magnum/src/Magnum/Math/Test/Matrix4Test.cpp

/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
                2020 Vladimír Vondruš <mosra@centrum.cz>

    Permission is hereby granted, free of charge, to any person obtaining a
    copy of this software and associated documentation files (the "Software"),
    to deal in the Software without restriction, including without limitation
    the rights to use, copy, modify, merge, publish, distribute, sublicense,
    and/or sell copies of the Software, and to permit persons to whom the
    Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included
    in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
    DEALINGS IN THE SOFTWARE.
*/

#include <sstream>
#include <Corrade/TestSuite/Tester.h>
#include <Corrade/TestSuite/Compare/Numeric.h>
#include <Corrade/Utility/DebugStl.h>

#include "Magnum/Math/Matrix4.h"
#include "Magnum/Math/StrictWeakOrdering.h"

struct Mat4 {
    float a[16];
};

namespace Magnum { namespace Math {

namespace Implementation {

template<> struct RectangularMatrixConverter<4, 4, float, Mat4> {
    constexpr static RectangularMatrix<4, 4, Float> from(const Mat4& other) {
        return RectangularMatrix<4, 4, Float>(
            Vector<4, Float>(other.a[0], other.a[1], other.a[2], other.a[3]),
            Vector<4, Float>(other.a[4], other.a[5], other.a[6], other.a[7]),
            Vector<4, Float>(other.a[8], other.a[9], other.a[10], other.a[11]),
            Vector<4, Float>(other.a[12], other.a[13], other.a[14], other.a[15]));
    }

    constexpr static Mat4 to(const RectangularMatrix<4, 4, Float>& other) {
        return Mat4{{other[0][0], other[0][1], other[0][2], other[0][3],
                     other[1][0], other[1][1], other[1][2], other[1][3],
                     other[2][0], other[2][1], other[2][2], other[2][3],
                     other[3][0], other[3][1], other[3][2], other[3][3]}};
    }
};

}

namespace Test { namespace {

struct Matrix4Test: Corrade::TestSuite::Tester {
    explicit Matrix4Test();

    void construct();
    void constructIdentity();
    void constructZero();
    void constructNoInit();
    void constructOneValue();
    void constructConversion();
    void constructFromDifferentSize();
    void constructCopy();
    void convert();

    void isRigidTransformation();

    void translation();
    void scaling();
    void rotation();
    void rotationNotNormalized();
    void rotationX();
    void rotationY();
    void rotationZ();
    void reflection();
    void reflectionNotNormalized();
    void reflectionIsScaling();
    void shearingXY();
    void shearingXZ();
    void shearingYZ();
    void orthographicProjection();
    void perspectiveProjection();
    void perspectiveProjectionInfiniteFar();
    void perspectiveProjectionFov();
    void perspectiveProjectionFovInfiniteFar();
    void perspectiveProjectionOffCenter();
    void perspectiveProjectionOffCenterInfiniteFar();
    void lookAt();

    void fromParts();
    void rotationScalingPart();
    void rotationShearPart();
    void rotationPart();
    void rotationPartNotOrthogonal();
    void rotationNormalizedPart();
    void rotationNormalizedPartNotOrthogonal();
    void scalingPart();
    void rotationScalingPartNegative();
    void uniformScalingPart();
    void uniformScalingPartNotUniform();
    void normalMatrixPart();
    void vectorParts();
    void invertedRigid();
    void invertedRigidNotRigid();
    void transform();
    void transformProjection();

    void strictWeakOrdering();

    void debug();
};

typedef Math::Deg<Float> Deg;
typedef Math::Rad<Float> Rad;
typedef Math::Matrix<2, Float> Matrix2x2;
typedef Math::Matrix<3, Float> Matrix3x3;
typedef Math::Matrix4<Float> Matrix4;
typedef Math::Matrix4<Int> Matrix4i;
typedef Math::Vector2<Float> Vector2;
typedef Math::Vector3<Float> Vector3;
typedef Math::Vector4<Float> Vector4;
typedef Math::Constants<Float> Constants;

Matrix4Test::Matrix4Test() {
    addTests({&Matrix4Test::construct,
              &Matrix4Test::constructIdentity,
              &Matrix4Test::constructZero,
              &Matrix4Test::constructNoInit,
              &Matrix4Test::constructOneValue,
              &Matrix4Test::constructConversion,
              &Matrix4Test::constructFromDifferentSize,
              &Matrix4Test::constructCopy,
              &Matrix4Test::convert,

              &Matrix4Test::isRigidTransformation,

              &Matrix4Test::translation,
              &Matrix4Test::scaling,
              &Matrix4Test::rotation,
              &Matrix4Test::rotationNotNormalized,
              &Matrix4Test::rotationX,
              &Matrix4Test::rotationY,
              &Matrix4Test::rotationZ,
              &Matrix4Test::reflection,
              &Matrix4Test::reflectionNotNormalized,
              &Matrix4Test::reflectionIsScaling,
              &Matrix4Test::shearingXY,
              &Matrix4Test::shearingXZ,
              &Matrix4Test::shearingYZ,
              &Matrix4Test::orthographicProjection,
              &Matrix4Test::perspectiveProjection,
              &Matrix4Test::perspectiveProjectionInfiniteFar,
              &Matrix4Test::perspectiveProjectionFov,
              &Matrix4Test::perspectiveProjectionFovInfiniteFar,
              &Matrix4Test::perspectiveProjectionOffCenter,
              &Matrix4Test::perspectiveProjectionOffCenterInfiniteFar,
              &Matrix4Test::lookAt,

              &Matrix4Test::fromParts,
              &Matrix4Test::rotationScalingPart,
              &Matrix4Test::rotationShearPart,
              &Matrix4Test::rotationPart,
              &Matrix4Test::rotationPartNotOrthogonal,
              &Matrix4Test::rotationNormalizedPart,
              &Matrix4Test::rotationNormalizedPartNotOrthogonal,
              &Matrix4Test::scalingPart,
              &Matrix4Test::rotationScalingPartNegative,
              &Matrix4Test::uniformScalingPart,
              &Matrix4Test::uniformScalingPartNotUniform,
              &Matrix4Test::normalMatrixPart,
              &Matrix4Test::vectorParts,
              &Matrix4Test::invertedRigid,
              &Matrix4Test::invertedRigidNotRigid,
              &Matrix4Test::transform,
              &Matrix4Test::transformProjection,

