MatrixTest.cpp revision 311a3cda9457d50cc7c2a0fc9f153a9ce2c8cb8e 
1/*
2 * Copyright 2011 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8#include "SkMath.h"
9#include "SkMatrix.h"
10#include "SkMatrixUtils.h"
11#include "SkRandom.h"
12#include "Test.h"
13
14static bool nearly_equal_scalar(SkScalar a, SkScalar b) {
15    const SkScalar tolerance = SK_Scalar1 / 200000;
16    return SkScalarAbs(a - b) <= tolerance;
17}
18
19static bool nearly_equal(const SkMatrix& a, const SkMatrix& b) {
20    for (int i = 0; i < 9; i++) {
21        if (!nearly_equal_scalar(a[i], b[i])) {
22            SkDebugf("not equal %g %g\n", (float)a[i], (float)b[i]);
23            return false;
24        }
25    }
26    return true;
27}
28
29static bool are_equal(skiatest::Reporter* reporter,
30                      const SkMatrix& a,
31                      const SkMatrix& b) {
32    bool equal = a == b;
33    bool cheapEqual = a.cheapEqualTo(b);
34    if (equal != cheapEqual) {
35        if (equal) {
36            bool foundZeroSignDiff = false;
37            for (int i = 0; i < 9; ++i) {
38                float aVal = a.get(i);
39                float bVal = b.get(i);
40                int aValI = *SkTCast<int*>(&aVal);
41                int bValI = *SkTCast<int*>(&bVal);
42                if (0 == aVal && 0 == bVal && aValI != bValI) {
43                    foundZeroSignDiff = true;
44                } else {
45                    REPORTER_ASSERT(reporter, aVal == bVal && aValI == aValI);
46                }
47            }
48            REPORTER_ASSERT(reporter, foundZeroSignDiff);
49        } else {
50            bool foundNaN = false;
51            for (int i = 0; i < 9; ++i) {
52                float aVal = a.get(i);
53                float bVal = b.get(i);
54                int aValI = *SkTCast<int*>(&aVal);
55                int bValI = *SkTCast<int*>(&bVal);
56                if (sk_float_isnan(aVal) && aValI == bValI) {
57                    foundNaN = true;
58                } else {
59                    REPORTER_ASSERT(reporter, aVal == bVal && aValI == bValI);
60                }
61            }
62            REPORTER_ASSERT(reporter, foundNaN);
63        }
64    }
65    return equal;
66}
67
68static bool is_identity(const SkMatrix& m) {
69    SkMatrix identity;
70    identity.reset();
71    return nearly_equal(m, identity);
72}
73
74static void test_matrix_recttorect(skiatest::Reporter* reporter) {
75    SkRect src, dst;
76    SkMatrix matrix;
77
78    src.set(0, 0, SK_Scalar1*10, SK_Scalar1*10);
79    dst = src;
80    matrix.setRectToRect(src, dst, SkMatrix::kFill_ScaleToFit);
81    REPORTER_ASSERT(reporter, SkMatrix::kIdentity_Mask == matrix.getType());
82    REPORTER_ASSERT(reporter, matrix.rectStaysRect());
83
84    dst.offset(SK_Scalar1, SK_Scalar1);
85    matrix.setRectToRect(src, dst, SkMatrix::kFill_ScaleToFit);
86    REPORTER_ASSERT(reporter, SkMatrix::kTranslate_Mask == matrix.getType());
87    REPORTER_ASSERT(reporter, matrix.rectStaysRect());
88
89    dst.fRight += SK_Scalar1;
90    matrix.setRectToRect(src, dst, SkMatrix::kFill_ScaleToFit);
91    REPORTER_ASSERT(reporter,
92                    (SkMatrix::kTranslate_Mask | SkMatrix::kScale_Mask) == matrix.getType());
93    REPORTER_ASSERT(reporter, matrix.rectStaysRect());
94
95    dst = src;
96    dst.fRight = src.fRight * 2;
97    matrix.setRectToRect(src, dst, SkMatrix::kFill_ScaleToFit);
98    REPORTER_ASSERT(reporter, SkMatrix::kScale_Mask == matrix.getType());
99    REPORTER_ASSERT(reporter, matrix.rectStaysRect());
