1 /*
2 * Copyright 2020 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 "include/core/SkM44.h"
9 #include "include/utils/SkRandom.h"
10 #include "src/core/SkMatrixPriv.h"
11 #include "tests/Test.h"
12
eq(const SkM44 & a,const SkM44 & b,float tol)13 static bool eq(const SkM44& a, const SkM44& b, float tol) {
14 float fa[16], fb[16];
15 a.getColMajor(fa);
16 b.getColMajor(fb);
17 for (int i = 0; i < 16; ++i) {
18 if (!SkScalarNearlyEqual(fa[i], fb[i], tol)) {
19 return false;
20 }
21 }
22 return true;
23 }
24
DEF_TEST(M44,reporter)25 DEF_TEST(M44, reporter) {
26 SkM44 m, im;
27
28 REPORTER_ASSERT(reporter, SkM44(1, 0, 0, 0,
29 0, 1, 0, 0,
30 0, 0, 1, 0,
31 0, 0, 0, 1) == m);
32 REPORTER_ASSERT(reporter, SkM44() == m);
33 REPORTER_ASSERT(reporter, m.invert(&im));
34 REPORTER_ASSERT(reporter, SkM44() == im);
35
36 m.setTranslate(3, 4, 2);
37 REPORTER_ASSERT(reporter, SkM44(1, 0, 0, 3,
38 0, 1, 0, 4,
39 0, 0, 1, 2,
40 0, 0, 0, 1) == m);
41
42 const float f[] = { 1, 0, 0, 2, 3, 1, 2, 5, 0, 5, 3, 0, 0, 1, 0, 2 };
43 m = SkM44::ColMajor(f);
44 REPORTER_ASSERT(reporter, SkM44(f[0], f[4], f[ 8], f[12],
45 f[1], f[5], f[ 9], f[13],
46 f[2], f[6], f[10], f[14],
47 f[3], f[7], f[11], f[15]) == m);
48
49 {
50 SkM44 t = m.transpose();
51 REPORTER_ASSERT(reporter, t != m);
52 REPORTER_ASSERT(reporter, t.rc(1,0) == m.rc(0,1));
53 SkM44 tt = t.transpose();
54 REPORTER_ASSERT(reporter, tt == m);
55 }
56
57 m = SkM44::RowMajor(f);
58 REPORTER_ASSERT(reporter, SkM44(f[ 0], f[ 1], f[ 2], f[ 3],
59 f[ 4], f[ 5], f[ 6], f[ 7],
60 f[ 8], f[ 9], f[10], f[14],
61 f[12], f[13], f[14], f[15]) == m);
62
63 REPORTER_ASSERT(reporter, m.invert(&im));
64
65 m = m * im;
66 // m should be identity now, but our calc is not perfect...
67 REPORTER_ASSERT(reporter, eq(SkM44(), m, 0.0000005f));
68 REPORTER_ASSERT(reporter, SkM44() != m);
69 }
70
DEF_TEST(M44_v3,reporter)71 DEF_TEST(M44_v3, reporter) {
72 SkV3 a = {1, 2, 3},
73 b = {1, 2, 2};
74
75 REPORTER_ASSERT(reporter, a.lengthSquared() == 1 + 4 + 9);
76 REPORTER_ASSERT(reporter, b.length() == 3);
77 REPORTER_ASSERT(reporter, a.dot(b) == 1 + 4 + 6);
78 REPORTER_ASSERT(reporter, b.dot(a) == 1 + 4 + 6);
