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

/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016
              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 "Magnum/Math/Matrix4.h"
#include "Magnum/Math/Quaternion.h"

struct Quat {
    float x, y, z, w;
};

namespace Magnum { namespace Math {

namespace Implementation {

template<> struct QuaternionConverter<Float, Quat> {
    #if !defined(__GNUC__) || defined(__clang__)
    constexpr /* See the convert() test case */
    #endif
    static Quaternion<Float> from(const Quat& other) {
        return {{other.x, other.y, other.z}, other.w};
    }

    constexpr static Quat to(const Quaternion<Float>& other) {
        return {other.vector().x(), other.vector().y(), other.vector().z(), other.scalar() };
    }
};

}

namespace Test {

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

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

    void compare();
    void isNormalized();
    template<class T> void isNormalizedEpsilon();

    void addSubtract();
    void negated();
    void multiplyDivideScalar();
    void multiply();

    void dot();
    void dotSelf();
    void length();
    void normalized();
    template<class T> void normalizedIterative();

    void conjugated();
    void inverted();
    void invertedNormalized();

    void rotation();
    void angle();
    void matrix();
    void lerp();
    void slerp();
    void transformVector();
    void transformVectorNormalized();

    void debug();
};

typedef Math::Deg<Float> Deg;
typedef Math::Rad<Float> Rad;
typedef Math::Matrix<3, Float> Matrix3x3;
typedef Math::Matrix4<Float> Matrix4;
typedef Math::Quaternion<Float> Quaternion;
typedef Math::Vector3<Float> Vector3;
typedef Math::Vector4<Float> Vector4;

QuaternionTest::QuaternionTest() {
    addTests({&QuaternionTest::construct,
              &QuaternionTest::constructIdentity,
              &QuaternionTest::constructZero,
              &QuaternionTest::constructNoInit,
              &QuaternionTest::constructFromVector,
              &QuaternionTest::constructConversion,
              &QuaternionTest::constructCopy,
              &QuaternionTest::convert,

              &QuaternionTest::compare,
              &QuaternionTest::isNormalized,
              &QuaternionTest::isNormalizedEpsilon<Float>,
              &QuaternionTest::isNormalizedEpsilon<Double>,

              &QuaternionTest::addSubtract,
              &QuaternionTest::negated,
              &QuaternionTest::multiplyDivideScalar,
              &QuaternionTest::multiply,

              &QuaternionTest::dot,
              &QuaternionTest::dotSelf,
              &QuaternionTest::length,
              &QuaternionTest::normalized});

    addRepeatedTests<QuaternionTest>({
        &QuaternionTest::normalizedIterative<Float>,
        &QuaternionTest::normalizedIterative<Double>}, 1000);

    addTests({&QuaternionTest::conjugated,
              &QuaternionTest::inverted,
              &QuaternionTest::invertedNormalized,

              &QuaternionTest::rotation,
              &QuaternionTest::angle,
              &QuaternionTest::matrix,
              &QuaternionTest::lerp,
              &QuaternionTest::slerp,
              &QuaternionTest::transformVector,
              &QuaternionTest::transformVectorNormalized,

              &QuaternionTest::debug});
}

void QuaternionTest::construct() {
    constexpr Quaternion a = {{1.0f, 2.0f, 3.0f}, -4.0f};
    CORRADE_COMPARE(a, Quaternion({1.0f, 2.0f, 3.0f}, -4.0f));

    constexpr Vector3 b = a.vector();
    constexpr Float c = a.scalar();
    CORRADE_COMPARE(b, Vector3(1.0f, 2.0f, 3.0f));
    CORRADE_COMPARE(c, -4.0f);

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

void QuaternionTest::constructIdentity() {
    constexpr Quaternion a;
    constexpr Quaternion b{IdentityInit};
    CORRADE_COMPARE(a, Quaternion({0.0f, 0.0f, 0.0f}, 1.0f));
    CORRADE_COMPARE(b, Quaternion({0.0f, 0.0f, 0.0f}, 1.0f));
    CORRADE_COMPARE(a.length(), 1.0f);
    CORRADE_COMPARE(b.length(), 1.0f);

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

void QuaternionTest::constructZero() {
    constexpr Quaternion a{ZeroInit};
    CORRADE_COMPARE(a, Quaternion({0.0f, 0.0f, 0.0f}, 0.0f));

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

void QuaternionTest::constructNoInit() {
    Quaternion a{{1.0f, 2.0f, 3.0f}, -4.0f};
    new(&a) Quaternion{NoInit};
    CORRADE_COMPARE(a, Quaternion({1.0f, 2.0f, 3.0f}, -4.0f));