100}
101
102static void test_flatten(skiatest::Reporter* reporter, const SkMatrix& m) {
103    // add 100 in case we have a bug, I don't want to kill my stack in the test
104    static const size_t kBufferSize = SkMatrix::kMaxFlattenSize + 100;
105    char buffer[kBufferSize];
106    size_t size1 = m.writeToMemory(NULL);
107    size_t size2 = m.writeToMemory(buffer);
108    REPORTER_ASSERT(reporter, size1 == size2);
109    REPORTER_ASSERT(reporter, size1 <= SkMatrix::kMaxFlattenSize);
110
111    SkMatrix m2;
112    size_t size3 = m2.readFromMemory(buffer, kBufferSize);
113    REPORTER_ASSERT(reporter, size1 == size3);
114    REPORTER_ASSERT(reporter, are_equal(reporter, m, m2));
115
116    char buffer2[kBufferSize];
117    size3 = m2.writeToMemory(buffer2);
118    REPORTER_ASSERT(reporter, size1 == size3);
119    REPORTER_ASSERT(reporter, memcmp(buffer, buffer2, size1) == 0);
120}
121
122static void test_matrix_min_max_scale(skiatest::Reporter* reporter) {
123    SkScalar scales[2];
124    bool success;
125
126    SkMatrix identity;
127    identity.reset();
128    REPORTER_ASSERT(reporter, SK_Scalar1 == identity.getMinScale());
129    REPORTER_ASSERT(reporter, SK_Scalar1 == identity.getMaxScale());
130    success = identity.getMinMaxScales(scales);
131    REPORTER_ASSERT(reporter, success && SK_Scalar1 == scales[0] && SK_Scalar1 == scales[1]);
132
133    SkMatrix scale;
134    scale.setScale(SK_Scalar1 * 2, SK_Scalar1 * 4);
135    REPORTER_ASSERT(reporter, SK_Scalar1 * 2 == scale.getMinScale());
136    REPORTER_ASSERT(reporter, SK_Scalar1 * 4 == scale.getMaxScale());
137    success = scale.getMinMaxScales(scales);
138    REPORTER_ASSERT(reporter, success && SK_Scalar1 * 2 == scales[0] && SK_Scalar1 * 4 == scales[1]);
139
140    SkMatrix rot90Scale;
141    rot90Scale.setRotate(90 * SK_Scalar1);
142    rot90Scale.postScale(SK_Scalar1 / 4, SK_Scalar1 / 2);
143    REPORTER_ASSERT(reporter, SK_Scalar1 / 4 == rot90Scale.getMinScale());
144    REPORTER_ASSERT(reporter, SK_Scalar1 / 2 == rot90Scale.getMaxScale());
145    success = rot90Scale.getMinMaxScales(scales);
146    REPORTER_ASSERT(reporter, success && SK_Scalar1 / 4  == scales[0] && SK_Scalar1 / 2 == scales[1]);
147
148    SkMatrix rotate;
149    rotate.setRotate(128 * SK_Scalar1);
150    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(SK_Scalar1, rotate.getMinScale(), SK_ScalarNearlyZero));
151    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(SK_Scalar1, rotate.getMaxScale(), SK_ScalarNearlyZero));
152    success = rotate.getMinMaxScales(scales);
153    REPORTER_ASSERT(reporter, success);
154    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(SK_Scalar1, scales[0], SK_ScalarNearlyZero));
155    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(SK_Scalar1, scales[1], SK_ScalarNearlyZero));
156
157    SkMatrix translate;
158    translate.setTranslate(10 * SK_Scalar1, -5 * SK_Scalar1);
159    REPORTER_ASSERT(reporter, SK_Scalar1 == translate.getMinScale());
160    REPORTER_ASSERT(reporter, SK_Scalar1 == translate.getMaxScale());
161    success = translate.getMinMaxScales(scales);
162    REPORTER_ASSERT(reporter, success && SK_Scalar1 == scales[0] && SK_Scalar1 == scales[1]);
163
164    SkMatrix perspX;
165    perspX.reset();
166    perspX.setPerspX(SkScalarToPersp(SK_Scalar1 / 1000));
167    REPORTER_ASSERT(reporter, -SK_Scalar1 == perspX.getMinScale());
168    REPORTER_ASSERT(reporter, -SK_Scalar1 == perspX.getMaxScale());
169    // Verify that getMinMaxScales() doesn't update the scales array on failure.
