magnum/src/Math/Test/DualQuaternionTest.cpp

/*
    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>

    This file is part of Magnum.

    Magnum is free software: you can redistribute it and/or modify
    it under the terms of the GNU Lesser General Public License version 3
    only, as published by the Free Software Foundation.

    Magnum is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    GNU Lesser General Public License version 3 for more details.
*/

#include <sstream>
#include <TestSuite/Tester.h>

#include "Math/DualQuaternion.h"

namespace Magnum { namespace Math { namespace Test {

class DualQuaternionTest: public Corrade::TestSuite::Tester {
    public:
        explicit DualQuaternionTest();

        void construct();
        void constructDefault();
        void constructFromVector();

        void constExpressions();

        void lengthSquared();
        void length();
        void normalized();

        void quaternionConjugated();
        void dualConjugated();
        void conjugated();
        void inverted();

        void rotation();
        void translation();
        void combinedTransformParts();
        void matrix();
        void transformPoint();
        void transformPointNormalized();

        void debug();
};

typedef Math::Deg<float> Deg;
typedef Math::Rad<float> Rad;
typedef Math::Dual<float> Dual;
typedef Math::Matrix4<float> Matrix4;
typedef Math::DualQuaternion<float> DualQuaternion;
typedef Math::Quaternion<float> Quaternion;
typedef Math::Vector3<float> Vector3;

DualQuaternionTest::DualQuaternionTest() {
    addTests(&DualQuaternionTest::construct,
             &DualQuaternionTest::constructDefault,
             &DualQuaternionTest::constructFromVector,

             &DualQuaternionTest::constExpressions,

             &DualQuaternionTest::lengthSquared,
             &DualQuaternionTest::length,
             &DualQuaternionTest::normalized,

             &DualQuaternionTest::quaternionConjugated,
             &DualQuaternionTest::dualConjugated,
             &DualQuaternionTest::conjugated,
             &DualQuaternionTest::inverted,

             &DualQuaternionTest::rotation,
             &DualQuaternionTest::translation,
             &DualQuaternionTest::combinedTransformParts,
             &DualQuaternionTest::matrix,
             &DualQuaternionTest::transformPoint,
             &DualQuaternionTest::transformPointNormalized,

             &DualQuaternionTest::debug);
}

void DualQuaternionTest::construct() {
    DualQuaternion q({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.5f, -3.1f, 3.3f}, 2.0f});
    CORRADE_COMPARE(q.real(), Quaternion({1.0f, 2.0f, 3.0f}, -4.0f));
    CORRADE_COMPARE(q.dual(), Quaternion({0.5f, -3.1f, 3.3f}, 2.0f));
}

void DualQuaternionTest::constructDefault() {
    CORRADE_COMPARE(DualQuaternion(), DualQuaternion({{0.0f, 0.0f, 0.0f}, 1.0f}, {{0.0f, 0.0f, 0.0f}, 0.0f}));
    CORRADE_COMPARE(DualQuaternion().length(), 1.0f);
}

void DualQuaternionTest::constructFromVector() {
    CORRADE_COMPARE(DualQuaternion(Vector3(1.0f, 2.0f, 3.0f)), DualQuaternion({{0.0f, 0.0f, 0.0f}, 1.0f}, {{1.0f, 2.0f, 3.0f}, 0.0f}));
}

void DualQuaternionTest::constExpressions() {
    /* Default constructor */
    constexpr DualQuaternion a;
    CORRADE_COMPARE(a, DualQuaternion({{0.0f, 0.0f, 0.0f}, 1.0f}, {{0.0f, 0.0f, 0.0f}, 0.0f}));

    /* Value constructor */
    constexpr DualQuaternion b({{1.0f, 2.0f, -3.0f}, -3.5f}, {{4.5f, -7.0f, 2.0f}, 1.0f});
    CORRADE_COMPARE(b, DualQuaternion({{1.0f, 2.0f, -3.0f}, -3.5f}, {{4.5f, -7.0f, 2.0f}, 1.0f}));

    /* Vector constructor */
    constexpr DualQuaternion c(Vector3(1.5f, -5.0f, 3.0f));
    CORRADE_COMPARE(c, DualQuaternion({{0.0f, 0.0f, 0.0f}, 1.0f}, {{1.5f, -5.0f, 3.0f}, 0.0f}));

