 SkDoubleToMScalar(1 / expectedEndOfAnimation.matrix().get(3.0, 3.0)));
1307 normalizationMatrix.matrix().set(
1308 2.0,
1309 2.0,
1310 SkDoubleToMScalar(1 / expectedEndOfAnimation.matrix().get(3.0, 3.0)));
1311 normalizationMatrix.matrix().set(
1312 3.0,
1313 3.0,
1314 SkDoubleToMScalar(1 / expectedEndOfAnimation.matrix().get(3.0, 3.0)));
1315 normalizedExpectedEndOfAnimation.PreconcatTransform(normalizationMatrix);
1316
1317 EXPECT_TRUE(MatricesAreNearlyEqual(normalizedExpectedEndOfAnimation, to));
1318 }
1319
1320 TEST(XFormTest, DecomposedTransformCtor) {
1321 DecomposedTransform decomp;
1322 for (int i = 0; i < 3; ++i) {
1323 EXPECT_EQ(0.0, decomp.translate[i]);
1324 EXPECT_EQ(1.0, decomp.scale[i]);
1325 EXPECT_EQ(0.0, decomp.skew[i]);
1326 EXPECT_EQ(0.0, decomp.quaternion[i]);
1327 EXPECT_EQ(0.0, decomp.perspective[i]);
1328 }
1329 EXPECT_EQ(1.0, decomp.quaternion[3]);
1330 EXPECT_EQ(1.0, decomp.perspective[3]);
1331 Transform identity;
1332 Transform composed = ComposeTransform(decomp);
1333 EXPECT_TRUE(MatricesAreNearlyEqual(identity, composed));
1334 }
1335
1336 TEST(XFormTest, FactorTRS) {
1337 for (int degrees = 0; degrees < 180; ++degrees) {
1338 // build a transformation matrix.
1339 gfx::Transform transform;
1340 transform.Translate(degrees * 2, -degrees * 3);
1341 transform.Rotate(degrees);
1342 transform.Scale(degrees + 1, 2 * degrees + 1);
1343
1344 // factor the matrix
1345 DecomposedTransform decomp;
1346 bool success = DecomposeTransform(&decomp, transform);
1347 EXPECT_TRUE(success);
1348 EXPECT_FLOAT_EQ(decomp.translate[0], degrees * 2);
1349 EXPECT_FLOAT_EQ(decomp.translate[1], -degrees * 3);
1350 double rotation =
1351 std::acos(SkMScalarToDouble(decomp.quaternion[3])) * 360.0 / M_PI;
1352 while (rotation < 0.0)
1353 rotation += 360.0;
1354 while (rotation > 360.0)
1355 rotation -= 360.0;
1356
1357 const float epsilon = 0.00015f;
1358 EXPECT_NEAR(rotation, degrees, epsilon);
1359 EXPECT_NEAR(decomp.scale[0], degrees + 1, epsilon);
1360 EXPECT_NEAR(decomp.scale[1], 2 * degrees + 1, epsilon);
1361 }
1362 }
1363
1364 TEST(XFormTest, IntegerTranslation) {
1365 gfx::Transform transform;
1366 EXPECT_TRUE(transform.IsIdentityOrIntegerTranslation());
1367
1368 transform.Translate3d(1, 2, 3);
1369 EXPECT_TRUE(transform.IsIdentityOrIntegerTranslation());
1370
1371 transform.MakeIdentity();
1372 transform.Translate3d(-1, -2, -3);
1373 EXPECT_TRUE(transform.IsIdentityOrIntegerTranslation());
1374
1375 transform.MakeIdentity();
1376 transform.Translate3d(4.5f, 0, 0);
1377 EXPECT_FALSE(transform.IsIdentityOrIntegerTranslation());
1378
1379 transform.MakeIdentity();
1380 transform.Translate3d(0, -6.7f, 0);
1381 EXPECT_FALSE(transform.IsIdentityOrIntegerTranslation());
1382
1383 transform.MakeIdentity();
1384 transform.Translate3d(0, 0, 8.9f);
1385 EXPECT_FALSE(transform.IsIdentityOrIntegerTranslation());
1386 }
1387
1388 TEST(XFormTest, verifyMatrixInversion) {
1389 {
1390 // Invert a translation
1391 gfx::Transform translation;
1392 translation.Translate3d(2.0, 3.0, 4.0);
1393 EXPECT_TRUE(translation.IsInvertible());
1394
1395 gfx::Transform inverse_translation;
1396 bool is_invertible = translation.GetInverse(&inverse_translation);
1397 EXPECT_TRUE(is_invertible);
1398 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, -2.0f, inverse_translation);
1399 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, -3.0f, inverse_translation);
1400 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, -4.0f, inverse_translation);
1401 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, inverse_translation);
1402 }
1403
1404 {
1405 // Invert a non-uniform scale
1406 gfx::Transform scale;
1407 scale.Scale3d(4.0, 10.0, 100.0);
1408 EXPECT_TRUE(scale.IsInvertible());
1409
1410 gfx::Transform inverse_scale;
1411 bool is_invertible = scale.GetInverse(&inverse_scale);
1412 EXPECT_TRUE(is_invertible);
1413 EXPECT_ROW1_EQ(0.25f, 0.0f, 0.0f, 0.0f, inverse_scale);
1414 EXPECT_ROW2_EQ(0.0f, 0.1f, 0.0f, 0.0f, inverse_scale);
1415 EXPECT_ROW3_EQ(0.0f, 0.0f, 0.01f, 0.0f, inverse_scale);
1416 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, inverse_scale);
1417 }
1418
1419 {
1420 // Try to invert a matrix that is not invertible.
1421 // The inverse() function should reset the output matrix to identity.
1422 gfx::Transform uninvertible;
1423 uninvertible.matrix().set(0, 0, 0.f);
1424 uninvertible.matrix().set(1, 1, 0.f);
1425 uninvertible.matrix().set(2, 2, 0.f);
1426 uninvertible.matrix().set(3, 3, 0.f);
1427 EXPECT_FALSE(uninvertible.IsInvertible());
1428
1429 gfx::Transform inverse_of_uninvertible;
1430
1431 // Add a scale just to more easily ensure that inverse_of_uninvertible is
1432 // reset to identity.
1433 inverse_of_uninvertible.Scale3d(4.0, 10.0, 100.0);
1434
1435 bool is_invertible = uninvertible.GetInverse(&inverse_of_uninvertible);
1436 EXPECT_FALSE(is_invertible);
1437 EXPECT_TRUE(inverse_of_uninvertible.IsIdentity());
1438 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, inverse_of_uninvertible);
1439 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, inverse_of_uninvertible);
1440 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, inverse_of_uninvertible);
1441 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, inverse_of_uninvertible);
1442 }
1443 }
1444
1445 TEST(XFormTest, verifyBackfaceVisibilityBasicCases) {
1446 Transform transform;
1447
1448 transform.MakeIdentity();
1449 EXPECT_FALSE(transform.IsBackFaceVisible());
1450
1451 transform.MakeIdentity();
1452 transform.RotateAboutYAxis(80.0);
1453 EXPECT_FALSE(transform.IsBackFaceVisible());
1454
1455 transform.MakeIdentity();
1456 transform.RotateAboutYAxis(100.0);
1457 EXPECT_TRUE(transform.IsBackFaceVisible());
1458
1459 // Edge case, 90 degree rotation should return false.