              &Matrix4Test::strictWeakOrdering,

              &Matrix4Test::debug});
}

using namespace Literals;

void Matrix4Test::construct() {
    constexpr Matrix4 a = {{3.0f,  5.0f, 8.0f, -3.0f},
                           {4.5f,  4.0f, 7.0f,  2.0f},
                           {1.0f,  2.0f, 3.0f, -1.0f},
                           {7.9f, -1.0f, 8.0f, -1.5f}};
    CORRADE_COMPARE(a, Matrix4({3.0f,  5.0f, 8.0f, -3.0f},
                               {4.5f,  4.0f, 7.0f,  2.0f},
                               {1.0f,  2.0f, 3.0f, -1.0f},
                               {7.9f, -1.0f, 8.0f, -1.5f}));

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix4, Vector4, Vector4, Vector4, Vector4>::value));
}

void Matrix4Test::constructIdentity() {
    constexpr Matrix4 identity;
    constexpr Matrix4 identity2{IdentityInit};
    constexpr Matrix4 identity3{IdentityInit, 4.0f};

    Matrix4 identityExpected({1.0f, 0.0f, 0.0f, 0.0f},
                             {0.0f, 1.0f, 0.0f, 0.0f},
                             {0.0f, 0.0f, 1.0f, 0.0f},
                             {0.0f, 0.0f, 0.0f, 1.0f});

    Matrix4 identity3Expected({4.0f, 0.0f, 0.0f, 0.0f},
                              {0.0f, 4.0f, 0.0f, 0.0f},
                              {0.0f, 0.0f, 4.0f, 0.0f},
                              {0.0f, 0.0f, 0.0f, 4.0f});

    CORRADE_COMPARE(identity, identityExpected);
    CORRADE_COMPARE(identity2, identityExpected);
    CORRADE_COMPARE(identity3, identity3Expected);

    CORRADE_VERIFY(std::is_nothrow_default_constructible<Matrix4>::value);
    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix4, IdentityInitT>::value));

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<IdentityInitT, Matrix4>::value));
}

void Matrix4Test::constructZero() {
    constexpr Matrix4 a{ZeroInit};
    CORRADE_COMPARE(a, Matrix4({0.0f, 0.0f, 0.0f, 0.0f},
                               {0.0f, 0.0f, 0.0f, 0.0f},
                               {0.0f, 0.0f, 0.0f, 0.0f},
                               {0.0f, 0.0f, 0.0f, 0.0f}));

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix4, ZeroInitT>::value));

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<ZeroInitT, Matrix4>::value));
}

void Matrix4Test::constructNoInit() {
    Matrix4 a = {{3.0f,  5.0f, 8.0f, -3.0f},
                 {4.5f,  4.0f, 7.0f,  2.0f},
                 {1.0f,  2.0f, 3.0f, -1.0f},
                 {7.9f, -1.0f, 8.0f, -1.5f}};
    new(&a) Matrix4{Magnum::NoInit};
    {
        #if defined(__GNUC__) && __GNUC__*100 + __GNUC_MINOR__ >= 601 && __OPTIMIZE__
        CORRADE_EXPECT_FAIL("GCC 6.1+ misoptimizes and overwrites the value.");
        #endif
        CORRADE_COMPARE(a, Matrix4({3.0f,  5.0f, 8.0f, -3.0f},
                                   {4.5f,  4.0f, 7.0f,  2.0f},
                                   {1.0f,  2.0f, 3.0f, -1.0f},
                                   {7.9f, -1.0f, 8.0f, -1.5f}));
    }

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix4, Magnum::NoInitT>::value));

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Magnum::NoInitT, Matrix4>::value));
}

void Matrix4Test::constructOneValue() {
    constexpr Matrix4 a{1.5f};
    CORRADE_COMPARE(a, (Matrix4{{1.5f, 1.5f, 1.5f, 1.5f},
                                {1.5f, 1.5f, 1.5f, 1.5f},
                                {1.5f, 1.5f, 1.5f, 1.5f},
                                {1.5f, 1.5f, 1.5f, 1.5f}}));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Float, Matrix4>::value));

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix4, Float>::value));
}

void Matrix4Test::constructConversion() {
    constexpr Matrix4 a({3.0f,  5.0f, 8.0f, -3.0f},
                        {4.5f,  4.0f, 7.0f,  2.0f},
                        {1.0f,  2.0f, 3.0f, -1.0f},
                        {7.9f, -1.0f, 8.0f, -1.5f});
    constexpr Matrix4i b(a);
    CORRADE_COMPARE(b, Matrix4i({3,  5, 8, -3},
                                {4,  4, 7,  2},
                                {1,  2, 3, -1},
                                {7, -1, 8, -1}));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Matrix4, Matrix4i>::value));

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix4, Matrix4i>::value));
}

void Matrix4Test::constructFromDifferentSize() {
    constexpr Matrix4 a{{3.0f,  5.0f, 8.0f, -3.0f},
                        {4.5f,  4.0f, 7.0f,  2.0f},
                        {1.0f,  2.0f, 3.0f, -1.0f},
                        {7.9f, -1.0f, 8.0f, -1.5f}};
    constexpr Matrix2x2 b{Vector2{3.0f,  5.0f},
                          Vector2{4.5f,  4.0f}};
    constexpr Matrix4 c{{3.0f, 5.0f, 0.0f, 0.0f},
                        {4.5f, 4.0f, 0.0f, 0.0f},
                        {0.0f, 0.0f, 1.0f, 0.0f},
                        {0.0f, 0.0f, 0.0f, 1.0f}};

    constexpr Matrix4 larger{b};
    CORRADE_COMPARE(larger, c);
    CORRADE_COMPARE(Matrix4{b}, c);

    constexpr Matrix2x2 smaller{a};
    CORRADE_COMPARE(smaller, b);
    CORRADE_COMPARE(Matrix2x2{a}, b);
}

void Matrix4Test::constructCopy() {
    constexpr Matrix<4, Float> a(Vector<4, Float>(3.0f,  5.0f, 8.0f, -3.0f),
                                 Vector<4, Float>(4.5f,  4.0f, 7.0f,  2.0f),
                                 Vector<4, Float>(1.0f,  2.0f, 3.0f, -1.0f),
                                 Vector<4, Float>(7.9f, -1.0f, 8.0f, -1.5f));
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Why can't be copy constexpr? */
    constexpr
    #endif
    Matrix4 b(a);
    CORRADE_COMPARE(b, Matrix4({3.0f,  5.0f, 8.0f, -3.0f},
                               {4.5f,  4.0f, 7.0f,  2.0f},
                               {1.0f,  2.0f, 3.0f, -1.0f},
                               {7.9f, -1.0f, 8.0f, -1.5f}));