170    scales[0] = -5;
171    scales[1] = -5;
172    success = perspX.getMinMaxScales(scales);
173    REPORTER_ASSERT(reporter, !success && -5 * SK_Scalar1 == scales[0] && -5 * SK_Scalar1  == scales[1]);
174
175    SkMatrix perspY;
176    perspY.reset();
177    perspY.setPerspY(SkScalarToPersp(-SK_Scalar1 / 500));
178    REPORTER_ASSERT(reporter, -SK_Scalar1 == perspY.getMinScale());
179    REPORTER_ASSERT(reporter, -SK_Scalar1 == perspY.getMaxScale());
180    scales[0] = -5;
181    scales[1] = -5;
182    success = perspY.getMinMaxScales(scales);
183    REPORTER_ASSERT(reporter, !success && -5 * SK_Scalar1 == scales[0] && -5 * SK_Scalar1  == scales[1]);
184
185    SkMatrix baseMats[] = {scale, rot90Scale, rotate,
186                           translate, perspX, perspY};
187    SkMatrix mats[2*SK_ARRAY_COUNT(baseMats)];
188    for (size_t i = 0; i < SK_ARRAY_COUNT(baseMats); ++i) {
189        mats[i] = baseMats[i];
190        bool invertable = mats[i].invert(&mats[i + SK_ARRAY_COUNT(baseMats)]);
191        REPORTER_ASSERT(reporter, invertable);
192    }
193    SkRandom rand;
194    for (int m = 0; m < 1000; ++m) {
195        SkMatrix mat;
196        mat.reset();
197        for (int i = 0; i < 4; ++i) {
198            int x = rand.nextU() % SK_ARRAY_COUNT(mats);
199            mat.postConcat(mats[x]);
200        }
201
202        SkScalar minScale = mat.getMinScale();
203        SkScalar maxScale = mat.getMaxScale();
204        REPORTER_ASSERT(reporter, (minScale < 0) == (maxScale < 0));
205        REPORTER_ASSERT(reporter, (maxScale < 0) == mat.hasPerspective());
206
207        SkScalar scales[2];
208        bool success = mat.getMinMaxScales(scales);
209        REPORTER_ASSERT(reporter, success == !mat.hasPerspective());
210        REPORTER_ASSERT(reporter, !success || (scales[0] == minScale && scales[1] == maxScale));
211
212        if (mat.hasPerspective()) {
213            m -= 1; // try another non-persp matrix
214            continue;
215        }
216
217        // test a bunch of vectors. All should be scaled by between minScale and maxScale
218        // (modulo some error) and we should find a vector that is scaled by almost each.
219        static const SkScalar gVectorScaleTol = (105 * SK_Scalar1) / 100;
220        static const SkScalar gCloseScaleTol = (97 * SK_Scalar1) / 100;
221        SkScalar max = 0, min = SK_ScalarMax;
222        SkVector vectors[1000];
223        for (size_t i = 0; i < SK_ARRAY_COUNT(vectors); ++i) {
224            vectors[i].fX = rand.nextSScalar1();
225            vectors[i].fY = rand.nextSScalar1();
226            if (!vectors[i].normalize()) {
227                i -= 1;
228                continue;
229            }
230        }
231        mat.mapVectors(vectors, SK_ARRAY_COUNT(vectors));
232        for (size_t i = 0; i < SK_ARRAY_COUNT(vectors); ++i) {
233            SkScalar d = vectors[i].length();
234            REPORTER_ASSERT(reporter, SkScalarDiv(d, maxScale) < gVectorScaleTol);
235            REPORTER_ASSERT(reporter, SkScalarDiv(minScale, d) < gVectorScaleTol);
236            if (max < d) {
237                max = d;
238            }
239            if (min > d) {
240                min = d;
241            }
242        }
243        REPORTER_ASSERT(reporter, SkScalarDiv(max, maxScale) >= gCloseScaleTol);
244        REPORTER_ASSERT(reporter, SkScalarDiv(minScale, min) >= gCloseScaleTol);
245    }
246}
247
248static void test_matrix_is_similarity(skiatest::Reporter* reporter) {
249    SkMatrix mat;
250
251    // identity
252    mat.setIdentity();
253    REPORTER_ASSERT(reporter, mat.isSimilarity());
254
255    // translation only
256    mat.reset();
257    mat.setTranslate(SkIntToScalar(100), SkIntToScalar(100));
258    REPORTER_ASSERT(reporter, mat.isSimilarity());
