2 * Copyright 2011 Google Inc.
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
8 #include "SkMatrix44.h"
11 static bool nearly_equal_double(double a, double b) {
12 const double tolerance = 1e-7;
16 return diff <= tolerance;
19 static bool nearly_equal_mscalar(SkMScalar a, SkMScalar b) {
20 const SkMScalar tolerance = SK_MScalar1 / 200000;
22 return SkTAbs<SkMScalar>(a - b) <= tolerance;
25 static bool nearly_equal_scalar(SkScalar a, SkScalar b) {
26 const SkScalar tolerance = SK_Scalar1 / 200000;
27 return SkScalarAbs(a - b) <= tolerance;
30 template <typename T> void assert16(skiatest::Reporter* reporter, const T data[],
31 T m0, T m1, T m2, T m3,
32 T m4, T m5, T m6, T m7,
33 T m8, T m9, T m10, T m11,
34 T m12, T m13, T m14, T m15) {
35 REPORTER_ASSERT(reporter, data[0] == m0);
36 REPORTER_ASSERT(reporter, data[1] == m1);
37 REPORTER_ASSERT(reporter, data[2] == m2);
38 REPORTER_ASSERT(reporter, data[3] == m3);
40 REPORTER_ASSERT(reporter, data[4] == m4);
41 REPORTER_ASSERT(reporter, data[5] == m5);
42 REPORTER_ASSERT(reporter, data[6] == m6);
43 REPORTER_ASSERT(reporter, data[7] == m7);
45 REPORTER_ASSERT(reporter, data[8] == m8);
46 REPORTER_ASSERT(reporter, data[9] == m9);
47 REPORTER_ASSERT(reporter, data[10] == m10);
48 REPORTER_ASSERT(reporter, data[11] == m11);
50 REPORTER_ASSERT(reporter, data[12] == m12);
51 REPORTER_ASSERT(reporter, data[13] == m13);
52 REPORTER_ASSERT(reporter, data[14] == m14);
53 REPORTER_ASSERT(reporter, data[15] == m15);
56 static bool nearly_equal(const SkMatrix44& a, const SkMatrix44& b) {
57 for (int i = 0; i < 4; ++i) {
58 for (int j = 0; j < 4; ++j) {
59 if (!nearly_equal_mscalar(a.get(i, j), b.get(i, j))) {
60 SkDebugf("not equal %g %g\n", a.get(i, j), b.get(i, j));
68 static bool is_identity(const SkMatrix44& m) {
69 SkMatrix44 identity(SkMatrix44::kIdentity_Constructor);
70 return nearly_equal(m, identity);
73 ///////////////////////////////////////////////////////////////////////////////
74 static bool bits_isonly(int value, int mask) {
75 return 0 == (value & ~mask);
78 static void test_constructor(skiatest::Reporter* reporter) {
79 // Allocate a matrix on the heap
80 SkMatrix44* placeholderMatrix = new SkMatrix44(SkMatrix44::kUninitialized_Constructor);
81 SkAutoTDelete<SkMatrix44> deleteMe(placeholderMatrix);
83 for (int row = 0; row < 4; ++row) {
84 for (int col = 0; col < 4; ++col) {
85 placeholderMatrix->setDouble(row, col, row * col);
89 // Use placement-new syntax to trigger the constructor on top of the heap
90 // address we already initialized. This allows us to check that the
91 // constructor did avoid initializing the matrix contents.
92 SkMatrix44* testMatrix = new(placeholderMatrix) SkMatrix44(SkMatrix44::kUninitialized_Constructor);
93 REPORTER_ASSERT(reporter, testMatrix == placeholderMatrix);
94 REPORTER_ASSERT(reporter, !testMatrix->isIdentity());
95 for (int row = 0; row < 4; ++row) {
96 for (int col = 0; col < 4; ++col) {
97 REPORTER_ASSERT(reporter, nearly_equal_double(row * col, testMatrix->getDouble(row, col)));
101 // Verify that kIdentity_Constructor really does initialize to an identity matrix.
