magnum/src/Magnum/Math/Test/Matrix3Test.cpp

/*
    This file is part of Magnum.

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

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    the rights to use, copy, modify, merge, publish, distribute, sublicense,
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    Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included
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    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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*/

#include <sstream>
#include <Corrade/TestSuite/Tester.h>
#include <Corrade/Utility/Configuration.h>

#include "Magnum/Math/Matrix3.h"

struct Mat3 {
    float a[9];
};

namespace Magnum { namespace Math {

namespace Implementation {

template<> struct RectangularMatrixConverter<3, 3, float, Mat3> {
    constexpr static RectangularMatrix<3, 3, Float> from(const Mat3& other) {
        return RectangularMatrix<3, 3, Float>(
            Vector<3, Float>(other.a[0], other.a[1], other.a[2]),
            Vector<3, Float>(other.a[3], other.a[4], other.a[5]),
            Vector<3, Float>(other.a[6], other.a[7], other.a[8]));
    }

    constexpr static Mat3 to(const RectangularMatrix<3, 3, Float>& other) {
        return Mat3{{other[0][0], other[0][1], other[0][2],
                     other[1][0], other[1][1], other[1][2],
                     other[2][0], other[2][1], other[2][2]}};
    }
};

}

namespace Test {

struct Matrix3Test: Corrade::TestSuite::Tester {
    explicit Matrix3Test();

    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 reflection();
    void reflectionIsScaling();
    void shearingX();
    void shearingY();
    void projection();
    void fromParts();
    void rotationScalingPart();
    void rotationNormalizedPart();
    void rotationPart();
    void uniformScalingPart();
    void vectorParts();
    void invertedRigid();
    void transform();

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

typedef Math::Deg<Float> Deg;
typedef Math::Matrix3<Float> Matrix3;
typedef Math::Matrix3<Int> Matrix3i;
typedef Math::Matrix2x2<Float> Matrix2x2;
typedef Math::Vector3<Float> Vector3;
typedef Math::Vector2<Float> Vector2;

Matrix3Test::Matrix3Test() {
    addTests({&Matrix3Test::construct,
              &Matrix3Test::constructIdentity,
              &Matrix3Test::constructZero,
              &Matrix3Test::constructNoInit,
              &Matrix3Test::constructOneValue,
              &Matrix3Test::constructConversion,
              &Matrix3Test::constructCopy,
              &Matrix3Test::convert,

              &Matrix3Test::isRigidTransformation,

              &Matrix3Test::translation,
              &Matrix3Test::scaling,
              &Matrix3Test::rotation,
              &Matrix3Test::reflection,
              &Matrix3Test::reflectionIsScaling,
              &Matrix3Test::shearingX,
              &Matrix3Test::shearingY,
              &Matrix3Test::projection,
              &Matrix3Test::fromParts,
              &Matrix3Test::rotationScalingPart,
              &Matrix3Test::rotationNormalizedPart,
              &Matrix3Test::rotationPart,
              &Matrix3Test::uniformScalingPart,
              &Matrix3Test::vectorParts,
              &Matrix3Test::invertedRigid,
              &Matrix3Test::transform,

              &Matrix3Test::debug,
              &Matrix3Test::configuration});
}

void Matrix3Test::construct() {
    constexpr Matrix3 a = {{3.0f,  5.0f, 8.0f},
                           {4.5f,  4.0f, 7.0f},
                           {7.9f, -1.0f, 8.0f}};
    CORRADE_COMPARE(a, Matrix3({3.0f,  5.0f, 8.0f},
                               {4.5f,  4.0f, 7.0f},
                               {7.9f, -1.0f, 8.0f}));

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix3, Vector3, Vector3, Vector3>::value));
}

void Matrix3Test::constructIdentity() {
    constexpr Matrix3 identity;
    constexpr Matrix3 identity2{IdentityInit};
    constexpr Matrix3 identity3{IdentityInit, 4.0f};

    Matrix3 identityExpected({1.0f, 0.0f, 0.0f},
                             {0.0f, 1.0f, 0.0f},
                             {0.0f, 0.0f, 1.0f});

    Matrix3 identity3Expected({4.0f, 0.0f, 0.0f},
                              {0.0f, 4.0f, 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<Matrix3>::value);
    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix3, IdentityInitT>::value));
}

void Matrix3Test::constructZero() {
    constexpr Matrix3 a{ZeroInit};
    CORRADE_COMPARE(a, Matrix3({0.0f, 0.0f, 0.0f},
                               {0.0f, 0.0f, 0.0f},
                               {0.0f, 0.0f, 0.0f}));