259
260    // scale with same size
261    mat.reset();
262    mat.setScale(SkIntToScalar(15), SkIntToScalar(15));
263    REPORTER_ASSERT(reporter, mat.isSimilarity());
264
265    // scale with one negative
266    mat.reset();
267    mat.setScale(SkIntToScalar(-15), SkIntToScalar(15));
268    REPORTER_ASSERT(reporter, mat.isSimilarity());
269
270    // scale with different size
271    mat.reset();
272    mat.setScale(SkIntToScalar(15), SkIntToScalar(20));
273    REPORTER_ASSERT(reporter, !mat.isSimilarity());
274
275    // scale with same size at a pivot point
276    mat.reset();
277    mat.setScale(SkIntToScalar(15), SkIntToScalar(15),
278                 SkIntToScalar(2), SkIntToScalar(2));
279    REPORTER_ASSERT(reporter, mat.isSimilarity());
280
281    // scale with different size at a pivot point
282    mat.reset();
283    mat.setScale(SkIntToScalar(15), SkIntToScalar(20),
284                 SkIntToScalar(2), SkIntToScalar(2));
285    REPORTER_ASSERT(reporter, !mat.isSimilarity());
286
287    // skew with same size
288    mat.reset();
289    mat.setSkew(SkIntToScalar(15), SkIntToScalar(15));
290    REPORTER_ASSERT(reporter, !mat.isSimilarity());
291
292    // skew with different size
293    mat.reset();
294    mat.setSkew(SkIntToScalar(15), SkIntToScalar(20));
295    REPORTER_ASSERT(reporter, !mat.isSimilarity());
296
297    // skew with same size at a pivot point
298    mat.reset();
299    mat.setSkew(SkIntToScalar(15), SkIntToScalar(15),
300                SkIntToScalar(2), SkIntToScalar(2));
301    REPORTER_ASSERT(reporter, !mat.isSimilarity());
302
303    // skew with different size at a pivot point
304    mat.reset();
305    mat.setSkew(SkIntToScalar(15), SkIntToScalar(20),
306                SkIntToScalar(2), SkIntToScalar(2));
307    REPORTER_ASSERT(reporter, !mat.isSimilarity());
308
309    // perspective x
310    mat.reset();
311    mat.setPerspX(SkScalarToPersp(SK_Scalar1 / 2));
312    REPORTER_ASSERT(reporter, !mat.isSimilarity());
313
314    // perspective y
315    mat.reset();
316    mat.setPerspY(SkScalarToPersp(SK_Scalar1 / 2));
317    REPORTER_ASSERT(reporter, !mat.isSimilarity());
318
319    // rotate
320    for (int angle = 0; angle < 360; ++angle) {
321        mat.reset();
322        mat.setRotate(SkIntToScalar(angle));
323        REPORTER_ASSERT(reporter, mat.isSimilarity());
324    }
325
326    // see if there are any accumulated precision issues
327    mat.reset();
328    for (int i = 1; i < 360; i++) {
329        mat.postRotate(SkIntToScalar(1));
330    }
331    REPORTER_ASSERT(reporter, mat.isSimilarity());
332
333    // rotate + translate
334    mat.reset();
335    mat.setRotate(SkIntToScalar(30));
336    mat.postTranslate(SkIntToScalar(10), SkIntToScalar(20));
337    REPORTER_ASSERT(reporter, mat.isSimilarity());
338
339    // rotate + uniform scale
340    mat.reset();
341    mat.setRotate(SkIntToScalar(30));
342    mat.postScale(SkIntToScalar(2), SkIntToScalar(2));
343    REPORTER_ASSERT(reporter, mat.isSimilarity());
344
345    // rotate + non-uniform scale
346    mat.reset();
347    mat.setRotate(SkIntToScalar(30));
348    mat.postScale(SkIntToScalar(3), SkIntToScalar(2));
349    REPORTER_ASSERT(reporter, !mat.isSimilarity());
350
351    // all zero
352    mat.setAll(0, 0, 0, 0, 0, 0, 0, 0, 0);
353    REPORTER_ASSERT(reporter, !mat.isSimilarity());
354
355    // all zero except perspective
356    mat.setAll(0, 0, 0, 0, 0, 0, 0, 0, SK_Scalar1);
357    REPORTER_ASSERT(reporter, !mat.isSimilarity());
358
359    // scales zero, only skews
360    mat.setAll(0, SK_Scalar1, 0,
361               SK_Scalar1, 0, 0,
362               0, 0, SkMatrix::I()[8]);
363    REPORTER_ASSERT(reporter, mat.isSimilarity());
364}
365
366// For test_matrix_decomposition, below.