    CORRADE_VERIFY(std::is_nothrow_copy_constructible<Matrix4>::value);
    CORRADE_VERIFY(std::is_nothrow_copy_assignable<Matrix4>::value);
}

void Matrix4Test::convert() {
    constexpr Mat4 a{{3.0f,  5.0f, 8.0f, -3.0f,
                      4.5f,  4.0f, 7.0f,  2.0f,
                      1.0f,  2.0f, 3.0f, -1.0f,
                      7.9f, -1.0f, 8.0f, -1.5f}};
    constexpr Matrix4 b({3.0f,  5.0f, 8.0f, -3.0f},
                        {4.5f,  4.0f, 7.0f,  2.0f},
                        {1.0f,  2.0f, 3.0f, -1.0f},
                        {7.9f, -1.0f, 8.0f, -1.5f});

    constexpr Matrix4 c(b);
    CORRADE_COMPARE(c, b);

    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Why can't be conversion constexpr? */
    constexpr
    #endif
    Mat4 d(b);
    for(std::size_t i = 0; i != 16; ++i)
        CORRADE_COMPARE(d.a[i], a.a[i]);

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Mat4, Matrix4>::value));
    CORRADE_VERIFY(!(std::is_convertible<Matrix4, Mat4>::value));
}

void Matrix4Test::isRigidTransformation() {
    CORRADE_VERIFY(!Matrix4({1.0f, 0.0f, 0.0f, 0.0f},
                            {0.0f, 1.0f, 0.0f, 0.0f},
                            {0.0f, 0.1f, 1.0f, 0.0f},
                            {5.0f, 4.0f, 0.5f, 1.0f}).isRigidTransformation());
    CORRADE_VERIFY(!Matrix4({1.0f, 0.0f, 0.0f, 0.0f},
                            {0.1f, 1.0f, 0.0f, 0.0f},
                            {0.0f, 0.0f, 1.0f, 1.0f},
                            {5.0f, 4.0f, 0.5f, 0.0f}).isRigidTransformation());
    CORRADE_VERIFY(Matrix4({1.0f, 0.0f, 0.0f, 0.0f},
                           {0.0f, 1.0f, 0.0f, 0.0f},
                           {0.0f, 0.0f, 1.0f, 0.0f},
                           {5.0f, 4.0f, 0.5f, 1.0f}).isRigidTransformation());
}

void Matrix4Test::translation() {
    constexpr Matrix4 a = Matrix4::translation({3.0f, 1.0f, 2.0f});
    CORRADE_COMPARE(a, Matrix4({1.0f, 0.0f, 0.0f, 0.0f},
                               {0.0f, 1.0f, 0.0f, 0.0f},
                               {0.0f, 0.0f, 1.0f, 0.0f},
                               {3.0f, 1.0f, 2.0f, 1.0f}));
}

void Matrix4Test::scaling() {
    constexpr Matrix4 a = Matrix4::scaling({3.0f, 1.5f, 2.0f});
    CORRADE_COMPARE(a, Matrix4({3.0f, 0.0f, 0.0f, 0.0f},
                               {0.0f, 1.5f, 0.0f, 0.0f},
                               {0.0f, 0.0f, 2.0f, 0.0f},
                               {0.0f, 0.0f, 0.0f, 1.0f}));
}

void Matrix4Test::rotation() {
    Matrix4 matrix({ 0.35612202f, -0.80181062f, 0.47987163f, 0.0f},
                   { 0.47987163f,  0.59757626f,  0.6423596f, 0.0f},
                   {-0.80181062f,  0.00151846f, 0.59757626f, 0.0f},
                   {        0.0f,         0.0f,        0.0f, 1.0f});
    CORRADE_COMPARE(Matrix4::rotation(Deg(-74.0f), Vector3(-1.0f, 2.0f, 2.0f).normalized()), matrix);
}

void Matrix4Test::rotationNotNormalized() {
    #ifdef CORRADE_NO_ASSERT
    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
    #endif

    std::ostringstream out;
    Error redirectError{&out};

    Matrix4::rotation(Deg(-74.0f), {-1.0f, 2.0f, 2.0f});
    CORRADE_COMPARE(out.str(), "Math::Matrix4::rotation(): axis Vector(-1, 2, 2) is not normalized\n");
}

void Matrix4Test::rotationX() {
    Matrix4 matrix({1.0f,         0.0f,        0.0f, 0.0f},
                   {0.0f,  0.90096887f, 0.43388374f, 0.0f},
                   {0.0f, -0.43388374f, 0.90096887f, 0.0f},
                   {0.0f,         0.0f,        0.0f, 1.0f});
    CORRADE_COMPARE(Matrix4::rotation(Rad(Constants::pi()/7), Vector3::xAxis()), matrix);
    CORRADE_COMPARE(Matrix4::rotationX(Rad(Constants::pi()/7)), matrix);
}

void Matrix4Test::rotationY() {
    Matrix4 matrix({0.90096887f, 0.0f, -0.43388374f, 0.0f},
                   {       0.0f, 1.0f,         0.0f, 0.0f},
                   {0.43388374f, 0.0f,  0.90096887f, 0.0f},
                   {       0.0f, 0.0f,         0.0f, 1.0f});
    CORRADE_COMPARE(Matrix4::rotation(Rad(Constants::pi()/7), Vector3::yAxis()), matrix);
    CORRADE_COMPARE(Matrix4::rotationY(Rad(Constants::pi()/7)), matrix);
}

void Matrix4Test::rotationZ() {
    Matrix4 matrix({ 0.90096887f, 0.43388374f, 0.0f, 0.0f},
                   {-0.43388374f, 0.90096887f, 0.0f, 0.0f},
                   {        0.0f,        0.0f, 1.0f, 0.0f},
                   {        0.0f,        0.0f, 0.0f, 1.0f});
    CORRADE_COMPARE(Matrix4::rotation(Rad(Constants::pi()/7), Vector3::zAxis()), matrix);
    CORRADE_COMPARE(Matrix4::rotationZ(Rad(Constants::pi()/7)), matrix);
}

void Matrix4Test::reflection() {
    Vector3 normal(-1.0f, 2.0f, 2.0f);
    Matrix4 actual = Matrix4::reflection(normal.normalized());
    Matrix4 expected({0.777778f,  0.444444f,  0.444444f, 0.0f},
                     {0.444444f,  0.111111f, -0.888889f, 0.0f},
                     {0.444444f, -0.888889f,  0.111111f, 0.0f},
                     {     0.0f,       0.0f,       0.0f, 1.0f});