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix3, ZeroInitT>::value));
}

void Matrix3Test::constructNoInit() {
    Matrix3 a{{3.0f,  5.0f, 8.0f},
              {4.5f,  4.0f, 7.0f},
              {7.9f, -1.0f, 8.0f}};
    new(&a) Matrix3{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, Matrix3({3.0f,  5.0f, 8.0f},
                                   {4.5f,  4.0f, 7.0f},
                                   {7.9f, -1.0f, 8.0f}));
    }

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix3, NoInitT>::value));

    /* Implicit construction is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<NoInitT, Matrix3>::value));
}

void Matrix3Test::constructOneValue() {
    constexpr Matrix3 a{1.5f};
    CORRADE_COMPARE(a, (Matrix3{Vector3{1.5f, 1.5f, 1.5f},
                                Vector3{1.5f, 1.5f, 1.5f},
                                Vector3{1.5f, 1.5f, 1.5f}}));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Float, Matrix3>::value));

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix3, Float>::value));
}

void Matrix3Test::constructConversion() {
    constexpr Matrix3 a({3.0f,  5.0f, 8.0f},
                        {4.5f,  4.0f, 7.0f},
                        {7.9f, -1.0f, 8.0f});
    constexpr Matrix3i b(a);
    CORRADE_COMPARE(b, Matrix3i({3,  5, 8},
                                {4,  4, 7},
                                {7, -1, 8}));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Matrix3, Matrix3i>::value));

    CORRADE_VERIFY((std::is_nothrow_constructible<Matrix3, Matrix3i>::value));
}

void Matrix3Test::constructCopy() {
    constexpr RectangularMatrix<3, 3, Float> a(Vector<3, Float>(3.0f,  5.0f, 8.0f),
                                               Vector<3, Float>(4.5f,  4.0f, 7.0f),
                                               Vector<3, Float>(7.9f, -1.0f, 8.0f));
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Why can't be copy constexpr? */
    constexpr
    #endif
    Matrix3 b(a);
    CORRADE_COMPARE(b, Matrix3({3.0f,  5.0f, 8.0f},
                               {4.5f,  4.0f, 7.0f},
                               {7.9f, -1.0f, 8.0f}));

    CORRADE_VERIFY(std::is_nothrow_copy_constructible<Matrix3>::value);
    CORRADE_VERIFY(std::is_nothrow_copy_assignable<Matrix3>::value);
}

void Matrix3Test::convert() {
    constexpr Mat3 a{{1.5f,  2.0f, -3.5f,
                      2.0f, -3.1f,  0.4f,
                      9.5f, -1.5f,  0.1f}};
    constexpr Matrix3 b(Vector3(1.5f, 2.0f, -3.5f),
                        Vector3(2.0f, -3.1f,  0.4f),
                        Vector3(9.5f, -1.5f,  0.1f));

    constexpr Matrix3 c(b);
    CORRADE_COMPARE(c, b);

    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Why can't be conversion constexpr? */
    constexpr
    #endif
    Mat3 d(b);
    for(std::size_t i = 0; i != 9; ++i)
        CORRADE_COMPARE(d.a[0], a.a[0]);

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Mat3, Matrix3>::value));
    CORRADE_VERIFY(!(std::is_convertible<Matrix3, Mat3>::value));
}

void Matrix3Test::isRigidTransformation() {
    CORRADE_VERIFY(!Matrix3({1.0f, 0.0f, 0.0f},
                            {0.1f, 1.0f, 0.0f},
                            {5.0f, 4.0f, 1.0f}).isRigidTransformation());
    CORRADE_VERIFY(!Matrix3({1.0f, 0.0f, 0.0f},
                            {0.0f, 1.0f, 1.0f},
                            {5.0f, 4.0f, 0.0f}).isRigidTransformation());
    CORRADE_VERIFY(Matrix3({1.0f, 0.0f, 0.0f},
                           {0.0f, 1.0f, 0.0f},
                           {5.0f, 4.0f, 1.0f}).isRigidTransformation());
}

void Matrix3Test::translation() {
    constexpr Matrix3 a = Matrix3::translation({3.0f, 1.0f});
    CORRADE_COMPARE(a, Matrix3({1.0f, 0.0f, 0.0f},
                               {0.0f, 1.0f, 0.0f},
                               {3.0f, 1.0f, 1.0f}));
}

void Matrix3Test::scaling() {
    constexpr Matrix3 a = Matrix3::scaling({3.0f, 1.5f});
    CORRADE_COMPARE(a, Matrix3({3.0f, 0.0f, 0.0f},
                               {0.0f, 1.5f, 0.0f},
                               {0.0f, 0.0f, 1.0f}));
}

void Matrix3Test::rotation() {
    Matrix3 matrix({ 0.965926f, 0.258819f, 0.0f},
                   {-0.258819f, 0.965926f, 0.0f},
                   {      0.0f,      0.0f, 1.0f});

