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3294bb64a5bda2fc86cb8ce13ff9ea52257152fd
filament/libs/math/tests/test_mat.cpp
Mathias Agopian 1b0db0fca2 fix a couple shadow stability bugs 
- shadows are now stable (in stable mode) when an IBL rotation is
  used.

- fix the shadow transform option which didn't work when an IBL rotation
  was used

- also use the x-axis as a reference for the "up" direction when
  computing the light space matrix so that we don't fall into the
  degenerate case when the light points straight down, which is a
  common case

FIXES=[299310624]
2023-10-17 12:26:43 -07:00

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27 KiB
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/*
* Copyright 2013 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <gtest/gtest.h>
#include <limits>
#include <random>
#include <functional>
#include <math/mat2.h>
#include <math/mat4.h>
#include <math/mat3.h>
#include <math/quat.h>
#include <math/scalar.h>
using namespace filament::math;
class MatTest : public testing::Test {
protected:
};
//------------------------------------------------------------------------------
// A macro to help with vector comparisons within floating point range.
#define EXPECT_VEC_EQ(VEC1, VEC2) \
do { \
const decltype(VEC1) v1 = VEC1; \
const decltype(VEC2) v2 = VEC2; \
if (std::is_same<TypeParam,float>::value) { \
for (int i = 0; i < v1.size(); ++i) { \
EXPECT_FLOAT_EQ(v1[i], v2[i]); \
} \
} else if (std::is_same<TypeParam,double>::value) { \
for (int i = 0; i < v1.size(); ++i) { \
EXPECT_DOUBLE_EQ(v1[i], v2[i]); \
} \
} else { \
for (int i = 0; i < v1.size(); ++i) { \
EXPECT_EQ(v1[i], v2[i]); \
} \
} \
} while(0)
//------------------------------------------------------------------------------
// A macro to help with vector comparisons within a range.
#define EXPECT_VEC_NEAR(VEC1, VEC2, eps) \
do { \
const decltype(VEC1) v1 = VEC1; \
const decltype(VEC2) v2 = VEC2; \
for (int i = 0; i < v1.size(); ++i) { \
EXPECT_NEAR(v1[i], v2[i], eps); \
} \
} while(0)
//------------------------------------------------------------------------------
// A macro to help with type comparisons within floating point range.
#define ASSERT_TYPE_EQ(T1, T2) \
do { \
const decltype(T1) t1 = T1; \
const decltype(T2) t2 = T2; \
if (std::is_same<TypeParam,float>::value) { \
ASSERT_FLOAT_EQ(t1, t2); \
} else if (std::is_same<TypeParam,double>::value) { \
ASSERT_DOUBLE_EQ(t1, t2); \
} else { \
ASSERT_EQ(t1, t2); \
} \
} while(0)
TEST_F(MatTest, LargeFloatRotationsWithOrthogonalization) {
double3 const t = { 2304097.1410110965, -4688442.9915525438, -3639452.5611694567 };
mat4 const T = mat4::translation(t);
for (float d = 0; d < 90; d = d + 1.0) {
mat3f const R = mat3f::rotation(d * f::DEG_TO_RAD, float3{ 0, 1, 0 });
mat3 RR = orthogonalize(mat3{ R });
ASSERT_NEAR(dot(RR[0], RR[0]), 1.0, 1e-12);