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

void QuaternionTest::constructFromVector() {
    constexpr Quaternion a(Vector3(1.0f, 2.0f, 3.0f));
    CORRADE_COMPARE(a, Quaternion({1.0f, 2.0f, 3.0f}, 0.0f));

    /* Implicit conversion is not allowed */
    CORRADE_VERIFY(!(std::is_convertible<Vector3, Quaternion>::value));

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

void QuaternionTest::constructConversion() {
    typedef Math::Quaternion<Int> Quaternioni;

    constexpr Quaternion a{{1.3f, 2.7f, -15.0f}, 7.0f};
    constexpr Quaternioni b{a};

    CORRADE_COMPARE(b, (Quaternioni{{1, 2, -15}, 7}));

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

    CORRADE_VERIFY((std::is_nothrow_constructible<Quaternion, Quaternioni>::value));
}

void QuaternionTest::constructCopy() {
    constexpr Quaternion a({1.0f, -3.0f, 7.0f}, 2.5f);
    constexpr Quaternion b(a);
    CORRADE_COMPARE(b, Quaternion({1.0f, -3.0f, 7.0f}, 2.5f));

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

void QuaternionTest::convert() {
    constexpr Quat a{1.5f, -3.5f, 7.0f, -0.5f};
    constexpr Quaternion b{{1.5f, -3.5f, 7.0f}, -0.5f};

    /* GCC 5.1 fills the result with zeros instead of properly calling
       delegated copy constructor if using constexpr. Reported here:
       https://gcc.gnu.org/bugzilla/show_bug.cgi?id=66450 */
    #if !defined(__GNUC__) || defined(__clang__)
    constexpr
    #endif
    Quaternion c{a};
    CORRADE_COMPARE(c, b);

    constexpr Quat d(b);
    CORRADE_COMPARE(d.x, a.x);
    CORRADE_COMPARE(d.y, a.y);
    CORRADE_COMPARE(d.z, a.z);
    CORRADE_COMPARE(d.w, a.w);

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

void QuaternionTest::compare() {
    CORRADE_VERIFY(Quaternion({1.0f+TypeTraits<Float>::epsilon()/2, 2.0f, 3.0f}, -4.0f) == Quaternion({1.0f, 2.0f, 3.0f}, -4.0f));
    CORRADE_VERIFY(Quaternion({1.0f+TypeTraits<Float>::epsilon()*2, 2.0f, 3.0f}, -4.0f) != Quaternion({1.0f, 2.0f, 3.0f}, -4.0f));
    CORRADE_VERIFY(Quaternion({4.0f, 2.0f, 3.0f}, -1.0f+TypeTraits<Float>::epsilon()/2) == Quaternion({4.0f, 2.0f, 3.0f}, -1.0f));
    CORRADE_VERIFY(Quaternion({4.0f, 2.0f, 3.0f}, -1.0f+TypeTraits<Float>::epsilon()*2) != Quaternion({4.0f, 2.0f, 3.0f}, -1.0f));
}

void QuaternionTest::isNormalized() {
    CORRADE_VERIFY(!Quaternion({1.0f, 2.0f, 3.0f}, 4.0f).isNormalized());
    CORRADE_VERIFY(Quaternion::rotation(Deg(23.0f), Vector3::xAxis()).isNormalized());
}

template<class T> void QuaternionTest::isNormalizedEpsilon() {
    setTestCaseName(std::string{"isNormalizedEpsilon<"} + TypeTraits<T>::name() + ">");

    CORRADE_VERIFY((Math::Quaternion<T>{{T(0.0106550719778129), T(0.311128101752138), T(-0.0468823167023769)}, T(0.949151106053128) + TypeTraits<T>::epsilon()/T(2.0)}.isNormalized()));
    CORRADE_VERIFY(!(Math::Quaternion<T>{{T(0.0106550719778129), T(0.311128101752138), T(-0.0468823167023769)}, T(0.949151106053128) + TypeTraits<T>::epsilon()*T(2.0)}.isNormalized()));
}

void QuaternionTest::addSubtract() {
    Quaternion a({ 1.0f, 3.0f, -2.0f}, -4.0f);
    Quaternion b({-0.5f, 1.4f,  3.0f}, 12.0f);
    Quaternion c({ 0.5f, 4.4f,  1.0f},  8.0f);