79 REPORTER_ASSERT(reporter, (a.cross(b) == SkV3{-2, 1, 0}));
80 REPORTER_ASSERT(reporter, (b.cross(a) == SkV3{ 2, -1, 0}));
81
82 SkM44 m = {
83 2, 0, 0, 3,
84 0, 1, 0, 5,
85 0, 0, 3, 1,
86 0, 0, 0, 1
87 };
88
89 SkV3 c = m * a;
90 REPORTER_ASSERT(reporter, (c == SkV3{2, 2, 9}));
91 SkV4 d = m.map(4, 3, 2, 1);
92 REPORTER_ASSERT(reporter, (d == SkV4{11, 8, 7, 1}));
93 }
94
DEF_TEST(M44_v4,reporter)95 DEF_TEST(M44_v4, reporter) {
96 SkM44 m( 1, 2, 3, 4,
97 5, 6, 7, 8,
98 9, 10, 11, 12,
99 13, 14, 15, 16);
100
101 SkV4 r0 = m.row(0),
102 r1 = m.row(1),
103 r2 = m.row(2),
104 r3 = m.row(3);
105
106 REPORTER_ASSERT(reporter, (r0 == SkV4{ 1, 2, 3, 4}));
107 REPORTER_ASSERT(reporter, (r1 == SkV4{ 5, 6, 7, 8}));
108 REPORTER_ASSERT(reporter, (r2 == SkV4{ 9, 10, 11, 12}));
109 REPORTER_ASSERT(reporter, (r3 == SkV4{13, 14, 15, 16}));
110
111 REPORTER_ASSERT(reporter, SkM44::Rows(r0, r1, r2, r3) == m);
112
113 SkV4 c0 = m.col(0),
114 c1 = m.col(1),
115 c2 = m.col(2),
116 c3 = m.col(3);
117
118 REPORTER_ASSERT(reporter, (c0 == SkV4{1, 5, 9, 13}));
119 REPORTER_ASSERT(reporter, (c1 == SkV4{2, 6, 10, 14}));
120 REPORTER_ASSERT(reporter, (c2 == SkV4{3, 7, 11, 15}));
121 REPORTER_ASSERT(reporter, (c3 == SkV4{4, 8, 12, 16}));
122
123 REPORTER_ASSERT(reporter, SkM44::Cols(c0, c1, c2, c3) == m);
124
125 // implement matrix * vector using column vectors
126 SkV4 v = {1, 2, 3, 4};
127 SkV4 v1 = m * v;
128 SkV4 v2 = c0 * v.x + c1 * v.y + c2 * v.z + c3 * v.w;
129 REPORTER_ASSERT(reporter, v1 == v2);
130
131 REPORTER_ASSERT(reporter, (c0 + r0 == SkV4{c0.x+r0.x, c0.y+r0.y, c0.z+r0.z, c0.w+r0.w}));
132 REPORTER_ASSERT(reporter, (c0 - r0 == SkV4{c0.x-r0.x, c0.y-r0.y, c0.z-r0.z, c0.w-r0.w}));
133 REPORTER_ASSERT(reporter, (c0 * r0 == SkV4{c0.x*r0.x, c0.y*r0.y, c0.z*r0.z, c0.w*r0.w}));
134 }
135
DEF_TEST(M44_rotate,reporter)136 DEF_TEST(M44_rotate, reporter) {
137 const SkV3 x = {1, 0, 0},
138 y = {0, 1, 0},
139 z = {0, 0, 1};
140
141 // We have radians version of setRotateAbout methods, but even with our best approx
142 // for PI, sin(SK_ScalarPI) != 0, so to make the comparisons in the unittest clear,
143 // I'm using the variants that explicitly take the sin,cos values.