ASSERT_NEAR(dot(RR[1], RR[1]), 1.0, 1e-12);
ASSERT_NEAR(dot(RR[2], RR[2]), 1.0, 1e-12);
mat4 M = mat4{ RR } * T;
double3 const t2 = transpose(M.upperLeft()) * M[3].xyz;
EXPECT_VEC_NEAR(t, t2, 0.0001); // 0.1mm
}
}
TEST_F(MatTest, ConstexprMat2) {
constexpr float a = F_PI;
constexpr mat2f M;
constexpr mat2f M0(a);
constexpr mat2f M1(float2{a, a});
constexpr mat2f M2(1,2,3,4);
constexpr mat2f M3(M2);
constexpr mat2f M4(float2{1,2}, float2{3,4});
constexpr float2 f0 = M0 * float2{1,2};
constexpr float2 f1 = float2{1,2} * M1;
CONSTEXPR_IF_NOT_MSVC mat2f M5 = M2 * 2;
CONSTEXPR_IF_NOT_MSVC mat2f M7 = 2 * M2;
constexpr float2 f3 = diag(M0);
constexpr mat2f M8 = transpose(M0);
constexpr mat2f M9 = inverse(M0);
constexpr mat2f M12 = abs(M0);
constexpr mat2f M11 = details::matrix::cof(M0);
constexpr mat2f M10 = M8 * M9;
constexpr float s0 = trace(M0);
constexpr float f4 = M[0][0];
constexpr float f5 = M(0, 0);
}
TEST_F(MatTest, ConstexprMat3) {
constexpr float a = F_PI;
constexpr mat3f M;
constexpr mat3f M0(a);
constexpr mat3f M1(float3{a, a, a});
constexpr mat3f M2(1,2,3,4,5,6,7,8,9);
constexpr mat3f M3(M2);
constexpr mat3f M4(float3{1,2,3}, float3{4,5,6}, float3{7,8,9});
constexpr float3 f0 = M0 * float3{1,2,3};
constexpr float3 f1 = float3{1,2,3} * M1;
CONSTEXPR_IF_NOT_MSVC mat3f M5 = M2 * 2;
CONSTEXPR_IF_NOT_MSVC mat3f M7 = 2 * M2;
constexpr float3 f3 = diag(M0);
constexpr mat3f M8 = transpose(M0);
constexpr mat3f M9 = inverse(M0);
constexpr mat3f M12 = details::matrix::cof(M0);
constexpr mat3f M10 = M8 * M9;
constexpr float s0 = trace(M0);
constexpr quatf q;
constexpr mat3f M11{q};
}
TEST_F(MatTest, ConstexprMat4) {
constexpr float a = F_PI;
constexpr mat4f M;
constexpr mat4f M0(a);
constexpr mat4f M1(float4{a, a, a, a});
constexpr mat4f M2(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);
constexpr mat4f M3(M2);
constexpr mat4f M4(float4{1,2,3,4}, float4{5,6,7,8}, float4{9,10,11,12}, float4{13,14,15,16});
constexpr float4 f0 = M0 * float4{1,2,3,4};
constexpr float4 f1 = float4{1,2,3,4} * M1;
CONSTEXPR_IF_NOT_MSVC mat4f M5 = M2 * 2;
CONSTEXPR_IF_NOT_MSVC mat4f M7 = 2 * M2;
constexpr float4 f3 = diag(M0);
constexpr mat4f M8 = transpose(M0);
constexpr mat4f M9 = inverse(M0);
constexpr mat4f M16 = details::matrix::cof(M0);
constexpr mat4f M10 = M8 * M9;
constexpr float s0 = trace(M0);
constexpr quatf q;
constexpr mat4f M11{q};
constexpr mat4f M13{mat3f{}};
constexpr mat4f M14{mat3f{}, float3{}};
constexpr mat4f M15{mat3f{}, float4{}};
constexpr mat4f O = mat4f::ortho(0, 1, 0, 1, -1, 1);
constexpr mat4f F = mat4f::frustum(0, 1, 0, 1, -1, 1);
constexpr float4 f4 = mat4f::project(F, float4{1,2,3,1});
constexpr float3 f5 = mat4f::project(F, float3{1,2,3});
constexpr mat3f U = M11.upperLeft();
constexpr mat4f T = mat4f::translation(f5);
constexpr mat4f S = mat4f::scaling(f5);