    CORRADE_COMPARE(actual*actual, Matrix4());
    CORRADE_COMPARE(actual.transformVector(normal), -normal);
    CORRADE_COMPARE(actual, expected);
}

void Matrix4Test::reflectionNotNormalized() {
    #ifdef CORRADE_NO_ASSERT
    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
    #endif

    std::ostringstream out;
    Error redirectError{&out};

    Matrix4::reflection({-1.0f, 2.0f, 2.0f});
    CORRADE_COMPARE(out.str(), "Math::Matrix4::reflection(): normal Vector(-1, 2, 2) is not normalized\n");
}

void Matrix4Test::reflectionIsScaling() {
    CORRADE_COMPARE(Matrix4::reflection(Vector3::yAxis()), Matrix4::scaling(Vector3::yScale(-1.0f)));
}

void Matrix4Test::shearingXY() {
    constexpr Matrix4 a = Matrix4::shearingXY(3.0f, -5.0f);
    CORRADE_COMPARE(a, Matrix4({1.0f,  0.0f, 0.0f, 0.0f},
                               {0.0f,  1.0f, 0.0f, 0.0f},
                               {3.0f, -5.0f, 1.0f, 0.0f},
                               {0.0f,  0.0f, 0.0f, 1.0f}));
    CORRADE_COMPARE(a.transformPoint(Vector3(1.0f)), Vector3(4.0f, -4.0f, 1.0f));
}

void Matrix4Test::shearingXZ() {
    constexpr Matrix4 a = Matrix4::shearingXZ(3.0f, -5.0f);
    CORRADE_COMPARE(a, Matrix4({1.0f, 0.0f,  0.0f, 0.0f},
                               {3.0f, 1.0f, -5.0f, 0.0f},
                               {0.0f, 0.0f,  1.0f, 0.0f},
                               {0.0f, 0.0f,  0.0f, 1.0f}));
    CORRADE_COMPARE(a.transformPoint(Vector3(1.0f)), Vector3(4.0f, 1.0f, -4.0f));
}

void Matrix4Test::shearingYZ() {
    constexpr Matrix4 a = Matrix4::shearingYZ(3.0f, -5.0f);
    CORRADE_COMPARE(a, Matrix4({1.0f, 3.0f, -5.0f, 0.0f},
                               {0.0f, 1.0f,  0.0f, 0.0f},
                               {0.0f, 0.0f,  1.0f, 0.0f},
                               {0.0f, 0.0f,  0.0f, 1.0f}));
    CORRADE_COMPARE(a.transformPoint(Vector3(1.0f)), Vector3(1.0f, 4.0f, -4.0f));
}

void Matrix4Test::orthographicProjection() {
    Matrix4 expected({0.4f, 0.0f,   0.0f, 0.0f},
                     {0.0f, 0.5f,   0.0f, 0.0f},
                     {0.0f, 0.0f, -0.25f, 0.0f},
                     {0.0f, 0.0f, -1.25f, 1.0f});
    Matrix4 actual = Matrix4::orthographicProjection({5.0f, 4.0f}, 1.0f, 9.0f);
    CORRADE_COMPARE(actual, expected);

    /* NDC is left-handed, so point on near plane should be -1, far +1 */
    CORRADE_COMPARE(actual.transformPoint({0.0f, 0.0f, -1.0f}), Vector3(0.0f, 0.0f, -1.0f));
    CORRADE_COMPARE(actual.transformPoint({0.0f, 0.0f, -9.0f}), Vector3(0.0f, 0.0f, +1.0f));
}

void Matrix4Test::perspectiveProjection() {
    Matrix4 expected({4.0f,      0.0f,         0.0f,  0.0f},
                     {0.0f, 7.111111f,         0.0f,  0.0f},
                     {0.0f,      0.0f,  -1.9411764f, -1.0f},
                     {0.0f,      0.0f, -94.1176452f,  0.0f});
    Matrix4 actual = Matrix4::perspectiveProjection({16.0f, 9.0f}, 32.0f, 100.0f);
    CORRADE_COMPARE(actual, expected);

    /* NDC is left-handed, so point on near plane should be -1, far +1 */
    CORRADE_COMPARE(actual.transformPoint({0.0f, 0.0f, -32.0f}), Vector3(0.0f, 0.0f, -1.0f));
    CORRADE_COMPARE(actual.transformPoint({0.0f, 0.0f, -100.0f}), Vector3(0.0f, 0.0f, +1.0f));

    /* The version with bottom/left/top/right should give the same result if
       it's centered */
    CORRADE_COMPARE(Matrix4::perspectiveProjection({-8.0f, -4.5f}, {8.0f, 4.5f}, 32.0f, 100.0f), expected);
}

void Matrix4Test::perspectiveProjectionInfiniteFar() {
    Matrix4 expected({4.0f,      0.0f,   0.0f,  0.0f},
                     {0.0f, 7.111111f,   0.0f,  0.0f},
                     {0.0f,      0.0f,  -1.0f, -1.0f},
                     {0.0f,      0.0f, -64.0f,  0.0f});
    Matrix4 actual = Matrix4::perspectiveProjection({16.0f, 9.0f}, 32.0f, Constants::inf());
    CORRADE_COMPARE(actual, expected);

    /* NDC is left-handed, so point on near plane should be -1 and a *vector*
       in direction of far plane +1 */
    CORRADE_COMPARE(actual.transformPoint({0.0f, 0.0f, -32.0f}), Vector3(0.0f, 0.0f, -1.0f));
    CORRADE_COMPARE(actual.transformVector({0.0f, 0.0f, -1.0f}), Vector3(0.0f, 0.0f, +1.0f));