144
145 struct {
146 SkScalar sinAngle, cosAngle;
147 SkV3 aboutAxis;
148 SkV3 expectedX, expectedY, expectedZ;
149 } recs[] = {
150 { 0, 1, x, x, y, z}, // angle = 0
151 { 0, 1, y, x, y, z}, // angle = 0
152 { 0, 1, z, x, y, z}, // angle = 0
153
154 { 0,-1, x, x,-y,-z}, // angle = 180
155 { 0,-1, y, -x, y,-z}, // angle = 180
156 { 0,-1, z, -x,-y, z}, // angle = 180
157
158 // Skia coordinate system is right-handed
159
160 { 1, 0, x, x, z,-y}, // angle = 90
161 { 1, 0, y, -z, y, x}, // angle = 90
162 { 1, 0, z, y,-x, z}, // angle = 90
163
164 {-1, 0, x, x,-z, y}, // angle = -90
165 {-1, 0, y, z, y,-x}, // angle = -90
166 {-1, 0, z, -y, x, z}, // angle = -90
167 };
168
169 for (const auto& r : recs) {
170 SkM44 m(SkM44::kNaN_Constructor);
171 m.setRotateUnitSinCos(r.aboutAxis, r.sinAngle, r.cosAngle);
172
173 auto mx = m * x;
174 auto my = m * y;
175 auto mz = m * z;
176 REPORTER_ASSERT(reporter, mx == r.expectedX);
177 REPORTER_ASSERT(reporter, my == r.expectedY);
178 REPORTER_ASSERT(reporter, mz == r.expectedZ);
179
180 // flipping the axis-of-rotation should flip the results
181 mx = m * -x;
182 my = m * -y;
183 mz = m * -z;
184 REPORTER_ASSERT(reporter, mx == -r.expectedX);
185 REPORTER_ASSERT(reporter, my == -r.expectedY);
186 REPORTER_ASSERT(reporter, mz == -r.expectedZ);
187 }
188 }
189
DEF_TEST(M44_rectToRect,reporter)190 DEF_TEST(M44_rectToRect, reporter) {
191 SkV2 dstScales[] = {
192 {1.f, 1.f}, // no aspect ratio change, nor up/down scaling
193 {0.25f, 0.5f}, // aspect ratio narrows, downscale x and y
194 {0.5f, 0.25f}, // aspect ratio widens, downscale x and y
195 {0.5f, 0.5f}, // no aspect ratio change, downscale x and y
196 {2.f, 3.f}, // aspect ratio narrows, upscale x and y
197 {3.f, 2.f}, // aspect ratio widens, upscale x and y
198 {2.f, 2.f}, // no aspect ratio change, upscale x and y
199 {0.5f, 2.f}, // aspect ratio narrows, downscale x and upscale y
200 {2.f, 0.5f} // aspect ratio widens, upscale x and downscale y
201 };
202
203 auto map2d = [&](const SkM44& m, SkV2 p) {
204 SkV4 mapped = m.map(p.x, p.y, 0.f, 1.f);
205 REPORTER_ASSERT(reporter, mapped.z == 0.f);
206 REPORTER_ASSERT(reporter, mapped.w == 1.f);
207 return SkV2{mapped.x, mapped.y};
208 };
209 auto assertNearlyEqual = [&](float actual, float expected) {
210 REPORTER_ASSERT(reporter, SkScalarNearlyEqual(actual, expected),
211 "Expected %g == %g", actual, expected);
212 };
213 auto assertEdges = [&](float actualLow, float actualHigh,
214 float expectedLow, float expectedHigh) {
215 SkASSERT(expectedLow < expectedHigh);
216 REPORTER_ASSERT(reporter, actualLow < actualHigh,
217 "Expected %g < %g", actualLow, actualHigh);
218
219 assertNearlyEqual(actualLow, expectedLow);
220 assertNearlyEqual(actualHigh, expectedHigh);
221 };
222
223 SkRandom rand;
224 for (const auto& r : dstScales) {
225 SkRect src = SkRect::MakeXYWH(rand.nextRangeF(-10.f, 10.f),
226 rand.nextRangeF(-10.f, 10.f),
227 rand.nextRangeF(1.f, 10.f),
228 rand.nextRangeF(1.f, 10.f));
229 SkRect dst = SkRect::MakeXYWH(rand.nextRangeF(-10.f, 10.f),
230 rand.nextRangeF(-10.f, 10.f),
231 r.x * src.width(),
232 r.y * src.height());
233
234 SkM44 m = SkM44::RectToRect(src, dst);
235
236 // Regardless of the factory, center of src maps to center of dst
237 SkV2 center = map2d(m, {src.centerX(), src.centerY()});
238 assertNearlyEqual(center.x, dst.centerX());