367static bool scalar_nearly_equal_relative(SkScalar a, SkScalar b,
368                                         SkScalar tolerance = SK_ScalarNearlyZero) {
369    // from Bruce Dawson
370    // absolute check
371    SkScalar diff = SkScalarAbs(a - b);
372    if (diff < tolerance) {
373        return true;
374    }
375
376    // relative check
377    a = SkScalarAbs(a);
378    b = SkScalarAbs(b);
379    SkScalar largest = (b > a) ? b : a;
380
381    if (diff <= largest*tolerance) {
382        return true;
383    }
384
385    return false;
386}
387
388static bool check_matrix_recomposition(const SkMatrix& mat,
389                                       const SkPoint& rotation1,
390                                       const SkPoint& scale,
391                                       const SkPoint& rotation2) {
392    SkScalar c1 = rotation1.fX;
393    SkScalar s1 = rotation1.fY;
394    SkScalar scaleX = scale.fX;
395    SkScalar scaleY = scale.fY;
396    SkScalar c2 = rotation2.fX;
397    SkScalar s2 = rotation2.fY;
398
399    // We do a relative check here because large scale factors cause problems with an absolute check
400    bool result = scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
401                                               scaleX*c1*c2 - scaleY*s1*s2) &&
402                  scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
403                                               -scaleX*s1*c2 - scaleY*c1*s2) &&
404                  scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
405                                               scaleX*c1*s2 + scaleY*s1*c2) &&
406                  scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
407                                               -scaleX*s1*s2 + scaleY*c1*c2);
408    return result;
409}
410
411static void test_matrix_decomposition(skiatest::Reporter* reporter) {
412    SkMatrix mat;
413    SkPoint rotation1, scale, rotation2;
414
415    const float kRotation0 = 15.5f;
416    const float kRotation1 = -50.f;
417    const float kScale0 = 5000.f;
418    const float kScale1 = 0.001f;
419
420    // identity
421    mat.reset();
422    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
423    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
424    // make sure it doesn't crash if we pass in NULLs
425    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, NULL, NULL, NULL));
426
427    // rotation only
428    mat.setRotate(kRotation0);
429    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
430    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
431
432    // uniform scale only
433    mat.setScale(kScale0, kScale0);
434    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
435    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
436
437    // anisotropic scale only
438    mat.setScale(kScale1, kScale0);
439    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
440    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
441
442    // rotation then uniform scale
443    mat.setRotate(kRotation1);
444    mat.postScale(kScale0, kScale0);
445    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
446    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
447
448    // uniform scale then rotation
449    mat.setScale(kScale0, kScale0);
450    mat.postRotate(kRotation1);
451    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
452    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
453
454    // rotation then uniform scale+reflection
455    mat.setRotate(kRotation0);
456    mat.postScale(kScale1, -kScale1);
457    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
458    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
459
460    // uniform scale+reflection, then rotate
461    mat.setScale(kScale0, -kScale0);
462    mat.postRotate(kRotation1);
463    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
464    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
465
466    // rotation then anisotropic scale
467    mat.setRotate(kRotation1);
468    mat.postScale(kScale1, kScale0);
469    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
470    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
471
472    // rotation then anisotropic scale
473    mat.setRotate(90);
474    mat.postScale(kScale1, kScale0);
475    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
476    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
477
478    // anisotropic scale then rotation
479    mat.setScale(kScale1, kScale0);
480    mat.postRotate(kRotation0);
481    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
482    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
483
484    // anisotropic scale then rotation
485    mat.setScale(kScale1, kScale0);
486    mat.postRotate(90);
487    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
488    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
489
490    // rotation, uniform scale, then different rotation
491    mat.setRotate(kRotation1);
492    mat.postScale(kScale0, kScale0);
493    mat.postRotate(kRotation0);
494    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
495    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
496
497    // rotation, anisotropic scale, then different rotation
498    mat.setRotate(kRotation0);
499    mat.postScale(kScale1, kScale0);
500    mat.postRotate(kRotation1);
501    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
502    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
503
504    // rotation, anisotropic scale + reflection, then different rotation
505    mat.setRotate(kRotation0);
506    mat.postScale(-kScale1, kScale0);
507    mat.postRotate(kRotation1);
508    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
509    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
510
511    // try some random matrices
512    SkRandom rand;
513    for (int m = 0; m < 1000; ++m) {
514        SkScalar rot0 = rand.nextRangeF(-180, 180);
515        SkScalar sx = rand.nextRangeF(-3000.f, 3000.f);
516        SkScalar sy = rand.nextRangeF(-3000.f, 3000.f);
517        SkScalar rot1 = rand.nextRangeF(-180, 180);
518        mat.setRotate(rot0);
519        mat.postScale(sx, sy);
520        mat.postRotate(rot1);
521
522        if (SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2)) {
523            REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
524        } else {
525            // if the matrix is degenerate, the basis vectors should be near-parallel or near-zero
526            SkScalar perpdot = mat[SkMatrix::kMScaleX]*mat[SkMatrix::kMScaleY] -
527                               mat[SkMatrix::kMSkewX]*mat[SkMatrix::kMSkewY];
528            REPORTER_ASSERT(reporter, SkScalarNearlyZero(perpdot));
529        }
530    }
531
532    // translation shouldn't affect this
533    mat.postTranslate(-1000.f, 1000.f);
534    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
535    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
536
537    // perspective shouldn't affect this
538    mat[SkMatrix::kMPersp0] = 12.f;
539    mat[SkMatrix::kMPersp1] = 4.f;
540    mat[SkMatrix::kMPersp2] = 1872.f;
541    REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
542    REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
543
544    // degenerate matrices
545    // mostly zero entries
546    mat.reset();
547    mat[SkMatrix::kMScaleX] = 0.f;
548    REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
549    mat.reset();
550    mat[SkMatrix::kMScaleY] = 0.f;
551    REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
552    mat.reset();
553    // linearly dependent entries
554    mat[SkMatrix::kMScaleX] = 1.f;
555    mat[SkMatrix::kMSkewX] = 2.f;
556    mat[SkMatrix::kMSkewY] = 4.f;
557    mat[SkMatrix::kMScaleY] = 8.f;
558    REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
559}
560
561// For test_matrix_homogeneous, below.