    /* The version with bottom/left/top/right should give the same result if
       it's centered */
    CORRADE_COMPARE(Matrix4::perspectiveProjection({-8.0f, -4.5f}, {8.0f, 4.5f}, 32.0f, Constants::inf()), expected);
}

void Matrix4Test::perspectiveProjectionFov() {
    Matrix4 expected({4.1652994f,      0.0f,         0.0f,  0.0f},
                     {      0.0f, 9.788454f,         0.0f,  0.0f},
                     {      0.0f,      0.0f,  -1.9411764f, -1.0f},
                     {      0.0f,      0.0f, -94.1176452f,  0.0f});
    CORRADE_COMPARE(Matrix4::perspectiveProjection(Deg(27.0f), 2.35f, 32.0f, 100.0f), expected);
}

void Matrix4Test::perspectiveProjectionFovInfiniteFar() {
    Matrix4 expected({4.1652994f,      0.0f,   0.0f,  0.0f},
                     {      0.0f, 9.788454f,   0.0f,  0.0f},
                     {      0.0f,      0.0f,  -1.0f, -1.0f},
                     {      0.0f,      0.0f, -64.0f,  0.0f});
    CORRADE_COMPARE(Matrix4::perspectiveProjection(Deg(27.0f), 2.35f, 32.0f, Constants::inf()), expected);
}

void Matrix4Test::perspectiveProjectionOffCenter() {
    Matrix4 expected({   4.0f,        0.0f,         0.0f,  0.0f},
                     {   0.0f,   7.111111f,         0.0f,  0.0f},
                     {-0.125f, -0.1111111f,  -1.9411764f, -1.0f},
                     {   0.0f,        0.0f, -94.1176452f,  0.0f});
    /* Shifted by (-1, -0.5) compared to the perspectiveProjection() test */
    Matrix4 actual = Matrix4::perspectiveProjection({-9.0f, -5.0f}, {7.0f, 4.0f}, 32.0f, 100.0f);
    CORRADE_COMPARE(actual, expected);

    /* NDC is left-handed, so point on the near plane top right corner should
       be (1, 1, -1), and a point in the center on the far plane roughly (0, 0,
       +1) due to the "off-centerness" */
    CORRADE_COMPARE(actual.transformPoint({7.0f, 4.0f, -32.0f}), Vector3(1.0f, 1.0f, -1.0f));
    CORRADE_COMPARE(actual.transformPoint({0.0f, 0.0f, -100.0f}), Vector3(0.125f, 0.1111111f, +1.0f));
}

void Matrix4Test::perspectiveProjectionOffCenterInfiniteFar() {
    Matrix4 expected({   4.0f,        0.0f,   0.0f,  0.0f},
                     {   0.0f,   7.111111f,   0.0f,  0.0f},
                     {-0.125f, -0.1111111f,  -1.0f, -1.0f},
                     {   0.0f,        0.0f, -64.0f,  0.0f});
    /* Shifted by (-1, -0.5) compared to perspectiveProjectionInfiniteFar() */
    Matrix4 actual = Matrix4::perspectiveProjection({-9.0f, -5.0f}, {7.0f, 4.0f}, 32.0f, Constants::inf());
    CORRADE_COMPARE(actual, expected);

    /* NDC is left-handed, so point on the near plane bottom left corner should
       be (1, 1, -1) and a *vector* in the direction of the far plane roughly
       (0, 0, +1) due to the "off-centerness" */
    CORRADE_COMPARE(actual.transformPoint({-9.0f, -5.0f, -32.0f}), Vector3(-1.0f, -1.0f, -1.0f));
    CORRADE_COMPARE(actual.transformVector({0.0f, 0.0f, -1.0f}), Vector3(0.125f, 0.1111111f, +1.0f));
}

void Matrix4Test::lookAt() {
    Vector3 translation{5.3f, -8.9f, -10.0f};
    Vector3 target{19.0f, 29.3f, 0.0f};
    Matrix4 a = Matrix4::lookAt(translation, target, Vector3::xAxis());

    /* It's just a translation and rotation */
    CORRADE_VERIFY(a.isRigidTransformation());

    /* The matrix should translate to the position */
    CORRADE_COMPARE(a.translation(), translation);

    /* Forward vector should point in direction of the target */
    CORRADE_COMPARE(dot(-a.backward(), (target - translation).normalized()), 1.0f);

    /* Up vector should be in the same direction as X axis */
    CORRADE_COMPARE_AS(dot(Vector3::xAxis(), a.up()), 0.0f, Corrade::TestSuite::Compare::Greater);

    /* Just to be sure */
    CORRADE_COMPARE(a, Matrix4({     0.0f,  0.253247f,  -0.967402f, 0.0f},
                               {0.944754f, -0.317095f, -0.0830092f, 0.0f},
                               {-0.32778f, -0.913957f,  -0.239256f, 0.0f},
                               {     5.3f,      -8.9f,      -10.0f, 1.0f}));
}

void Matrix4Test::fromParts() {
    #ifndef CORRADE_MSVC2017_COMPATIBILITY
    constexpr Matrix3x3 rotationScaling(Vector3(3.0f,  5.0f, 8.0f),
                                        Vector3(4.0f,  4.0f, 7.0f),
                                        Vector3(7.0f, -1.0f, 8.0f));
    #else
    /* https://developercommunity.visualstudio.com/content/problem/259204/1572-regression-ice-in-constexpr-code-involving-de.html */
    constexpr Matrix3x3 rotationScaling{Vector<3, Float>{3.0f,  5.0f, 8.0f},
                                        Vector<3, Float>{4.0f,  4.0f, 7.0f},
                                        Vector<3, Float>{7.0f, -1.0f, 8.0f}};
    #endif
    constexpr Vector3 translation(9.0f, 4.0f, 5.0f);
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Matrix4 a = Matrix4::from(rotationScaling, translation);

    CORRADE_COMPARE(a, Matrix4({3.0f,  5.0f, 8.0f, 0.0f},
                               {4.0f,  4.0f, 7.0f, 0.0f},
                               {7.0f, -1.0f, 8.0f, 0.0f},
                               {9.0f,  4.0f, 5.0f, 1.0f}));
}

void Matrix4Test::rotationScalingPart() {
    constexpr Matrix4 a({3.0f,  5.0f, 8.0f, 4.0f},
                        {4.0f,  4.0f, 7.0f, 3.0f},
                        {7.0f, -1.0f, 8.0f, 0.0f},
                        {9.0f,  4.0f, 5.0f, 9.0f});
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Matrix3x3 b = a.rotationScaling();

    CORRADE_COMPARE(b, Matrix3x3(Vector3(3.0f, 5.0f, 8.0f),
                                 Vector3(4.0f, 4.0f, 7.0f),
                                 Vector3(7.0f, -1.0f, 8.0f)));
}

void Matrix4Test::rotationShearPart() {
    Matrix4 rotation = Matrix4::rotation(-74.0_degf, Vector3{-1.0f, 2.0f, 2.0f}.normalized());
    Matrix4 rotationScalingTranslation = rotation*
        Matrix4::scaling(Vector3::yScale(3.5f))*
        Matrix4::translation({2.0f, 5.0f, -3.0f});