1460 transform.MakeIdentity();
1461 transform.RotateAboutYAxis(90.0);
1462 EXPECT_FALSE(transform.IsBackFaceVisible());
1463 }
1464
1465 TEST(XFormTest, verifyBackfaceVisibilityForPerspective) {
1466 Transform layer_space_to_projection_plane;
1467
1468 // This tests if IsBackFaceVisible works properly under perspective
1469 // transforms. Specifically, layers that may have their back face visible in
1470 // orthographic projection, may not actually have back face visible under
1471 // perspective projection.
1472
1473 // Case 1: Layer is rotated by slightly more than 90 degrees, at the center
1474 // of the prespective projection. In this case, the layer's back-side
1475 // is visible to the camera.
1476 layer_space_to_projection_plane.MakeIdentity();
1477 layer_space_to_projection_plane.ApplyPerspectiveDepth(1.0);
1478 layer_space_to_projection_plane.Translate3d(0.0, 0.0, 0.0);
1479 layer_space_to_projection_plane.RotateAboutYAxis(100.0);
1480 EXPECT_TRUE(layer_space_to_projection_plane.IsBackFaceVisible());
1481
1482 // Case 2: Layer is rotated by slightly more than 90 degrees, but shifted off
1483 // to the side of the camera. Because of the wide field-of-view, the
1484 // layer's front side is still visible.
1485 //
1486 // |<-- front side of layer is visible to camera
1487 // \ | /
1488 // \ | /
1489 // \| /
1490 // | /
1491 // |\ /<-- camera field of view
1492 // | \ /
1493 // back side of layer -->| \ /
1494 // \./ <-- camera origin
1495 //
1496 layer_space_to_projection_plane.MakeIdentity();
1497 layer_space_to_projection_plane.ApplyPerspectiveDepth(1.0);
1498 layer_space_to_projection_plane.Translate3d(-10.0, 0.0, 0.0);
1499 layer_space_to_projection_plane.RotateAboutYAxis(100.0);
1500 EXPECT_FALSE(layer_space_to_projection_plane.IsBackFaceVisible());
1501
1502 // Case 3: Additionally rotating the layer by 180 degrees should of course
1503 // show the opposite result of case 2.
1504 layer_space_to_projection_plane.RotateAboutYAxis(180.0);
1505 EXPECT_TRUE(layer_space_to_projection_plane.IsBackFaceVisible());
1506 }
1507
1508 TEST(XFormTest, verifyDefaultConstructorCreatesIdentityMatrix) {
1509 Transform A;
1510 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1511 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1512 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1513 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1514 EXPECT_TRUE(A.IsIdentity());
1515 }
1516
1517 TEST(XFormTest, verifyCopyConstructor) {
1518 Transform A;
1519 InitializeTestMatrix(&A);
1520
1521 // Copy constructor should produce exact same elements as matrix A.
1522 Transform B(A);
1523 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, B);
1524 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, B);
1525 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, B);
1526 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, B);
1527 }
1528
1529 TEST(XFormTest, verifyConstructorFor16Elements) {
1530 Transform transform(1.0, 2.0, 3.0, 4.0,
1531 5.0, 6.0, 7.0, 8.0,
1532 9.0, 10.0, 11.0, 12.0,
1533 13.0, 14.0, 15.0, 16.0);
1534
1535 EXPECT_ROW1_EQ(1.0f, 2.0f, 3.0f, 4.0f, transform);
1536 EXPECT_ROW2_EQ(5.0f, 6.0f, 7.0f, 8.0f, transform);
1537 EXPECT_ROW3_EQ(9.0f, 10.0f, 11.0f, 12.0f, transform);
1538 EXPECT_ROW4_EQ(13.0f, 14.0f, 15.0f, 16.0f, transform);
1539 }
1540
1541 TEST(XFormTest, verifyConstructorFor2dElements) {
1542 Transform transform(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
1543
1544 EXPECT_ROW1_EQ(1.0f, 2.0f, 0.0f, 5.0f, transform);
1545 EXPECT_ROW2_EQ(3.0f, 4.0f, 0.0f, 6.0f, transform);
1546 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, transform);
1547 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, transform);
1548 }
1549
1550
1551 TEST(XFormTest, verifyAssignmentOperator) {
1552 Transform A;
1553 InitializeTestMatrix(&A);
1554 Transform B;
1555 InitializeTestMatrix2(&B);
1556 Transform C;
1557 InitializeTestMatrix2(&C);
1558 C = B = A;
1559
1560 // Both B and C should now have been re-assigned to the value of A.
1561 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, B);
1562 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, B);
1563 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, B);
1564 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, B);
1565
1566 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, C);
1567 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, C);
1568 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, C);
1569 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, C);
1570 }
1571
1572 TEST(XFormTest, verifyEqualsBooleanOperator) {
1573 Transform A;
1574 InitializeTestMatrix(&A);
1575
1576 Transform B;
1577 InitializeTestMatrix(&B);
1578 EXPECT_TRUE(A == B);
1579
1580 // Modifying multiple elements should cause equals operator to return false.
1581 Transform C;
1582 InitializeTestMatrix2(&C);
1583 EXPECT_FALSE(A == C);
1584
1585 // Modifying any one individual element should cause equals operator to
1586 // return false.
1587 Transform D;
1588 D = A;
1589 D.matrix().set(0, 0, 0.f);
1590 EXPECT_FALSE(A == D);
1591
1592 D = A;
1593 D.matrix().set(1, 0, 0.f);
1594 EXPECT_FALSE(A == D);
1595
1596 D = A;
1597 D.matrix().set(2, 0, 0.f);
1598 EXPECT_FALSE(A == D);
1599
1600 D = A;
1601 D.matrix().set(3, 0, 0.f);
1602 EXPECT_FALSE(A == D);
1603
1604 D = A;
1605 D.matrix().set(0, 1, 0.f);
1606 EXPECT_FALSE(A == D);
1607
1608 D = A;
1609 D.matrix().set(1, 1, 0.f);
1610 EXPECT_FALSE(A == D);
1611
1612 D = A;
1613 D.matrix().set(2, 1, 0.f);
1614 EXPECT_FALSE(A == D);
1615
1616 D = A;
1617 D.matrix().set(3, 1, 0.f);
1618 EXPECT_FALSE(A == D);
1619
1620 D = A;
1621 D.matrix().set(0, 2, 0.f);
1622 EXPECT_FALSE(A == D);
1623
1624 D = A;
1625 D.matrix().set(1, 2, 0.f);
1626 EXPECT_FALSE(A == D);
1627
1628 D = A;
1629 D.matrix().set(2, 2, 0.f);
1630 EXPECT_FALSE(A == D);
1631
1632 D = A;
1633 D.matrix().set(3, 2, 0.f);
1634 EXPECT_FALSE(A == D);
1635
1636 D = A;
1637 D.matrix().set(0, 3, 0.f);
1638 EXPECT_FALSE(A == D);
1639
1640 D = A;
1641 D.matrix().set(1, 3, 0.f);
1642 EXPECT_FALSE(A == D);
1643
1644 D = A;
1645 D.matrix().set(2, 3, 0.f);
1646 EXPECT_FALSE(A == D);
1647
1648 D = A;
1649 D.matrix().set(3, 3, 0.f);
1650 EXPECT_FALSE(A == D);
1651 }
1652
1653 TEST(XFormTest, verifyMultiplyOperator) {
1654 Transform A;
1655 InitializeTestMatrix(&A);
1656
1657 Transform B;
1658 InitializeTestMatrix2(&B);
1659
1660 Transform C = A * B;
1661 EXPECT_ROW1_EQ(2036.0f, 2292.0f, 2548.0f, 2804.0f, C);
1662 EXPECT_ROW2_EQ(2162.0f, 2434.0f, 2706.0f, 2978.0f, C);
1663 EXPECT_ROW3_EQ(2288.0f, 2576.0f, 2864.0f, 3152.0f, C);
1664 EXPECT_ROW4_EQ(2414.0f, 2718.0f, 3022.0f, 3326.0f, C);
1665
1666 // Just an additional sanity check; matrix multiplication is not commutative.