    CORRADE_COMPARE(a + b, c);
    CORRADE_COMPARE(c - b, a);
}

void QuaternionTest::negated() {
    CORRADE_COMPARE(-Quaternion({1.0f, 2.0f, -3.0f}, -4.0f), Quaternion({-1.0f, -2.0f, 3.0f}, 4.0f));
}

void QuaternionTest::multiplyDivideScalar() {
    Quaternion a({ 1.0f,  3.0f, -2.0f}, -4.0f);
    Quaternion b({-1.5f, -4.5f,  3.0f},  6.0f);

    CORRADE_COMPARE(a*-1.5f, b);
    CORRADE_COMPARE(-1.5f*a, b);
    CORRADE_COMPARE(b/-1.5f, a);

    CORRADE_COMPARE(2.0f/a, Quaternion({2.0f, 0.666666f, -1.0f}, -0.5f));
}

void QuaternionTest::multiply() {
    CORRADE_COMPARE(Quaternion({-6.0f, -9.0f, 15.0f}, 0.5f)*Quaternion({2.0f, 3.0f, -5.0f}, 2.0f),
                    Quaternion({-11.0f, -16.5f, 27.5f}, 115.0f));
}

void QuaternionTest::dot() {
    Quaternion a({ 1.0f, 3.0f, -2.0f}, -4.0f);
    Quaternion b({-0.5f, 1.5f,  3.0f}, 12.0f);

    CORRADE_COMPARE(Math::dot(a, b), -50.0f);
}

void QuaternionTest::dotSelf() {
    CORRADE_COMPARE(Quaternion({1.0f, 2.0f, -3.0f}, -4.0f).dot(), 30.0f);
}

void QuaternionTest::length() {
    CORRADE_COMPARE(Quaternion({1.0f, 3.0f, -2.0f}, -4.0f).length(), std::sqrt(30.0f));
}

void QuaternionTest::normalized() {
    Quaternion normalized = Quaternion({1.0f, 3.0f, -2.0f}, -4.0f).normalized();
    CORRADE_COMPARE(normalized.length(), 1.0f);
    CORRADE_COMPARE(normalized, Quaternion({1.0f, 3.0f, -2.0f}, -4.0f)/std::sqrt(30.0f));
}

template<class T> void QuaternionTest::normalizedIterative() {
    setTestCaseName(std::string{"normalizedIterative<"} + TypeTraits<T>::name() + ">");

    const auto axis = Math::Vector3<T>{T(0.5), T(7.9), T(0.1)}.normalized();
    auto a = Math::Quaternion<T>::rotation(Math::Deg<T>{T(36.7)}, Math::Vector3<T>{T(0.25), T(7.3), T(-1.1)}.normalized());
    for(std::size_t i = 0; i != testCaseRepeatId(); ++i) {
        a = Math::Quaternion<T>::rotation(Math::Deg<T>{T(87.1)}, axis)*a;
        a = a.normalized();
    }

    CORRADE_VERIFY(a.isNormalized());
}

void QuaternionTest::conjugated() {
    CORRADE_COMPARE(Quaternion({ 1.0f,  3.0f, -2.0f}, -4.0f).conjugated(),
                    Quaternion({-1.0f, -3.0f,  2.0f}, -4.0f));
}

void QuaternionTest::inverted() {
    Quaternion a = Quaternion({1.0f, 3.0f, -2.0f}, -4.0f);
    Quaternion inverted = a.inverted();

    CORRADE_COMPARE(a*inverted, Quaternion());
    CORRADE_COMPARE(inverted*a, Quaternion());
    CORRADE_COMPARE(inverted, Quaternion({-1.0f, -3.0f, 2.0f}, -4.0f)/30.0f);
}

void QuaternionTest::invertedNormalized() {
    Quaternion a = Quaternion({1.0f, 3.0f, -2.0f}, -4.0f);

    std::ostringstream o;
    Error redirectError{&o};
    a.invertedNormalized();
    CORRADE_COMPARE(o.str(), "Math::Quaternion::invertedNormalized(): quaternion must be normalized\n");

    Quaternion aNormalized = a.normalized();
    Quaternion inverted = aNormalized.invertedNormalized();
    CORRADE_COMPARE(aNormalized*inverted, Quaternion());
    CORRADE_COMPARE(inverted*aNormalized, Quaternion());
    CORRADE_COMPARE(inverted, Quaternion({-1.0f, -3.0f, 2.0f}, -4.0f)/std::sqrt(30.0f));
}

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

    Vector3 axis(1.0f/Constants<Float>::sqrt3());