    Matrix3x3 a = rotationScalingTranslation.rotationShear();
    CORRADE_COMPARE(a, rotation.rotationScaling());
    CORRADE_COMPARE(a, (Matrix3x3{
        Vector3{ 0.35612206f, -0.80181074f, 0.47987169f},
        Vector3{ 0.47987163f,  0.59757626f, 0.64235962f},
        Vector3{-0.80181062f,  0.00151846f, 0.59757626f}}));
}

void Matrix4Test::rotationPart() {
    Matrix4 rotation = Matrix4::rotation(-74.0_degf, Vector3{-1.0f, 2.0f, 2.0f}.normalized());
    Matrix3x3 expectedRotationPart{
        Vector3( 0.35612206f, -0.80181074f, 0.47987169f),
        Vector3( 0.47987163f,  0.59757626f, 0.64235962f),
        Vector3(-0.80181062f,  0.00151846f, 0.59757626f)};

    /* For rotation and translation this is the same as rotationScaling() */
    Matrix4 rotationTranslation = rotation*
        Matrix4::translation({2.0f, 5.0f, -3.0f});
    Matrix3x3 rotationTranslationPart = rotationTranslation.rotation();
    CORRADE_COMPARE(rotationTranslationPart, rotationTranslation.rotationScaling());
    CORRADE_COMPARE(rotationTranslationPart, expectedRotationPart);

    /* Uniform scaling */
    Matrix4 rotationUniformScalingTranslation = rotation*
        Matrix4::scaling(Vector3(3.0f))*
        Matrix4::translation({2.0f, 5.0f, -3.0f});
    Matrix3x3 rotationUniformScalingPart = rotationUniformScalingTranslation.rotation();
    CORRADE_COMPARE(rotationUniformScalingPart.determinant(), 1.0f);
    CORRADE_COMPARE(rotationUniformScalingPart*rotationUniformScalingPart.transposed(), Matrix3x3());
    CORRADE_COMPARE(rotationUniformScalingPart, expectedRotationPart);

    /* Non-uniform scaling */
    Matrix4 rotationScalingTranslation = rotation*
        Matrix4::scaling(Vector3::yScale(3.5f))*
        Matrix4::translation({2.0f, 5.0f, -3.0f});
    Matrix3x3 rotationScalingPart = rotationScalingTranslation.rotation();
    CORRADE_COMPARE(rotationScalingPart.determinant(), 1.0f);
    CORRADE_COMPARE(rotationScalingPart*rotationScalingPart.transposed(), Matrix3x3());
    CORRADE_COMPARE(rotationScalingPart, expectedRotationPart);
}

void Matrix4Test::rotationPartNotOrthogonal() {
    #ifdef CORRADE_NO_ASSERT
    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
    #endif

    std::ostringstream out;
    Error redirectError{&out};

    /* Test both non-orthogonality and "unnormalizable" scaling */
    Matrix4::shearingXY(1.5f, 0.0f).rotation();
    Matrix4::scaling(Vector3::yScale(0.0f)).rotation();

    #if defined(CORRADE_TARGET_APPLE) || (defined(CORRADE_TARGET_WINDOWS) && defined(__MINGW32__)) || defined(CORRADE_TARGET_ANDROID)
    CORRADE_COMPARE(out.str(),
        "Math::Matrix4::rotation(): the normalized rotation part is not orthogonal:\n"
        "Matrix(1, 0, 0.83205,\n"
        "       0, 1, 0,\n"
        "       0, 0, 0.5547)\n"
        "Math::Matrix4::rotation(): the normalized rotation part is not orthogonal:\n"
        "Matrix(1, nan, 0,\n"
        "       0, nan, 0,\n"
        "       0, nan, 1)\n");
    #elif defined(CORRADE_TARGET_WINDOWS) && defined(_MSC_VER)
    CORRADE_COMPARE(out.str(),
        "Math::Matrix4::rotation(): the normalized rotation part is not orthogonal:\n"
        "Matrix(1, 0, 0.83205,\n"
        "       0, 1, 0,\n"
        "       0, 0, 0.5547)\n"
        "Math::Matrix4::rotation(): the normalized rotation part is not orthogonal:\n"
        "Matrix(1, -nan(ind), 0,\n"
        "       0, -nan(ind), 0,\n"
        "       0, -nan(ind), 1)\n");
    #else
    CORRADE_COMPARE(out.str(),
        "Math::Matrix4::rotation(): the normalized rotation part is not orthogonal:\n"
        "Matrix(1, 0, 0.83205,\n"
        "       0, 1, 0,\n"
        "       0, 0, 0.5547)\n"
        "Math::Matrix4::rotation(): the normalized rotation part is not orthogonal:\n"
        "Matrix(1, -nan, 0,\n"
        "       0, -nan, 0,\n"
        "       0, -nan, 1)\n");
    #endif
}

void Matrix4Test::rotationNormalizedPart() {
    Matrix4 a({ 0.35612214f,  -0.80181062f, 0.47987163f, 1.0f},
              { 0.47987163f,   0.59757638f,  0.6423595f, 3.0f},
              {-0.80181062f, 0.0015183985f, 0.59757638f, 4.0f},
              {        0.0f,          0.0f,        0.0f, 1.0f});
    CORRADE_COMPARE(a.rotationNormalized(),
        (Matrix3x3{Vector3{ 0.35612214f,  -0.80181062f, 0.47987163f},
                   Vector3{ 0.47987163f,   0.59757638f,  0.6423595f},
                   Vector3{-0.80181062f, 0.0015183985f, 0.59757638f}}));
}

void Matrix4Test::rotationNormalizedPartNotOrthogonal() {
    #ifdef CORRADE_NO_ASSERT
    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
    #endif

    std::ostringstream out;
    Error redirectError{&out};

    Matrix4 a({0.0f,  0.0f, 1.0f, 4.0f},
              {1.0f,  0.0f, 0.0f, 3.0f},
              {0.0f, -1.0f, 0.1f, 0.0f},
              {9.0f,  4.0f, 5.0f, 9.0f});
    a.rotationNormalized();
    CORRADE_COMPARE(out.str(),
        "Math::Matrix4::rotationNormalized(): the rotation part is not orthogonal:\n"
        "Matrix(0, 1, 0,\n"
        "       0, 0, -1,\n"
        "       1, 0, 0.1)\n");
}

void Matrix4Test::scalingPart() {
    Matrix4 translationRotationScaling =
        Matrix4::translation({2.0f, 5.0f, -3.0f})*
        Matrix4::rotation(-74.0_degf, Vector3(-1.0f, 2.0f, 2.0f).normalized())*
        Matrix4::scaling({0.5f, 3.5f, 1.2f});