1667 EXPECT_FALSE(A * B == B * A);
1668 }
1669
1670 TEST(XFormTest, verifyMultiplyAndAssignOperator) {
1671 Transform A;
1672 InitializeTestMatrix(&A);
1673
1674 Transform B;
1675 InitializeTestMatrix2(&B);
1676
1677 A *= B;
1678 EXPECT_ROW1_EQ(2036.0f, 2292.0f, 2548.0f, 2804.0f, A);
1679 EXPECT_ROW2_EQ(2162.0f, 2434.0f, 2706.0f, 2978.0f, A);
1680 EXPECT_ROW3_EQ(2288.0f, 2576.0f, 2864.0f, 3152.0f, A);
1681 EXPECT_ROW4_EQ(2414.0f, 2718.0f, 3022.0f, 3326.0f, A);
1682
1683 // Just an additional sanity check; matrix multiplication is not commutative.
1684 Transform C = A;
1685 C *= B;
1686 Transform D = B;
1687 D *= A;
1688 EXPECT_FALSE(C == D);
1689 }
1690
1691 TEST(XFormTest, verifyMatrixMultiplication) {
1692 Transform A;
1693 InitializeTestMatrix(&A);
1694
1695 Transform B;
1696 InitializeTestMatrix2(&B);
1697
1698 A.PreconcatTransform(B);
1699 EXPECT_ROW1_EQ(2036.0f, 2292.0f, 2548.0f, 2804.0f, A);
1700 EXPECT_ROW2_EQ(2162.0f, 2434.0f, 2706.0f, 2978.0f, A);
1701 EXPECT_ROW3_EQ(2288.0f, 2576.0f, 2864.0f, 3152.0f, A);
1702 EXPECT_ROW4_EQ(2414.0f, 2718.0f, 3022.0f, 3326.0f, A);
1703 }
1704
1705 TEST(XFormTest, verifyMakeIdentiy) {
1706 Transform A;
1707 InitializeTestMatrix(&A);
1708 A.MakeIdentity();
1709 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1710 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1711 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1712 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1713 EXPECT_TRUE(A.IsIdentity());
1714 }
1715
1716 TEST(XFormTest, verifyTranslate) {
1717 Transform A;
1718 A.Translate(2.0, 3.0);
1719 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 2.0f, A);
1720 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 3.0f, A);
1721 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1722 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1723
1724 // Verify that Translate() post-multiplies the existing matrix.
1725 A.MakeIdentity();
1726 A.Scale(5.0, 5.0);
1727 A.Translate(2.0, 3.0);
1728 EXPECT_ROW1_EQ(5.0f, 0.0f, 0.0f, 10.0f, A);
1729 EXPECT_ROW2_EQ(0.0f, 5.0f, 0.0f, 15.0f, A);
1730 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1731 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1732 }
1733
1734 TEST(XFormTest, verifyTranslate3d) {
1735 Transform A;
1736 A.Translate3d(2.0, 3.0, 4.0);
1737 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 2.0f, A);
1738 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 3.0f, A);
1739 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 4.0f, A);
1740 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1741
1742 // Verify that Translate3d() post-multiplies the existing matrix.
1743 A.MakeIdentity();
1744 A.Scale3d(6.0, 7.0, 8.0);
1745 A.Translate3d(2.0, 3.0, 4.0);
1746 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 12.0f, A);
1747 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 21.0f, A);
1748 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 32.0f, A);
1749 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1750 }
1751
1752 TEST(XFormTest, verifyScale) {
1753 Transform A;
1754 A.Scale(6.0, 7.0);
1755 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 0.0f, A);
1756 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 0.0f, A);
1757 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1758 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1759
1760 // Verify that Scale() post-multiplies the existing matrix.
1761 A.MakeIdentity();
1762 A.Translate3d(2.0, 3.0, 4.0);
1763 A.Scale(6.0, 7.0);
1764 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 2.0f, A);
1765 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 3.0f, A);
1766 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 4.0f, A);
1767 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1768 }
1769
1770 TEST(XFormTest, verifyScale3d) {
1771 Transform A;
1772 A.Scale3d(6.0, 7.0, 8.0);
1773 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 0.0f, A);
1774 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 0.0f, A);
1775 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1776 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1777
1778 // Verify that scale3d() post-multiplies the existing matrix.
1779 A.MakeIdentity();
1780 A.Translate3d(2.0, 3.0, 4.0);
1781 A.Scale3d(6.0, 7.0, 8.0);
1782 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 2.0f, A);
1783 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 3.0f, A);
1784 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 4.0f, A);
1785 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1786 }
1787
1788 TEST(XFormTest, verifyRotate) {
1789 Transform A;
1790 A.Rotate(90.0);
1791 EXPECT_ROW1_NEAR(0.0, -1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1792 EXPECT_ROW2_NEAR(1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1793 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1794 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1795
1796 // Verify that Rotate() post-multiplies the existing matrix.
1797 A.MakeIdentity();
1798 A.Scale3d(6.0, 7.0, 8.0);
1799 A.Rotate(90.0);
1800 EXPECT_ROW1_NEAR(0.0, -6.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1801 EXPECT_ROW2_NEAR(7.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1802 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1803 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1804 }
1805
1806 TEST(XFormTest, verifyRotateAboutXAxis) {
1807 Transform A;
1808 double sin45 = 0.5 * sqrt(2.0);
1809 double cos45 = sin45;
1810
1811 A.MakeIdentity();
1812 A.RotateAboutXAxis(90.0);
1813 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1814 EXPECT_ROW2_NEAR(0.0, 0.0, -1.0, 0.0, A, ERROR_THRESHOLD);
1815 EXPECT_ROW3_NEAR(0.0, 1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1816 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1817
1818 A.MakeIdentity();
1819 A.RotateAboutXAxis(45.0);
1820 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1821 EXPECT_ROW2_NEAR(0.0, cos45, -sin45, 0.0, A, ERROR_THRESHOLD);
1822 EXPECT_ROW3_NEAR(0.0, sin45, cos45, 0.0, A, ERROR_THRESHOLD);
1823 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1824
1825 // Verify that RotateAboutXAxis(angle) post-multiplies the existing matrix.