constexpr mat4f V = mat4f::scaling(s0);
}
TEST_F(MatTest, Basics) {
EXPECT_EQ(sizeof(mat4), sizeof(double)*16);
}
TEST_F(MatTest, ComparisonOps) {
mat4 m0;
mat4 m1(2);
EXPECT_TRUE(m0 == m0);
EXPECT_TRUE(m0 != m1);
EXPECT_FALSE(m0 != m0);
EXPECT_FALSE(m0 == m1);
}
TEST_F(MatTest, Constructors) {
mat4 m0;
ASSERT_EQ(m0[0].x, 1);
ASSERT_EQ(m0[0].y, 0);
ASSERT_EQ(m0[0].z, 0);
ASSERT_EQ(m0[0].w, 0);
ASSERT_EQ(m0[1].x, 0);
ASSERT_EQ(m0[1].y, 1);
ASSERT_EQ(m0[1].z, 0);
ASSERT_EQ(m0[1].w, 0);
ASSERT_EQ(m0[2].x, 0);
ASSERT_EQ(m0[2].y, 0);
ASSERT_EQ(m0[2].z, 1);
ASSERT_EQ(m0[2].w, 0);
ASSERT_EQ(m0[3].x, 0);
ASSERT_EQ(m0[3].y, 0);
ASSERT_EQ(m0[3].z, 0);
ASSERT_EQ(m0[3].w, 1);
mat4 m1(2);
mat4 m2(double4(2));
mat4 m3(m2);
EXPECT_EQ(m1, m2);
EXPECT_EQ(m2, m3);
EXPECT_EQ(m3, m1);
}
TEST_F(MatTest, ArithmeticOps) {
mat4 m0;
mat4 m1(2);
mat4 m2(double4(2));
m1 += m2;
EXPECT_EQ(mat4(4), m1);
m2 -= m1;
EXPECT_EQ(mat4(-2), m2);
m1 *= 2;
EXPECT_EQ(mat4(8), m1);
m1 /= 2;
EXPECT_EQ(mat4(4), m1);
m0 = -m0;
EXPECT_EQ(mat4(-1), m0);
}
TEST_F(MatTest, UnaryOps) {
const mat4 identity;
mat4 m0;
m0 = -m0;
EXPECT_EQ(mat4(double4(-1, 0, 0, 0),
double4(0, -1, 0, 0),
double4(0, 0, -1, 0),
double4(0, 0, 0, -1)), m0);
m0 = -m0;
EXPECT_EQ(identity, m0);
}
TEST_F(MatTest, MiscOps) {
const mat4 identity;
mat4 m0;
EXPECT_EQ(4, trace(m0));
mat4 m1(double4(1, 2, 3, 4), double4(5, 6, 7, 8), double4(9, 10, 11, 12), double4(13, 14, 15, 16));
mat4 m2(double4(1, 5, 9, 13), double4(2, 6, 10, 14), double4(3, 7, 11, 15), double4(4, 8, 12, 16));
EXPECT_EQ(m1, transpose(m2));
EXPECT_EQ(m2, transpose(m1));
EXPECT_EQ(double4(1, 6, 11, 16), diag(m1));
EXPECT_EQ(identity, inverse(identity));
mat4 m3(double4(4, 3, 0, 0), double4(3, 2, 0, 0), double4(0, 0, 1, 0), double4(0, 0, 0, 1));
mat4 m3i(inverse(m3));
EXPECT_FLOAT_EQ(-2, m3i[0][0]);
EXPECT_FLOAT_EQ(3, m3i[0][1]);
EXPECT_FLOAT_EQ(3, m3i[1][0]);
EXPECT_FLOAT_EQ(-4, m3i[1][1]);
mat4 m3ii(inverse(m3i));
EXPECT_FLOAT_EQ(m3[0][0], m3ii[0][0]);
EXPECT_FLOAT_EQ(m3[0][1], m3ii[0][1]);
EXPECT_FLOAT_EQ(m3[1][0], m3ii[1][0]);
EXPECT_FLOAT_EQ(m3[1][1], m3ii[1][1]);
EXPECT_EQ(m1, m1*identity);
for (size_t c=0 ; c<4 ; c++) {
for (size_t r=0 ; r<4 ; r++) {
EXPECT_FLOAT_EQ(m1[c][r], m1(r, c));
}
}
}
TEST_F(MatTest, ElementAccess) {
mat4 m(double4(1, 2, 3, 4), double4(5, 6, 7, 8), double4(9, 10, 11, 12), double4(13, 14, 15, 16));
for (size_t c=0 ; c<4 ; c++) {
for (size_t r=0 ; r<4 ; r++) {
EXPECT_FLOAT_EQ(m[c][r], m(r, c));
}
}
m(3,2) = 100;
EXPECT_FLOAT_EQ(m[2][3], 100);
EXPECT_FLOAT_EQ(m(3, 2), 100);
}
//------------------------------------------------------------------------------
// MAT 3
//------------------------------------------------------------------------------
class Mat3Test : public testing::Test {
protected:
};
TEST_F(Mat3Test, Basics) {
EXPECT_EQ(sizeof(mat3), sizeof(double)*9);
}
TEST_F(Mat3Test, ComparisonOps) {
