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
PointsAreNearlyEqual(const Point3F & lhs,const Point3F & rhs)73 bool PointsAreNearlyEqual(const Point3F& lhs,
74 const Point3F& rhs) {
75 float epsilon = 0.0001f;
76 return lhs.SquaredDistanceTo(rhs) < epsilon;
77 }
78
MatricesAreNearlyEqual(const Transform & lhs,const Transform & rhs)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
InitializeTestMatrix(Transform * transform)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
InitializeTestMatrix2(Transform * transform)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
InitializeApproxIdentityMatrix(Transform * transform)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
TEST(XFormTest,Equality)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
TEST(XFormTest,ConcatTranslate)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
TEST(XFormTest,ConcatScale)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
TEST(XFormTest,ConcatRotate)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
TEST(XFormTest,SetTranslate)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
TEST(XFormTest,SetScale)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
TEST(XFormTest,SetRotate)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
TEST(XFormTest,ConcatTranslate2D)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
TEST(XFormTest,ConcatScale2D)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
TEST(XFormTest,ConcatRotate2D)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
TEST(XFormTest,SetTranslate2D)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
TEST(XFormTest,SetScale2D)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
TEST(XFormTest,SetRotate2D)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
TEST(XFormTest,TransformPointWithExtremePerspective)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
TEST(XFormTest,BlendTranslate)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
TEST(XFormTest,BlendRotate)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
TEST(XFormTest,BlendRotateFollowsShortestPath)738 TEST(XFormTest, BlendRotateFollowsShortestPath) {
739 // Verify that we interpolate along the shortest path regardless of whether
740 // this path crosses the 180-degree point.
741 Vector3dF axes[] = {
742 Vector3dF(1, 0, 0),
743 Vector3dF(0, 1, 0),
744 Vector3dF(0, 0, 1),
745 Vector3dF(1, 1, 1)
746 };
747 for (size_t index = 0; index < ARRAYSIZE_UNSAFE(axes); ++index) {
748 for (int i = -5; i < 15; ++i) {
749 Transform from1;
750 from1.RotateAbout(axes[index], 130.0);
751 Transform to1;
752 to1.RotateAbout(axes[index], 175.0);
753
754 Transform from2;
755 from2.RotateAbout(axes[index], 140.0);
756 Transform to2;
757 to2.RotateAbout(axes[index], 185.0);
758
759 double t = i / 9.0;
760 EXPECT_TRUE(to1.Blend(from1, t));
761 EXPECT_TRUE(to2.Blend(from2, t));
762
763 Transform expected1;
764 expected1.RotateAbout(axes[index], 130.0 + 45.0 * t);
765
766 Transform expected2;
767 expected2.RotateAbout(axes[index], 140.0 + 45.0 * t);
768
769 EXPECT_TRUE(MatricesAreNearlyEqual(expected1, to1));
770 EXPECT_TRUE(MatricesAreNearlyEqual(expected2, to2));
771 }
772 }
773 }
774
TEST(XFormTest,CanBlend180DegreeRotation)775 TEST(XFormTest, CanBlend180DegreeRotation) {
776 Vector3dF axes[] = {
777 Vector3dF(1, 0, 0),
778 Vector3dF(0, 1, 0),
779 Vector3dF(0, 0, 1),
780 Vector3dF(1, 1, 1)
781 };
782 Transform from;
783 for (size_t index = 0; index < ARRAYSIZE_UNSAFE(axes); ++index) {
784 for (int i = -5; i < 15; ++i) {
785 Transform to;
786 to.RotateAbout(axes[index], 180.0);
787 double t = i / 9.0;
788 EXPECT_TRUE(to.Blend(from, t));
789
790 // A 180 degree rotation is exactly opposite on the sphere, therefore
791 // either great circle arc to it is equivalent (and numerical precision
792 // will determine which is closer). Test both directions.
793 Transform expected1;
794 expected1.RotateAbout(axes[index], 180.0 * t);
795 Transform expected2;
796 expected2.RotateAbout(axes[index], -180.0 * t);
797
798 EXPECT_TRUE(MatricesAreNearlyEqual(expected1, to) ||
799 MatricesAreNearlyEqual(expected2, to))
800 << "axis: " << index << ", i: " << i;
801 }
802 }
803 }
804
TEST(XFormTest,BlendScale)805 TEST(XFormTest, BlendScale) {
806 Transform from;
807 for (int i = -5; i < 15; ++i) {
808 Transform to;
809 to.Scale3d(5, 4, 3);
810 double t = i / 9.0;
811 EXPECT_TRUE(to.Blend(from, t));
812 EXPECT_FLOAT_EQ(t * 4 + 1, to.matrix().get(0, 0)) << "i: " << i;
813 EXPECT_FLOAT_EQ(t * 3 + 1, to.matrix().get(1, 1)) << "i: " << i;
814 EXPECT_FLOAT_EQ(t * 2 + 1, to.matrix().get(2, 2)) << "i: " << i;
815 }
816 }
817
TEST(XFormTest,BlendSkew)818 TEST(XFormTest, BlendSkew) {
819 Transform from;
820 for (int i = 0; i < 2; ++i) {
821 Transform to;
822 to.SkewX(10);
823 to.SkewY(5);
824 double t = i;
825 Transform expected;
826 expected.SkewX(t * 10);
827 expected.SkewY(t * 5);
828 EXPECT_TRUE(to.Blend(from, t));
829 EXPECT_TRUE(MatricesAreNearlyEqual(expected, to));
830 }
831 }
832
TEST(XFormTest,ExtrapolateSkew)833 TEST(XFormTest, ExtrapolateSkew) {
834 Transform from;
835 for (int i = -1; i < 2; ++i) {
836 Transform to;
837 to.SkewX(20);
838 double t = i;
839 Transform expected;
840 expected.SkewX(t * 20);
841 EXPECT_TRUE(to.Blend(from, t));
842 EXPECT_TRUE(MatricesAreNearlyEqual(expected, to));
843 }
844 }
845
TEST(XFormTest,BlendPerspective)846 TEST(XFormTest, BlendPerspective) {
847 Transform from;
848 from.ApplyPerspectiveDepth(200);
849 for (int i = -1; i < 3; ++i) {
850 Transform to;
851 to.ApplyPerspectiveDepth(800);
852 double t = i;
853 double depth = 1.0 / ((1.0 / 200) * (1.0 - t) + (1.0 / 800) * t);
854 Transform expected;
855 expected.ApplyPerspectiveDepth(depth);
856 EXPECT_TRUE(to.Blend(from, t));
857 EXPECT_TRUE(MatricesAreNearlyEqual(expected, to));
858 }
859 }
860
TEST(XFormTest,BlendIdentity)861 TEST(XFormTest, BlendIdentity) {
862 Transform from;
863 Transform to;
864 EXPECT_TRUE(to.Blend(from, 0.5));
865 EXPECT_EQ(to, from);
866 }
867
TEST(XFormTest,CannotBlendSingularMatrix)868 TEST(XFormTest, CannotBlendSingularMatrix) {
869 Transform from;
870 Transform to;
871 to.matrix().set(1, 1, SkDoubleToMScalar(0));
872 EXPECT_FALSE(to.Blend(from, 0.5));
873 }
874
TEST(XFormTest,VerifyBlendForTranslation)875 TEST(XFormTest, VerifyBlendForTranslation) {
876 Transform from;
877 from.Translate3d(100.0, 200.0, 100.0);
878
879 Transform to;
880
881 to.Translate3d(200.0, 100.0, 300.0);
882 to.Blend(from, 0.0);
883 EXPECT_EQ(from, to);
884
885 to = Transform();
886 to.Translate3d(200.0, 100.0, 300.0);
887 to.Blend(from, 0.25);
888 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 125.0f, to);
889 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 175.0f, to);
890 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 150.0f, to);
891 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
892
893 to = Transform();
894 to.Translate3d(200.0, 100.0, 300.0);
895 to.Blend(from, 0.5);
896 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 150.0f, to);
897 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 150.0f, to);
898 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 200.0f, to);
899 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
900
901 to = Transform();
902 to.Translate3d(200.0, 100.0, 300.0);
903 to.Blend(from, 1.0);
904 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 200.0f, to);
905 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 100.0f, to);
906 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 300.0f, to);
907 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
908 }
909
TEST(XFormTest,VerifyBlendForScale)910 TEST(XFormTest, VerifyBlendForScale) {
911 Transform from;
912 from.Scale3d(100.0, 200.0, 100.0);
913
914 Transform to;
915
916 to.Scale3d(200.0, 100.0, 300.0);
917 to.Blend(from, 0.0);
918 EXPECT_EQ(from, to);
919
920 to = Transform();
921 to.Scale3d(200.0, 100.0, 300.0);
922 to.Blend(from, 0.25);
923 EXPECT_ROW1_EQ(125.0f, 0.0f, 0.0f, 0.0f, to);
924 EXPECT_ROW2_EQ(0.0f, 175.0f, 0.0f, 0.0f, to);
925 EXPECT_ROW3_EQ(0.0f, 0.0f, 150.0f, 0.0f, to);
926 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
927
928 to = Transform();
929 to.Scale3d(200.0, 100.0, 300.0);
930 to.Blend(from, 0.5);
931 EXPECT_ROW1_EQ(150.0f, 0.0f, 0.0f, 0.0f, to);
932 EXPECT_ROW2_EQ(0.0f, 150.0f, 0.0f, 0.0f, to);
933 EXPECT_ROW3_EQ(0.0f, 0.0f, 200.0f, 0.0f, to);
934 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
935
936 to = Transform();
937 to.Scale3d(200.0, 100.0, 300.0);
938 to.Blend(from, 1.0);
939 EXPECT_ROW1_EQ(200.0f, 0.0f, 0.0f, 0.0f, to);
940 EXPECT_ROW2_EQ(0.0f, 100.0f, 0.0f, 0.0f, to);
941 EXPECT_ROW3_EQ(0.0f, 0.0f, 300.0f, 0.0f, to);
942 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
943 }
944
TEST(XFormTest,VerifyBlendForSkewX)945 TEST(XFormTest, VerifyBlendForSkewX) {
946 Transform from;
947 from.SkewX(0.0);
948
949 Transform to;
950
951 to.SkewX(45.0);
952 to.Blend(from, 0.0);
953 EXPECT_EQ(from, to);
954
955 to = Transform();
956 to.SkewX(45.0);
957 to.Blend(from, 0.5);
958 EXPECT_ROW1_EQ(1.0f, 0.5f, 0.0f, 0.0f, to);
959 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, to);
960 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
961 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
962
963 to = Transform();
964 to.SkewX(45.0);
965 to.Blend(from, 0.25);
966 EXPECT_ROW1_EQ(1.0f, 0.25f, 0.0f, 0.0f, to);
967 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, to);
968 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
969 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
970
971 to = Transform();
972 to.SkewX(45.0);
973 to.Blend(from, 1.0);
974 EXPECT_ROW1_EQ(1.0f, 1.0f, 0.0f, 0.0f, to);
975 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, to);
976 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
977 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
978 }
979
TEST(XFormTest,VerifyBlendForSkewY)980 TEST(XFormTest, VerifyBlendForSkewY) {
981 // NOTE CAREFULLY: Decomposition of skew and rotation terms of the matrix
982 // is inherently underconstrained, and so it does not always compute the
983 // originally intended skew parameters. The current implementation uses QR
984 // decomposition, which decomposes the shear into a rotation + non-uniform
985 // scale.