    CORRADE_COMPARE(translationRotationScaling.scaling(), (Vector3{0.5f, 3.5f, 1.2f}));
    CORRADE_COMPARE(translationRotationScaling.scalingSquared(), (Vector3{0.25f, 12.25f, 1.44f}));
}

void Matrix4Test::rotationScalingPartNegative() {
    /* Large angle */
    Matrix4 largeAngle =
        Matrix4::rotationY(215.0_degf)*
        Matrix4::scaling({0.5f, 3.5f, 1.2f});
    CORRADE_COMPARE(Matrix4::from(largeAngle.rotation(), {}),
        Matrix4::rotationY(215.0_degf));
    CORRADE_COMPARE(largeAngle.scaling(), (Vector3{0.5f, 3.5f, 1.2f}));
    /* The parts should combine back to the same matrix */
    CORRADE_COMPARE(
        Matrix4::from(largeAngle.rotation(), {})*
        Matrix4::scaling(largeAngle.scaling()),
        largeAngle);

    /* The sign gets contained in the rotation */
    Matrix4 negativeScaling =
        Matrix4::rotationY(15.0_degf)*
        Matrix4::scaling({0.5f, -3.5f, 1.2f});
    CORRADE_COMPARE(Matrix4::from(negativeScaling.rotation(), {}),
        Matrix4::rotationY(15.0_degf)*
        Matrix4::scaling(Vector3::yScale(-1)));
    CORRADE_COMPARE(negativeScaling.scaling(), (Vector3{0.5f, 3.5f, 1.2f}));
    /* The parts should combine back to the same matrix */
    CORRADE_COMPARE(
        Matrix4::from(negativeScaling.rotation(), {})*
        Matrix4::scaling(negativeScaling.scaling()),
        negativeScaling);
}

void Matrix4Test::uniformScalingPart() {
    const Matrix4 rotation = Matrix4::rotation(-74.0_degf, Vector3(-1.0f, 2.0f, 2.0f).normalized());

    CORRADE_COMPARE((rotation*Matrix4::scaling(Vector3(3.0f))).uniformScaling(), 3.0f);
}

void Matrix4Test::uniformScalingPartNotUniform() {
    #ifdef CORRADE_NO_ASSERT
    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
    #endif

    std::ostringstream out;
    Error redirectError{&out}; Matrix4::scaling(Vector3::yScale(3.0f)).uniformScaling();
    CORRADE_COMPARE(out.str(), "Math::Matrix4::uniformScaling(): the matrix doesn't have uniform scaling:\n"
        "Matrix(1, 0, 0,\n"
        "       0, 3, 0,\n"
        "       0, 0, 1)\n");
}

namespace {

/* FFS. https://gcc.gnu.org/bugzilla/show_bug.cgi?id=60491 */
#ifdef minor
#undef minor
#endif

/* From https://github.com/graphitemaster/normals_revisited#sample-code */
float minor(const float* m, int r0, int r1, int r2, int c0, int c1, int c2) {
  return m[4*r0+c0] * (m[4*r1+c1] * m[4*r2+c2] - m[4*r2+c1] * m[4*r1+c2]) -
         m[4*r0+c1] * (m[4*r1+c0] * m[4*r2+c2] - m[4*r2+c0] * m[4*r1+c2]) +
         m[4*r0+c2] * (m[4*r1+c0] * m[4*r2+c1] - m[4*r2+c0] * m[4*r1+c1]);
}

void cofactor(const float* src, float* dst) {
  dst[ 0] =  minor(src, 1, 2, 3, 1, 2, 3);
  dst[ 1] = -minor(src, 1, 2, 3, 0, 2, 3);
  dst[ 2] =  minor(src, 1, 2, 3, 0, 1, 3);
  dst[ 3] = -minor(src, 1, 2, 3, 0, 1, 2);
  dst[ 4] = -minor(src, 0, 2, 3, 1, 2, 3);
  dst[ 5] =  minor(src, 0, 2, 3, 0, 2, 3);
  dst[ 6] = -minor(src, 0, 2, 3, 0, 1, 3);
  dst[ 7] =  minor(src, 0, 2, 3, 0, 1, 2);
  dst[ 8] =  minor(src, 0, 1, 3, 1, 2, 3);
  dst[ 9] = -minor(src, 0, 1, 3, 0, 2, 3);
  dst[10] =  minor(src, 0, 1, 3, 0, 1, 3);
  dst[11] = -minor(src, 0, 1, 3, 0, 1, 2);
  dst[12] = -minor(src, 0, 1, 2, 1, 2, 3);
  dst[13] =  minor(src, 0, 1, 2, 0, 2, 3);
  dst[14] = -minor(src, 0, 1, 2, 0, 1, 3);
  dst[15] =  minor(src, 0, 1, 2, 0, 1, 2);
}

Matrix4 cofactorGroundTruth(const Matrix4& src) {
    Matrix4 out;
    cofactor(src.data(), out.data());
    return out;
}

}

void Matrix4Test::normalMatrixPart() {
    /* Comparing normalized matrices -- we care only about orientation, not
       scaling as that's renormalized in the shader anyway */
    auto unit = [](const Matrix3x3& a) {
        return Matrix3x3{a[0].normalized(),
                         a[1].normalized(),
                         a[2].normalized()};
    };

    /* For just a rotation, normalMatrix is the same as the upper-left part
       (and the same as the "classic" calculation) */
    auto a = Matrix4::rotationY(35.0_degf);
    CORRADE_COMPARE(a.normalMatrix(), a.rotationScaling());
    CORRADE_COMPARE(a.normalMatrix(), a.rotationScaling().inverted().transposed());
    /* It should be also the same result as the original code */
    CORRADE_COMPARE(a.normalMatrix(), cofactorGroundTruth(a).rotationScaling());

    /* For rotation + uniform scaling, normalMatrix is the same as the
       normalized upper-left part (and the same as the "classic" calculation) */
    auto b = Matrix4::rotationZ(35.0_degf)*Matrix4::scaling(Vector3{3.5f});
    CORRADE_COMPARE(unit(b.normalMatrix()), unit(b.rotation()));
    CORRADE_COMPARE(unit(b.normalMatrix()), unit(b.rotationScaling().inverted().transposed()));
    /* It should be also the same result as the original code */
    CORRADE_COMPARE(b.normalMatrix(), cofactorGroundTruth(b).rotationScaling());