1826 A.MakeIdentity();
1827 A.Scale3d(6.0, 7.0, 8.0);
1828 A.RotateAboutXAxis(90.0);
1829 EXPECT_ROW1_NEAR(6.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1830 EXPECT_ROW2_NEAR(0.0, 0.0, -7.0, 0.0, A, ERROR_THRESHOLD);
1831 EXPECT_ROW3_NEAR(0.0, 8.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1832 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1833 }
1834
1835 TEST(XFormTest, verifyRotateAboutYAxis) {
1836 Transform A;
1837 double sin45 = 0.5 * sqrt(2.0);
1838 double cos45 = sin45;
1839
1840 // Note carefully, the expected pattern is inverted compared to rotating
1841 // about x axis or z axis.
1842 A.MakeIdentity();
1843 A.RotateAboutYAxis(90.0);
1844 EXPECT_ROW1_NEAR(0.0, 0.0, 1.0, 0.0, A, ERROR_THRESHOLD);
1845 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1846 EXPECT_ROW3_NEAR(-1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1847 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1848
1849 A.MakeIdentity();
1850 A.RotateAboutYAxis(45.0);
1851 EXPECT_ROW1_NEAR(cos45, 0.0, sin45, 0.0, A, ERROR_THRESHOLD);
1852 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1853 EXPECT_ROW3_NEAR(-sin45, 0.0, cos45, 0.0, A, ERROR_THRESHOLD);
1854 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1855
1856 // Verify that RotateAboutYAxis(angle) post-multiplies the existing matrix.
1857 A.MakeIdentity();
1858 A.Scale3d(6.0, 7.0, 8.0);
1859 A.RotateAboutYAxis(90.0);
1860 EXPECT_ROW1_NEAR(0.0, 0.0, 6.0, 0.0, A, ERROR_THRESHOLD);
1861 EXPECT_ROW2_NEAR(0.0, 7.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1862 EXPECT_ROW3_NEAR(-8.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1863 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1864 }
1865
1866 TEST(XFormTest, verifyRotateAboutZAxis) {
1867 Transform A;
1868 double sin45 = 0.5 * sqrt(2.0);
1869 double cos45 = sin45;
1870
1871 A.MakeIdentity();
1872 A.RotateAboutZAxis(90.0);
1873 EXPECT_ROW1_NEAR(0.0, -1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1874 EXPECT_ROW2_NEAR(1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1875 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1876 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1877
1878 A.MakeIdentity();
1879 A.RotateAboutZAxis(45.0);
1880 EXPECT_ROW1_NEAR(cos45, -sin45, 0.0, 0.0, A, ERROR_THRESHOLD);
1881 EXPECT_ROW2_NEAR(sin45, cos45, 0.0, 0.0, A, ERROR_THRESHOLD);
1882 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1883 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1884
1885 // Verify that RotateAboutZAxis(angle) post-multiplies the existing matrix.
1886 A.MakeIdentity();
1887 A.Scale3d(6.0, 7.0, 8.0);
1888 A.RotateAboutZAxis(90.0);
1889 EXPECT_ROW1_NEAR(0.0, -6.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1890 EXPECT_ROW2_NEAR(7.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1891 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1892 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1893 }
1894
1895 TEST(XFormTest, verifyRotateAboutForAlignedAxes) {
1896 Transform A;
1897
1898 // Check rotation about z-axis
1899 A.MakeIdentity();
1900 A.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1901 EXPECT_ROW1_NEAR(0.0, -1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1902 EXPECT_ROW2_NEAR(1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1903 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1904 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1905
1906 // Check rotation about x-axis
1907 A.MakeIdentity();
1908 A.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1909 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1910 EXPECT_ROW2_NEAR(0.0, 0.0, -1.0, 0.0, A, ERROR_THRESHOLD);
1911 EXPECT_ROW3_NEAR(0.0, 1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1912 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1913
1914 // Check rotation about y-axis. Note carefully, the expected pattern is
1915 // inverted compared to rotating about x axis or z axis.
1916 A.MakeIdentity();
1917 A.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1918 EXPECT_ROW1_NEAR(0.0, 0.0, 1.0, 0.0, A, ERROR_THRESHOLD);
1919 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1920 EXPECT_ROW3_NEAR(-1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1921 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1922
1923 // Verify that rotate3d(axis, angle) post-multiplies the existing matrix.
1924 A.MakeIdentity();
1925 A.Scale3d(6.0, 7.0, 8.0);
1926 A.RotateAboutZAxis(90.0);
1927 EXPECT_ROW1_NEAR(0.0, -6.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1928 EXPECT_ROW2_NEAR(7.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1929 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1930 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1931 }
1932
1933 TEST(XFormTest, verifyRotateAboutForArbitraryAxis) {
1934 // Check rotation about an arbitrary non-axis-aligned vector.
1935 Transform A;
1936 A.RotateAbout(Vector3dF(1.0, 1.0, 1.0), 90.0);
1937 EXPECT_ROW1_NEAR(0.3333333333333334258519187,
1938 -0.2440169358562924717404030,
1939 0.9106836025229592124219380,
1940 0.0, A, ERROR_THRESHOLD);
1941 EXPECT_ROW2_NEAR(0.9106836025229592124219380,
1942 0.3333333333333334258519187,
1943 -0.2440169358562924717404030,
1944 0.0, A, ERROR_THRESHOLD);
1945 EXPECT_ROW3_NEAR(-0.2440169358562924717404030,
1946 0.9106836025229592124219380,
1947 0.3333333333333334258519187,
1948 0.0, A, ERROR_THRESHOLD);
1949 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1950 }
1951
1952 TEST(XFormTest, verifyRotateAboutForDegenerateAxis) {
1953 // Check rotation about a degenerate zero vector.
1954 // It is expected to skip applying the rotation.
1955 Transform A;
1956
1957 A.RotateAbout(Vector3dF(0.0, 0.0, 0.0), 45.0);
1958 // Verify that A remains unchanged.
1959 EXPECT_TRUE(A.IsIdentity());
1960
1961 InitializeTestMatrix(&A);
1962 A.RotateAbout(Vector3dF(0.0, 0.0, 0.0), 35.0);
1963
1964 // Verify that A remains unchanged.
1965 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, A);
1966 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, A);
1967 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, A);
1968 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, A);
1969 }
1970
1971 TEST(XFormTest, verifySkewX) {
1972 Transform A;
1973 A.SkewX(45.0);
1974 EXPECT_ROW1_EQ(1.0f, 1.0f, 0.0f, 0.0f, A);
1975 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1976 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1977 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1978
1979 // Verify that skewX() post-multiplies the existing matrix. Row 1, column 2,
1980 // would incorrectly have value "7" if the matrix is pre-multiplied instead
1981 // of post-multiplied.