562static bool scalar_array_nearly_equal_relative(const SkScalar a[], const SkScalar b[], int count) {
563    for (int i = 0; i < count; ++i) {
564        if (!scalar_nearly_equal_relative(a[i], b[i])) {
565            return false;
566        }
567    }
568    return true;
569}
570
571// For test_matrix_homogeneous, below.
572// Maps a single triple in src using m and compares results to those in dst
573static bool naive_homogeneous_mapping(const SkMatrix& m, const SkScalar src[3],
574                                      const SkScalar dst[3]) {
575    SkScalar res[3];
576    SkScalar ms[9] = {m[0], m[1], m[2],
577                      m[3], m[4], m[5],
578                      m[6], m[7], m[8]};
579    res[0] = src[0] * ms[0] + src[1] * ms[1] + src[2] * ms[2];
580    res[1] = src[0] * ms[3] + src[1] * ms[4] + src[2] * ms[5];
581    res[2] = src[0] * ms[6] + src[1] * ms[7] + src[2] * ms[8];
582    return scalar_array_nearly_equal_relative(res, dst, 3);
583}
584
585static void test_matrix_homogeneous(skiatest::Reporter* reporter) {
586    SkMatrix mat;
587
588    const float kRotation0 = 15.5f;
589    const float kRotation1 = -50.f;
590    const float kScale0 = 5000.f;
591
592    const int kTripleCount = 1000;
593    const int kMatrixCount = 1000;
594    SkRandom rand;
595
596    SkScalar randTriples[3*kTripleCount];
597    for (int i = 0; i < 3*kTripleCount; ++i) {
598        randTriples[i] = rand.nextRangeF(-3000.f, 3000.f);
599    }
600
601    SkMatrix mats[kMatrixCount];
602    for (int i = 0; i < kMatrixCount; ++i) {
603        for (int j = 0; j < 9; ++j) {
604            mats[i].set(j, rand.nextRangeF(-3000.f, 3000.f));
605        }
606    }
607
608    // identity
609    {
610    mat.reset();
611    SkScalar dst[3*kTripleCount];
612    mat.mapHomogeneousPoints(dst, randTriples, kTripleCount);
613    REPORTER_ASSERT(reporter, scalar_array_nearly_equal_relative(randTriples, dst, kTripleCount*3));
614    }
615
616    // zero matrix
617    {
618    mat.setAll(0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, 0.f);
619    SkScalar dst[3*kTripleCount];
620    mat.mapHomogeneousPoints(dst, randTriples, kTripleCount);
621    SkScalar zeros[3] = {0.f, 0.f, 0.f};
622    for (int i = 0; i < kTripleCount; ++i) {
623        REPORTER_ASSERT(reporter, scalar_array_nearly_equal_relative(&dst[i*3], zeros, 3));
624    }
625    }
626
627    // zero point
628    {
629    SkScalar zeros[3] = {0.f, 0.f, 0.f};
630    for (int i = 0; i < kMatrixCount; ++i) {
631        SkScalar dst[3];
632        mats[i].mapHomogeneousPoints(dst, zeros, 1);
633        REPORTER_ASSERT(reporter, scalar_array_nearly_equal_relative(dst, zeros, 3));
634    }
635    }
636
637    // doesn't crash with null dst, src, count == 0
638    {
639    mats[0].mapHomogeneousPoints(NULL, NULL, 0);
640    }
641
642    // uniform scale of point
643    {
644    mat.setScale(kScale0, kScale0);
645    SkScalar dst[3];
646    SkScalar src[3] = {randTriples[0], randTriples[1], 1.f};
647    SkPoint pnt;
648    pnt.set(src[0], src[1]);
649    mat.mapHomogeneousPoints(dst, src, 1);
650    mat.mapPoints(&pnt, &pnt, 1);
651    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[0], pnt.fX));
652    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[1], pnt.fY));
653    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[2], SK_Scalar1));
654    }
655
656    // rotation of point
657    {
658    mat.setRotate(kRotation0);
659    SkScalar dst[3];