mat3 m0;
mat3 m1(2);
EXPECT_TRUE(m0 == m0);
EXPECT_TRUE(m0 != m1);
EXPECT_FALSE(m0 != m0);
EXPECT_FALSE(m0 == m1);
}
TEST_F(Mat3Test, Constructors) {
mat3 m0;
ASSERT_EQ(m0[0].x, 1);
ASSERT_EQ(m0[0].y, 0);
ASSERT_EQ(m0[0].z, 0);
ASSERT_EQ(m0[1].x, 0);
ASSERT_EQ(m0[1].y, 1);
ASSERT_EQ(m0[1].z, 0);
ASSERT_EQ(m0[2].x, 0);
ASSERT_EQ(m0[2].y, 0);
ASSERT_EQ(m0[2].z, 1);
mat3 m1(2);
mat3 m2(double3(2));
mat3 m3(m2);
EXPECT_EQ(m1, m2);
EXPECT_EQ(m2, m3);
EXPECT_EQ(m3, m1);
}
TEST_F(Mat3Test, ArithmeticOps) {
mat3 m0;
mat3 m1(2);
mat3 m2(double3(2));
m1 += m2;
EXPECT_EQ(mat3(4), m1);
m2 -= m1;
EXPECT_EQ(mat3(-2), m2);
m1 *= 2;
EXPECT_EQ(mat3(8), m1);
m1 /= 2;
EXPECT_EQ(mat3(4), m1);
m0 = -m0;
EXPECT_EQ(mat3(-1), m0);
}
TEST_F(Mat3Test, UnaryOps) {
const mat3 identity;
mat3 m0;
m0 = -m0;
EXPECT_EQ(mat3(double3(-1, 0, 0),
double3(0, -1, 0),
double3(0, 0, -1)), m0);
m0 = -m0;
EXPECT_EQ(identity, m0);
}
TEST_F(Mat3Test, MiscOps) {
const mat3 identity;
mat3 m0;
EXPECT_EQ(3, trace(m0));
mat3 m1(double3(1, 2, 3), double3(4, 5, 6), double3(7, 8, 9));
mat3 m2(double3(1, 4, 7), double3(2, 5, 8), double3(3, 6, 9));
EXPECT_EQ(m1, transpose(m2));
EXPECT_EQ(m2, transpose(m1));
EXPECT_EQ(double3(1, 5, 9), diag(m1));
EXPECT_EQ(identity, inverse(identity));
mat3 m3(double3(4, 3, 0), double3(3, 2, 0), double3(0, 0, 1));
mat3 m3i(inverse(m3));
EXPECT_FLOAT_EQ(-2, m3i[0][0]);
EXPECT_FLOAT_EQ(3, m3i[0][1]);
EXPECT_FLOAT_EQ(3, m3i[1][0]);
EXPECT_FLOAT_EQ(-4, m3i[1][1]);
mat3 m3ii(inverse(m3i));
EXPECT_FLOAT_EQ(m3[0][0], m3ii[0][0]);
EXPECT_FLOAT_EQ(m3[0][1], m3ii[0][1]);
EXPECT_FLOAT_EQ(m3[1][0], m3ii[1][0]);
EXPECT_FLOAT_EQ(m3[1][1], m3ii[1][1]);
EXPECT_EQ(m1, m1*identity);
}
//------------------------------------------------------------------------------
// MAT 2
//------------------------------------------------------------------------------
class Mat2Test : public testing::Test {
protected:
};
TEST_F(Mat2Test, Basics) {
EXPECT_EQ(sizeof(mat2), sizeof(double)*4);
}
TEST_F(Mat2Test, ComparisonOps) {
mat2 m0;
mat2 m1(2);
EXPECT_TRUE(m0 == m0);
EXPECT_TRUE(m0 != m1);
EXPECT_FALSE(m0 != m0);
EXPECT_FALSE(m0 == m1);
}
TEST_F(Mat2Test, Constructors) {
mat2 m0;
ASSERT_EQ(m0[0].x, 1);
ASSERT_EQ(m0[0].y, 0);
ASSERT_EQ(m0[1].x, 0);
ASSERT_EQ(m0[1].y, 1);
mat2 m1(2);
mat2 m2(double2(2));
mat2 m3(m2);
EXPECT_EQ(m1, m2);
EXPECT_EQ(m2, m3);
EXPECT_EQ(m3, m1);
}
TEST_F(Mat2Test, ArithmeticOps) {
mat2 m0;
mat2 m1(2);
mat2 m2(double2(2));
m1 += m2;
EXPECT_EQ(mat2(4), m1);
m2 -= m1;
EXPECT_EQ(mat2(-2), m2);
m1 *= 2;
EXPECT_EQ(mat2(8), m1);
m1 /= 2;
EXPECT_EQ(mat2(4), m1);
m0 = -m0;
EXPECT_EQ(mat2(-1), m0);
}
TEST_F(Mat2Test, UnaryOps) {
const mat2 identity;
mat2 m0;
m0 = -m0;
EXPECT_EQ(mat2(double2(-1, 0),
double2(0, -1)), m0);
m0 = -m0;
EXPECT_EQ(identity, m0);
}
TEST_F(Mat2Test, MiscOps) {
const mat2 identity;
mat2 m0;
