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// Copyright 2017 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.
#define _USE_MATH_DEFINES // For VC++ to get M_PI. This has to be first.
#include <cmath>
#include "base/macros.h"
#include "testing/gtest/include/gtest/gtest.h"
#include "ui/gfx/geometry/quaternion.h"
#include "ui/gfx/geometry/vector3d_f.h"
namespace gfx {
namespace {
const double kEpsilon = 1e-7;
void CompareQuaternions(const Quaternion& a, const Quaternion& b) {
EXPECT_FLOAT_EQ(a.x(), b.x());
EXPECT_FLOAT_EQ(a.y(), b.y());
EXPECT_FLOAT_EQ(a.z(), b.z());
EXPECT_FLOAT_EQ(a.w(), b.w());
}
} // namespace
TEST(QuatTest, DefaultConstruction) {
CompareQuaternions(Quaternion(0, 0, 0, 1), Quaternion());
}
TEST(QuatTest, AxisAngleCommon) {
double radians = 0.5;
Quaternion q(Vector3dF(1, 0, 0), radians);
CompareQuaternions(
Quaternion(std::sin(radians / 2), 0, 0, std::cos(radians / 2)), q);
}
TEST(QuatTest, VectorToVectorRotation) {
Quaternion q(Vector3dF(1.0f, 0.0f, 0.0f), Vector3dF(0.0f, 1.0f, 0.0f));
Quaternion r(Vector3dF(0.0f, 0.0f, 1.0f), M_PI_2);
EXPECT_FLOAT_EQ(r.x(), q.x());
EXPECT_FLOAT_EQ(r.y(), q.y());
EXPECT_FLOAT_EQ(r.z(), q.z());
EXPECT_FLOAT_EQ(r.w(), q.w());
}
TEST(QuatTest, AxisAngleWithZeroLengthAxis) {
Quaternion q(Vector3dF(0, 0, 0), 0.5);
// If the axis of zero length, we should assume the default values.
CompareQuaternions(q, Quaternion());
}
TEST(QuatTest, Addition) {
double values[] = {0, 1, 100};
for (size_t i = 0; i < arraysize(values); ++i) {
float t = values[i];
Quaternion a(t, 2 * t, 3 * t, 4 * t);
Quaternion b(5 * t, 4 * t, 3 * t, 2 * t);
Quaternion sum = a + b;
CompareQuaternions(Quaternion(t, t, t, t) * 6, sum);
}
}
TEST(QuatTest, Multiplication) {
struct {
Quaternion a;
Quaternion b;
Quaternion expected;
} cases[] = {
{Quaternion(1, 0, 0, 0), Quaternion(1, 0, 0, 0), Quaternion(0, 0, 0, -1)},
{Quaternion(0, 1, 0, 0), Quaternion(0, 1, 0, 0), Quaternion(0, 0, 0, -1)},
{Quaternion(0, 0, 1, 0), Quaternion(0, 0, 1, 0), Quaternion(0, 0, 0, -1)},
{Quaternion(0, 0, 0, 1), Quaternion(0, 0, 0, 1), Quaternion(0, 0, 0, 1)},
{Quaternion(1, 2, 3, 4), Quaternion(5, 6, 7, 8),
Quaternion(24, 48, 48, -6)},
{Quaternion(5, 6, 7, 8), Quaternion(1, 2, 3, 4),
Quaternion(32, 32, 56, -6)},
};
for (size_t i = 0; i < arraysize(cases); ++i) {
Quaternion product = cases[i].a * cases[i].b;
CompareQuaternions(cases[i].expected, product);
}
}
TEST(QuatTest, Scaling) {
double values[] = {0, 10, 100};
for (size_t i = 0; i < arraysize(values); ++i) {
double s = values[i];
Quaternion q(1, 2, 3, 4);
Quaternion expected(s, 2 * s, 3 * s, 4 * s);
CompareQuaternions(expected, q * s);
CompareQuaternions(expected, s * q);
if (s > 0)
CompareQuaternions(expected, q / (1 / s));
}
}
TEST(QuatTest, Normalization) {
Quaternion q(1, -1, 1, -1);
EXPECT_NEAR(q.Length(), 4, kEpsilon);
q = q.Normalized();
EXPECT_NEAR(q.Length(), 1, kEpsilon);
EXPECT_NEAR(q.x(), 0.5, kEpsilon);
EXPECT_NEAR(q.y(), -0.5, kEpsilon);
EXPECT_NEAR(q.z(), 0.5, kEpsilon);
EXPECT_NEAR(q.w(), -0.5, kEpsilon);
}
TEST(QuatTest, Lerp) {
for (size_t i = 1; i < 100; ++i) {
Quaternion a(0, 0, 0, 0);
Quaternion b(1, 2, 3, 4);
float t = static_cast<float>(i) / 100.0f;
Quaternion interpolated = a.Lerp(b, t);
double s = 1.0 / sqrt(30.0);
CompareQuaternions(Quaternion(1, 2, 3, 4) * s, interpolated);
}
Quaternion a(4, 3, 2, 1);
Quaternion b(1, 2, 3, 4);
CompareQuaternions(a.Normalized(), a.Lerp(b, 0));
CompareQuaternions(b.Normalized(), a.Lerp(b, 1));
CompareQuaternions(Quaternion(1, 1, 1, 1).Normalized(), a.Lerp(b, 0.5));
}
TEST(QuatTest, Slerp) {
Vector3dF axis(1, 1, 1);
double start_radians = -0.5;
double stop_radians = 0.5;
Quaternion start(axis, start_radians);
Quaternion stop(axis, stop_radians);
for (size_t i = 0; i < 100; ++i) {
float t = static_cast<float>(i) / 100.0f;
double radians = (1.0 - t) * start_radians + t * stop_radians;
Quaternion expected(axis, radians);
Quaternion interpolated = start.Slerp(stop, t);
EXPECT_NEAR(expected.x(), interpolated.x(), kEpsilon);
EXPECT_NEAR(expected.y(), interpolated.y(), kEpsilon);
EXPECT_NEAR(expected.z(), interpolated.z(), kEpsilon);
EXPECT_NEAR(expected.w(), interpolated.w(), kEpsilon);
}
}
TEST(QuatTest, SlerpOppositeAngles) {
Vector3dF axis(1, 1, 1);
double start_radians = -M_PI_2;
double stop_radians = M_PI_2;
Quaternion start(axis, start_radians);
Quaternion stop(axis, stop_radians);
// When quaternions are pointed in the fully opposite direction, this is
// ambiguous, so we rotate as per https://www.w3.org/TR/css-transforms-1/
Quaternion expected(axis, 0);
Quaternion interpolated = start.Slerp(stop, 0.5f);
EXPECT_NEAR(expected.x(), interpolated.x(), kEpsilon);
EXPECT_NEAR(expected.y(), interpolated.y(), kEpsilon);
EXPECT_NEAR(expected.z(), interpolated.z(), kEpsilon);
EXPECT_NEAR(expected.w(), interpolated.w(), kEpsilon);
}
} // namespace gfx
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