660    SkScalar src[3] = {randTriples[0], randTriples[1], 1.f};
661    SkPoint pnt;
662    pnt.set(src[0], src[1]);
663    mat.mapHomogeneousPoints(dst, src, 1);
664    mat.mapPoints(&pnt, &pnt, 1);
665    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[0], pnt.fX));
666    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[1], pnt.fY));
667    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[2], SK_Scalar1));
668    }
669
670    // rotation, scale, rotation of point
671    {
672    mat.setRotate(kRotation1);
673    mat.postScale(kScale0, kScale0);
674    mat.postRotate(kRotation0);
675    SkScalar dst[3];
676    SkScalar src[3] = {randTriples[0], randTriples[1], 1.f};
677    SkPoint pnt;
678    pnt.set(src[0], src[1]);
679    mat.mapHomogeneousPoints(dst, src, 1);
680    mat.mapPoints(&pnt, &pnt, 1);
681    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[0], pnt.fX));
682    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[1], pnt.fY));
683    REPORTER_ASSERT(reporter, SkScalarNearlyEqual(dst[2], SK_Scalar1));
684    }
685
686    // compare with naive approach
687    {
688    for (int i = 0; i < kMatrixCount; ++i) {
689        for (int j = 0; j < kTripleCount; ++j) {
690            SkScalar dst[3];
691            mats[i].mapHomogeneousPoints(dst, &randTriples[j*3], 1);
692            REPORTER_ASSERT(reporter, naive_homogeneous_mapping(mats[i], &randTriples[j*3], dst));
693        }
694    }
695    }
696
697}
698
699DEF_TEST(Matrix, reporter) {
700    SkMatrix    mat, inverse, iden1, iden2;
701
702    mat.reset();
703    mat.setTranslate(SK_Scalar1, SK_Scalar1);
704    REPORTER_ASSERT(reporter, mat.invert(&inverse));
705    iden1.setConcat(mat, inverse);
706    REPORTER_ASSERT(reporter, is_identity(iden1));
707
708    mat.setScale(SkIntToScalar(2), SkIntToScalar(4));
709    REPORTER_ASSERT(reporter, mat.invert(&inverse));
710    iden1.setConcat(mat, inverse);
711    REPORTER_ASSERT(reporter, is_identity(iden1));
712    test_flatten(reporter, mat);
713
714    mat.setScale(SK_Scalar1/2, SkIntToScalar(2));
715    REPORTER_ASSERT(reporter, mat.invert(&inverse));
716    iden1.setConcat(mat, inverse);
717    REPORTER_ASSERT(reporter, is_identity(iden1));
718    test_flatten(reporter, mat);
719
720    mat.setScale(SkIntToScalar(3), SkIntToScalar(5), SkIntToScalar(20), 0);
721    mat.postRotate(SkIntToScalar(25));
722    REPORTER_ASSERT(reporter, mat.invert(NULL));
723    REPORTER_ASSERT(reporter, mat.invert(&inverse));
724    iden1.setConcat(mat, inverse);
725    REPORTER_ASSERT(reporter, is_identity(iden1));
726    iden2.setConcat(inverse, mat);
727    REPORTER_ASSERT(reporter, is_identity(iden2));
728    test_flatten(reporter, mat);
729    test_flatten(reporter, iden2);
730
731    mat.setScale(0, SK_Scalar1);
732    REPORTER_ASSERT(reporter, !mat.invert(NULL));
733    REPORTER_ASSERT(reporter, !mat.invert(&inverse));
734    mat.setScale(SK_Scalar1, 0);
735    REPORTER_ASSERT(reporter, !mat.invert(NULL));
736    REPORTER_ASSERT(reporter, !mat.invert(&inverse));
737
738    // rectStaysRect test
739    {
740        static const struct {
741            SkScalar    m00, m01, m10, m11;
742            bool        mStaysRect;
743        }
744        gRectStaysRectSamples[] = {
745            {          0,          0,          0,           0, false },
746            {          0,          0,          0,  SK_Scalar1, false },
747            {          0,          0, SK_Scalar1,           0, false },