986 //
987 // It is unlikely that the decomposition implementation will need to change
988 // very often, so to get any test coverage, the compromise is to verify the
989 // exact matrix that the.Blend() operation produces.
990 //
991 // This problem also potentially exists for skewX, but the current QR
992 // decomposition implementation just happens to decompose those test
993 // matrices intuitively.
994 //
995 // Unfortunately, this case suffers from uncomfortably large precision
996 // error.
997
998 Transform from;
999 from.SkewY(0.0);
1000
1001 Transform to;
1002
1003 to.SkewY(45.0);
1004 to.Blend(from, 0.0);
1005 EXPECT_EQ(from, to);
1006
1007 to = Transform();
1008 to.SkewY(45.0);
1009 to.Blend(from, 0.25);
1010 EXPECT_ROW1_NEAR(1.0823489449280947471976333,
1011 0.0464370719145053845178239,
1012 0.0,
1013 0.0,
1014 to,
1015 LOOSE_ERROR_THRESHOLD);
1016 EXPECT_ROW2_NEAR(0.2152925909665224513123150,
1017 0.9541702441750861130032035,
1018 0.0,
1019 0.0,
1020 to,
1021 LOOSE_ERROR_THRESHOLD);
1022 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
1023 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1024
1025 to = Transform();
1026 to.SkewY(45.0);
1027 to.Blend(from, 0.5);
1028 EXPECT_ROW1_NEAR(1.1152212925809066312865525,
1029 0.0676495144007326631996335,
1030 0.0,
1031 0.0,
1032 to,
1033 LOOSE_ERROR_THRESHOLD);
1034 EXPECT_ROW2_NEAR(0.4619397844342648662419037,
1035 0.9519009045724774464858342,
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, 1.0);
1046 EXPECT_ROW1_NEAR(1.0, 0.0, 0.0, 0.0, to, LOOSE_ERROR_THRESHOLD);
1047 EXPECT_ROW2_NEAR(1.0, 1.0, 0.0, 0.0, to, LOOSE_ERROR_THRESHOLD);
1048 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, to);
1049 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1050 }
1051
TEST(XFormTest,VerifyBlendForRotationAboutX)1052 TEST(XFormTest, VerifyBlendForRotationAboutX) {
1053 // Even though.Blending uses quaternions, axis-aligned rotations should.
1054 // Blend the same with quaternions or Euler angles. So we can test
1055 // rotation.Blending by comparing against manually specified matrices from
1056 // Euler angles.
1057
1058 Transform from;
1059 from.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 0.0);
1060
1061 Transform to;
1062
1063 to.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1064 to.Blend(from, 0.0);
1065 EXPECT_EQ(from, to);
1066
1067 double expectedRotationAngle = 22.5 * M_PI / 180.0;
1068 to = Transform();
1069 to.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1070 to.Blend(from, 0.25);
1071 EXPECT_ROW1_NEAR(1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1072 EXPECT_ROW2_NEAR(0.0,
1073 std::cos(expectedRotationAngle),
1074 -std::sin(expectedRotationAngle),
1075 0.0,
1076 to,
1077 ERROR_THRESHOLD);
1078 EXPECT_ROW3_NEAR(0.0,
1079 std::sin(expectedRotationAngle),
1080 std::cos(expectedRotationAngle),
1081 0.0,
1082 to,
1083 ERROR_THRESHOLD);
1084 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1085
1086 expectedRotationAngle = 45.0 * M_PI / 180.0;
1087 to = Transform();
1088 to.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1089 to.Blend(from, 0.5);
1090 EXPECT_ROW1_NEAR(1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1091 EXPECT_ROW2_NEAR(0.0,
1092 std::cos(expectedRotationAngle),
1093 -std::sin(expectedRotationAngle),
1094 0.0,
1095 to,
1096 ERROR_THRESHOLD);
1097 EXPECT_ROW3_NEAR(0.0,
1098 std::sin(expectedRotationAngle),
1099 std::cos(expectedRotationAngle),
1100 0.0,
1101 to,
1102 ERROR_THRESHOLD);
1103 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1104
1105 to = Transform();
1106 to.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1107 to.Blend(from, 1.0);
1108 EXPECT_ROW1_NEAR(1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1109 EXPECT_ROW2_NEAR(0.0, 0.0, -1.0, 0.0, to, ERROR_THRESHOLD);
1110 EXPECT_ROW3_NEAR(0.0, 1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1111 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1112 }
1113
TEST(XFormTest,VerifyBlendForRotationAboutY)1114 TEST(XFormTest, VerifyBlendForRotationAboutY) {
1115 Transform from;
1116 from.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 0.0);
1117
1118 Transform to;
1119
1120 to.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1121 to.Blend(from, 0.0);
1122 EXPECT_EQ(from, to);
1123
1124 double expectedRotationAngle = 22.5 * M_PI / 180.0;
1125 to = Transform();
1126 to.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1127 to.Blend(from, 0.25);
1128 EXPECT_ROW1_NEAR(std::cos(expectedRotationAngle),
1129 0.0,
1130 std::sin(expectedRotationAngle),
1131 0.0,
1132 to,
1133 ERROR_THRESHOLD);
1134 EXPECT_ROW2_NEAR(0.0, 1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1135 EXPECT_ROW3_NEAR(-std::sin(expectedRotationAngle),
1136 0.0,
1137 std::cos(expectedRotationAngle),
1138 0.0,
1139 to,
1140 ERROR_THRESHOLD);
1141 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1142
1143 expectedRotationAngle = 45.0 * M_PI / 180.0;
1144 to = Transform();
1145 to.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1146 to.Blend(from, 0.5);
1147 EXPECT_ROW1_NEAR(std::cos(expectedRotationAngle),
1148 0.0,
1149 std::sin(expectedRotationAngle),
1150 0.0,
1151 to,
1152 ERROR_THRESHOLD);
1153 EXPECT_ROW2_NEAR(0.0, 1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1154 EXPECT_ROW3_NEAR(-std::sin(expectedRotationAngle),
1155 0.0,
1156 std::cos(expectedRotationAngle),
1157 0.0,
1158 to,
1159 ERROR_THRESHOLD);
1160 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1161
1162 to = Transform();
1163 to.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1164 to.Blend(from, 1.0);
1165 EXPECT_ROW1_NEAR(0.0, 0.0, 1.0, 0.0, to, ERROR_THRESHOLD);
1166 EXPECT_ROW2_NEAR(0.0, 1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1167 EXPECT_ROW3_NEAR(-1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1168 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1169 }
1170
TEST(XFormTest,VerifyBlendForRotationAboutZ)1171 TEST(XFormTest, VerifyBlendForRotationAboutZ) {
1172 Transform from;
1173 from.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 0.0);
1174
1175 Transform to;
1176
1177 to.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1178 to.Blend(from, 0.0);
1179 EXPECT_EQ(from, to);
1180
1181 double expectedRotationAngle = 22.5 * M_PI / 180.0;
1182 to = Transform();
1183 to.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1184 to.Blend(from, 0.25);
1185 EXPECT_ROW1_NEAR(std::cos(expectedRotationAngle),
1186 -std::sin(expectedRotationAngle),
1187 0.0,
1188 0.0,
1189 to,
1190 ERROR_THRESHOLD);
1191 EXPECT_ROW2_NEAR(std::sin(expectedRotationAngle),
1192 std::cos(expectedRotationAngle),
1193 0.0,
1194 0.0,
1195 to,
1196 ERROR_THRESHOLD);
1197 EXPECT_ROW3_NEAR(0.0, 0.0, 1.0, 0.0, to, ERROR_THRESHOLD);
1198 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1199
1200 expectedRotationAngle = 45.0 * M_PI / 180.0;
1201 to = Transform();
1202 to.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1203 to.Blend(from, 0.5);
1204 EXPECT_ROW1_NEAR(std::cos(expectedRotationAngle),
1205 -std::sin(expectedRotationAngle),
1206 0.0,
1207 0.0,
1208 to,
1209 ERROR_THRESHOLD);
1210 EXPECT_ROW2_NEAR(std::sin(expectedRotationAngle),
1211 std::cos(expectedRotationAngle),
1212 0.0,
1213 0.0,
1214 to,
1215 ERROR_THRESHOLD);
1216 EXPECT_ROW3_NEAR(0.0, 0.0, 1.0, 0.0, to, ERROR_THRESHOLD);
1217 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1218
1219 to = Transform();
1220 to.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1221 to.Blend(from, 1.0);
1222 EXPECT_ROW1_NEAR(0.0, -1.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1223 EXPECT_ROW2_NEAR(1.0, 0.0, 0.0, 0.0, to, ERROR_THRESHOLD);
1224 EXPECT_ROW3_NEAR(0.0, 0.0, 1.0, 0.0, to, ERROR_THRESHOLD);
1225 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, to);
1226 }
1227
TEST(XFormTest,VerifyBlendForCompositeTransform)1228 TEST(XFormTest, VerifyBlendForCompositeTransform) {
1229 // Verify that the.Blending was done with a decomposition in correct order
1230 // by blending a composite transform. Using matrix x vector notation
1231 // (Ax = b, where x is column vector), the ordering should be:
1232 // perspective * translation * rotation * skew * scale
1233 //
1234 // It is not as important (or meaningful) to check intermediate
1235 // interpolations; order of operations will be tested well enough by the
1236 // end cases that are easier to specify.