1982 A.MakeIdentity();
1983 A.Scale3d(6.0, 7.0, 8.0);
1984 A.SkewX(45.0);
1985 EXPECT_ROW1_EQ(6.0f, 6.0f, 0.0f, 0.0f, A);
1986 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 0.0f, A);
1987 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1988 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1989 }
1990
1991 TEST(XFormTest, verifySkewY) {
1992 Transform A;
1993 A.SkewY(45.0);
1994 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1995 EXPECT_ROW2_EQ(1.0f, 1.0f, 0.0f, 0.0f, A);
1996 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1997 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1998
1999 // Verify that skewY() post-multiplies the existing matrix. Row 2, column 1 ,
2000 // would incorrectly have value "6" if the matrix is pre-multiplied instead
2001 // of post-multiplied.
2002 A.MakeIdentity();
2003 A.Scale3d(6.0, 7.0, 8.0);
2004 A.SkewY(45.0);
2005 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 0.0f, A);
2006 EXPECT_ROW2_EQ(7.0f, 7.0f, 0.0f, 0.0f, A);
2007 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
2008 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
2009 }
2010
2011 TEST(XFormTest, verifyPerspectiveDepth) {
2012 Transform A;
2013 A.ApplyPerspectiveDepth(1.0);
2014 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
2015 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
2016 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
2017 EXPECT_ROW4_EQ(0.0f, 0.0f, -1.0f, 1.0f, A);
2018
2019 // Verify that PerspectiveDepth() post-multiplies the existing matrix.
2020 A.MakeIdentity();
2021 A.Translate3d(2.0, 3.0, 4.0);
2022 A.ApplyPerspectiveDepth(1.0);
2023 EXPECT_ROW1_EQ(1.0f, 0.0f, -2.0f, 2.0f, A);
2024 EXPECT_ROW2_EQ(0.0f, 1.0f, -3.0f, 3.0f, A);
2025 EXPECT_ROW3_EQ(0.0f, 0.0f, -3.0f, 4.0f, A);
2026 EXPECT_ROW4_EQ(0.0f, 0.0f, -1.0f, 1.0f, A);
2027 }
2028
2029 TEST(XFormTest, verifyHasPerspective) {
2030 Transform A;
2031 A.ApplyPerspectiveDepth(1.0);
2032 EXPECT_TRUE(A.HasPerspective());
2033
2034 A.MakeIdentity();
2035 A.ApplyPerspectiveDepth(0.0);
2036 EXPECT_FALSE(A.HasPerspective());
2037
2038 A.MakeIdentity();
2039 A.matrix().set(3, 0, -1.f);
2040 EXPECT_TRUE(A.HasPerspective());
2041
2042 A.MakeIdentity();
2043 A.matrix().set(3, 1, -1.f);
2044 EXPECT_TRUE(A.HasPerspective());
2045
2046 A.MakeIdentity();
2047 A.matrix().set(3, 2, -0.3f);
2048 EXPECT_TRUE(A.HasPerspective());
2049
2050 A.MakeIdentity();
2051 A.matrix().set(3, 3, 0.5f);
2052 EXPECT_TRUE(A.HasPerspective());
2053
2054 A.MakeIdentity();
2055 A.matrix().set(3, 3, 0.f);
2056 EXPECT_TRUE(A.HasPerspective());
2057 }
2058
2059 TEST(XFormTest, verifyIsInvertible) {
2060 Transform A;
2061
2062 // Translations, rotations, scales, skews and arbitrary combinations of them
2063 // are invertible.
2064 A.MakeIdentity();
2065 EXPECT_TRUE(A.IsInvertible());
2066
2067 A.MakeIdentity();
2068 A.Translate3d(2.0, 3.0, 4.0);
2069 EXPECT_TRUE(A.IsInvertible());
2070
2071 A.MakeIdentity();
2072 A.Scale3d(6.0, 7.0, 8.0);
2073 EXPECT_TRUE(A.IsInvertible());
2074
2075 A.MakeIdentity();
2076 A.RotateAboutXAxis(10.0);
2077 A.RotateAboutYAxis(20.0);
2078 A.RotateAboutZAxis(30.0);
2079 EXPECT_TRUE(A.IsInvertible());
2080
2081 A.MakeIdentity();
2082 A.SkewX(45.0);
2083 EXPECT_TRUE(A.IsInvertible());
2084
2085 // A perspective matrix (projection plane at z=0) is invertible. The
2086 // intuitive explanation is that perspective is eqivalent to a skew of the
2087 // w-axis; skews are invertible.
2088 A.MakeIdentity();
2089 A.ApplyPerspectiveDepth(1.0);
2090 EXPECT_TRUE(A.IsInvertible());
2091
2092 // A "pure" perspective matrix derived by similar triangles, with m44() set
2093 // to zero (i.e. camera positioned at the origin), is not invertible.
2094 A.MakeIdentity();
2095 A.ApplyPerspectiveDepth(1.0);
2096 A.matrix().set(3, 3, 0.f);
2097 EXPECT_FALSE(A.IsInvertible());
2098
2099 // Adding more to a non-invertible matrix will not make it invertible in the
2100 // general case.
2101 A.MakeIdentity();
2102 A.ApplyPerspectiveDepth(1.0);
2103 A.matrix().set(3, 3, 0.f);
2104 A.Scale3d(6.0, 7.0, 8.0);
2105 A.RotateAboutXAxis(10.0);
2106 A.RotateAboutYAxis(20.0);
2107 A.RotateAboutZAxis(30.0);
2108 A.Translate3d(6.0, 7.0, 8.0);
2109 EXPECT_FALSE(A.IsInvertible());
2110
2111 // A degenerate matrix of all zeros is not invertible.
2112 A.MakeIdentity();
2113 A.matrix().set(0, 0, 0.f);
2114 A.matrix().set(1, 1, 0.f);
2115 A.matrix().set(2, 2, 0.f);
2116 A.matrix().set(3, 3, 0.f);
2117 EXPECT_FALSE(A.IsInvertible());
2118 }
2119
2120 TEST(XFormTest, verifyIsIdentity) {
2121 Transform A;
2122
2123 InitializeTestMatrix(&A);
2124 EXPECT_FALSE(A.IsIdentity());
2125
2126 A.MakeIdentity();
2127 EXPECT_TRUE(A.IsIdentity());
2128
2129 // Modifying any one individual element should cause the matrix to no longer
2130 // be identity.
