1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
|
// Copyright 2012 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
#include "config.h"
#include "cc/math_util.h"
#include <cmath>
#include "cc/test/geometry_test_utils.h"
#include "testing/gmock/include/gmock/gmock.h"
#include "testing/gtest/include/gtest/gtest.h"
#include "ui/gfx/rect.h"
#include "ui/gfx/rect_f.h"
#include <public/WebTransformationMatrix.h>
using namespace cc;
using WebKit::WebTransformationMatrix;
namespace {
TEST(MathUtilTest, verifyBackfaceVisibilityBasicCases)
{
WebTransformationMatrix transform;
transform.makeIdentity();
EXPECT_FALSE(transform.isBackFaceVisible());
transform.makeIdentity();
transform.rotate3d(0, 80, 0);
EXPECT_FALSE(transform.isBackFaceVisible());
transform.makeIdentity();
transform.rotate3d(0, 100, 0);
EXPECT_TRUE(transform.isBackFaceVisible());
// Edge case, 90 degree rotation should return false.
transform.makeIdentity();
transform.rotate3d(0, 90, 0);
EXPECT_FALSE(transform.isBackFaceVisible());
}
TEST(MathUtilTest, verifyBackfaceVisibilityForPerspective)
{
WebTransformationMatrix layerSpaceToProjectionPlane;
// This tests if isBackFaceVisible works properly under perspective transforms.
// Specifically, layers that may have their back face visible in orthographic
// projection, may not actually have back face visible under perspective projection.
// Case 1: Layer is rotated by slightly more than 90 degrees, at the center of the
// prespective projection. In this case, the layer's back-side is visible to
// the camera.
layerSpaceToProjectionPlane.makeIdentity();
layerSpaceToProjectionPlane.applyPerspective(1);
layerSpaceToProjectionPlane.translate3d(0, 0, 0);
layerSpaceToProjectionPlane.rotate3d(0, 100, 0);
EXPECT_TRUE(layerSpaceToProjectionPlane.isBackFaceVisible());
// Case 2: Layer is rotated by slightly more than 90 degrees, but shifted off to the
// side of the camera. Because of the wide field-of-view, the layer's front
// side is still visible.
//
// |<-- front side of layer is visible to perspective camera
// \ | /
// \ | /
// \| /
// | /
// |\ /<-- camera field of view
// | \ /
// back side of layer -->| \ /
// \./ <-- camera origin
//
layerSpaceToProjectionPlane.makeIdentity();
layerSpaceToProjectionPlane.applyPerspective(1);
layerSpaceToProjectionPlane.translate3d(-10, 0, 0);
layerSpaceToProjectionPlane.rotate3d(0, 100, 0);
EXPECT_FALSE(layerSpaceToProjectionPlane.isBackFaceVisible());
// Case 3: Additionally rotating the layer by 180 degrees should of course show the
// opposite result of case 2.
layerSpaceToProjectionPlane.rotate3d(0, 180, 0);
EXPECT_TRUE(layerSpaceToProjectionPlane.isBackFaceVisible());
}
TEST(MathUtilTest, verifyProjectionOfPerpendicularPlane)
{
// In this case, the m33() element of the transform becomes zero, which could cause a
// divide-by-zero when projecting points/quads.
WebTransformationMatrix transform;
transform.makeIdentity();
transform.setM33(0);
gfx::RectF rect = gfx::RectF(0, 0, 1, 1);
gfx::RectF projectedRect = MathUtil::projectClippedRect(transform, rect);
EXPECT_EQ(0, projectedRect.x());
EXPECT_EQ(0, projectedRect.y());
EXPECT_TRUE(projectedRect.IsEmpty());
}
TEST(MathUtilTest, verifyEnclosingClippedRectUsesCorrectInitialBounds)
{
HomogeneousCoordinate h1(-100, -100, 0, 1);
HomogeneousCoordinate h2(-10, -10, 0, 1);
HomogeneousCoordinate h3(10, 10, 0, -1);
HomogeneousCoordinate h4(100, 100, 0, -1);
// The bounds of the enclosing clipped rect should be -100 to -10 for both x and y.