103 testMatrix = new(placeholderMatrix) SkMatrix44(SkMatrix44::kIdentity_Constructor);
104 REPORTER_ASSERT(reporter, testMatrix == placeholderMatrix);
105 REPORTER_ASSERT(reporter, testMatrix->isIdentity());
106 REPORTER_ASSERT(reporter, *testMatrix == SkMatrix44::I());
109 static void test_translate(skiatest::Reporter* reporter) {
110 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
111 SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor);
113 mat.setTranslate(0, 0, 0);
114 REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kIdentity_Mask));
115 mat.setTranslate(1, 2, 3);
116 REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kTranslate_Mask));
117 REPORTER_ASSERT(reporter, mat.invert(&inverse));
118 REPORTER_ASSERT(reporter, bits_isonly(inverse.getType(), SkMatrix44::kTranslate_Mask));
120 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
121 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
122 SkMatrix44 c(SkMatrix44::kUninitialized_Constructor);
123 a.set3x3(1, 2, 3, 4, 5, 6, 7, 8, 9);
124 b.setTranslate(10, 11, 12);
128 mat.preTranslate(10, 11, 12);
129 REPORTER_ASSERT(reporter, mat == c);
133 mat.postTranslate(10, 11, 12);
134 REPORTER_ASSERT(reporter, mat == c);
137 static void test_scale(skiatest::Reporter* reporter) {
138 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
139 SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor);
141 mat.setScale(1, 1, 1);
142 REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kIdentity_Mask));
143 mat.setScale(1, 2, 3);
144 REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kScale_Mask));
145 REPORTER_ASSERT(reporter, mat.invert(&inverse));
146 REPORTER_ASSERT(reporter, bits_isonly(inverse.getType(), SkMatrix44::kScale_Mask));
148 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
149 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
150 SkMatrix44 c(SkMatrix44::kUninitialized_Constructor);
151 a.set3x3(1, 2, 3, 4, 5, 6, 7, 8, 9);
152 b.setScale(10, 11, 12);
156 mat.preScale(10, 11, 12);
157 REPORTER_ASSERT(reporter, mat == c);
161 mat.postScale(10, 11, 12);
162 REPORTER_ASSERT(reporter, mat == c);
165 static void make_i(SkMatrix44* mat) { mat->setIdentity(); }
166 static void make_t(SkMatrix44* mat) { mat->setTranslate(1, 2, 3); }
167 static void make_s(SkMatrix44* mat) { mat->setScale(1, 2, 3); }
168 static void make_st(SkMatrix44* mat) {
169 mat->setScale(1, 2, 3);
170 mat->postTranslate(1, 2, 3);
172 static void make_a(SkMatrix44* mat) {
173 mat->setRotateDegreesAbout(1, 2, 3, 45);
175 static void make_p(SkMatrix44* mat) {
177 1, 2, 3, 4, 5, 6, 7, 8,
178 1, 2, 3, 4, 5, 6, 7, 8,
180 mat->setRowMajor(data);
183 typedef void (*Make44Proc)(SkMatrix44*);
185 static const Make44Proc gMakeProcs[] = {
186 make_i, make_t, make_s, make_st, make_a, make_p
189 static void test_map2(skiatest::Reporter* reporter, const SkMatrix44& mat) {
190 SkMScalar src2[] = { 1, 2 };
191 SkMScalar src4[] = { src2[0], src2[1], 0, 1 };
192 SkMScalar dstA[4], dstB[4];
194 for (int i = 0; i < 4; ++i) {
199 mat.map2(src2, 1, dstA);
200 mat.mapMScalars(src4, dstB);
202 for (int i = 0; i < 4; ++i) {
203 REPORTER_ASSERT(reporter, dstA[i] == dstB[i]);
207 static void test_map2(skiatest::Reporter* reporter) {
208 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
210 for (size_t i = 0; i < SK_ARRAY_COUNT(gMakeProcs); ++i) {
212 test_map2(reporter, mat);
216 static void test_gettype(skiatest::Reporter* reporter) {
217 SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
219 REPORTER_ASSERT(reporter, matrix.isIdentity());
220 REPORTER_ASSERT(reporter, SkMatrix44::kIdentity_Mask == matrix.getType());
225 expectedMask = SkMatrix44::kScale_Mask;
226 REPORTER_ASSERT(reporter, matrix.getType() == expectedMask);