1237
1238 Transform from;
1239 Transform to;
1240
1241 Transform expectedEndOfAnimation;
1242 expectedEndOfAnimation.ApplyPerspectiveDepth(1.0);
1243 expectedEndOfAnimation.Translate3d(10.0, 20.0, 30.0);
1244 expectedEndOfAnimation.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 25.0);
1245 expectedEndOfAnimation.SkewY(45.0);
1246 expectedEndOfAnimation.Scale3d(6.0, 7.0, 8.0);
1247
1248 to = expectedEndOfAnimation;
1249 to.Blend(from, 0.0);
1250 EXPECT_EQ(from, to);
1251
1252 to = expectedEndOfAnimation;
1253 // We short circuit if blend is >= 1, so to check the numerics, we will
1254 // check that we get close to what we expect when we're nearly done
1255 // interpolating.
1256 to.Blend(from, .99999f);
1257
1258 // Recomposing the matrix results in a normalized matrix, so to verify we
1259 // need to normalize the expectedEndOfAnimation before comparing elements.
1260 // Normalizing means dividing everything by expectedEndOfAnimation.m44().
1261 Transform normalizedExpectedEndOfAnimation = expectedEndOfAnimation;
1262 Transform normalizationMatrix;
1263 normalizationMatrix.matrix().set(
1264 0.0,
1265 0.0,
1266 SkDoubleToMScalar(1 / expectedEndOfAnimation.matrix().get(3.0, 3.0)));
1267 normalizationMatrix.matrix().set(
1268 1.0,
1269 1.0,
1270 SkDoubleToMScalar(1 / expectedEndOfAnimation.matrix().get(3.0, 3.0)));
1271 normalizationMatrix.matrix().set(
1272 2.0,
1273 2.0,
1274 SkDoubleToMScalar(1 / expectedEndOfAnimation.matrix().get(3.0, 3.0)));
1275 normalizationMatrix.matrix().set(
1276 3.0,
1277 3.0,
1278 SkDoubleToMScalar(1 / expectedEndOfAnimation.matrix().get(3.0, 3.0)));
1279 normalizedExpectedEndOfAnimation.PreconcatTransform(normalizationMatrix);
1280
1281 EXPECT_TRUE(MatricesAreNearlyEqual(normalizedExpectedEndOfAnimation, to));
1282 }
1283
TEST(XFormTest,DecomposedTransformCtor)1284 TEST(XFormTest, DecomposedTransformCtor) {
1285 DecomposedTransform decomp;
1286 for (int i = 0; i < 3; ++i) {
1287 EXPECT_EQ(0.0, decomp.translate[i]);
1288 EXPECT_EQ(1.0, decomp.scale[i]);
1289 EXPECT_EQ(0.0, decomp.skew[i]);
1290 EXPECT_EQ(0.0, decomp.quaternion[i]);
1291 EXPECT_EQ(0.0, decomp.perspective[i]);
1292 }
1293 EXPECT_EQ(1.0, decomp.quaternion[3]);
1294 EXPECT_EQ(1.0, decomp.perspective[3]);
1295 Transform identity;
1296 Transform composed = ComposeTransform(decomp);
1297 EXPECT_TRUE(MatricesAreNearlyEqual(identity, composed));
1298 }
1299
TEST(XFormTest,FactorTRS)1300 TEST(XFormTest, FactorTRS) {
1301 for (int degrees = 0; degrees < 180; ++degrees) {
1302 // build a transformation matrix.
1303 gfx::Transform transform;
1304 transform.Translate(degrees * 2, -degrees * 3);
1305 transform.Rotate(degrees);
1306 transform.Scale(degrees + 1, 2 * degrees + 1);
1307
1308 // factor the matrix
1309 DecomposedTransform decomp;
1310 bool success = DecomposeTransform(&decomp, transform);
1311 EXPECT_TRUE(success);
1312 EXPECT_FLOAT_EQ(decomp.translate[0], degrees * 2);
1313 EXPECT_FLOAT_EQ(decomp.translate[1], -degrees * 3);
1314 double rotation =
1315 std::acos(SkMScalarToDouble(decomp.quaternion[3])) * 360.0 / M_PI;
1316 while (rotation < 0.0)
1317 rotation += 360.0;
1318 while (rotation > 360.0)
1319 rotation -= 360.0;
1320
1321 const float epsilon = 0.00015f;
1322 EXPECT_NEAR(rotation, degrees, epsilon);
1323 EXPECT_NEAR(decomp.scale[0], degrees + 1, epsilon);
1324 EXPECT_NEAR(decomp.scale[1], 2 * degrees + 1, epsilon);
1325 }
1326 }
1327
TEST(XFormTest,IntegerTranslation)1328 TEST(XFormTest, IntegerTranslation) {
1329 gfx::Transform transform;
1330 EXPECT_TRUE(transform.IsIdentityOrIntegerTranslation());
1331
1332 transform.Translate3d(1, 2, 3);
1333 EXPECT_TRUE(transform.IsIdentityOrIntegerTranslation());
1334
1335 transform.MakeIdentity();
1336 transform.Translate3d(-1, -2, -3);
1337 EXPECT_TRUE(transform.IsIdentityOrIntegerTranslation());
1338
1339 transform.MakeIdentity();
1340 transform.Translate3d(4.5f, 0, 0);
1341 EXPECT_FALSE(transform.IsIdentityOrIntegerTranslation());
1342
1343 transform.MakeIdentity();
1344 transform.Translate3d(0, -6.7f, 0);
1345 EXPECT_FALSE(transform.IsIdentityOrIntegerTranslation());
1346
1347 transform.MakeIdentity();
1348 transform.Translate3d(0, 0, 8.9f);
1349 EXPECT_FALSE(transform.IsIdentityOrIntegerTranslation());
1350 }
1351
TEST(XFormTest,verifyMatrixInversion)1352 TEST(XFormTest, verifyMatrixInversion) {
1353 {
1354 // Invert a translation
1355 gfx::Transform translation;
1356 translation.Translate3d(2.0, 3.0, 4.0);
1357 EXPECT_TRUE(translation.IsInvertible());
1358
1359 gfx::Transform inverse_translation;
1360 bool is_invertible = translation.GetInverse(&inverse_translation);
1361 EXPECT_TRUE(is_invertible);
1362 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, -2.0f, inverse_translation);
1363 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, -3.0f, inverse_translation);
1364 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, -4.0f, inverse_translation);
1365 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, inverse_translation);
1366 }
1367
1368 {
1369 // Invert a non-uniform scale
1370 gfx::Transform scale;
1371 scale.Scale3d(4.0, 10.0, 100.0);
1372 EXPECT_TRUE(scale.IsInvertible());
1373
1374 gfx::Transform inverse_scale;
1375 bool is_invertible = scale.GetInverse(&inverse_scale);
1376 EXPECT_TRUE(is_invertible);
1377 EXPECT_ROW1_EQ(0.25f, 0.0f, 0.0f, 0.0f, inverse_scale);
1378 EXPECT_ROW2_EQ(0.0f, 0.1f, 0.0f, 0.0f, inverse_scale);
1379 EXPECT_ROW3_EQ(0.0f, 0.0f, 0.01f, 0.0f, inverse_scale);
1380 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, inverse_scale);
1381 }
1382
1383 {
1384 // Try to invert a matrix that is not invertible.
1385 // The inverse() function should reset the output matrix to identity.
1386 gfx::Transform uninvertible;
1387 uninvertible.matrix().set(0, 0, 0.f);
1388 uninvertible.matrix().set(1, 1, 0.f);
1389 uninvertible.matrix().set(2, 2, 0.f);
1390 uninvertible.matrix().set(3, 3, 0.f);
1391 EXPECT_FALSE(uninvertible.IsInvertible());
1392
1393 gfx::Transform inverse_of_uninvertible;
1394
1395 // Add a scale just to more easily ensure that inverse_of_uninvertible is
1396 // reset to identity.
1397 inverse_of_uninvertible.Scale3d(4.0, 10.0, 100.0);
1398
1399 bool is_invertible = uninvertible.GetInverse(&inverse_of_uninvertible);
1400 EXPECT_FALSE(is_invertible);
1401 EXPECT_TRUE(inverse_of_uninvertible.IsIdentity());
1402 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, inverse_of_uninvertible);
1403 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, inverse_of_uninvertible);
1404 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, inverse_of_uninvertible);
1405 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, inverse_of_uninvertible);
1406 }
1407 }
1408
TEST(XFormTest,verifyBackfaceVisibilityBasicCases)1409 TEST(XFormTest, verifyBackfaceVisibilityBasicCases) {
1410 Transform transform;
1411
1412 transform.MakeIdentity();
1413 EXPECT_FALSE(transform.IsBackFaceVisible());
1414
1415 transform.MakeIdentity();
1416 transform.RotateAboutYAxis(80.0);
1417 EXPECT_FALSE(transform.IsBackFaceVisible());
1418
1419 transform.MakeIdentity();
1420 transform.RotateAboutYAxis(100.0);
1421 EXPECT_TRUE(transform.IsBackFaceVisible());
1422
1423 // Edge case, 90 degree rotation should return false.
1424 transform.MakeIdentity();
1425 transform.RotateAboutYAxis(90.0);
1426 EXPECT_FALSE(transform.IsBackFaceVisible());
1427 }
1428
TEST(XFormTest,verifyBackfaceVisibilityForPerspective)1429 TEST(XFormTest, verifyBackfaceVisibilityForPerspective) {
1430 Transform layer_space_to_projection_plane;
1431
1432 // This tests if IsBackFaceVisible works properly under perspective
1433 // transforms. Specifically, layers that may have their back face visible in
1434 // orthographic projection, may not actually have back face visible under
1435 // perspective projection.
1436
1437 // Case 1: Layer is rotated by slightly more than 90 degrees, at the center
1438 // of the prespective projection. In this case, the layer's back-side
1439 // is visible to the camera.
1440 layer_space_to_projection_plane.MakeIdentity();
1441 layer_space_to_projection_plane.ApplyPerspectiveDepth(1.0);
1442 layer_space_to_projection_plane.Translate3d(0.0, 0.0, 0.0);
1443 layer_space_to_projection_plane.RotateAboutYAxis(100.0);
1444 EXPECT_TRUE(layer_space_to_projection_plane.IsBackFaceVisible());
1445
1446 // Case 2: Layer is rotated by slightly more than 90 degrees, but shifted off
1447 // to the side of the camera. Because of the wide field-of-view, the
1448 // layer's front side is still visible.