// However, if there is a bug where the initial xmin/xmax/ymin/ymax are initialized to
// numeric_limits<float>::min() (which is zero, not -flt_max) then the enclosing
// clipped rect will be computed incorrectly.
gfx::RectF result = MathUtil::computeEnclosingClippedRect(h1, h2, h3, h4);
EXPECT_FLOAT_RECT_EQ(gfx::RectF(gfx::PointF(-100, -100), gfx::SizeF(90, 90)), result);
}
TEST(MathUtilTest, verifyEnclosingRectOfVerticesUsesCorrectInitialBounds)
{
gfx::PointF vertices[3];
int numVertices = 3;
vertices[0] = gfx::PointF(-10, -100);
vertices[1] = gfx::PointF(-100, -10);
vertices[2] = gfx::PointF(-30, -30);
// The bounds of the enclosing rect should be -100 to -10 for both x and y. However,
// if there is a bug where the initial xmin/xmax/ymin/ymax are initialized to
// numeric_limits<float>::min() (which is zero, not -flt_max) then the enclosing
// clipped rect will be computed incorrectly.
gfx::RectF result = MathUtil::computeEnclosingRectOfVertices(vertices, numVertices);
EXPECT_FLOAT_RECT_EQ(gfx::RectF(gfx::PointF(-100, -100), gfx::SizeF(90, 90)), result);
}
TEST(MathUtilTest, smallestAngleBetweenVectors)
{
gfx::Vector2dF x(1, 0);
gfx::Vector2dF y(0, 1);
gfx::Vector2dF testVector(0.5, 0.5);
// Orthogonal vectors are at an angle of 90 degress.
EXPECT_EQ(90, MathUtil::smallestAngleBetweenVectors(x, y));
// A vector makes a zero angle with itself.
EXPECT_EQ(0, MathUtil::smallestAngleBetweenVectors(x, x));
EXPECT_EQ(0, MathUtil::smallestAngleBetweenVectors(y, y));
EXPECT_EQ(0, MathUtil::smallestAngleBetweenVectors(testVector, testVector));
// Parallel but reversed vectors are at 180 degrees.
EXPECT_FLOAT_EQ(180, MathUtil::smallestAngleBetweenVectors(x, -x));
EXPECT_FLOAT_EQ(180, MathUtil::smallestAngleBetweenVectors(y, -y));
EXPECT_FLOAT_EQ(180, MathUtil::smallestAngleBetweenVectors(testVector, -testVector));
// The test vector is at a known angle.
EXPECT_FLOAT_EQ(45, std::floor(MathUtil::smallestAngleBetweenVectors(testVector, x)));
EXPECT_FLOAT_EQ(45, std::floor(MathUtil::smallestAngleBetweenVectors(testVector, y)));
}
TEST(MathUtilTest, vectorProjection)
{
gfx::Vector2dF x(1, 0);
gfx::Vector2dF y(0, 1);
gfx::Vector2dF testVector(0.3f, 0.7f);
// Orthogonal vectors project to a zero vector.
EXPECT_VECTOR_EQ(gfx::Vector2dF(0, 0), MathUtil::projectVector(x, y));
EXPECT_VECTOR_EQ(gfx::Vector2dF(0, 0), MathUtil::projectVector(y, x));
// Projecting a vector onto the orthonormal basis gives the corresponding component of the
// vector.
EXPECT_VECTOR_EQ(gfx::Vector2dF(testVector.x(), 0), MathUtil::projectVector(testVector, x));
EXPECT_VECTOR_EQ(gfx::Vector2dF(0, testVector.y()), MathUtil::projectVector(testVector, y));
// Finally check than an arbitrary vector projected to another one gives a vector parallel to
// the second vector.
gfx::Vector2dF targetVector(0.5, 0.2f);
gfx::Vector2dF projectedVector = MathUtil::projectVector(testVector, targetVector);
EXPECT_EQ(projectedVector.x() / targetVector.x(),
projectedVector.y() / targetVector.y());
}
} // namespace
|