228 matrix.set(0, 3, 1); // translate-x
229 expectedMask |= SkMatrix44::kTranslate_Mask;
230 REPORTER_ASSERT(reporter, matrix.getType() == expectedMask);
233 expectedMask |= SkMatrix44::kAffine_Mask;
234 REPORTER_ASSERT(reporter, matrix.getType() == expectedMask);
237 REPORTER_ASSERT(reporter, matrix.getType() & SkMatrix44::kPerspective_Mask);
239 // ensure that negative zero is treated as zero
243 matrix.setTranslate(-dx, -dy, -dz);
244 REPORTER_ASSERT(reporter, matrix.isIdentity());
245 matrix.preTranslate(-dx, -dy, -dz);
246 REPORTER_ASSERT(reporter, matrix.isIdentity());
247 matrix.postTranslate(-dx, -dy, -dz);
248 REPORTER_ASSERT(reporter, matrix.isIdentity());
251 static void test_common_angles(skiatest::Reporter* reporter) {
252 SkMatrix44 rot(SkMatrix44::kUninitialized_Constructor);
253 // Test precision of rotation in common cases
254 int common_angles[] = { 0, 90, -90, 180, -180, 270, -270, 360, -360 };
255 for (int i = 0; i < 9; ++i) {
256 rot.setRotateDegreesAbout(0, 0, -1, SkIntToScalar(common_angles[i]));
258 SkMatrix rot3x3 = rot;
259 REPORTER_ASSERT(reporter, rot3x3.rectStaysRect());
263 static void test_concat(skiatest::Reporter* reporter) {
265 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
266 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
267 SkMatrix44 c(SkMatrix44::kUninitialized_Constructor);
268 SkMatrix44 d(SkMatrix44::kUninitialized_Constructor);
270 a.setTranslate(10, 10, 10);
283 REPORTER_ASSERT(reporter, d == c);
285 c.mapScalars(src, dst); c.mapScalars(src + 4, dst + 4);
286 for (i = 0; i < 3; ++i) {
287 REPORTER_ASSERT(reporter, 10 == dst[i]);
288 REPORTER_ASSERT(reporter, 12 == dst[i + 4]);
295 REPORTER_ASSERT(reporter, d == c);
297 c.mapScalars(src, dst); c.mapScalars(src + 4, dst + 4);
298 for (i = 0; i < 3; ++i) {
299 REPORTER_ASSERT(reporter, 20 == dst[i]);
300 REPORTER_ASSERT(reporter, 22 == dst[i + 4]);
304 static void test_determinant(skiatest::Reporter* reporter) {
305 SkMatrix44 a(SkMatrix44::kIdentity_Constructor);
306 REPORTER_ASSERT(reporter, nearly_equal_double(1, a.determinant()));
308 REPORTER_ASSERT(reporter, nearly_equal_double(2, a.determinant()));
309 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
310 REPORTER_ASSERT(reporter, a.invert(&b));
311 REPORTER_ASSERT(reporter, nearly_equal_double(0.5, b.determinant()));
312 SkMatrix44 c = b = a;
315 REPORTER_ASSERT(reporter,
316 nearly_equal_double(a.determinant(),
320 REPORTER_ASSERT(reporter, nearly_equal_double(16, d.determinant()));
324 REPORTER_ASSERT(reporter, nearly_equal_double(32, e.determinant()));
326 REPORTER_ASSERT(reporter, nearly_equal_double(0, e.determinant()));
329 static void test_invert(skiatest::Reporter* reporter) {
330 SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor);
331 double inverseData[16];
333 SkMatrix44 identity(SkMatrix44::kIdentity_Constructor);
334 identity.invert(&inverse);
335 inverse.asRowMajord(inverseData);
336 assert16<double>(reporter, inverseData,
342 SkMatrix44 translation(SkMatrix44::kUninitialized_Constructor);
343 translation.setTranslate(2, 3, 4);
344 translation.invert(&inverse);
345 inverse.asRowMajord(inverseData);
346 assert16<double>(reporter, inverseData,
352 SkMatrix44 scale(SkMatrix44::kUninitialized_Constructor);
353 scale.setScale(2, 4, 8);
354 scale.invert(&inverse);
355 inverse.asRowMajord(inverseData);
356 assert16<double>(reporter, inverseData,
362 SkMatrix44 scaleTranslation(SkMatrix44::kUninitialized_Constructor);
363 scaleTranslation.setScale(10, 100, 1000);
364 scaleTranslation.preTranslate(2, 3, 4);
365 scaleTranslation.invert(&inverse);
366 inverse.asRowMajord(inverseData);
367 assert16<double>(reporter, inverseData,