EXPECT_EQ(2, trace(m0));
mat2 m1(double2(1, 2), double2(3, 4));
mat2 m2(double2(1, 3), double2(2, 4));
EXPECT_EQ(m1, transpose(m2));
EXPECT_EQ(m2, transpose(m1));
EXPECT_EQ(double2(1, 4), diag(m1));
EXPECT_EQ(identity, inverse(identity));
EXPECT_EQ(m1, m1*identity);
}
//------------------------------------------------------------------------------
// MORE MATRIX TESTS
//------------------------------------------------------------------------------
template <typename T>
class MatTestT : public ::testing::Test {
public:
};
typedef ::testing::Types<float,double> TestMatrixValueTypes;
TYPED_TEST_SUITE(MatTestT, TestMatrixValueTypes);
#define TEST_MATRIX_INVERSE(MATRIX, EPSILON) \
{ \
typedef decltype(MATRIX) MatrixType; \
MatrixType inv1 = inverse(MATRIX); \
MatrixType ident1 = MATRIX * inv1; \
MatrixType inv2 = transpose(cof(MATRIX))/det(MATRIX); \
MatrixType ident2 = MATRIX * inv2; \
static const MatrixType IDENTITY; \
for (int row = 0; row < MatrixType::ROW_SIZE; ++row) { \
for (int col = 0; col < MatrixType::COL_SIZE; ++col) { \
EXPECT_NEAR(ident1[row][col], IDENTITY[row][col], EPSILON); \
EXPECT_NEAR(ident2[row][col], IDENTITY[row][col], EPSILON); \
} \
} \
}
TYPED_TEST(MatTestT, Inverse4) {
typedef filament::math::details::TMat44<TypeParam> M44T;
M44T m1(1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1);
M44T m2(0, -1, 0, 0,
1, 0, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1);
M44T m3(1, 0, 0, 0,
0, 2, 0, 0,
0, 0, 0, 1,
0, 0, -1, 0);
M44T m4(
4.683281e-01, 1.251189e-02, -8.834660e-01, -4.726541e+00,
-8.749647e-01, 1.456563e-01, -4.617587e-01, 3.044795e+00,
1.229049e-01, 9.892561e-01, 7.916244e-02, -6.737138e+00,
0.000000e+00, 0.000000e+00, 0.000000e+00, 1.000000e+00);
M44T m5(
4.683281e-01, 1.251189e-02, -8.834660e-01, -4.726541e+00,
-8.749647e-01, 1.456563e-01, -4.617587e-01, 3.044795e+00,
1.229049e-01, 9.892561e-01, 7.916244e-02, -6.737138e+00,
1.000000e+00, 2.000000e+00, 3.000000e+00, 4.000000e+00);
TEST_MATRIX_INVERSE(m1, 0);
TEST_MATRIX_INVERSE(m2, 0);
TEST_MATRIX_INVERSE(m3, 0);
TEST_MATRIX_INVERSE(m4, 20.0 * std::numeric_limits<TypeParam>::epsilon());
TEST_MATRIX_INVERSE(m5, 20.0 * std::numeric_limits<TypeParam>::epsilon());
}
//------------------------------------------------------------------------------
TYPED_TEST(MatTestT, Inverse3) {
typedef filament::math::details::TMat33<TypeParam> M33T;
M33T m1(1, 0, 0,
0, 1, 0,
0, 0, 1);
M33T m2(0, -1, 0,
1, 0, 0,
0, 0, 1);
M33T m3(2, 0, 0,
0, 0, 1,
0, -1, 0);
M33T m4(
4.683281e-01, 1.251189e-02, 0.000000e+00,
-8.749647e-01, 1.456563e-01, 0.000000e+00,
0.000000e+00, 0.000000e+00, 1.000000e+00);
M33T m5(
4.683281e-01, 1.251189e-02, -8.834660e-01,
-8.749647e-01, 1.456563e-01, -4.617587e-01,
1.229049e-01, 9.892561e-01, 7.916244e-02);
TEST_MATRIX_INVERSE(m1, 0);
TEST_MATRIX_INVERSE(m2, 0);
TEST_MATRIX_INVERSE(m3, 0);