    CORRADE_COMPARE(Matrix3::rotation(Deg(15.0f)), matrix);
}

void Matrix3Test::reflection() {
    std::ostringstream o;
    Error redirectError{&o};

    Vector2 normal(-1.0f, 2.0f);

    CORRADE_COMPARE(Matrix3::reflection(normal), Matrix3());
    CORRADE_COMPARE(o.str(), "Math::Matrix3::reflection(): normal must be normalized\n");

    Matrix3 actual = Matrix3::reflection(normal.normalized());
    Matrix3 expected({0.6f,  0.8f, 0.0f},
                     {0.8f, -0.6f, 0.0f},
                     {0.0f,  0.0f, 1.0f});

    CORRADE_COMPARE(actual*actual, Matrix3());
    CORRADE_COMPARE(actual.transformVector(normal), -normal);
    CORRADE_COMPARE(actual, expected);
}

void Matrix3Test::reflectionIsScaling() {
    CORRADE_COMPARE(Matrix3::reflection(Vector2::yAxis()), Matrix3::scaling(Vector2::yScale(-1.0f)));
}

void Matrix3Test::shearingX() {
    constexpr Matrix3 a = Matrix3::shearingX(3.0f);
    CORRADE_COMPARE(a, Matrix3({1.0f, 0.0f, 0.0f},
                               {3.0f, 1.0f, 0.0f},
                               {0.0f, 0.0f, 1.0f}));
    CORRADE_COMPARE(a.transformPoint(Vector2(1.0f)), Vector2(4.0f, 1.0f));
}

void Matrix3Test::shearingY() {
    constexpr Matrix3 a = Matrix3::shearingY(3.0f);
    CORRADE_COMPARE(a, Matrix3({1.0f, 3.0f, 0.0f},
                               {0.0f, 1.0f, 0.0f},
                               {0.0f, 0.0f, 1.0f}));
    CORRADE_COMPARE(a.transformPoint(Vector2(1.0f)), Vector2(1.0f, 4.0f));
}

void Matrix3Test::projection() {
    Matrix3 expected({2.0f/4.0f,      0.0f, 0.0f},
                     {     0.0f, 2.0f/3.0f, 0.0f},
                     {     0.0f,      0.0f, 1.0f});

    CORRADE_COMPARE(Matrix3::projection({4.0f, 3.0f}), expected);
}

void Matrix3Test::fromParts() {
    constexpr Matrix2x2 rotationScaling(Vector2(3.0f, 5.0f),
                                        Vector2(4.0f, 4.0f));
    constexpr Vector2 translation(7.0f, -1.0f);
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Matrix3 a = Matrix3::from(rotationScaling, translation);

    CORRADE_COMPARE(a, Matrix3({3.0f,  5.0f, 0.0f},
                               {4.0f,  4.0f, 0.0f},
                               {7.0f, -1.0f, 1.0f}));
}

void Matrix3Test::rotationScalingPart() {
    constexpr Matrix3 a({3.0f,  5.0f, 8.0f},
                        {4.0f,  4.0f, 7.0f},
                        {7.0f, -1.0f, 8.0f});
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Matrix2x2 b = a.rotationScaling();

    CORRADE_COMPARE(b, Matrix2x2(Vector2(3.0f, 5.0f),
                                 Vector2(4.0f, 4.0f)));
}

void Matrix3Test::rotationNormalizedPart() {
    std::ostringstream o;
    Error redirectError{&o};

    Matrix3 a({1.0f,  0.0f, 8.0f},
              {1.0f,  0.1f, 7.0f},
              {7.0f, -1.0f, 8.0f});
    a.rotationNormalized();

    CORRADE_COMPARE(o.str(), "Math::Matrix3::rotationNormalized(): the rotation part is not normalized\n");

    Matrix3 b({ 0.965926f, 0.258819f, 1.0f},
              {-0.258819f, 0.965926f, 3.0f},
              {      0.0f,      0.0f, 1.0f});
    CORRADE_COMPARE(b.rotationNormalized(), Matrix2x2(Vector2( 0.965926f, 0.258819f),
                                                      Vector2(-0.258819f, 0.965926f)));
}

void Matrix3Test::rotationPart() {
    Matrix3 rotation = Matrix3::rotation(Deg(15.0f));
    Matrix2x2 expectedRotationPart(Vector2( 0.965926f, 0.258819f),
                                   Vector2(-0.258819f, 0.965926f));