373 SkMatrix44 rotation(SkMatrix44::kUninitialized_Constructor);
374 rotation.setRotateDegreesAbout(0, 0, 1, 90);
375 rotation.invert(&inverse);
376 SkMatrix44 expected(SkMatrix44::kUninitialized_Constructor);
377 double expectedInverseRotation[16] =
382 expected.setRowMajord(expectedInverseRotation);
383 REPORTER_ASSERT(reporter, nearly_equal(expected, inverse));
385 SkMatrix44 affine(SkMatrix44::kUninitialized_Constructor);
386 affine.setRotateDegreesAbout(0, 0, 1, 90);
387 affine.preScale(10, 20, 100);
388 affine.preTranslate(2, 3, 4);
389 affine.invert(&inverse);
390 double expectedInverseAffine[16] =
395 expected.setRowMajord(expectedInverseAffine);
396 REPORTER_ASSERT(reporter, nearly_equal(expected, inverse));
398 SkMatrix44 perspective(SkMatrix44::kIdentity_Constructor);
399 perspective.setDouble(3, 2, 1.0);
400 perspective.invert(&inverse);
401 double expectedInversePerspective[16] =
406 expected.setRowMajord(expectedInversePerspective);
407 REPORTER_ASSERT(reporter, nearly_equal(expected, inverse));
409 SkMatrix44 affineAndPerspective(SkMatrix44::kIdentity_Constructor);
410 affineAndPerspective.setDouble(3, 2, 1.0);
411 affineAndPerspective.preScale(10, 20, 100);
412 affineAndPerspective.preTranslate(2, 3, 4);
413 affineAndPerspective.invert(&inverse);
414 double expectedInverseAffineAndPerspective[16] =
419 expected.setRowMajord(expectedInverseAffineAndPerspective);
420 REPORTER_ASSERT(reporter, nearly_equal(expected, inverse));
423 static void test_transpose(skiatest::Reporter* reporter) {
424 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
425 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
428 for (int row = 0; row < 4; ++row) {
429 for (int col = 0; col < 4; ++col) {
430 a.setDouble(row, col, i);
431 b.setDouble(col, row, i++);
436 REPORTER_ASSERT(reporter, nearly_equal(a, b));
439 static void test_get_set_double(skiatest::Reporter* reporter) {
440 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
441 for (int row = 0; row < 4; ++row) {
442 for (int col = 0; col < 4; ++col) {
443 a.setDouble(row, col, 3.141592653589793);
444 REPORTER_ASSERT(reporter,
445 nearly_equal_double(3.141592653589793,
446 a.getDouble(row, col)));
447 a.setDouble(row, col, 0);
448 REPORTER_ASSERT(reporter,
449 nearly_equal_double(0, a.getDouble(row, col)));
454 static void test_set_row_col_major(skiatest::Reporter* reporter) {
455 SkMatrix44 a(SkMatrix44::kUninitialized_Constructor);
456 SkMatrix44 b(SkMatrix44::kUninitialized_Constructor);
458 for (int row = 0; row < 4; ++row) {
459 for (int col = 0; col < 4; ++col) {
460 a.setDouble(row, col, row * 4 + col);
466 a.asColMajord(bufferd);
467 b.setColMajord(bufferd);
468 REPORTER_ASSERT(reporter, nearly_equal(a, b));
469 b.setRowMajord(bufferd);
471 REPORTER_ASSERT(reporter, nearly_equal(a, b));
472 a.asColMajorf(bufferf);
473 b.setColMajorf(bufferf);
474 REPORTER_ASSERT(reporter, nearly_equal(a, b));
475 b.setRowMajorf(bufferf);
477 REPORTER_ASSERT(reporter, nearly_equal(a, b));
480 static void test_3x3_conversion(skiatest::Reporter* reporter) {
481 SkMScalar values4x4[16] = { 1, 2, 3, 4,
485 SkScalar values3x3[9] = { 1, 2, 4,
488 SkMScalar values4x4flattened[16] = { 1, 2, 0, 4,
492 SkMatrix44 a44(SkMatrix44::kUninitialized_Constructor);
493 a44.setRowMajor(values4x4);
497 for (int i = 0; i < 9; i++) expected33[i] = values3x3[i];
498 REPORTER_ASSERT(reporter, expected33 == a33);
500 SkMatrix44 a44flattened = a33;
501 SkMatrix44 expected44flattened(SkMatrix44::kUninitialized_Constructor);
502 expected44flattened.setRowMajor(values4x4flattened);
503 REPORTER_ASSERT(reporter, nearly_equal(a44flattened, expected44flattened));
505 // Test that a point with a Z value of 0 is transformed the same way.