    /* Rotation and non-uniform scaling (= shear) is the same as the
       "classic" calculation */
    auto c = Matrix4::rotationX(35.0_degf)*Matrix4::scaling({0.3f, 1.1f, 3.5f});
    CORRADE_COMPARE(unit(c.normalMatrix()), unit(c.rotationScaling().inverted().transposed()));
    /* It should be also the same result as the original code */
    CORRADE_COMPARE(c.normalMatrix(), cofactorGroundTruth(c).rotationScaling());

    /* Reflection (or scaling by -1) is not -- the "classic" way has the sign
       flipped */
    auto d = Matrix4::rotationZ(35.0_degf)*Matrix4::reflection(Vector3{1.0f/Constants::sqrt3()});
    CORRADE_COMPARE(-unit(d.normalMatrix()), unit(d.rotationScaling().inverted().transposed()));
    /* It should be also the same result as the original code */
    CORRADE_COMPARE(d.normalMatrix(), cofactorGroundTruth(d).rotationScaling());
}

void Matrix4Test::vectorParts() {
    constexpr Matrix4 a({-1.0f,  0.0f,  0.0f, 0.0f},
                        { 0.0f, 12.0f,  0.0f, 0.0f},
                        { 0.0f,  0.0f, 35.0f, 0.0f},
                        {-5.0f, 12.0f,  0.5f, 1.0f});
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Vector3 right = a.right();
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Vector3 up = a.up();
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Vector3 backward = a.backward();
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Vector3 translation = a.translation();

    CORRADE_COMPARE(right, Vector3::xAxis(-1.0f));
    CORRADE_COMPARE(up, Vector3::yAxis(12.0f));
    CORRADE_COMPARE(backward, Vector3::zAxis(35.0f));
    CORRADE_COMPARE(translation, Vector3(-5.0f, 12.0f, 0.5f));
}

void Matrix4Test::invertedRigid() {
    Matrix4 actual = Matrix4::rotation(Deg(-74.0f), Vector3(-1.0f, 0.5f, 2.0f).normalized())*
                     Matrix4::reflection(Vector3(0.5f, -2.0f, 2.0f).normalized())*
                     Matrix4::translation({1.0f, 2.0f, -3.0f});
    Matrix4 expected = Matrix4::translation({-1.0f, -2.0f, 3.0f})*
                       Matrix4::reflection(Vector3(0.5f, -2.0f, 2.0f).normalized())*
                       Matrix4::rotation(Deg(74.0f), Vector3(-1.0f, 0.5f, 2.0f).normalized());


    CORRADE_COMPARE(actual.invertedRigid(), expected);
    CORRADE_COMPARE(actual.invertedRigid(), actual.inverted());
}

void Matrix4Test::invertedRigidNotRigid() {
    #ifdef CORRADE_NO_ASSERT
    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
    #endif

    std::ostringstream out;
    Error redirectError{&out};

    (Matrix4::rotationX(-60.0_degf)*2.0f).invertedRigid();
    CORRADE_COMPARE(out.str(),
        "Math::Matrix4::invertedRigid(): the matrix doesn't represent a rigid transformation:\n"
        "Matrix(2, 0, 0, 0,\n"
        "       0, 1, 1.73205, 0,\n"
        "       0, -1.73205, 1, 0,\n"
        "       0, 0, 0, 2)\n");
}

void Matrix4Test::transform() {
    Matrix4 a = Matrix4::translation({1.0f, -5.0f, 3.5f})*Matrix4::rotation(Deg(90.0f), Vector3::zAxis());
    Vector3 v(1.0f, -2.0f, 5.5f);

    CORRADE_COMPARE(a.transformVector(v), Vector3(2.0f, 1.0f, 5.5f));
    CORRADE_COMPARE(a.transformPoint(v), Vector3(3.0f, -4.0f, 9.0f));
}

void Matrix4Test::transformProjection() {
    Matrix4 a = Matrix4::perspectiveProjection({2.0f, 2.0f}, 1.0f, 100.0f);
    Vector3 v{0.0f, 0.0f, -100.0f};

    CORRADE_COMPARE(a.transformPoint(v), Vector3(0.0f, 0.0f, 1.0f));
}

void Matrix4Test::strictWeakOrdering() {
    StrictWeakOrdering o;
    const Matrix4 a(Vector4{1.0f, 1.0f, 2.0f, 2.0f}, Vector4{5.0f, 5.0f, 6.0f, 5.0f}, Vector4{5.0f, 5.0f, 6.0f, 5.0f}, Vector4{3.0f, 1.0f, 2.0f, 4.0f});
    const Matrix4 b(Vector4{2.0f, 1.0f, 2.0f, 3.0f}, Vector4{5.0f, 5.0f, 6.0f, 5.0f}, Vector4{5.0f, 5.0f, 6.0f, 5.0f}, Vector4{4.0f, 1.0f, 2.0f, 5.0f});
    const Matrix4 c(Vector4{1.0f, 1.0f, 2.0f, 2.0f}, Vector4{5.0f, 5.0f, 6.0f, 5.0f}, Vector4{5.0f, 5.0f, 6.0f, 5.0f}, Vector4{3.0f, 1.0f, 2.0f, 5.0f});

    CORRADE_VERIFY( o(a, b));
    CORRADE_VERIFY(!o(b, a));
    CORRADE_VERIFY( o(a, c));
    CORRADE_VERIFY(!o(c, a));
    CORRADE_VERIFY( o(c, b));
    CORRADE_VERIFY(!o(b, c));

    CORRADE_VERIFY(!o(a, a));
}

void Matrix4Test::debug() {
    Matrix4 m({3.0f,  5.0f, 8.0f, 4.0f},
              {4.0f,  4.0f, 7.0f, 3.0f},
              {7.0f, -1.0f, 8.0f, 0.0f},
              {9.0f,  4.0f, 5.0f, 9.0f});

    std::ostringstream o;
    Debug(&o) << m;
    CORRADE_COMPARE(o.str(), "Matrix(3, 4, 7, 9,\n"
                             "       5, 4, -1, 4,\n"
                             "       8, 7, 8, 5,\n"
                             "       4, 3, 0, 9)\n");
}

}}}}

CORRADE_TEST_MAIN(Magnum::Math::Test::Matrix4Test)