2131 A.MakeIdentity();
2132 A.matrix().set(0, 0, 2.f);
2133 EXPECT_FALSE(A.IsIdentity());
2134
2135 A.MakeIdentity();
2136 A.matrix().set(1, 0, 2.f);
2137 EXPECT_FALSE(A.IsIdentity());
2138
2139 A.MakeIdentity();
2140 A.matrix().set(2, 0, 2.f);
2141 EXPECT_FALSE(A.IsIdentity());
2142
2143 A.MakeIdentity();
2144 A.matrix().set(3, 0, 2.f);
2145 EXPECT_FALSE(A.IsIdentity());
2146
2147 A.MakeIdentity();
2148 A.matrix().set(0, 1, 2.f);
2149 EXPECT_FALSE(A.IsIdentity());
2150
2151 A.MakeIdentity();
2152 A.matrix().set(1, 1, 2.f);
2153 EXPECT_FALSE(A.IsIdentity());
2154
2155 A.MakeIdentity();
2156 A.matrix().set(2, 1, 2.f);
2157 EXPECT_FALSE(A.IsIdentity());
2158
2159 A.MakeIdentity();
2160 A.matrix().set(3, 1, 2.f);
2161 EXPECT_FALSE(A.IsIdentity());
2162
2163 A.MakeIdentity();
2164 A.matrix().set(0, 2, 2.f);
2165 EXPECT_FALSE(A.IsIdentity());
2166
2167 A.MakeIdentity();
2168 A.matrix().set(1, 2, 2.f);
2169 EXPECT_FALSE(A.IsIdentity());
2170
2171 A.MakeIdentity();
2172 A.matrix().set(2, 2, 2.f);
2173 EXPECT_FALSE(A.IsIdentity());
2174
2175 A.MakeIdentity();
2176 A.matrix().set(3, 2, 2.f);
2177 EXPECT_FALSE(A.IsIdentity());
2178
2179 A.MakeIdentity();
2180 A.matrix().set(0, 3, 2.f);
2181 EXPECT_FALSE(A.IsIdentity());
2182
2183 A.MakeIdentity();
2184 A.matrix().set(1, 3, 2.f);
2185 EXPECT_FALSE(A.IsIdentity());
2186
2187 A.MakeIdentity();
2188 A.matrix().set(2, 3, 2.f);
2189 EXPECT_FALSE(A.IsIdentity());
2190
2191 A.MakeIdentity();
2192 A.matrix().set(3, 3, 2.f);
2193 EXPECT_FALSE(A.IsIdentity());
2194 }
2195
2196 TEST(XFormTest, verifyIsIdentityOrTranslation) {
2197 Transform A;
2198
2199 InitializeTestMatrix(&A);
2200 EXPECT_FALSE(A.IsIdentityOrTranslation());
2201
2202 A.MakeIdentity();
2203 EXPECT_TRUE(A.IsIdentityOrTranslation());
2204
2205 // Modifying any non-translation components should cause
2206 // IsIdentityOrTranslation() to return false. NOTE: (0, 3), (1, 3), and
2207 // (2, 3) are the translation components, so modifying them should still
2208 // return true.
2209 A.MakeIdentity();
2210 A.matrix().set(0, 0, 2.f);
2211 EXPECT_FALSE(A.IsIdentityOrTranslation());
2212
2213 A.MakeIdentity();
2214 A.matrix().set(1, 0, 2.f);
2215 EXPECT_FALSE(A.IsIdentityOrTranslation());
2216
2217 A.MakeIdentity();
2218 A.matrix().set(2, 0, 2.f);
2219 EXPECT_FALSE(A.IsIdentityOrTranslation());
2220
2221 A.MakeIdentity();
2222 A.matrix().set(3, 0, 2.f);
2223 EXPECT_FALSE(A.IsIdentityOrTranslation());
2224
2225 A.MakeIdentity();
2226 A.matrix().set(0, 1, 2.f);
2227 EXPECT_FALSE(A.IsIdentityOrTranslation());
2228
2229 A.MakeIdentity();
2230 A.matrix().set(1, 1, 2.f);
2231 EXPECT_FALSE(A.IsIdentityOrTranslation());
2232
2233 A.MakeIdentity();
2234 A.matrix().set(2, 1, 2.f);
2235 EXPECT_FALSE(A.IsIdentityOrTranslation());
2236
2237 A.MakeIdentity();
2238 A.matrix().set(3, 1, 2.f);
2239 EXPECT_FALSE(A.IsIdentityOrTranslation());
2240
2241 A.MakeIdentity();
2242 A.matrix().set(0, 2, 2.f);
2243 EXPECT_FALSE(A.IsIdentityOrTranslation());
2244
2245 A.MakeIdentity();
2246 A.matrix().set(1, 2, 2.f);
2247 EXPECT_FALSE(A.IsIdentityOrTranslation());
2248
2249 A.MakeIdentity();
2250 A.matrix().set(2, 2, 2.f);
2251 EXPECT_FALSE(A.IsIdentityOrTranslation());
2252
2253 A.MakeIdentity();
2254 A.matrix().set(3, 2, 2.f);
2255 EXPECT_FALSE(A.IsIdentityOrTranslation());
2256
2257 // Note carefully - expecting true here.
2258 A.MakeIdentity();
2259 A.matrix().set(0, 3, 2.f);
2260 EXPECT_TRUE(A.IsIdentityOrTranslation());
2261
2262 // Note carefully - expecting true here.
2263 A.MakeIdentity();
2264 A.matrix().set(1, 3, 2.f);
2265 EXPECT_TRUE(A.IsIdentityOrTranslation());
2266
2267 // Note carefully - expecting true here.
2268 A.MakeIdentity();
2269 A.matrix().set(2, 3, 2.f);
2270 EXPECT_TRUE(A.IsIdentityOrTranslation());
2271
2272 A.MakeIdentity();
2273 A.matrix().set(3, 3, 2.f);
2274 EXPECT_FALSE(A.IsIdentityOrTranslation());
2275 }
2276
2277 TEST(XFormTest, verifyIsApproximatelyIdentityOrTranslation) {
2278 Transform A;
2279 SkMatrix44& matrix = A.matrix();
2280
2281 // Exact pure translation.
2282 A.MakeIdentity();
2283
2284 // Set translate values to values other than 0 or 1.
2285 matrix.set(0, 3, 3.4f);
2286 matrix.set(1, 3, 4.4f);
2287 matrix.set(2, 3, 5.6f);
2288
2289 EXPECT_TRUE(A.IsApproximatelyIdentityOrTranslation(0));
2290 EXPECT_TRUE(A.IsApproximatelyIdentityOrTranslation(kApproxZero));
2291
2292 // Approximately pure translation.
2293 InitializeApproxIdentityMatrix(&A);
2294
2295 // Some values must be exact.
2296 matrix.set(3, 0, 0);
2297 matrix.set(3, 1, 0);
2298 matrix.set(3, 2, 0);
2299 matrix.set(3, 3, 1);
2300
2301 // Set translate values to values other than 0 or 1.
2302 matrix.set(0, 3, 3.4f);
2303 matrix.set(1, 3, 4.4f);
2304 matrix.set(2, 3, 5.6f);
2305
2306 EXPECT_FALSE(A.IsApproximatelyIdentityOrTranslation(0));
2307 EXPECT_TRUE(A.IsApproximatelyIdentityOrTranslation(kApproxZero));
2308
2309 // Not approximately pure translation.
2310 InitializeApproxIdentityMatrix(&A);
2311
2312 // Some values must be exact.
2313 matrix.set(3, 0, 0);
2314 matrix.set(3, 1, 0);
2315 matrix.set(3, 2, 0);
2316 matrix.set(3, 3, 1);
2317
2318 // Set some values (not translate values) to values other than 0 or 1.
2319 matrix.set(0, 1, 3.4f);
2320 matrix.set(3, 2, 4.4f);
2321 matrix.set(2, 0, 5.6f);
2322
2323 EXPECT_FALSE(A.IsApproximatelyIdentityOrTranslation(0));
2324 EXPECT_FALSE(A.IsApproximatelyIdentityOrTranslation(kApproxZero));
2325 }
2326
2327 TEST(XFormTest, verifyIsScaleOrTranslation) {
2328 Transform A;
2329
2330 InitializeTestMatrix(&A);
2331 EXPECT_FALSE(A.IsScaleOrTranslation());
2332
2333 A.MakeIdentity();
2334 EXPECT_TRUE(A.IsScaleOrTranslation());
2335
2336 // Modifying any non-scale or non-translation components should cause
2337 // IsScaleOrTranslation() to return false. (0, 0), (1, 1), (2, 2), (0, 3),
2338 // (1, 3), and (2, 3) are the scale and translation components, so
2339 // modifying them should still return true.