1449 //
1450 // |<-- front side of layer is visible to camera
1451 // \ | /
1452 // \ | /
1453 // \| /
1454 // | /
1455 // |\ /<-- camera field of view
1456 // | \ /
1457 // back side of layer -->| \ /
1458 // \./ <-- camera origin
1459 //
1460 layer_space_to_projection_plane.MakeIdentity();
1461 layer_space_to_projection_plane.ApplyPerspectiveDepth(1.0);
1462 layer_space_to_projection_plane.Translate3d(-10.0, 0.0, 0.0);
1463 layer_space_to_projection_plane.RotateAboutYAxis(100.0);
1464 EXPECT_FALSE(layer_space_to_projection_plane.IsBackFaceVisible());
1465
1466 // Case 3: Additionally rotating the layer by 180 degrees should of course
1467 // show the opposite result of case 2.
1468 layer_space_to_projection_plane.RotateAboutYAxis(180.0);
1469 EXPECT_TRUE(layer_space_to_projection_plane.IsBackFaceVisible());
1470 }
1471
TEST(XFormTest,verifyDefaultConstructorCreatesIdentityMatrix)1472 TEST(XFormTest, verifyDefaultConstructorCreatesIdentityMatrix) {
1473 Transform A;
1474 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1475 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1476 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1477 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1478 EXPECT_TRUE(A.IsIdentity());
1479 }
1480
TEST(XFormTest,verifyCopyConstructor)1481 TEST(XFormTest, verifyCopyConstructor) {
1482 Transform A;
1483 InitializeTestMatrix(&A);
1484
1485 // Copy constructor should produce exact same elements as matrix A.
1486 Transform B(A);
1487 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, B);
1488 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, B);
1489 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, B);
1490 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, B);
1491 }
1492
TEST(XFormTest,verifyConstructorFor16Elements)1493 TEST(XFormTest, verifyConstructorFor16Elements) {
1494 Transform transform(1.0, 2.0, 3.0, 4.0,
1495 5.0, 6.0, 7.0, 8.0,
1496 9.0, 10.0, 11.0, 12.0,
1497 13.0, 14.0, 15.0, 16.0);
1498
1499 EXPECT_ROW1_EQ(1.0f, 2.0f, 3.0f, 4.0f, transform);
1500 EXPECT_ROW2_EQ(5.0f, 6.0f, 7.0f, 8.0f, transform);
1501 EXPECT_ROW3_EQ(9.0f, 10.0f, 11.0f, 12.0f, transform);
1502 EXPECT_ROW4_EQ(13.0f, 14.0f, 15.0f, 16.0f, transform);
1503 }
1504
TEST(XFormTest,verifyConstructorFor2dElements)1505 TEST(XFormTest, verifyConstructorFor2dElements) {
1506 Transform transform(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
1507
1508 EXPECT_ROW1_EQ(1.0f, 2.0f, 0.0f, 5.0f, transform);
1509 EXPECT_ROW2_EQ(3.0f, 4.0f, 0.0f, 6.0f, transform);
1510 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, transform);
1511 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, transform);
1512 }
1513
1514
TEST(XFormTest,verifyAssignmentOperator)1515 TEST(XFormTest, verifyAssignmentOperator) {
1516 Transform A;
1517 InitializeTestMatrix(&A);
1518 Transform B;
1519 InitializeTestMatrix2(&B);
1520 Transform C;
1521 InitializeTestMatrix2(&C);
1522 C = B = A;
1523
1524 // Both B and C should now have been re-assigned to the value of A.
1525 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, B);
1526 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, B);
1527 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, B);
1528 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, B);
1529
1530 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, C);
1531 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, C);
1532 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, C);
1533 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, C);
1534 }
1535
TEST(XFormTest,verifyEqualsBooleanOperator)1536 TEST(XFormTest, verifyEqualsBooleanOperator) {
1537 Transform A;
1538 InitializeTestMatrix(&A);
1539
1540 Transform B;
1541 InitializeTestMatrix(&B);
1542 EXPECT_TRUE(A == B);
1543
1544 // Modifying multiple elements should cause equals operator to return false.
1545 Transform C;
1546 InitializeTestMatrix2(&C);
1547 EXPECT_FALSE(A == C);
1548
1549 // Modifying any one individual element should cause equals operator to
1550 // return false.
1551 Transform D;
1552 D = A;
1553 D.matrix().set(0, 0, 0.f);
1554 EXPECT_FALSE(A == D);
1555
1556 D = A;
1557 D.matrix().set(1, 0, 0.f);
1558 EXPECT_FALSE(A == D);
1559
1560 D = A;
1561 D.matrix().set(2, 0, 0.f);
1562 EXPECT_FALSE(A == D);
1563
1564 D = A;
1565 D.matrix().set(3, 0, 0.f);
1566 EXPECT_FALSE(A == D);
1567
1568 D = A;
1569 D.matrix().set(0, 1, 0.f);
1570 EXPECT_FALSE(A == D);
1571
1572 D = A;
1573 D.matrix().set(1, 1, 0.f);
1574 EXPECT_FALSE(A == D);
1575
1576 D = A;
1577 D.matrix().set(2, 1, 0.f);
1578 EXPECT_FALSE(A == D);
1579
1580 D = A;
1581 D.matrix().set(3, 1, 0.f);
1582 EXPECT_FALSE(A == D);
1583
1584 D = A;
1585 D.matrix().set(0, 2, 0.f);
1586 EXPECT_FALSE(A == D);
1587
1588 D = A;
1589 D.matrix().set(1, 2, 0.f);
1590 EXPECT_FALSE(A == D);
1591
1592 D = A;
1593 D.matrix().set(2, 2, 0.f);
1594 EXPECT_FALSE(A == D);
1595
1596 D = A;
1597 D.matrix().set(3, 2, 0.f);
1598 EXPECT_FALSE(A == D);
1599
1600 D = A;
1601 D.matrix().set(0, 3, 0.f);
1602 EXPECT_FALSE(A == D);
1603
1604 D = A;
1605 D.matrix().set(1, 3, 0.f);
1606 EXPECT_FALSE(A == D);
1607
1608 D = A;
1609 D.matrix().set(2, 3, 0.f);
1610 EXPECT_FALSE(A == D);
1611
1612 D = A;
1613 D.matrix().set(3, 3, 0.f);
1614 EXPECT_FALSE(A == D);
1615 }
1616
TEST(XFormTest,verifyMultiplyOperator)1617 TEST(XFormTest, verifyMultiplyOperator) {
1618 Transform A;
1619 InitializeTestMatrix(&A);
1620
1621 Transform B;
1622 InitializeTestMatrix2(&B);
1623
1624 Transform C = A * B;
1625 EXPECT_ROW1_EQ(2036.0f, 2292.0f, 2548.0f, 2804.0f, C);
1626 EXPECT_ROW2_EQ(2162.0f, 2434.0f, 2706.0f, 2978.0f, C);
1627 EXPECT_ROW3_EQ(2288.0f, 2576.0f, 2864.0f, 3152.0f, C);
1628 EXPECT_ROW4_EQ(2414.0f, 2718.0f, 3022.0f, 3326.0f, C);
1629
1630 // Just an additional sanity check; matrix multiplication is not commutative.
1631 EXPECT_FALSE(A * B == B * A);
1632 }
1633
TEST(XFormTest,verifyMultiplyAndAssignOperator)1634 TEST(XFormTest, verifyMultiplyAndAssignOperator) {
1635 Transform A;
1636 InitializeTestMatrix(&A);
1637
1638 Transform B;
1639 InitializeTestMatrix2(&B);
1640
1641 A *= B;
1642 EXPECT_ROW1_EQ(2036.0f, 2292.0f, 2548.0f, 2804.0f, A);
1643 EXPECT_ROW2_EQ(2162.0f, 2434.0f, 2706.0f, 2978.0f, A);
1644 EXPECT_ROW3_EQ(2288.0f, 2576.0f, 2864.0f, 3152.0f, A);
1645 EXPECT_ROW4_EQ(2414.0f, 2718.0f, 3022.0f, 3326.0f, A);
1646
1647 // Just an additional sanity check; matrix multiplication is not commutative.
1648 Transform C = A;
1649 C *= B;
1650 Transform D = B;
1651 D *= A;
1652 EXPECT_FALSE(C == D);
1653 }
1654
TEST(XFormTest,verifyMatrixMultiplication)1655 TEST(XFormTest, verifyMatrixMultiplication) {
1656 Transform A;
1657 InitializeTestMatrix(&A);
1658
1659 Transform B;
1660 InitializeTestMatrix2(&B);
1661
1662 A.PreconcatTransform(B);
1663 EXPECT_ROW1_EQ(2036.0f, 2292.0f, 2548.0f, 2804.0f, A);
1664 EXPECT_ROW2_EQ(2162.0f, 2434.0f, 2706.0f, 2978.0f, A);
1665 EXPECT_ROW3_EQ(2288.0f, 2576.0f, 2864.0f, 3152.0f, A);
1666 EXPECT_ROW4_EQ(2414.0f, 2718.0f, 3022.0f, 3326.0f, A);
1667 }
1668
TEST(XFormTest,verifyMakeIdentiy)1669 TEST(XFormTest, verifyMakeIdentiy) {
1670 Transform A;
1671 InitializeTestMatrix(&A);
1672 A.MakeIdentity();
1673 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1674 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1675 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1676 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1677 EXPECT_TRUE(A.IsIdentity());
1678 }
1679
TEST(XFormTest,verifyTranslate)1680 TEST(XFormTest, verifyTranslate) {
1681 Transform A;
1682 A.Translate(2.0, 3.0);
1683 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 2.0f, A);
1684 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 3.0f, A);
1685 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1686 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1687
1688 // Verify that Translate() post-multiplies the existing matrix.
1689 A.MakeIdentity();
1690 A.Scale(5.0, 5.0);
1691 A.Translate(2.0, 3.0);
1692 EXPECT_ROW1_EQ(5.0f, 0.0f, 0.0f, 10.0f, A);
1693 EXPECT_ROW2_EQ(0.0f, 5.0f, 0.0f, 15.0f, A);
1694 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1695 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1696 }
1697
TEST(XFormTest,verifyTranslate3d)1698 TEST(XFormTest, verifyTranslate3d) {
1699 Transform A;
1700 A.Translate3d(2.0, 3.0, 4.0);
1701 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 2.0f, A);
1702 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 3.0f, A);
1703 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 4.0f, A);
1704 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1705
1706 // Verify that Translate3d() post-multiplies the existing matrix.