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

    Quaternion q = Quaternion::rotation(Deg(120.0f), axis);
    CORRADE_COMPARE(q.length(), 1.0f);
    CORRADE_COMPARE(q, Quaternion(Vector3(0.5f, 0.5f, 0.5f), 0.5f));
    CORRADE_COMPARE_AS(q.angle(), Deg(120.0f), Deg);
    CORRADE_COMPARE(q.axis(), axis);
    CORRADE_COMPARE(q.axis().length(), 1.0f);

    /* Verify negative angle */
    Quaternion q2 = Quaternion::rotation(Deg(-120.0f), axis);
    CORRADE_COMPARE(q2, Quaternion(Vector3(-0.5f, -0.5f, -0.5f), 0.5f));
    CORRADE_COMPARE_AS(q2.angle(), Deg(120.0f), Deg);
    CORRADE_COMPARE(q2.axis(), -axis);

    /* Default-constructed quaternion has zero angle and NaN axis */
    CORRADE_COMPARE_AS(Quaternion().angle(), Deg(0.0f), Deg);
    CORRADE_VERIFY(Quaternion().axis() != Quaternion().axis());
}

void QuaternionTest::angle() {
    std::ostringstream o;
    Error redirectError{&o};
    Math::angle(Quaternion({1.0f, 2.0f, -3.0f}, -4.0f).normalized(), {{4.0f, -3.0f, 2.0f}, -1.0f});
    CORRADE_COMPARE(o.str(), "Math::angle(): quaternions must be normalized\n");

    o.str({});
    Math::angle({{1.0f, 2.0f, -3.0f}, -4.0f}, Quaternion({4.0f, -3.0f, 2.0f}, -1.0f).normalized());
    CORRADE_COMPARE(o.str(), "Math::angle(): quaternions must be normalized\n");

    /* Verify also that the angle is the same as angle between 4D vectors */
    Rad angle = Math::angle(Quaternion({1.0f, 2.0f, -3.0f}, -4.0f).normalized(),
                            Quaternion({4.0f, -3.0f, 2.0f}, -1.0f).normalized());
    CORRADE_COMPARE(angle, Math::angle(Vector4(1.0f, 2.0f, -3.0f, -4.0f).normalized(),
                                 Vector4(4.0f, -3.0f, 2.0f, -1.0f).normalized()));
    CORRADE_COMPARE(angle, Rad(1.704528f));
}

void QuaternionTest::matrix() {
    Vector3 axis = Vector3(-3.0f, 1.0f, 5.0f).normalized();

    Quaternion q = Quaternion::rotation(Deg(37.0f), axis);
    Matrix3x3 m = Matrix4::rotation(Deg(37.0f), axis).rotationScaling();

    /* Verify that negated quaternion gives the same rotation */
    CORRADE_COMPARE(q.toMatrix(), m);
    CORRADE_COMPARE((-q).toMatrix(), m);

    std::ostringstream o;
    Error redirectError{&o};
    Quaternion::fromMatrix(m*2);
    CORRADE_COMPARE(o.str(), "Math::Quaternion::fromMatrix(): the matrix is not orthogonal\n");

    /* Trace > 0 */
    CORRADE_VERIFY(m.trace() > 0.0f);
    CORRADE_COMPARE(Quaternion::fromMatrix(m), q);

    /* Trace < 0, max is diagonal[2] */
    Matrix3x3 m2 = Matrix4::rotation(Deg(130.0f), axis).rotationScaling();
    Quaternion q2 = Quaternion::rotation(Deg(130.0f), axis);
    CORRADE_VERIFY(m2.trace() < 0.0f);
    CORRADE_VERIFY(m2.diagonal()[2] > std::max(m2.diagonal()[0], m2.diagonal()[1]));
    CORRADE_COMPARE(Quaternion::fromMatrix(m2), q2);

    /* Trace < 0, max is diagonal[1] */
    Vector3 axis2 = Vector3(-3.0f, 5.0f, 1.0f).normalized();
    Matrix3x3 m3 = Matrix4::rotation(Deg(130.0f), axis2).rotationScaling();
    Quaternion q3 = Quaternion::rotation(Deg(130.0f), axis2);
    CORRADE_VERIFY(m3.trace() < 0.0f);
    CORRADE_VERIFY(m3.diagonal()[1] > std::max(m3.diagonal()[0], m3.diagonal()[2]));
    CORRADE_COMPARE(Quaternion::fromMatrix(m3), q3);