TEST_MATRIX_INVERSE(m4, 20.0 * std::numeric_limits<TypeParam>::epsilon());
TEST_MATRIX_INVERSE(m5, 20.0 * std::numeric_limits<TypeParam>::epsilon());
}
//------------------------------------------------------------------------------
TYPED_TEST(MatTestT, Inverse2) {
typedef filament::math::details::TMat22<TypeParam> M22T;
M22T m1(1, 0,
0, 1);
M22T m2(0, -1,
1, 0);
M22T m3(
4.683281e-01, 1.251189e-02,
-8.749647e-01, 1.456563e-01);
M22T m4(
4.683281e-01, 1.251189e-02,
-8.749647e-01, 1.456563e-01);
TEST_MATRIX_INVERSE(m1, 0);
TEST_MATRIX_INVERSE(m2, 0);
TEST_MATRIX_INVERSE(m3, 20.0 * std::numeric_limits<TypeParam>::epsilon());
TEST_MATRIX_INVERSE(m4, 20.0 * std::numeric_limits<TypeParam>::epsilon());
}
TYPED_TEST(MatTestT, NormalsNegativeScale) {
typedef filament::math::details::TMat33<TypeParam> M33T;
typedef filament::math::details::TVec3<TypeParam> V3T;
M33T m(-1, 0, 0,
0, 1, 0,
0, 0, 1);
V3T n = V3T(0, 0, 1);
V3T n_prime = M33T::getTransformForNormals(m) * n;
// The normal should be flipped for mirroring transformations (ie when the det < 0).
//
// This is intuitive using Grassmann algebra, or when visualizing the mirroring of the
// tangent + bivector pair rather than the normal itself.
//
// Another way of thinking about this is in terms of polygon winding: since the winding is
// flipped, we render its underside and thus need to flip the shading normal.
//
// The following shadertoy is illuminating: https://www.shadertoy.com/view/3s33zj.
// The shadertoy is interesting for several reasons: (1) it uses the adjoint matrix for
// transforming normals and (2) it negates the normal when scale is negative (look for
// "isFlipped") and (3) it demonstrates that inverse-transpose computation is slow.
ASSERT_LT(det(m), 0);
EXPECT_VEC_EQ(n_prime, -n);
}
//------------------------------------------------------------------------------
// Test some translation stuff.
TYPED_TEST(MatTestT, Translation4) {
typedef filament::math::details::TMat44<TypeParam> M44T;
typedef filament::math::details::TVec4<TypeParam> V4T;
typedef filament::math::details::TVec3<TypeParam> V3T;
V3T translateBy(-7.3, 1.1, 14.4);
V3T translation(translateBy[0], translateBy[1], translateBy[2]);
M44T translation_matrix = M44T::translation(translation);
V4T p1(9.9, 3.1, 41.1, 1.0);
V4T p2(-18.0, 0.0, 1.77, 1.0);
V4T p3(0, 0, 0, 1);
V4T p4(-1000, -1000, 1000, 1.0);
EXPECT_VEC_EQ((translation_matrix * p1).xyz, translateBy + p1.xyz);
EXPECT_VEC_EQ((translation_matrix * p2).xyz, translateBy + p2.xyz);
EXPECT_VEC_EQ((translation_matrix * p3).xyz, translateBy + p3.xyz);
EXPECT_VEC_EQ((translation_matrix * p4).xyz, translateBy + p4.xyz);
translation_matrix = M44T::translation(V3T{2.7});
EXPECT_VEC_EQ((translation_matrix * p1).xyz, V3T{2.7} + p1.xyz);
}
//------------------------------------------------------------------------------
// Test some scale stuff.