1707 A.MakeIdentity();
1708 A.Scale3d(6.0, 7.0, 8.0);
1709 A.Translate3d(2.0, 3.0, 4.0);
1710 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 12.0f, A);
1711 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 21.0f, A);
1712 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 32.0f, A);
1713 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1714 }
1715
TEST(XFormTest,verifyScale)1716 TEST(XFormTest, verifyScale) {
1717 Transform A;
1718 A.Scale(6.0, 7.0);
1719 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 0.0f, A);
1720 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 0.0f, 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 Scale() post-multiplies the existing matrix.
1725 A.MakeIdentity();
1726 A.Translate3d(2.0, 3.0, 4.0);
1727 A.Scale(6.0, 7.0);
1728 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 2.0f, A);
1729 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 3.0f, A);
1730 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 4.0f, A);
1731 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1732 }
1733
TEST(XFormTest,verifyScale3d)1734 TEST(XFormTest, verifyScale3d) {
1735 Transform A;
1736 A.Scale3d(6.0, 7.0, 8.0);
1737 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 0.0f, A);
1738 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 0.0f, A);
1739 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1740 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1741
1742 // Verify that scale3d() post-multiplies the existing matrix.
1743 A.MakeIdentity();
1744 A.Translate3d(2.0, 3.0, 4.0);
1745 A.Scale3d(6.0, 7.0, 8.0);
1746 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 2.0f, A);
1747 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 3.0f, A);
1748 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 4.0f, A);
1749 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1750 }
1751
TEST(XFormTest,verifyRotate)1752 TEST(XFormTest, verifyRotate) {
1753 Transform A;
1754 A.Rotate(90.0);
1755 EXPECT_ROW1_NEAR(0.0, -1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1756 EXPECT_ROW2_NEAR(1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
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 Rotate() post-multiplies the existing matrix.
1761 A.MakeIdentity();
1762 A.Scale3d(6.0, 7.0, 8.0);
1763 A.Rotate(90.0);
1764 EXPECT_ROW1_NEAR(0.0, -6.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1765 EXPECT_ROW2_NEAR(7.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1766 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1767 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1768 }
1769
TEST(XFormTest,verifyRotateAboutXAxis)1770 TEST(XFormTest, verifyRotateAboutXAxis) {
1771 Transform A;
1772 double sin45 = 0.5 * sqrt(2.0);
1773 double cos45 = sin45;
1774
1775 A.MakeIdentity();
1776 A.RotateAboutXAxis(90.0);
1777 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1778 EXPECT_ROW2_NEAR(0.0, 0.0, -1.0, 0.0, A, ERROR_THRESHOLD);
1779 EXPECT_ROW3_NEAR(0.0, 1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1780 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1781
1782 A.MakeIdentity();
1783 A.RotateAboutXAxis(45.0);
1784 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1785 EXPECT_ROW2_NEAR(0.0, cos45, -sin45, 0.0, A, ERROR_THRESHOLD);
1786 EXPECT_ROW3_NEAR(0.0, sin45, cos45, 0.0, A, ERROR_THRESHOLD);
1787 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1788
1789 // Verify that RotateAboutXAxis(angle) post-multiplies the existing matrix.
1790 A.MakeIdentity();
1791 A.Scale3d(6.0, 7.0, 8.0);
1792 A.RotateAboutXAxis(90.0);
1793 EXPECT_ROW1_NEAR(6.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1794 EXPECT_ROW2_NEAR(0.0, 0.0, -7.0, 0.0, A, ERROR_THRESHOLD);
1795 EXPECT_ROW3_NEAR(0.0, 8.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1796 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1797 }
1798
TEST(XFormTest,verifyRotateAboutYAxis)1799 TEST(XFormTest, verifyRotateAboutYAxis) {
1800 Transform A;
1801 double sin45 = 0.5 * sqrt(2.0);
1802 double cos45 = sin45;
1803
1804 // Note carefully, the expected pattern is inverted compared to rotating
1805 // about x axis or z axis.
1806 A.MakeIdentity();
1807 A.RotateAboutYAxis(90.0);
1808 EXPECT_ROW1_NEAR(0.0, 0.0, 1.0, 0.0, A, ERROR_THRESHOLD);
1809 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1810 EXPECT_ROW3_NEAR(-1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1811 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1812
1813 A.MakeIdentity();
1814 A.RotateAboutYAxis(45.0);
1815 EXPECT_ROW1_NEAR(cos45, 0.0, sin45, 0.0, A, ERROR_THRESHOLD);
1816 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1817 EXPECT_ROW3_NEAR(-sin45, 0.0, cos45, 0.0, A, ERROR_THRESHOLD);
1818 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1819
1820 // Verify that RotateAboutYAxis(angle) post-multiplies the existing matrix.
1821 A.MakeIdentity();
1822 A.Scale3d(6.0, 7.0, 8.0);
1823 A.RotateAboutYAxis(90.0);
1824 EXPECT_ROW1_NEAR(0.0, 0.0, 6.0, 0.0, A, ERROR_THRESHOLD);
1825 EXPECT_ROW2_NEAR(0.0, 7.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1826 EXPECT_ROW3_NEAR(-8.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1827 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1828 }
1829
TEST(XFormTest,verifyRotateAboutZAxis)1830 TEST(XFormTest, verifyRotateAboutZAxis) {
1831 Transform A;
1832 double sin45 = 0.5 * sqrt(2.0);
1833 double cos45 = sin45;
1834
1835 A.MakeIdentity();
1836 A.RotateAboutZAxis(90.0);
1837 EXPECT_ROW1_NEAR(0.0, -1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1838 EXPECT_ROW2_NEAR(1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1839 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1840 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1841
1842 A.MakeIdentity();
1843 A.RotateAboutZAxis(45.0);
1844 EXPECT_ROW1_NEAR(cos45, -sin45, 0.0, 0.0, A, ERROR_THRESHOLD);
1845 EXPECT_ROW2_NEAR(sin45, cos45, 0.0, 0.0, A, ERROR_THRESHOLD);
1846 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1847 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1848
1849 // Verify that RotateAboutZAxis(angle) post-multiplies the existing matrix.
1850 A.MakeIdentity();
1851 A.Scale3d(6.0, 7.0, 8.0);
1852 A.RotateAboutZAxis(90.0);
1853 EXPECT_ROW1_NEAR(0.0, -6.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1854 EXPECT_ROW2_NEAR(7.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1855 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1856 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1857 }
1858
TEST(XFormTest,verifyRotateAboutForAlignedAxes)1859 TEST(XFormTest, verifyRotateAboutForAlignedAxes) {
1860 Transform A;
1861
1862 // Check rotation about z-axis
1863 A.MakeIdentity();
1864 A.RotateAbout(Vector3dF(0.0, 0.0, 1.0), 90.0);
1865 EXPECT_ROW1_NEAR(0.0, -1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1866 EXPECT_ROW2_NEAR(1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1867 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1868 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1869
1870 // Check rotation about x-axis
1871 A.MakeIdentity();
1872 A.RotateAbout(Vector3dF(1.0, 0.0, 0.0), 90.0);
1873 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1874 EXPECT_ROW2_NEAR(0.0, 0.0, -1.0, 0.0, A, ERROR_THRESHOLD);
1875 EXPECT_ROW3_NEAR(0.0, 1.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1876 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1877
1878 // Check rotation about y-axis. Note carefully, the expected pattern is
1879 // inverted compared to rotating about x axis or z axis.
1880 A.MakeIdentity();
1881 A.RotateAbout(Vector3dF(0.0, 1.0, 0.0), 90.0);
1882 EXPECT_ROW1_NEAR(0.0, 0.0, 1.0, 0.0, A, ERROR_THRESHOLD);
1883 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1884 EXPECT_ROW3_NEAR(-1.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1885 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1886
1887 // Verify that rotate3d(axis, angle) post-multiplies the existing matrix.
1888 A.MakeIdentity();
1889 A.Scale3d(6.0, 7.0, 8.0);
1890 A.RotateAboutZAxis(90.0);
1891 EXPECT_ROW1_NEAR(0.0, -6.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1892 EXPECT_ROW2_NEAR(7.0, 0.0, 0.0, 0.0, A, ERROR_THRESHOLD);
1893 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1894 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1895 }
1896
TEST(XFormTest,verifyRotateAboutForArbitraryAxis)1897 TEST(XFormTest, verifyRotateAboutForArbitraryAxis) {
1898 // Check rotation about an arbitrary non-axis-aligned vector.
1899 Transform A;
1900 A.RotateAbout(Vector3dF(1.0, 1.0, 1.0), 90.0);
1901 EXPECT_ROW1_NEAR(0.3333333333333334258519187,
1902 -0.2440169358562924717404030,
1903 0.9106836025229592124219380,
1904 0.0, A, ERROR_THRESHOLD);
1905 EXPECT_ROW2_NEAR(0.9106836025229592124219380,
1906 0.3333333333333334258519187,
1907 -0.2440169358562924717404030,
1908 0.0, A, ERROR_THRESHOLD);
1909 EXPECT_ROW3_NEAR(-0.2440169358562924717404030,
1910 0.9106836025229592124219380,
1911 0.3333333333333334258519187,
1912 0.0, A, ERROR_THRESHOLD);
1913 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1914 }
1915
TEST(XFormTest,verifyRotateAboutForDegenerateAxis)1916 TEST(XFormTest, verifyRotateAboutForDegenerateAxis) {
1917 // Check rotation about a degenerate zero vector.
1918 // It is expected to skip applying the rotation.
1919 Transform A;
1920
1921 A.RotateAbout(Vector3dF(0.0, 0.0, 0.0), 45.0);
1922 // Verify that A remains unchanged.
1923 EXPECT_TRUE(A.IsIdentity());
1924
1925 InitializeTestMatrix(&A);
1926 A.RotateAbout(Vector3dF(0.0, 0.0, 0.0), 35.0);
1927
1928 // Verify that A remains unchanged.