2340
2341 // Note carefully - expecting true here.
2342 A.MakeIdentity();
2343 A.matrix().set(0, 0, 2.f);
2344 EXPECT_TRUE(A.IsScaleOrTranslation());
2345
2346 A.MakeIdentity();
2347 A.matrix().set(1, 0, 2.f);
2348 EXPECT_FALSE(A.IsScaleOrTranslation());
2349
2350 A.MakeIdentity();
2351 A.matrix().set(2, 0, 2.f);
2352 EXPECT_FALSE(A.IsScaleOrTranslation());
2353
2354 A.MakeIdentity();
2355 A.matrix().set(3, 0, 2.f);
2356 EXPECT_FALSE(A.IsScaleOrTranslation());
2357
2358 A.MakeIdentity();
2359 A.matrix().set(0, 1, 2.f);
2360 EXPECT_FALSE(A.IsScaleOrTranslation());
2361
2362 // Note carefully - expecting true here.
2363 A.MakeIdentity();
2364 A.matrix().set(1, 1, 2.f);
2365 EXPECT_TRUE(A.IsScaleOrTranslation());
2366
2367 A.MakeIdentity();
2368 A.matrix().set(2, 1, 2.f);
2369 EXPECT_FALSE(A.IsScaleOrTranslation());
2370
2371 A.MakeIdentity();
2372 A.matrix().set(3, 1, 2.f);
2373 EXPECT_FALSE(A.IsScaleOrTranslation());
2374
2375 A.MakeIdentity();
2376 A.matrix().set(0, 2, 2.f);
2377 EXPECT_FALSE(A.IsScaleOrTranslation());
2378
2379 A.MakeIdentity();
2380 A.matrix().set(1, 2, 2.f);
2381 EXPECT_FALSE(A.IsScaleOrTranslation());
2382
2383 // Note carefully - expecting true here.
2384 A.MakeIdentity();
2385 A.matrix().set(2, 2, 2.f);
2386 EXPECT_TRUE(A.IsScaleOrTranslation());
2387
2388 A.MakeIdentity();
2389 A.matrix().set(3, 2, 2.f);
2390 EXPECT_FALSE(A.IsScaleOrTranslation());
2391
2392 // Note carefully - expecting true here.
2393 A.MakeIdentity();
2394 A.matrix().set(0, 3, 2.f);
2395 EXPECT_TRUE(A.IsScaleOrTranslation());
2396
2397 // Note carefully - expecting true here.
2398 A.MakeIdentity();
2399 A.matrix().set(1, 3, 2.f);
2400 EXPECT_TRUE(A.IsScaleOrTranslation());
2401
2402 // Note carefully - expecting true here.
2403 A.MakeIdentity();
2404 A.matrix().set(2, 3, 2.f);
2405 EXPECT_TRUE(A.IsScaleOrTranslation());
2406
2407 A.MakeIdentity();
2408 A.matrix().set(3, 3, 2.f);
2409 EXPECT_FALSE(A.IsScaleOrTranslation());
2410 }
2411
2412 TEST(XFormTest, verifyFlattenTo2d) {
2413 Transform A;
2414 InitializeTestMatrix(&A);
2415
2416 A.FlattenTo2d();
2417 EXPECT_ROW1_EQ(10.0f, 14.0f, 0.0f, 22.0f, A);
2418 EXPECT_ROW2_EQ(11.0f, 15.0f, 0.0f, 23.0f, A);
2419 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
2420 EXPECT_ROW4_EQ(13.0f, 17.0f, 0.0f, 25.0f, A);
2421 }
2422
2423 // Another implementation of Preserves2dAxisAlignment that isn't as fast,
2424 // good for testing the faster implementation.
2425 static bool EmpiricallyPreserves2dAxisAlignment(const Transform& transform) {
2426 Point3F p1(5.0f, 5.0f, 0.0f);
2427 Point3F p2(10.0f, 5.0f, 0.0f);
2428 Point3F p3(10.0f, 20.0f, 0.0f);
2429 Point3F p4(5.0f, 20.0f, 0.0f);
2430
2431 QuadF test_quad(PointF(p1.x(), p1.y()),
2432 PointF(p2.x(), p2.y()),
2433 PointF(p3.x(), p3.y()),
2434 PointF(p4.x(), p4.y()));
2435 EXPECT_TRUE(test_quad.IsRectilinear());
2436
2437 transform.TransformPoint(&p1);
2438 transform.TransformPoint(&p2);
2439 transform.TransformPoint(&p3);
2440 transform.TransformPoint(&p4);
2441
2442 QuadF transformedQuad(PointF(p1.x(), p1.y()),
2443 PointF(p2.x(), p2.y()),
2444 PointF(p3.x(), p3.y()),
2445 PointF(p4.x(), p4.y()));
2446 return transformedQuad.IsRectilinear();
2447 }
2448
2449 TEST(XFormTest, Preserves2dAxisAlignment) {
2450 static const struct TestCase {
2451 SkMScalar a; // row 1, column 1
2452 SkMScalar b; // row 1, column 2
2453 SkMScalar c; // row 2, column 1
2454 SkMScalar d; // row 2, column 2
2455 bool expected;
2456 } test_cases[] = {
2457 { 3.f, 0.f,
2458 0.f, 4.f, true }, // basic case
2459 { 0.f, 4.f,
2460 3.f, 0.f, true }, // rotate by 90
2461 { 0.f, 0.f,
2462 0.f, 4.f, true }, // degenerate x
2463 { 3.f, 0.f,
2464 0.f, 0.f, true }, // degenerate y
2465 { 0.f, 0.f,
2466 3.f, 0.f, true }, // degenerate x + rotate by 90
2467 { 0.f, 4.f,
2468 0.f, 0.f, true }, // degenerate y + rotate by 90
2469 { 3.f, 4.f,
2470 0.f, 0.f, false },
2471 { 0.f, 0.f,
2472 3.f, 4.f, false },
2473 { 0.f, 3.f,
2474 0.f, 4.f, false },
2475 { 3.f, 0.f,
2476 4.f, 0.f, false },
2477 { 3.f, 4.f,
2478 5.f, 0.f, false },
2479 { 3.f, 4.f,
2480 0.f, 5.f, false },
2481 { 3.f, 0.f,
2482 4.f, 5.f, false },
2483 { 0.f, 3.f,
2484 4.f, 5.f, false },
2485 { 2.f, 3.f,
2486 4.f, 5.f, false },
2487 };
2488
2489 Transform transform;
2490 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
2491 const TestCase& value = test_cases[i];
2492 transform.MakeIdentity();
2493 transform.matrix().set(0, 0, value.a);
2494 transform.matrix().set(0, 1, value.b);
2495 transform.matrix().set(1, 0, value.c);
2496 transform.matrix().set(1, 1, value.d);
2497
2498 if (value.expected) {
2499 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2500 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2501 } else {
2502 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2503 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2504 }
2505 }
2506
2507 // Try the same test cases again, but this time make sure that other matrix
2508 // elements (except perspective) have entries, to test that they are ignored.