TYPED_TEST(MatTestT, Scale4) {
typedef filament::math::details::TMat44<TypeParam> M44T;
typedef filament::math::details::TVec4<TypeParam> V4T;
typedef filament::math::details::TVec3<TypeParam> V3T;
V3T scaleBy(2.0, 3.0, 4.0);
V3T scale(scaleBy[0], scaleBy[1], scaleBy[2]);
M44T scale_matrix = M44T::scaling(scale);
V4T p1(9.9, 3.1, 41.1, 1.0);
V4T p2(-18.0, 0.0, 1.77, 1.0);
V4T p3(0, 0, 0, 1);
V4T p4(-1000, -1000, 1000, 1.0);
EXPECT_VEC_EQ((scale_matrix * p1).xyz, scaleBy * p1.xyz);
EXPECT_VEC_EQ((scale_matrix * p2).xyz, scaleBy * p2.xyz);
EXPECT_VEC_EQ((scale_matrix * p3).xyz, scaleBy * p3.xyz);
EXPECT_VEC_EQ((scale_matrix * p4).xyz, scaleBy * p4.xyz);
scale_matrix = M44T::scaling(3.0);
EXPECT_VEC_EQ((scale_matrix * p1).xyz, V3T{3.0} * p1.xyz);
}
//------------------------------------------------------------------------------
template <typename MATRIX>
static void verifyOrthonormal(const MATRIX& A) {
typedef typename MATRIX::value_type T;
static constexpr T value_eps = T(100) * std::numeric_limits<T>::epsilon();
const MATRIX prod = A * transpose(A);
for (int i = 0; i < MATRIX::NUM_COLS; ++i) {
for (int j = 0; j < MATRIX::NUM_ROWS; ++j) {
if (i == j) {
ASSERT_NEAR(prod[i][j], T(1), value_eps);
} else {
ASSERT_NEAR(prod[i][j], T(0), value_eps);
}
}
}
}
//------------------------------------------------------------------------------
// Test euler code.
TYPED_TEST(MatTestT, EulerZYX_44) {
typedef filament::math::details::TMat44<TypeParam> M44T;
std::default_random_engine generator(82828); // NOLINT
std::uniform_real_distribution<TypeParam> distribution(-6.0 * 2.0*F_PI, 6.0 * 2.0*F_PI);
auto rand_gen = std::bind(distribution, generator);
for (size_t i = 0; i < 100; ++i) {
M44T m = M44T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
verifyOrthonormal(m);
}
M44T m = M44T::eulerZYX(1, 2, 3);
verifyOrthonormal(m);
}
//------------------------------------------------------------------------------
// Test euler code.
TYPED_TEST(MatTestT, EulerZYX_33) {
typedef filament::math::details::TMat33<TypeParam> M33T;
std::default_random_engine generator(112233); // NOLINT
std::uniform_real_distribution<TypeParam> distribution(-6.0 * 2.0*F_PI, 6.0 * 2.0*F_PI);
auto rand_gen = std::bind(distribution, generator);
for (size_t i = 0; i < 100; ++i) {
M33T m = M33T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
verifyOrthonormal(m);
}
M33T m = M33T::eulerZYX(1, 2, 3);
verifyOrthonormal(m);
}
//------------------------------------------------------------------------------
// Test to quaternion with post translation.