1929 EXPECT_ROW1_EQ(10.0f, 14.0f, 18.0f, 22.0f, A);
1930 EXPECT_ROW2_EQ(11.0f, 15.0f, 19.0f, 23.0f, A);
1931 EXPECT_ROW3_EQ(12.0f, 16.0f, 20.0f, 24.0f, A);
1932 EXPECT_ROW4_EQ(13.0f, 17.0f, 21.0f, 25.0f, A);
1933 }
1934
TEST(XFormTest,verifySkewX)1935 TEST(XFormTest, verifySkewX) {
1936 Transform A;
1937 A.SkewX(45.0);
1938 EXPECT_ROW1_EQ(1.0f, 1.0f, 0.0f, 0.0f, A);
1939 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1940 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1941 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1942
1943 // Verify that skewX() post-multiplies the existing matrix. Row 1, column 2,
1944 // would incorrectly have value "7" if the matrix is pre-multiplied instead
1945 // of post-multiplied.
1946 A.MakeIdentity();
1947 A.Scale3d(6.0, 7.0, 8.0);
1948 A.SkewX(45.0);
1949 EXPECT_ROW1_EQ(6.0f, 6.0f, 0.0f, 0.0f, A);
1950 EXPECT_ROW2_EQ(0.0f, 7.0f, 0.0f, 0.0f, A);
1951 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1952 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1953 }
1954
TEST(XFormTest,verifySkewY)1955 TEST(XFormTest, verifySkewY) {
1956 Transform A;
1957 A.SkewY(45.0);
1958 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1959 EXPECT_ROW2_EQ(1.0f, 1.0f, 0.0f, 0.0f, A);
1960 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1961 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1962
1963 // Verify that skewY() post-multiplies the existing matrix. Row 2, column 1 ,
1964 // would incorrectly have value "6" if the matrix is pre-multiplied instead
1965 // of post-multiplied.
1966 A.MakeIdentity();
1967 A.Scale3d(6.0, 7.0, 8.0);
1968 A.SkewY(45.0);
1969 EXPECT_ROW1_EQ(6.0f, 0.0f, 0.0f, 0.0f, A);
1970 EXPECT_ROW2_EQ(7.0f, 7.0f, 0.0f, 0.0f, A);
1971 EXPECT_ROW3_EQ(0.0f, 0.0f, 8.0f, 0.0f, A);
1972 EXPECT_ROW4_EQ(0.0f, 0.0f, 0.0f, 1.0f, A);
1973 }
1974
TEST(XFormTest,verifyPerspectiveDepth)1975 TEST(XFormTest, verifyPerspectiveDepth) {
1976 Transform A;
1977 A.ApplyPerspectiveDepth(1.0);
1978 EXPECT_ROW1_EQ(1.0f, 0.0f, 0.0f, 0.0f, A);
1979 EXPECT_ROW2_EQ(0.0f, 1.0f, 0.0f, 0.0f, A);
1980 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
1981 EXPECT_ROW4_EQ(0.0f, 0.0f, -1.0f, 1.0f, A);
1982
1983 // Verify that PerspectiveDepth() post-multiplies the existing matrix.
1984 A.MakeIdentity();
1985 A.Translate3d(2.0, 3.0, 4.0);
1986 A.ApplyPerspectiveDepth(1.0);
1987 EXPECT_ROW1_EQ(1.0f, 0.0f, -2.0f, 2.0f, A);
1988 EXPECT_ROW2_EQ(0.0f, 1.0f, -3.0f, 3.0f, A);
1989 EXPECT_ROW3_EQ(0.0f, 0.0f, -3.0f, 4.0f, A);
1990 EXPECT_ROW4_EQ(0.0f, 0.0f, -1.0f, 1.0f, A);
1991 }
1992
TEST(XFormTest,verifyHasPerspective)1993 TEST(XFormTest, verifyHasPerspective) {
1994 Transform A;
1995 A.ApplyPerspectiveDepth(1.0);
1996 EXPECT_TRUE(A.HasPerspective());
1997
1998 A.MakeIdentity();
1999 A.ApplyPerspectiveDepth(0.0);
2000 EXPECT_FALSE(A.HasPerspective());
2001
2002 A.MakeIdentity();
2003 A.matrix().set(3, 0, -1.f);
2004 EXPECT_TRUE(A.HasPerspective());
2005
2006 A.MakeIdentity();
2007 A.matrix().set(3, 1, -1.f);
2008 EXPECT_TRUE(A.HasPerspective());
2009
2010 A.MakeIdentity();
2011 A.matrix().set(3, 2, -0.3f);
2012 EXPECT_TRUE(A.HasPerspective());
2013
2014 A.MakeIdentity();
2015 A.matrix().set(3, 3, 0.5f);
2016 EXPECT_TRUE(A.HasPerspective());
2017
2018 A.MakeIdentity();
2019 A.matrix().set(3, 3, 0.f);
2020 EXPECT_TRUE(A.HasPerspective());
2021 }
2022
TEST(XFormTest,verifyIsInvertible)2023 TEST(XFormTest, verifyIsInvertible) {
2024 Transform A;
2025
2026 // Translations, rotations, scales, skews and arbitrary combinations of them
2027 // are invertible.
2028 A.MakeIdentity();
2029 EXPECT_TRUE(A.IsInvertible());
2030
2031 A.MakeIdentity();
2032 A.Translate3d(2.0, 3.0, 4.0);
2033 EXPECT_TRUE(A.IsInvertible());
2034
2035 A.MakeIdentity();
2036 A.Scale3d(6.0, 7.0, 8.0);
2037 EXPECT_TRUE(A.IsInvertible());
2038
2039 A.MakeIdentity();
2040 A.RotateAboutXAxis(10.0);
2041 A.RotateAboutYAxis(20.0);
2042 A.RotateAboutZAxis(30.0);
2043 EXPECT_TRUE(A.IsInvertible());
2044
2045 A.MakeIdentity();
2046 A.SkewX(45.0);
2047 EXPECT_TRUE(A.IsInvertible());
2048
2049 // A perspective matrix (projection plane at z=0) is invertible. The
2050 // intuitive explanation is that perspective is eqivalent to a skew of the
2051 // w-axis; skews are invertible.
2052 A.MakeIdentity();
2053 A.ApplyPerspectiveDepth(1.0);
2054 EXPECT_TRUE(A.IsInvertible());
2055
2056 // A "pure" perspective matrix derived by similar triangles, with m44() set
2057 // to zero (i.e. camera positioned at the origin), is not invertible.
2058 A.MakeIdentity();
2059 A.ApplyPerspectiveDepth(1.0);
2060 A.matrix().set(3, 3, 0.f);
2061 EXPECT_FALSE(A.IsInvertible());
2062
2063 // Adding more to a non-invertible matrix will not make it invertible in the
2064 // general case.
2065 A.MakeIdentity();
2066 A.ApplyPerspectiveDepth(1.0);
2067 A.matrix().set(3, 3, 0.f);
2068 A.Scale3d(6.0, 7.0, 8.0);
2069 A.RotateAboutXAxis(10.0);
2070 A.RotateAboutYAxis(20.0);
2071 A.RotateAboutZAxis(30.0);
2072 A.Translate3d(6.0, 7.0, 8.0);
2073 EXPECT_FALSE(A.IsInvertible());
2074
2075 // A degenerate matrix of all zeros is not invertible.
2076 A.MakeIdentity();
2077 A.matrix().set(0, 0, 0.f);
2078 A.matrix().set(1, 1, 0.f);
2079 A.matrix().set(2, 2, 0.f);
2080 A.matrix().set(3, 3, 0.f);
2081 EXPECT_FALSE(A.IsInvertible());
2082 }
2083
TEST(XFormTest,verifyIsIdentity)2084 TEST(XFormTest, verifyIsIdentity) {
2085 Transform A;
2086
2087 InitializeTestMatrix(&A);
2088 EXPECT_FALSE(A.IsIdentity());
2089
2090 A.MakeIdentity();
2091 EXPECT_TRUE(A.IsIdentity());
2092
2093 // Modifying any one individual element should cause the matrix to no longer
2094 // be identity.
2095 A.MakeIdentity();
2096 A.matrix().set(0, 0, 2.f);
2097 EXPECT_FALSE(A.IsIdentity());
2098
2099 A.MakeIdentity();
2100 A.matrix().set(1, 0, 2.f);
2101 EXPECT_FALSE(A.IsIdentity());
2102
2103 A.MakeIdentity();
2104 A.matrix().set(2, 0, 2.f);
2105 EXPECT_FALSE(A.IsIdentity());
2106
2107 A.MakeIdentity();
2108 A.matrix().set(3, 0, 2.f);
2109 EXPECT_FALSE(A.IsIdentity());
2110
2111 A.MakeIdentity();
2112 A.matrix().set(0, 1, 2.f);
2113 EXPECT_FALSE(A.IsIdentity());
2114
2115 A.MakeIdentity();
2116 A.matrix().set(1, 1, 2.f);
2117 EXPECT_FALSE(A.IsIdentity());
2118
2119 A.MakeIdentity();
2120 A.matrix().set(2, 1, 2.f);
2121 EXPECT_FALSE(A.IsIdentity());
2122
2123 A.MakeIdentity();
2124 A.matrix().set(3, 1, 2.f);
2125 EXPECT_FALSE(A.IsIdentity());
2126
2127 A.MakeIdentity();
2128 A.matrix().set(0, 2, 2.f);
2129 EXPECT_FALSE(A.IsIdentity());
2130
2131 A.MakeIdentity();
2132 A.matrix().set(1, 2, 2.f);
2133 EXPECT_FALSE(A.IsIdentity());
2134
2135 A.MakeIdentity();
2136 A.matrix().set(2, 2, 2.f);
2137 EXPECT_FALSE(A.IsIdentity());
2138
2139 A.MakeIdentity();
2140 A.matrix().set(3, 2, 2.f);
2141 EXPECT_FALSE(A.IsIdentity());
2142
2143 A.MakeIdentity();
2144 A.matrix().set(0, 3, 2.f);
2145 EXPECT_FALSE(A.IsIdentity());
2146
2147 A.MakeIdentity();
2148 A.matrix().set(1, 3, 2.f);
2149 EXPECT_FALSE(A.IsIdentity());
2150
2151 A.MakeIdentity();
2152 A.matrix().set(2, 3, 2.f);
2153 EXPECT_FALSE(A.IsIdentity());
2154
2155 A.MakeIdentity();
2156 A.matrix().set(3, 3, 2.f);
2157 EXPECT_FALSE(A.IsIdentity());
2158 }
2159
TEST(XFormTest,verifyIsIdentityOrTranslation)2160 TEST(XFormTest, verifyIsIdentityOrTranslation) {
2161 Transform A;
2162
2163 InitializeTestMatrix(&A);
2164 EXPECT_FALSE(A.IsIdentityOrTranslation());
2165
2166 A.MakeIdentity();
2167 EXPECT_TRUE(A.IsIdentityOrTranslation());
2168
2169 // Modifying any non-translation components should cause
2170 // IsIdentityOrTranslation() to return false. NOTE: (0, 3), (1, 3), and
2171 // (2, 3) are the translation components, so modifying them should still
2172 // return true.