239 assertNearlyEqual(center.y, dst.centerY());
240
241 // Map the four corners of src and validate against expected edge mapping
242 SkV2 tl = map2d(m, {src.fLeft, src.fTop});
243 SkV2 tr = map2d(m, {src.fRight, src.fTop});
244 SkV2 br = map2d(m, {src.fRight, src.fBottom});
245 SkV2 bl = map2d(m, {src.fLeft, src.fBottom});
246
247 assertEdges(tl.x, tr.x, dst.fLeft, dst.fRight);
248 assertEdges(bl.x, br.x, dst.fLeft, dst.fRight);
249 assertEdges(tl.y, bl.y, dst.fTop, dst.fBottom);
250 assertEdges(tr.y, br.y, dst.fTop, dst.fBottom);
251 }
252 }
253
DEF_TEST(M44_mapRect,reporter)254 DEF_TEST(M44_mapRect, reporter) {
255 auto assertRectsNearlyEqual = [&](const SkRect& actual, const SkRect& expected,
256 const SkRect& e) {
257 REPORTER_ASSERT(reporter, SkScalarNearlyEqual(actual.fLeft, expected.fLeft, e.fLeft),
258 "Expected %g == %g", actual.fLeft, expected.fLeft);
259 REPORTER_ASSERT(reporter, SkScalarNearlyEqual(actual.fTop, expected.fTop, e.fTop),
260 "Expected %g == %g", actual.fTop, expected.fTop);
261 REPORTER_ASSERT(reporter, SkScalarNearlyEqual(actual.fRight, expected.fRight, e.fRight),
262 "Expected %g == %g", actual.fRight, expected.fRight);
263 REPORTER_ASSERT(reporter, SkScalarNearlyEqual(actual.fBottom, expected.fBottom, e.fBottom),
264 "Expected %g == %g", actual.fBottom, expected.fBottom);
265 };
266 auto assertMapRect = [&](const SkM44& m, const SkRect& src, const SkRect* expected) {
267 SkRect epsilon = {1e-5f, 1e-5f, 1e-5f, 1e-5f};
268
269 SkRect actual = SkMatrixPriv::MapRect(m, src);
270 REPORTER_ASSERT(reporter, !actual.isEmpty());
271
272 if (expected) {
273 assertRectsNearlyEqual(actual, *expected, epsilon);
274 }
275
276 SkV4 corners[4] = {{src.fLeft, src.fTop, 0.f, 1.f},
277 {src.fRight, src.fTop, 0.f, 1.f},
278 {src.fRight, src.fBottom, 0.f, 1.f},
279 {src.fLeft, src.fBottom, 0.f, 1.f}};
280 bool leftFound = false;
281 bool topFound = false;
282 bool rightFound = false;
283 bool bottomFound = false;
284 bool clipped = false;
285 for (int i = 0; i < 4; ++i) {
286 SkV4 mapped = m * corners[i];
287 if (mapped.w > 0.f) {
288 // Should be contained in actual and might be on one or two of actual's edges
289 float x = mapped.x / mapped.w;
290 float y = mapped.y / mapped.w;
291
292 // Can't use SkRect::contains() since it treats right and bottom edges as exclusive
293 REPORTER_ASSERT(reporter, actual.fLeft <= x && x <= actual.fRight,
294 "Expected %g contained in [%g, %g]",
295 x, actual.fLeft, actual.fRight);
296 REPORTER_ASSERT(reporter, actual.fTop <= y && y <= actual.fBottom,
297 "Expected %g contained in [%g, %g]",
298 y, actual.fTop, actual.fBottom);
299
300 leftFound |= SkScalarNearlyEqual(x, actual.fLeft);
301 topFound |= SkScalarNearlyEqual(y, actual.fTop);
302 rightFound |= SkScalarNearlyEqual(x, actual.fRight);
303 bottomFound |= SkScalarNearlyEqual(y, actual.fBottom);
304 } else {
305 // The mapped point would be clipped so the clipped mapped bounds don't necessarily
306 // contain it
307 clipped = true;
308 }
309 }
310
311 if (clipped) {
312 // At least one of the mapped corners should have contributed to the rect
313 REPORTER_ASSERT(reporter, leftFound || topFound || rightFound || bottomFound);
314 // For any edge that came from a clipped corner, increase its error tolerance relative
315 // to what SkPath::ApplyPerspectiveClip calculates.