748            {          0,          0, SK_Scalar1,  SK_Scalar1, false },
749            {          0, SK_Scalar1,          0,           0, false },
750            {          0, SK_Scalar1,          0,  SK_Scalar1, false },
751            {          0, SK_Scalar1, SK_Scalar1,           0, true },
752            {          0, SK_Scalar1, SK_Scalar1,  SK_Scalar1, false },
753            { SK_Scalar1,          0,          0,           0, false },
754            { SK_Scalar1,          0,          0,  SK_Scalar1, true },
755            { SK_Scalar1,          0, SK_Scalar1,           0, false },
756            { SK_Scalar1,          0, SK_Scalar1,  SK_Scalar1, false },
757            { SK_Scalar1, SK_Scalar1,          0,           0, false },
758            { SK_Scalar1, SK_Scalar1,          0,  SK_Scalar1, false },
759            { SK_Scalar1, SK_Scalar1, SK_Scalar1,           0, false },
760            { SK_Scalar1, SK_Scalar1, SK_Scalar1,  SK_Scalar1, false }
761        };
762
763        for (size_t i = 0; i < SK_ARRAY_COUNT(gRectStaysRectSamples); i++) {
764            SkMatrix    m;
765
766            m.reset();
767            m.set(SkMatrix::kMScaleX, gRectStaysRectSamples[i].m00);
768            m.set(SkMatrix::kMSkewX,  gRectStaysRectSamples[i].m01);
769            m.set(SkMatrix::kMSkewY,  gRectStaysRectSamples[i].m10);
770            m.set(SkMatrix::kMScaleY, gRectStaysRectSamples[i].m11);
771            REPORTER_ASSERT(reporter,
772                    m.rectStaysRect() == gRectStaysRectSamples[i].mStaysRect);
773        }
774    }
775
776    mat.reset();
777    mat.set(SkMatrix::kMScaleX, SkIntToScalar(1));
778    mat.set(SkMatrix::kMSkewX,  SkIntToScalar(2));
779    mat.set(SkMatrix::kMTransX, SkIntToScalar(3));
780    mat.set(SkMatrix::kMSkewY,  SkIntToScalar(4));
781    mat.set(SkMatrix::kMScaleY, SkIntToScalar(5));
782    mat.set(SkMatrix::kMTransY, SkIntToScalar(6));
783    SkScalar affine[6];
784    REPORTER_ASSERT(reporter, mat.asAffine(affine));
785
786    #define affineEqual(e) affine[SkMatrix::kA##e] == mat.get(SkMatrix::kM##e)
787    REPORTER_ASSERT(reporter, affineEqual(ScaleX));
788    REPORTER_ASSERT(reporter, affineEqual(SkewY));
789    REPORTER_ASSERT(reporter, affineEqual(SkewX));
790    REPORTER_ASSERT(reporter, affineEqual(ScaleY));
791    REPORTER_ASSERT(reporter, affineEqual(TransX));
792    REPORTER_ASSERT(reporter, affineEqual(TransY));
793    #undef affineEqual
794
795    mat.set(SkMatrix::kMPersp1, SkScalarToPersp(SK_Scalar1 / 2));
796    REPORTER_ASSERT(reporter, !mat.asAffine(affine));
797
798    SkMatrix mat2;
799    mat2.reset();
800    mat.reset();
801    SkScalar zero = 0;
802    mat.set(SkMatrix::kMSkewX, -zero);
803    REPORTER_ASSERT(reporter, are_equal(reporter, mat, mat2));
804
805    mat2.reset();
806    mat.reset();
807    mat.set(SkMatrix::kMSkewX, SK_ScalarNaN);
808    mat2.set(SkMatrix::kMSkewX, SK_ScalarNaN);
809    REPORTER_ASSERT(reporter, !are_equal(reporter, mat, mat2));
810
811    test_matrix_min_max_scale(reporter);
812    test_matrix_is_similarity(reporter);
813    test_matrix_recttorect(reporter);
814    test_matrix_decomposition(reporter);
815    test_matrix_homogeneous(reporter);
816}
817
818DEF_TEST(Matrix_Concat, r) {
819    SkMatrix a;
820    a.setTranslate(10, 20);
821
822    SkMatrix b;
823    b.setScale(3, 5);
824
825    SkMatrix expected;
826    expected.setConcat(a,b);
827
828    REPORTER_ASSERT(r, expected == SkMatrix::Concat(a, b));
829}
830