2173 A.MakeIdentity();
2174 A.matrix().set(0, 0, 2.f);
2175 EXPECT_FALSE(A.IsIdentityOrTranslation());
2176
2177 A.MakeIdentity();
2178 A.matrix().set(1, 0, 2.f);
2179 EXPECT_FALSE(A.IsIdentityOrTranslation());
2180
2181 A.MakeIdentity();
2182 A.matrix().set(2, 0, 2.f);
2183 EXPECT_FALSE(A.IsIdentityOrTranslation());
2184
2185 A.MakeIdentity();
2186 A.matrix().set(3, 0, 2.f);
2187 EXPECT_FALSE(A.IsIdentityOrTranslation());
2188
2189 A.MakeIdentity();
2190 A.matrix().set(0, 1, 2.f);
2191 EXPECT_FALSE(A.IsIdentityOrTranslation());
2192
2193 A.MakeIdentity();
2194 A.matrix().set(1, 1, 2.f);
2195 EXPECT_FALSE(A.IsIdentityOrTranslation());
2196
2197 A.MakeIdentity();
2198 A.matrix().set(2, 1, 2.f);
2199 EXPECT_FALSE(A.IsIdentityOrTranslation());
2200
2201 A.MakeIdentity();
2202 A.matrix().set(3, 1, 2.f);
2203 EXPECT_FALSE(A.IsIdentityOrTranslation());
2204
2205 A.MakeIdentity();
2206 A.matrix().set(0, 2, 2.f);
2207 EXPECT_FALSE(A.IsIdentityOrTranslation());
2208
2209 A.MakeIdentity();
2210 A.matrix().set(1, 2, 2.f);
2211 EXPECT_FALSE(A.IsIdentityOrTranslation());
2212
2213 A.MakeIdentity();
2214 A.matrix().set(2, 2, 2.f);
2215 EXPECT_FALSE(A.IsIdentityOrTranslation());
2216
2217 A.MakeIdentity();
2218 A.matrix().set(3, 2, 2.f);
2219 EXPECT_FALSE(A.IsIdentityOrTranslation());
2220
2221 // Note carefully - expecting true here.
2222 A.MakeIdentity();
2223 A.matrix().set(0, 3, 2.f);
2224 EXPECT_TRUE(A.IsIdentityOrTranslation());
2225
2226 // Note carefully - expecting true here.
2227 A.MakeIdentity();
2228 A.matrix().set(1, 3, 2.f);
2229 EXPECT_TRUE(A.IsIdentityOrTranslation());
2230
2231 // Note carefully - expecting true here.
2232 A.MakeIdentity();
2233 A.matrix().set(2, 3, 2.f);
2234 EXPECT_TRUE(A.IsIdentityOrTranslation());
2235
2236 A.MakeIdentity();
2237 A.matrix().set(3, 3, 2.f);
2238 EXPECT_FALSE(A.IsIdentityOrTranslation());
2239 }
2240
TEST(XFormTest,verifyIsApproximatelyIdentityOrTranslation)2241 TEST(XFormTest, verifyIsApproximatelyIdentityOrTranslation) {
2242 Transform A;
2243 SkMatrix44& matrix = A.matrix();
2244
2245 // Exact pure translation.
2246 A.MakeIdentity();
2247
2248 // Set translate values to values other than 0 or 1.
2249 matrix.set(0, 3, 3.4f);
2250 matrix.set(1, 3, 4.4f);
2251 matrix.set(2, 3, 5.6f);
2252
2253 EXPECT_TRUE(A.IsApproximatelyIdentityOrTranslation(0));
2254 EXPECT_TRUE(A.IsApproximatelyIdentityOrTranslation(kApproxZero));
2255
2256 // Approximately pure translation.
2257 InitializeApproxIdentityMatrix(&A);
2258
2259 // Some values must be exact.
2260 matrix.set(3, 0, 0);
2261 matrix.set(3, 1, 0);
2262 matrix.set(3, 2, 0);
2263 matrix.set(3, 3, 1);
2264
2265 // Set translate values to values other than 0 or 1.
2266 matrix.set(0, 3, 3.4f);
2267 matrix.set(1, 3, 4.4f);
2268 matrix.set(2, 3, 5.6f);
2269
2270 EXPECT_FALSE(A.IsApproximatelyIdentityOrTranslation(0));
2271 EXPECT_TRUE(A.IsApproximatelyIdentityOrTranslation(kApproxZero));
2272
2273 // Not approximately pure translation.
2274 InitializeApproxIdentityMatrix(&A);
2275
2276 // Some values must be exact.
2277 matrix.set(3, 0, 0);
2278 matrix.set(3, 1, 0);
2279 matrix.set(3, 2, 0);
2280 matrix.set(3, 3, 1);
2281
2282 // Set some values (not translate values) to values other than 0 or 1.
2283 matrix.set(0, 1, 3.4f);
2284 matrix.set(3, 2, 4.4f);
2285 matrix.set(2, 0, 5.6f);
2286
2287 EXPECT_FALSE(A.IsApproximatelyIdentityOrTranslation(0));
2288 EXPECT_FALSE(A.IsApproximatelyIdentityOrTranslation(kApproxZero));
2289 }
2290
TEST(XFormTest,verifyIsScaleOrTranslation)2291 TEST(XFormTest, verifyIsScaleOrTranslation) {
2292 Transform A;
2293
2294 InitializeTestMatrix(&A);
2295 EXPECT_FALSE(A.IsScaleOrTranslation());
2296
2297 A.MakeIdentity();
2298 EXPECT_TRUE(A.IsScaleOrTranslation());
2299
2300 // Modifying any non-scale or non-translation components should cause
2301 // IsScaleOrTranslation() to return false. (0, 0), (1, 1), (2, 2), (0, 3),
2302 // (1, 3), and (2, 3) are the scale and translation components, so
2303 // modifying them should still return true.
2304
2305 // Note carefully - expecting true here.
2306 A.MakeIdentity();
2307 A.matrix().set(0, 0, 2.f);
2308 EXPECT_TRUE(A.IsScaleOrTranslation());
2309
2310 A.MakeIdentity();
2311 A.matrix().set(1, 0, 2.f);
2312 EXPECT_FALSE(A.IsScaleOrTranslation());
2313
2314 A.MakeIdentity();
2315 A.matrix().set(2, 0, 2.f);
2316 EXPECT_FALSE(A.IsScaleOrTranslation());
2317
2318 A.MakeIdentity();
2319 A.matrix().set(3, 0, 2.f);
2320 EXPECT_FALSE(A.IsScaleOrTranslation());
2321
2322 A.MakeIdentity();
2323 A.matrix().set(0, 1, 2.f);
2324 EXPECT_FALSE(A.IsScaleOrTranslation());
2325
2326 // Note carefully - expecting true here.
2327 A.MakeIdentity();
2328 A.matrix().set(1, 1, 2.f);
2329 EXPECT_TRUE(A.IsScaleOrTranslation());
2330
2331 A.MakeIdentity();
2332 A.matrix().set(2, 1, 2.f);
2333 EXPECT_FALSE(A.IsScaleOrTranslation());
2334
2335 A.MakeIdentity();
2336 A.matrix().set(3, 1, 2.f);
2337 EXPECT_FALSE(A.IsScaleOrTranslation());
2338
2339 A.MakeIdentity();
2340 A.matrix().set(0, 2, 2.f);
2341 EXPECT_FALSE(A.IsScaleOrTranslation());
2342
2343 A.MakeIdentity();
2344 A.matrix().set(1, 2, 2.f);
2345 EXPECT_FALSE(A.IsScaleOrTranslation());
2346
2347 // Note carefully - expecting true here.
2348 A.MakeIdentity();
2349 A.matrix().set(2, 2, 2.f);
2350 EXPECT_TRUE(A.IsScaleOrTranslation());
2351
2352 A.MakeIdentity();
2353 A.matrix().set(3, 2, 2.f);
2354 EXPECT_FALSE(A.IsScaleOrTranslation());
2355
2356 // Note carefully - expecting true here.
2357 A.MakeIdentity();
2358 A.matrix().set(0, 3, 2.f);
2359 EXPECT_TRUE(A.IsScaleOrTranslation());
2360
2361 // Note carefully - expecting true here.
2362 A.MakeIdentity();
2363 A.matrix().set(1, 3, 2.f);
2364 EXPECT_TRUE(A.IsScaleOrTranslation());
2365
2366 // Note carefully - expecting true here.
2367 A.MakeIdentity();
2368 A.matrix().set(2, 3, 2.f);
2369 EXPECT_TRUE(A.IsScaleOrTranslation());
2370
2371 A.MakeIdentity();
2372 A.matrix().set(3, 3, 2.f);
2373 EXPECT_FALSE(A.IsScaleOrTranslation());
2374 }
2375
TEST(XFormTest,verifyFlattenTo2d)2376 TEST(XFormTest, verifyFlattenTo2d) {
2377 Transform A;
2378 InitializeTestMatrix(&A);
2379
2380 A.FlattenTo2d();
2381 EXPECT_ROW1_EQ(10.0f, 14.0f, 0.0f, 22.0f, A);
2382 EXPECT_ROW2_EQ(11.0f, 15.0f, 0.0f, 23.0f, A);
2383 EXPECT_ROW3_EQ(0.0f, 0.0f, 1.0f, 0.0f, A);
2384 EXPECT_ROW4_EQ(13.0f, 17.0f, 0.0f, 25.0f, A);
2385 }
2386
2387 // Another implementation of Preserves2dAxisAlignment that isn't as fast,
2388 // good for testing the faster implementation.