316 // TODO(michaelludwig): skbug.com/12335 required updating the w epsilon distance which
317 // greatly increased noise for coords projecting to infinity. They aren't "wrong", since
318 // the intent was clearly to pick a big number that's definitely offscreen, but
319 // MapRect should have a more robust solution than a fixed w > epsilon and when it does,
320 // these expectations for clipped points should be more accurate.
321 if (!leftFound) { epsilon.fLeft = .01f * actual.fLeft; }
322 if (!topFound) { epsilon.fTop = .01f * actual.fTop; }
323 if (!rightFound) { epsilon.fRight = .01f * actual.fRight; }
324 if (!bottomFound) { epsilon.fBottom = .01f * actual.fBottom; }
325 } else {
326 // The mapped corners should have contributed to all four edges of the returned rect
327 REPORTER_ASSERT(reporter, leftFound && topFound && rightFound && bottomFound);
328 }
329
330 SkPath path = SkPath::Rect(src);
331 path.transform(m.asM33(), SkApplyPerspectiveClip::kYes);
332 assertRectsNearlyEqual(actual, path.getBounds(), epsilon);
333 };
334
335 // src chosen arbitrarily
336 const SkRect src = SkRect::MakeLTRB(4.83f, -0.48f, 5.53f, 30.68f);
337
338 // Identity maps src to src
339 assertMapRect(SkM44(), src, &src);
340 // Scale+Translate just offsets src
341 SkRect st = SkRect::MakeLTRB(10.f + 2.f * src.fLeft, 8.f + 4.f * src.fTop,
342 10.f + 2.f * src.fRight, 8.f + 4.f * src.fBottom);
343 assertMapRect(SkM44::Scale(2.f, 4.f).postTranslate(10.f, 8.f), src, &st);
344 // Rotate 45 degrees about center
345 assertMapRect(SkM44::Rotate({0.f, 0.f, 1.f}, SK_ScalarPI / 4.f)
346 .preTranslate(-src.centerX(), -src.centerY())
347 .postTranslate(src.centerX(), src.centerY()),
348 src, nullptr);
349
350 // Perspective matrix where src does not need to be clipped w > 0
351 SkM44 p = SkM44::Perspective(0.01f, 10.f, SK_ScalarPI / 3.f);
352 p.preTranslate(0.f, 5.f, -0.1f);
353 p.preConcat(SkM44::Rotate({0.f, 1.f, 0.f}, 0.008f /* radians */));
354 assertMapRect(p, src, nullptr);
355
356 // Perspective matrix where src *does* need to be clipped w > 0
357 p.setIdentity();
358 p.setRow(3, {-.2f, -.6f, 0.f, 8.f});
359 assertMapRect(p, src, nullptr);
360 }
361
DEF_TEST(M44_mapRect_skbug12335,r)362 DEF_TEST(M44_mapRect_skbug12335, r) {
363 // Stripped down test case from skbug.com/12335. Essentially, the corners of this rect would
364 // map to homogoneous coords with very small w's (below the old value of kW0PlaneDistance) and
365 // so they would be clipped "behind" the plane, resulting in an empty mapped rect. Coordinates
366 // with positive that wouldn't overflow when divided by w should still be included in the mapped
367 // rectangle.
368 SkRect rect = SkRect::MakeLTRB(0, 0, 319, 620);
369 SkM44 m(SkMatrix::MakeAll( 0.000152695269f, 0.00000000f, -6.53848401e-05f,
370 -1.75697533e-05f, 0.000157153074f, -1.10847975e-06f,
371 -6.00415362e-08f, 0.00000000f, 0.000169880834f));
372 SkRect out = SkMatrixPriv::MapRect(m, rect);
373 REPORTER_ASSERT(r, !out.isEmpty());
374 }
375