    /* Copy constructor */
    constexpr DualQuaternion d(b);
    CORRADE_COMPARE(d, DualQuaternion({{1.0f, 2.0f, -3.0f}, -3.5f}, {{4.5f, -7.0f, 2.0f}, 1.0f}));
}

void DualQuaternionTest::lengthSquared() {
    DualQuaternion a({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.5f, -3.0f, 3.0f}, 2.0f});
    CORRADE_COMPARE(a.lengthSquared(), Dual(30.0f, -9.0f));
}

void DualQuaternionTest::length() {
    DualQuaternion a({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.5f, -3.0f, 3.0f}, 2.0f});
    CORRADE_COMPARE(a.length(), Dual(5.477226f, -0.821584f));
}

void DualQuaternionTest::normalized() {
    DualQuaternion a({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.5f, -3.0f, 3.0f}, 2.0f});
    DualQuaternion b({{0.182574f, 0.365148f, 0.547723f}, -0.730297f}, {{0.118673f, -0.49295f, 0.629881f}, 0.255604f});
    CORRADE_COMPARE(a.normalized().length(), 1.0f);
    CORRADE_COMPARE(a.normalized(), b);
}

void DualQuaternionTest::quaternionConjugated() {
    DualQuaternion a({{ 1.0f,  2.0f,  3.0f}, -4.0f}, {{ 0.5f, -3.1f,  3.3f}, 2.0f});
    DualQuaternion b({{-1.0f, -2.0f, -3.0f}, -4.0f}, {{-0.5f,  3.1f, -3.3f}, 2.0f});

    CORRADE_COMPARE(a.quaternionConjugated(), b);
}

void DualQuaternionTest::dualConjugated() {
    DualQuaternion a({{1.0f, 2.0f, 3.0f}, -4.0f}, {{ 0.5f, -3.1f,  3.3f},  2.0f});
    DualQuaternion b({{1.0f, 2.0f, 3.0f}, -4.0f}, {{-0.5f,  3.1f, -3.3f}, -2.0f});

    CORRADE_COMPARE(a.dualConjugated(), b);
}

void DualQuaternionTest::conjugated() {
    DualQuaternion a({{ 1.0f,  2.0f,  3.0f}, -4.0f}, {{ 0.5f, -3.1f,  3.3f},  2.0f});
    DualQuaternion b({{-1.0f, -2.0f, -3.0f}, -4.0f}, {{ 0.5f, -3.1f,  3.3f}, -2.0f});

    CORRADE_COMPARE(a.conjugated(), b);
}

void DualQuaternionTest::inverted() {
    DualQuaternion a({{ 1.0f,  2.0f,  3.0f}, -4.0f}, {{ 2.5f, -3.1f,  3.3f},  2.0f});
    DualQuaternion b({{-0.033333f, -0.066667f, -0.1f}, -0.133333f}, {{-0.087333f, 0.095333f, -0.122f}, 0.050667f});

    CORRADE_COMPARE(a*a.inverted(), DualQuaternion());
    CORRADE_COMPARE(a.inverted(), b);
}

void DualQuaternionTest::rotation() {
    std::ostringstream o;
    Error::setOutput(&o);

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

    CORRADE_COMPARE(DualQuaternion::rotation(Deg(120.0f), axis*2.0f), DualQuaternion());
    CORRADE_COMPARE(o.str(), "Math::Quaternion::rotation(): axis must be normalized\n");

    DualQuaternion q = DualQuaternion::rotation(Deg(120.0f), axis);
    CORRADE_COMPARE(q, DualQuaternion({Vector3(0.5f, 0.5f, 0.5f), 0.5f}, {{}, 0.0f}));
    CORRADE_COMPARE_AS(q.rotationAngle(), Deg(120.0f), Deg);
    CORRADE_COMPARE(q.rotationAxis(), axis);
}

void DualQuaternionTest::translation() {
    Vector3 vec(1.0f, -3.5f, 0.5f);
    DualQuaternion q = DualQuaternion::translation(vec);
    CORRADE_COMPARE(q, DualQuaternion({}, {{0.5f, -1.75f, 0.25f}, 0.0f}));
    CORRADE_COMPARE(q.translation(), vec);
}

void DualQuaternionTest::combinedTransformParts() {
    Vector3 translation = Vector3(-1.0f, 2.0f, 3.0f);
    DualQuaternion a = DualQuaternion::translation(translation)*DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis());
    DualQuaternion b = DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis())*DualQuaternion::translation(translation);