EmpiricallyPreserves2dAxisAlignment(const Transform & transform)2389 static bool EmpiricallyPreserves2dAxisAlignment(const Transform& transform) {
2390 Point3F p1(5.0f, 5.0f, 0.0f);
2391 Point3F p2(10.0f, 5.0f, 0.0f);
2392 Point3F p3(10.0f, 20.0f, 0.0f);
2393 Point3F p4(5.0f, 20.0f, 0.0f);
2394
2395 QuadF test_quad(PointF(p1.x(), p1.y()),
2396 PointF(p2.x(), p2.y()),
2397 PointF(p3.x(), p3.y()),
2398 PointF(p4.x(), p4.y()));
2399 EXPECT_TRUE(test_quad.IsRectilinear());
2400
2401 transform.TransformPoint(&p1);
2402 transform.TransformPoint(&p2);
2403 transform.TransformPoint(&p3);
2404 transform.TransformPoint(&p4);
2405
2406 QuadF transformedQuad(PointF(p1.x(), p1.y()),
2407 PointF(p2.x(), p2.y()),
2408 PointF(p3.x(), p3.y()),
2409 PointF(p4.x(), p4.y()));
2410 return transformedQuad.IsRectilinear();
2411 }
2412
TEST(XFormTest,Preserves2dAxisAlignment)2413 TEST(XFormTest, Preserves2dAxisAlignment) {
2414 static const struct TestCase {
2415 SkMScalar a; // row 1, column 1
2416 SkMScalar b; // row 1, column 2
2417 SkMScalar c; // row 2, column 1
2418 SkMScalar d; // row 2, column 2
2419 bool expected;
2420 } test_cases[] = {
2421 { 3.f, 0.f,
2422 0.f, 4.f, true }, // basic case
2423 { 0.f, 4.f,
2424 3.f, 0.f, true }, // rotate by 90
2425 { 0.f, 0.f,
2426 0.f, 4.f, true }, // degenerate x
2427 { 3.f, 0.f,
2428 0.f, 0.f, true }, // degenerate y
2429 { 0.f, 0.f,
2430 3.f, 0.f, true }, // degenerate x + rotate by 90
2431 { 0.f, 4.f,
2432 0.f, 0.f, true }, // degenerate y + rotate by 90
2433 { 3.f, 4.f,
2434 0.f, 0.f, false },
2435 { 0.f, 0.f,
2436 3.f, 4.f, false },
2437 { 0.f, 3.f,
2438 0.f, 4.f, false },
2439 { 3.f, 0.f,
2440 4.f, 0.f, false },
2441 { 3.f, 4.f,
2442 5.f, 0.f, false },
2443 { 3.f, 4.f,
2444 0.f, 5.f, false },
2445 { 3.f, 0.f,
2446 4.f, 5.f, false },
2447 { 0.f, 3.f,
2448 4.f, 5.f, false },
2449 { 2.f, 3.f,
2450 4.f, 5.f, false },
2451 };
2452
2453 Transform transform;
2454 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
2455 const TestCase& value = test_cases[i];
2456 transform.MakeIdentity();
2457 transform.matrix().set(0, 0, value.a);
2458 transform.matrix().set(0, 1, value.b);
2459 transform.matrix().set(1, 0, value.c);
2460 transform.matrix().set(1, 1, value.d);
2461
2462 if (value.expected) {
2463 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2464 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2465 } else {
2466 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2467 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2468 }
2469 }
2470
2471 // Try the same test cases again, but this time make sure that other matrix
2472 // elements (except perspective) have entries, to test that they are ignored.
2473 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
2474 const TestCase& value = test_cases[i];
2475 transform.MakeIdentity();
2476 transform.matrix().set(0, 0, value.a);
2477 transform.matrix().set(0, 1, value.b);
2478 transform.matrix().set(1, 0, value.c);
2479 transform.matrix().set(1, 1, value.d);
2480
2481 transform.matrix().set(0, 2, 1.f);
2482 transform.matrix().set(0, 3, 2.f);
2483 transform.matrix().set(1, 2, 3.f);
2484 transform.matrix().set(1, 3, 4.f);
2485 transform.matrix().set(2, 0, 5.f);
2486 transform.matrix().set(2, 1, 6.f);
2487 transform.matrix().set(2, 2, 7.f);
2488 transform.matrix().set(2, 3, 8.f);
2489
2490 if (value.expected) {
2491 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2492 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2493 } else {
2494 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2495 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2496 }
2497 }
2498
2499 // Try the same test cases again, but this time add perspective which is
2500 // always assumed to not-preserve axis alignment.
2501 for (size_t i = 0; i < ARRAYSIZE_UNSAFE(test_cases); ++i) {
2502 const TestCase& value = test_cases[i];
2503 transform.MakeIdentity();
2504 transform.matrix().set(0, 0, value.a);
2505 transform.matrix().set(0, 1, value.b);
2506 transform.matrix().set(1, 0, value.c);
2507 transform.matrix().set(1, 1, value.d);
2508
2509 transform.matrix().set(0, 2, 1.f);
2510 transform.matrix().set(0, 3, 2.f);
2511 transform.matrix().set(1, 2, 3.f);
2512 transform.matrix().set(1, 3, 4.f);
2513 transform.matrix().set(2, 0, 5.f);
2514 transform.matrix().set(2, 1, 6.f);
2515 transform.matrix().set(2, 2, 7.f);
2516 transform.matrix().set(2, 3, 8.f);
2517 transform.matrix().set(3, 0, 9.f);
2518 transform.matrix().set(3, 1, 10.f);
2519 transform.matrix().set(3, 2, 11.f);
2520 transform.matrix().set(3, 3, 12.f);
2521
2522 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2523 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2524 }
2525
2526 // Try a few more practical situations to check precision
2527 transform.MakeIdentity();
2528 transform.RotateAboutZAxis(90.0);
2529 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2530 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2531
2532 transform.MakeIdentity();
2533 transform.RotateAboutZAxis(180.0);
2534 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2535 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2536
2537 transform.MakeIdentity();
2538 transform.RotateAboutZAxis(270.0);
2539 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2540 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2541
2542 transform.MakeIdentity();
2543 transform.RotateAboutYAxis(90.0);
2544 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2545 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2546
2547 transform.MakeIdentity();
2548 transform.RotateAboutXAxis(90.0);
2549 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2550 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2551
2552 transform.MakeIdentity();
2553 transform.RotateAboutZAxis(90.0);
2554 transform.RotateAboutYAxis(90.0);
2555 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2556 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2557
2558 transform.MakeIdentity();
2559 transform.RotateAboutZAxis(90.0);
2560 transform.RotateAboutXAxis(90.0);
2561 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2562 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2563
2564 transform.MakeIdentity();
2565 transform.RotateAboutYAxis(90.0);
2566 transform.RotateAboutZAxis(90.0);
2567 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2568 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2569
2570 transform.MakeIdentity();
2571 transform.RotateAboutZAxis(45.0);
2572 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2573 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2574
2575 // 3-d case; In 2d after an orthographic projection, this case does
2576 // preserve 2d axis alignment. But in 3d, it does not preserve axis
2577 // alignment.
2578 transform.MakeIdentity();
2579 transform.RotateAboutYAxis(45.0);
2580 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2581 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2582
2583 transform.MakeIdentity();
2584 transform.RotateAboutXAxis(45.0);
2585 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2586 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2587
2588 // Perspective cases.
2589 transform.MakeIdentity();
2590 transform.ApplyPerspectiveDepth(10.0);
2591 transform.RotateAboutYAxis(45.0);
2592 EXPECT_FALSE(EmpiricallyPreserves2dAxisAlignment(transform));
2593 EXPECT_FALSE(transform.Preserves2dAxisAlignment());
2594
2595 transform.MakeIdentity();
2596 transform.ApplyPerspectiveDepth(10.0);
2597 transform.RotateAboutZAxis(90.0);
2598 EXPECT_TRUE(EmpiricallyPreserves2dAxisAlignment(transform));
2599 EXPECT_TRUE(transform.Preserves2dAxisAlignment());
2600 }
2601
TEST(XFormTest,To2dTranslation)2602 TEST(XFormTest, To2dTranslation) {
2603 Vector2dF translation(3.f, 7.f);
2604 Transform transform;
2605 transform.Translate(translation.x(), translation.y() + 1);
2606 EXPECT_NE(translation.ToString(), transform.To2dTranslation().ToString());
2607 transform.MakeIdentity();
2608 transform.Translate(translation.x(), translation.y());
2609 EXPECT_EQ(translation.ToString(), transform.To2dTranslation().ToString());
2610 }
2611
TEST(XFormTest,TransformRect)2612 TEST(XFormTest, TransformRect) {
2613 Transform translation;
2614 translation.Translate(3.f, 7.f);
2615 RectF rect(1.f, 2.f, 3.f, 4.f);
2616 RectF expected(4.f, 9.f, 3.f, 4.f);
2617 translation.TransformRect(&rect);
2618 EXPECT_EQ(expected.ToString(), rect.ToString());
2619 }
2620
TEST(XFormTest,TransformRectReverse)2621 TEST(XFormTest, TransformRectReverse) {
2622 Transform translation;
2623 translation.Translate(3.f, 7.f);
2624 RectF rect(1.f, 2.f, 3.f, 4.f);
2625 RectF expected(-2.f, -5.f, 3.f, 4.f);
2626 EXPECT_TRUE(translation.TransformRectReverse(&rect));
2627 EXPECT_EQ(expected.ToString(), rect.ToString());
2628
2629 Transform singular;
2630 singular.Scale3d(0.f, 0.f, 0.f);
2631 EXPECT_FALSE(singular.TransformRectReverse(&rect));
2632 }
2633
TEST(XFormTest,TransformBox)2634 TEST(XFormTest, TransformBox) {
2635 Transform translation;
2636 translation.Translate3d(3.f, 7.f, 6.f);
2637 BoxF box(1.f, 2.f, 3.f, 4.f, 5.f, 6.f);
2638 BoxF expected(4.f, 9.f, 9.f, 4.f, 5.f, 6.f);
2639 translation.TransformBox(&box);
2640 EXPECT_EQ(expected.ToString(), box.ToString());
2641 }
2642
TEST(XFormTest,TransformBoxReverse)2643 TEST(XFormTest, TransformBoxReverse) {
2644 Transform translation;
2645 translation.Translate3d(3.f, 7.f, 6.f);
2646 BoxF box(1.f, 2.f, 3.f, 4.f, 5.f, 6.f);
2647 BoxF expected(-2.f, -5.f, -3.f, 4.f, 5.f, 6.f);
2648 EXPECT_TRUE(translation.TransformBoxReverse(&box));
2649 EXPECT_EQ(expected.ToString(), box.ToString());
2650
2651 Transform singular;
2652 singular.Scale3d(0.f, 0.f, 0.f);
2653 EXPECT_FALSE(singular.TransformBoxReverse(&box));
2654 }
2655
2656 } // namespace
2657
2658 } // namespace gfx
2659