506 SkScalar vec4[4] = { 2, 4, 0, 8 };
507 SkScalar vec3[3] = { 2, 4, 8 };
509 SkScalar vec4transformed[4];
510 SkScalar vec3transformed[3];
511 SkScalar vec4transformed2[4];
512 a44.mapScalars(vec4, vec4transformed);
513 a33.mapHomogeneousPoints(vec3transformed, vec3, 1);
514 a44flattened.mapScalars(vec4, vec4transformed2);
515 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[0], vec3transformed[0]));
516 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[1], vec3transformed[1]));
517 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[3], vec3transformed[2]));
518 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[0], vec4transformed2[0]));
519 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[1], vec4transformed2[1]));
520 REPORTER_ASSERT(reporter, !nearly_equal_scalar(vec4transformed[2], vec4transformed2[2]));
521 REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[3], vec4transformed2[3]));
524 static void test_has_perspective(skiatest::Reporter* reporter) {
525 SkMatrix44 transform(SkMatrix44::kIdentity_Constructor);
527 transform.set(3, 2, -0.1);
528 REPORTER_ASSERT(reporter, transform.hasPerspective());
531 REPORTER_ASSERT(reporter, !transform.hasPerspective());
533 transform.set(3, 0, -1.0);
534 REPORTER_ASSERT(reporter, transform.hasPerspective());
537 transform.set(3, 1, -1.0);
538 REPORTER_ASSERT(reporter, transform.hasPerspective());
541 transform.set(3, 2, -0.3);
542 REPORTER_ASSERT(reporter, transform.hasPerspective());
545 transform.set(3, 3, 0.5);
546 REPORTER_ASSERT(reporter, transform.hasPerspective());
549 transform.set(3, 3, 0.0);
550 REPORTER_ASSERT(reporter, transform.hasPerspective());
553 DEF_TEST(Matrix44, reporter) {
554 SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor);
555 SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor);
556 SkMatrix44 iden1(SkMatrix44::kUninitialized_Constructor);
557 SkMatrix44 iden2(SkMatrix44::kUninitialized_Constructor);
558 SkMatrix44 rot(SkMatrix44::kUninitialized_Constructor);
560 mat.setTranslate(1, 1, 1);
561 mat.invert(&inverse);
562 iden1.setConcat(mat, inverse);
563 REPORTER_ASSERT(reporter, is_identity(iden1));
565 mat.setScale(2, 2, 2);
566 mat.invert(&inverse);
567 iden1.setConcat(mat, inverse);
568 REPORTER_ASSERT(reporter, is_identity(iden1));
570 mat.setScale(SK_MScalar1/2, SK_MScalar1/2, SK_MScalar1/2);
571 mat.invert(&inverse);
572 iden1.setConcat(mat, inverse);
573 REPORTER_ASSERT(reporter, is_identity(iden1));
575 mat.setScale(3, 3, 3);
576 rot.setRotateDegreesAbout(0, 0, -1, 90);
578 REPORTER_ASSERT(reporter, mat.invert(NULL));
579 mat.invert(&inverse);
580 iden1.setConcat(mat, inverse);
581 REPORTER_ASSERT(reporter, is_identity(iden1));
582 iden2.setConcat(inverse, mat);
583 REPORTER_ASSERT(reporter, is_identity(iden2));
585 // test tiny-valued matrix inverse
587 mat.setScale(1.0e-12, 1.0e-12, 1.0e-12);
588 rot.setRotateDegreesAbout(0, 0, -1, 90);
590 mat.postTranslate(1.0e-12, 1.0e-12, 1.0e-12);
591 REPORTER_ASSERT(reporter, mat.invert(NULL));
592 mat.invert(&inverse);
593 iden1.setConcat(mat, inverse);
594 REPORTER_ASSERT(reporter, is_identity(iden1));
596 // test mixed-valued matrix inverse
598 mat.setScale(1.0e-10, 3.0, 1.0e+10);
599 rot.setRotateDegreesAbout(0, 0, -1, 90);
601 mat.postTranslate(1.0e+10, 3.0, 1.0e-10);
602 REPORTER_ASSERT(reporter, mat.invert(NULL));
603 mat.invert(&inverse);
604 iden1.setConcat(mat, inverse);
605 REPORTER_ASSERT(reporter, is_identity(iden1));
607 // test degenerate matrix
609 mat.set3x3(1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0);
610 REPORTER_ASSERT(reporter, !mat.invert(NULL));
612 // test rol/col Major getters
614 mat.setTranslate(2, 3, 4);
618 mat.asColMajorf(dataf);
619 assert16<float>(reporter, dataf,
624 mat.asColMajord(datad);
625 assert16<double>(reporter, datad, 1, 0, 0, 0,
629 mat.asRowMajorf(dataf);
630 assert16<float>(reporter, dataf, 1, 0, 0, 2,
634 mat.asRowMajord(datad);
635 assert16<double>(reporter, datad, 1, 0, 0, 2,
641 test_concat(reporter);
643 if (false) { // avoid bit rot, suppress warning (working on making this pass)
644 test_common_angles(reporter);
647 test_constructor(reporter);
648 test_gettype(reporter);
649 test_determinant(reporter);
650 test_invert(reporter);
651 test_transpose(reporter);
652 test_get_set_double(reporter);
653 test_set_row_col_major(reporter);
654 test_translate(reporter);
655 test_scale(reporter);
657 test_3x3_conversion(reporter);
658 test_has_perspective(reporter);