2509 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
2510 const TestCase& value = test_cases[i];
2511 transform.MakeIdentity();
2512 transform.matrix().set(0, 0, value.a);
2513 transform.matrix().set(0, 1, value.b);
2514 transform.matrix().set(1, 0, value.c);
2515 transform.matrix().set(1, 1, value.d);
2516
2517 transform.matrix().set(0, 2, 1.f);
2518 transform.matrix().set(0, 3, 2.f);
2519 transform.matrix().set(1, 2, 3.f);
2520 transform.matrix().set(1, 3, 4.f);
2521 transform.matrix().set(2, 0, 5.f);
2522 transform.matrix().set(2, 1, 6.f);
2523 transform.matrix().set(2, 2, 7.f);
2524 transform.matrix().set(2, 3, 8.f);
2525
2526 if (value.expected) {
2527 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2528 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2529 } else {
2530 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2531 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2532 }
2533 }
2534
2535 // Try the same test cases again, but this time add perspective which is
2536 // always assumed to not-preserve axis alignment.
2537 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
2538 const TestCase& value = test_cases[i];
2539 transform.MakeIdentity();
2540 transform.matrix().set(0, 0, value.a);
2541 transform.matrix().set(0, 1, value.b);
2542 transform.matrix().set(1, 0, value.c);
2543 transform.matrix().set(1, 1, value.d);
2544
2545 transform.matrix().set(0, 2, 1.f);
2546 transform.matrix().set(0, 3, 2.f);
2547 transform.matrix().set(1, 2, 3.f);
2548 transform.matrix().set(1, 3, 4.f);
2549 transform.matrix().set(2, 0, 5.f);
2550 transform.matrix().set(2, 1, 6.f);
2551 transform.matrix().set(2, 2, 7.f);
2552 transform.matrix().set(2, 3, 8.f);
2553 transform.matrix().set(3, 0, 9.f);
2554 transform.matrix().set(3, 1, 10.f);
2555 transform.matrix().set(3, 2, 11.f);
2556 transform.matrix().set(3, 3, 12.f);
2557
2558 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2559 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2560 }
2561
2562 // Try a few more practical situations to check precision
2563 transform.MakeIdentity();
2564 transform.RotateAboutZAxis(90.0);
2565 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2566 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2567
2568 transform.MakeIdentity();
2569 transform.RotateAboutZAxis(180.0);
2570 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2571 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2572
2573 transform.MakeIdentity();
2574 transform.RotateAboutZAxis(270.0);
2575 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2576 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2577
2578 transform.MakeIdentity();
2579 transform.RotateAboutYAxis(90.0);
2580 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2581 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2582
2583 transform.MakeIdentity();
2584 transform.RotateAboutXAxis(90.0);
2585 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2586 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2587
2588 transform.MakeIdentity();
2589 transform.RotateAboutZAxis(90.0);
2590 transform.RotateAboutYAxis(90.0);
2591 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2592 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2593
2594 transform.MakeIdentity();
2595 transform.RotateAboutZAxis(90.0);
2596 transform.RotateAboutXAxis(90.0);
2597 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2598 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2599
2600 transform.MakeIdentity();
2601 transform.RotateAboutYAxis(90.0);
2602 transform.RotateAboutZAxis(90.0);
2603 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2604 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2605
2606 transform.MakeIdentity();
2607 transform.RotateAboutZAxis(45.0);
2608 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2609 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2610
2611 // 3-d case; In 2d after an orthographic projection, this case does
2612 // preserve 2d axis alignment. But in 3d, it does not preserve axis
2613 // alignment.
2614 transform.MakeIdentity();
2615 transform.RotateAboutYAxis(45.0);
2616 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2617 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2618
2619 transform.MakeIdentity();
2620 transform.RotateAboutXAxis(45.0);
2621 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2622 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2623
2624 // Perspective cases.
2625 transform.MakeIdentity();
2626 transform.ApplyPerspectiveDepth(10.0);
2627 transform.RotateAboutYAxis(45.0);
2628 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2629 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2630
2631 transform.MakeIdentity();
2632 transform.ApplyPerspectiveDepth(10.0);
2633 transform.RotateAboutZAxis(90.0);
2634 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2635 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2636 }
2637
2638 TEST(XFormTest, To2dTranslation) {
2639 Vector2dF translation(3.f, 7.f);
2640 Transform transform;
2641 transform.Translate(translation.x(), translation.y() + 1);
2642 EXPECT_NE(translation.ToString(), transform.To2dTranslation().ToString());
2643 transform.MakeIdentity();
2644 transform.Translate(translation.x(), translation.y());
2645 EXPECT_EQ(translation.ToString(), transform.To2dTranslation().ToString());
2646 }
2647
2648 TEST(XFormTest, TransformRect) {
2649 Transform translation;
2650 translation.Translate(3.f, 7.f);
2651 RectF rect(1.f, 2.f, 3.f, 4.f);
2652 RectF expected(4.f, 9.f, 3.f, 4.f);
2653 translation.TransformRect(&rect);
2654 EXPECT_EQ(expected.ToString(), rect.ToString());
2655 }
2656
2657 TEST(XFormTest, TransformRectReverse) {
2658 Transform translation;
2659 translation.Translate(3.f, 7.f);
2660 RectF rect(1.f, 2.f, 3.f, 4.f);
2661 RectF expected(-2.f, -5.f, 3.f, 4.f);
2662 EXPECT_TRUE(translation.TransformRectReverse(&rect));
2663 EXPECT_EQ(expected.ToString(), rect.ToString());
2664
2665 Transform singular;
2666 singular.Scale3d(0.f, 0.f, 0.f);
2667 EXPECT_FALSE(singular.TransformRectReverse(&rect));
2668 }
2669
2670 TEST(XFormTest, TransformBox) {
2671 Transform translation;
2672 translation.Translate3d(3.f, 7.f, 6.f);
2673 BoxF box(1.f, 2.f, 3.f, 4.f, 5.f, 6.f);
2674 BoxF expected(4.f, 9.f, 9.f, 4.f, 5.f, 6.f);
2675 translation.TransformBox(&box);
2676 EXPECT_EQ(expected.ToString(), box.ToString());
2677 }
2678
2679 TEST(XFormTest, TransformBoxReverse) {
2680 Transform translation;
2681 translation.Translate3d(3.f, 7.f, 6.f);
2682 BoxF box(1.f, 2.f, 3.f, 4.f, 5.f, 6.f);
2683 BoxF expected(-2.f, -5.f, -3.f, 4.f, 5.f, 6.f);
2684 EXPECT_TRUE(translation.TransformBoxReverse(&box));
2685 EXPECT_EQ(expected.ToString(), box.ToString());
2686
2687 Transform singular;
2688 singular.Scale3d(0.f, 0.f, 0.f);
2689 EXPECT_FALSE(singular.TransformBoxReverse(&box));
2690 }
2691
2692 } // namespace
2693
2694 } // namespace gfx