    /* For rotation and translation this is the same as rotationScaling() */
    Matrix3 rotationTranslation = rotation*Matrix3::translation({2.0f, 5.0f});
    Matrix2x2 rotationTranslationPart = rotationTranslation.rotation();
    CORRADE_COMPARE(rotationTranslationPart, rotationTranslation.rotationScaling());
    CORRADE_COMPARE(rotationTranslationPart, expectedRotationPart);

    /* Test uniform scaling */
    Matrix3 rotationScaling = rotation*Matrix3::scaling(Vector2(3.0f));
    Matrix2x2 rotationScalingPart = rotationScaling.rotation();
    CORRADE_COMPARE(rotationScalingPart.determinant(), 1.0f);
    CORRADE_COMPARE(rotationScalingPart*rotationScalingPart.transposed(), Matrix2x2());
    CORRADE_COMPARE(rotationScalingPart, expectedRotationPart);

    /* Fails on non-uniform scaling */
    std::ostringstream o;
    Error redirectError{&o};
    Matrix2x2 rotationScaling2 = (rotation*Matrix3::scaling(Vector2::yScale(3.5f))).rotation();
    CORRADE_COMPARE(o.str(), "Math::Matrix3::rotation(): the matrix doesn't have uniform scaling\n");
    CORRADE_COMPARE(rotationScaling2, Matrix2x2());
}

void Matrix3Test::uniformScalingPart() {
    const Matrix3 rotation = Matrix3::rotation(Deg(-74.0f));

    /* Test uniform scaling */
    CORRADE_COMPARE((rotation*Matrix3::scaling(Vector2(3.0f))).uniformScaling(), 3.0f);

    /* Fails on non-uniform scaling */
    std::ostringstream o;
    Error redirectError{&o};
    const Float nonUniformScaling = (rotation*Matrix3::scaling(Vector2::yScale(3.0f))).uniformScaling();
    CORRADE_COMPARE(o.str(), "Math::Matrix3::uniformScaling(): the matrix doesn't have uniform scaling\n");
    CORRADE_COMPARE(nonUniformScaling, 0.0f);
}

void Matrix3Test::vectorParts() {
    constexpr Matrix3 a({15.0f,  0.0f, 0.0f},
                        { 0.0f, -3.0f, 0.0f},
                        {-5.0f, 12.0f, 1.0f});
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Vector2 right = a.right();
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Vector2 up = a.up();
    #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Probably because copy is not constexpr */
    constexpr
    #endif
    Vector2 translation = a.translation();

    CORRADE_COMPARE(right, Vector2::xAxis(15.0f));
    CORRADE_COMPARE(up, Vector2::yAxis(-3.0f));
    CORRADE_COMPARE(translation, Vector2(-5.0f, 12.0f));
}

void Matrix3Test::invertedRigid() {
    Matrix3 actual = Matrix3::rotation(Deg(-74.0f))*
                     Matrix3::reflection(Vector2(0.5f, -2.0f).normalized())*
                     Matrix3::translation({2.0f, -3.0f});
    Matrix3 expected = Matrix3::translation({-2.0f, 3.0f})*
                       Matrix3::reflection(Vector2(0.5f, -2.0f).normalized())*
                       Matrix3::rotation(Deg(74.0f));

    std::ostringstream o;
    Error redirectError{&o};
    (2*actual).invertedRigid();
    CORRADE_COMPARE(o.str(), "Math::Matrix3::invertedRigid(): the matrix doesn't represent rigid transformation\n");

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

void Matrix3Test::transform() {
    Matrix3 a = Matrix3::translation({1.0f, -5.0f})*Matrix3::rotation(Deg(90.0f));
    Vector2 v(1.0f, -2.0f);

    CORRADE_COMPARE(a.transformVector(v), Vector2(2.0f, 1.0f));
    CORRADE_COMPARE(a.transformPoint(v), Vector2(3.0f, -4.0f));
}

void Matrix3Test::debug() {
    Matrix3 m({3.0f,  5.0f, 8.0f},
              {4.0f,  4.0f, 7.0f},
              {7.0f, -1.0f, 8.0f});

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

void Matrix3Test::configuration() {
    Corrade::Utility::Configuration c;

    Matrix3 m({5.0f, 8.0f,   4.0f},
              {4.0f, 7.0f, 3.125f},
              {4.0f, 5.0f,  9.55f});
    std::string value("5 4 4 8 7 5 4 3.125 9.55");

    c.setValue("matrix", m);
    CORRADE_COMPARE(c.value("matrix"), value);
    CORRADE_COMPARE(c.value<Matrix3>("matrix"), m);
}

}}}

CORRADE_TEST_MAIN(Magnum::Math::Test::Matrix3Test)