TYPED_TEST(MatTestT, ToQuaternionPostTranslation) {
typedef filament::math::details::TMat44<TypeParam> M44T;
typedef filament::math::details::TVec3<TypeParam> V3T;
typedef filament::math::details::TQuaternion<TypeParam> QuatT;
std::default_random_engine generator(112233); // NOLINT
std::uniform_real_distribution<TypeParam> distribution(-6.0 * 2.0*F_PI, 6.0 * 2.0*F_PI);
auto rand_gen = std::bind(distribution, generator);
for (size_t i = 0; i < 100; ++i) {
M44T r = M44T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
M44T t = M44T::translation(V3T(rand_gen(), rand_gen(), rand_gen()));
QuatT qr = r.toQuaternion();
M44T tr = t * r;
QuatT qtr = tr.toQuaternion();
ASSERT_TYPE_EQ(qr.x, qtr.x);
ASSERT_TYPE_EQ(qr.y, qtr.y);
ASSERT_TYPE_EQ(qr.z, qtr.z);
ASSERT_TYPE_EQ(qr.w, qtr.w);
}
M44T r = M44T::eulerZYX(1, 2, 3);
M44T t = M44T::translation(V3T(20, -15, 2));
QuatT qr = r.toQuaternion();
M44T tr = t * r;
QuatT qtr = tr.toQuaternion();
ASSERT_TYPE_EQ(qr.x, qtr.x);
ASSERT_TYPE_EQ(qr.y, qtr.y);
ASSERT_TYPE_EQ(qr.z, qtr.z);
ASSERT_TYPE_EQ(qr.w, qtr.w);
}
//------------------------------------------------------------------------------
// Test to quaternion with post translation.
TYPED_TEST(MatTestT, ToQuaternionPointTransformation33) {
static constexpr TypeParam value_eps =
TypeParam(1000) * std::numeric_limits<TypeParam>::epsilon();
typedef filament::math::details::TMat33<TypeParam> M33T;
typedef filament::math::details::TVec3<TypeParam> V3T;
typedef filament::math::details::TQuaternion<TypeParam> QuatT;
std::default_random_engine generator(112233); // NOLINT
std::uniform_real_distribution<TypeParam> distribution(-100.0, 100.0);
auto rand_gen = std::bind(distribution, generator);
for (size_t i = 0; i < 100; ++i) {
M33T r = M33T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
QuatT qr = r.toQuaternion();
V3T p(rand_gen(), rand_gen(), rand_gen());
V3T pr = r * p;
V3T pq = qr * p;
ASSERT_NEAR(pr.x, pq.x, value_eps);
ASSERT_NEAR(pr.y, pq.y, value_eps);
ASSERT_NEAR(pr.z, pq.z, value_eps);
}
}
//------------------------------------------------------------------------------
// Test to quaternion with post translation.
TYPED_TEST(MatTestT, ToQuaternionPointTransformation44) {
static constexpr TypeParam value_eps =
TypeParam(1000) * std::numeric_limits<TypeParam>::epsilon();
typedef filament::math::details::TMat44<TypeParam> M44T;
typedef filament::math::details::TVec4<TypeParam> V4T;
typedef filament::math::details::TVec3<TypeParam> V3T;
typedef filament::math::details::TQuaternion<TypeParam> QuatT;
std::default_random_engine generator(992626); // NOLINT
std::uniform_real_distribution<TypeParam> distribution(-100.0, 100.0);
auto rand_gen = std::bind(distribution, generator);
for (size_t i = 0; i < 100; ++i) {
M44T r = M44T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
QuatT qr = r.toQuaternion();
V3T p(rand_gen(), rand_gen(), rand_gen());
V4T pr = r * V4T(p.x, p.y, p.z, 1);
pr.x /= pr.w;
pr.y /= pr.w;
pr.z /= pr.w;
V3T pq = qr * p;
ASSERT_NEAR(pr.x, pq.x, value_eps);
ASSERT_NEAR(pr.y, pq.y, value_eps);
ASSERT_NEAR(pr.z, pq.z, value_eps);
}
}
TYPED_TEST(MatTestT, cofactor) {
static constexpr TypeParam value_eps =
TypeParam(1000) * std::numeric_limits<TypeParam>::epsilon();
typedef filament::math::details::TMat33<TypeParam> M33T;
std::default_random_engine generator(992626); // NOLINT
std::uniform_real_distribution<TypeParam> distribution(-100.0, 100.0);
auto rand_gen = std::bind(distribution, generator);
for (size_t i = 0; i < 100; ++i) {
M33T r = M33T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
M33T c0 = details::matrix::cofactor(r);
M33T c1 = details::matrix::fastCofactor3(r);
EXPECT_VEC_NEAR(c0[0], c1[0], value_eps);
EXPECT_VEC_NEAR(c0[1], c1[1], value_eps);
EXPECT_VEC_NEAR(c0[2], c1[2], value_eps);
}
}
#undef TEST_MATRIX_INVERSE
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