    /* Trace < 0, max is diagonal[0] */
    Vector3 axis3 = Vector3(5.0f, -3.0f, 1.0f).normalized();
    Matrix3x3 m4 = Matrix4::rotation(Deg(130.0f), axis3).rotationScaling();
    Quaternion q4 = Quaternion::rotation(Deg(130.0f), axis3);
    CORRADE_VERIFY(m4.trace() < 0.0f);
    CORRADE_VERIFY(m4.diagonal()[0] > std::max(m4.diagonal()[1], m4.diagonal()[2]));
    CORRADE_COMPARE(Quaternion::fromMatrix(m4), q4);
}

/* The crappy 4.9 20140827 (prerelease) in Android NDK segfaults when
   optimizing the following function. Dialing down the optimization helps. No
   problem when calling Math::lerp() anywhere else, so I won't dig further.
   Fuck this. */
#if defined(CORRADE_TARGET_ANDROID) && __GNUC__*100 + __GNUC_MINOR__*10 + __GNUC_PATCHLEVEL__ == 490
#pragma GCC push_options
#pragma GCC optimize("O0")
#endif
void QuaternionTest::lerp() {
    Quaternion a = Quaternion::rotation(Deg(15.0f), Vector3(1.0f/Constants<Float>::sqrt3()));
    Quaternion b = Quaternion::rotation(Deg(23.0f), Vector3::xAxis());

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

    Math::lerp(a*3.0f, b, 0.35f);
    CORRADE_COMPARE(o.str(), "Math::lerp(): quaternions must be normalized\n");

    o.str({});
    Math::lerp(a, b*-3.0f, 0.35f);
    CORRADE_COMPARE(o.str(), "Math::lerp(): quaternions must be normalized\n");

    Quaternion lerp = Math::lerp(a, b, 0.35f);
    CORRADE_COMPARE(lerp, Quaternion({0.119127f, 0.049134f, 0.049134f}, 0.990445f));
}
#if defined(CORRADE_TARGET_ANDROID) && __GNUC__*100 + __GNUC_MINOR__*10 + __GNUC_PATCHLEVEL__ == 490
#pragma GCC pop_options
#endif

void QuaternionTest::slerp() {
    Quaternion a = Quaternion::rotation(Deg(15.0f), Vector3(1.0f/Constants<Float>::sqrt3()));
    Quaternion b = Quaternion::rotation(Deg(23.0f), Vector3::xAxis());

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

    Math::slerp(a*3.0f, b, 0.35f);
    CORRADE_COMPARE(o.str(), "Math::slerp(): quaternions must be normalized\n");

    o.str({});
    Math::slerp(a, b*-3.0f, 0.35f);
    CORRADE_COMPARE(o.str(), "Math::slerp(): quaternions must be normalized\n");

    Quaternion slerp = Math::slerp(a, b, 0.35f);
    CORRADE_COMPARE(slerp, Quaternion({0.1191653f, 0.0491109f, 0.0491109f}, 0.9904423f));

    /* Avoid division by zero */
    CORRADE_COMPARE(Math::slerp(a, a, 0.25f), a);
    CORRADE_COMPARE(Math::slerp(a, -a, 0.42f), a);
}

void QuaternionTest::transformVector() {
    Quaternion a = Quaternion::rotation(Deg(23.0f), Vector3::xAxis());
    Matrix4 m = Matrix4::rotationX(Deg(23.0f));
    Vector3 v(5.0f, -3.6f, 0.7f);

    Vector3 rotated = a.transformVector(v);
    CORRADE_COMPARE(rotated, m.transformVector(v));
    CORRADE_COMPARE(rotated, Vector3(5.0f, -3.58733f, -0.762279f));
}

void QuaternionTest::transformVectorNormalized() {
    Quaternion a = Quaternion::rotation(Deg(23.0f), Vector3::xAxis());
    Matrix4 m = Matrix4::rotationX(Deg(23.0f));
    Vector3 v(5.0f, -3.6f, 0.7f);

    std::ostringstream o;
    Error redirectError{&o};
    (a*2).transformVectorNormalized(v);
    CORRADE_COMPARE(o.str(), "Math::Quaternion::transformVectorNormalized(): quaternion must be normalized\n");

    Vector3 rotated = a.transformVectorNormalized(v);
    CORRADE_COMPARE(rotated, m.transformVector(v));
    CORRADE_COMPARE(rotated, a.transformVector(v));
}

void QuaternionTest::debug() {
    std::ostringstream o;

    Debug(&o) << Quaternion({1.0f, 2.0f, 3.0f}, -4.0f);
    CORRADE_COMPARE(o.str(), "Quaternion({1, 2, 3}, -4)\n");
}

}}}

CORRADE_TEST_MAIN(Magnum::Math::Test::QuaternionTest)