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

/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018
              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/Configuration.h>

#include "Magnum/Math/Matrix4.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 {

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

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

    void isRigidTransformation();

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

    void fromParts();
    void rotationScalingPart();
    void rotationNormalizedPart();
    void rotationPart();
    void uniformScalingPart();
    void vectorParts();
    void invertedRigid();
    void transform();
    void transformProjection();

    void debug();
    void configuration();
};

typedef Math::Deg<Float> Deg;
typedef Math::Rad<Float> Rad;
typedef Math::Matrix4<Float> Matrix4;
typedef Math::Matrix4<Int> Matrix4i;
typedef Math::Matrix<3, Float> Matrix3x3;
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::constructCopy,
              &Matrix4Test::convert,

              &Matrix4Test::isRigidTransformation,

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

              &Matrix4Test::fromParts,
              &Matrix4Test::rotationScalingPart,
              &Matrix4Test::rotationNormalizedPart,
              &Matrix4Test::rotationPart,
              &Matrix4Test::uniformScalingPart,
              &Matrix4Test::vectorParts,
              &Matrix4Test::invertedRigid,
              &Matrix4Test::transform,
              &Matrix4Test::transformProjection,

              &Matrix4Test::debug,
              &Matrix4Test::configuration});
}

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));
}

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));
}

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{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, NoInitT>::value));

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<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::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() {
    std::ostringstream o;
    Error redirectError{&o};

    CORRADE_COMPARE(Matrix4::rotation(Deg(-74.0f), {-1.0f, 2.0f, 2.0f}), Matrix4());
    CORRADE_COMPARE(o.str(), "Math::Matrix4::rotation(): axis must be normalized\n");

    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::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() {
    std::ostringstream o;
    Error redirectError{&o};

    Vector3 normal(-1.0f, 2.0f, 2.0f);

    CORRADE_COMPARE(Matrix4::reflection(normal), Matrix4());
    CORRADE_COMPARE(o.str(), "Math::Matrix4::reflection(): normal must be normalized\n");

    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::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));
}

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));
}

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::fromParts() {
    constexpr Matrix3x3 rotationScaling(Vector3(3.0f,  5.0f, 8.0f),
                                        Vector3(4.0f,  4.0f, 7.0f),
                                        Vector3(7.0f, -1.0f, 8.0f));
    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::rotationNormalizedPart() {
    std::ostringstream o;
    Error redirectError{&o};

    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(o.str(), "Math::Matrix4::rotationNormalized(): the rotation part is not normalized\n");

    Matrix4 b({ 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(b.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::rotationPart() {
    Matrix4 rotation = Matrix4::rotation(Deg(-74.0f), 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);

    /* Test uniform scaling */
    Matrix4 rotationScaling = rotation*Matrix4::scaling(Vector3(3.0f));
    Matrix3x3 rotationScalingPart = rotationScaling.rotation();
    CORRADE_COMPARE(rotationScalingPart.determinant(), 1.0f);
    CORRADE_COMPARE(rotationScalingPart*rotationScalingPart.transposed(), Matrix3x3());
    CORRADE_COMPARE(rotationScalingPart, expectedRotationPart);

    /* Fails on non-uniform scaling */
    std::ostringstream o;
    Error redirectError{&o};
    Matrix3x3 rotationScaling2 = (rotation*Matrix4::scaling(Vector3::yScale(3.5f))).rotation();
    CORRADE_COMPARE(o.str(), "Math::Matrix4::rotation(): the matrix doesn't have uniform scaling\n");
    CORRADE_COMPARE(rotationScaling2, Matrix3x3());
}

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

    /* Test uniform scaling */
    CORRADE_COMPARE((rotation*Matrix4::scaling(Vector3(3.0f))).uniformScaling(), 3.0f);

    /* Fails on non-uniform scaling */
    std::ostringstream o;
    Error redirectError{&o};
    const Float nonUniformScaling = (rotation*Matrix4::scaling(Vector3::yScale(3.0f))).uniformScaling();
    CORRADE_COMPARE(o.str(), "Math::Matrix4::uniformScaling(): the matrix doesn't have uniform scaling\n");
    CORRADE_COMPARE(nonUniformScaling, 0.0f);
}

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());

    std::ostringstream o;
    Error redirectError{&o};
    (2*actual).invertedRigid();
    CORRADE_COMPARE(o.str(), "Math::Matrix4::invertedRigid(): the matrix doesn't represent rigid transformation\n");

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

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::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::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");
}

void Matrix4Test::configuration() {
    Corrade::Utility::Configuration c;

    Matrix4 m({3.0f,  5.0f, 8.0f,   4.0f},
              {4.0f,  4.0f, 7.0f, 3.125f},
              {7.0f, -1.0f, 8.0f,   0.0f},
              {9.0f,  4.0f, 5.0f,  9.55f});
    std::string value("3 4 7 9 5 4 -1 4 8 7 8 5 4 3.125 0 9.55");

    c.setValue("matrix", m);
    CORRADE_COMPARE(c.value("matrix"), value);
    CORRADE_COMPARE(c.value<Matrix4>("matrix"), m);
}

}}}

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