    CORRADE_COMPARE(a.rotationAxis(), Vector3::xAxis());
    CORRADE_COMPARE(b.rotationAxis(), Vector3::xAxis());
    CORRADE_COMPARE_AS(a.rotationAngle(), Deg(23.0f), Rad);
    CORRADE_COMPARE_AS(b.rotationAngle(), Deg(23.0f), Rad);

    CORRADE_COMPARE(a.translation(), translation);
    CORRADE_COMPARE(b.translation(), Quaternion::rotation(Deg(23.0f), Vector3::xAxis()).transformVector(translation));
}

void DualQuaternionTest::matrix() {
    DualQuaternion q = DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis())*DualQuaternion::translation({-1.0f, 2.0f, 3.0f});
    Matrix4 m = Matrix4::rotationX(Deg(23.0f))*Matrix4::translation({-1.0f, 2.0f, 3.0f});

    /* Verify that negated dual quaternion gives the same transformation */
    CORRADE_COMPARE(q.matrix(), m);
    CORRADE_COMPARE((-q).matrix(), m);
}

void DualQuaternionTest::transformPoint() {
    DualQuaternion a = DualQuaternion::translation({-1.0f, 2.0f, 3.0f})*DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis());
    DualQuaternion b = DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis())*DualQuaternion::translation({-1.0f, 2.0f, 3.0f});
    Matrix4 m = Matrix4::translation({-1.0f, 2.0f, 3.0f})*Matrix4::rotationX(Deg(23.0f));
    Matrix4 n = Matrix4::rotationX(Deg(23.0f))*Matrix4::translation({-1.0f, 2.0f, 3.0f});
    Vector3 v(0.0f, -3.6f, 0.7f);

    Vector3 transformedA = (a*Dual(2)).transformPoint(v);
    CORRADE_COMPARE(transformedA, m.transformPoint(v));
    CORRADE_COMPARE(transformedA, Vector3(-1.0f, -1.58733f, 2.237721f));

    Vector3 transformedB = (b*Dual(2)).transformPoint(v);
    CORRADE_COMPARE(transformedB, n.transformPoint(v));
    CORRADE_COMPARE(transformedB, Vector3(-1.0f, -2.918512f, 2.780698f));
}

void DualQuaternionTest::transformPointNormalized() {
    DualQuaternion a = DualQuaternion::translation({-1.0f, 2.0f, 3.0f})*DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis());
    DualQuaternion b = DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis())*DualQuaternion::translation({-1.0f, 2.0f, 3.0f});
    Matrix4 m = Matrix4::translation({-1.0f, 2.0f, 3.0f})*Matrix4::rotationX(Deg(23.0f));
    Matrix4 n = Matrix4::rotationX(Deg(23.0f))*Matrix4::translation({-1.0f, 2.0f, 3.0f});
    Vector3 v(0.0f, -3.6f, 0.7f);

    std::ostringstream o;
    Corrade::Utility::Error::setOutput(&o);
    Vector3 notTransformed = (a*Dual(2)).transformPointNormalized(v);
    CORRADE_VERIFY(notTransformed != notTransformed);
    CORRADE_COMPARE(o.str(), "Math::DualQuaternion::transformPointNormalized(): dual quaternion must be normalized\n");

    Vector3 transformedA = a.transformPointNormalized(v);
    CORRADE_COMPARE(transformedA, m.transformPoint(v));
    CORRADE_COMPARE(transformedA, Vector3(-1.0f, -1.58733f, 2.237721f));

    Vector3 transformedB = b.transformPointNormalized(v);
    CORRADE_COMPARE(transformedB, n.transformPoint(v));
    CORRADE_COMPARE(transformedB, Vector3(-1.0f, -2.918512f, 2.780698f));
}

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

    Debug(&o) << DualQuaternion({{1.0f, 2.0f, 3.0f}, -4.0f}, {{0.5f, -3.1f, 3.3f}, 2.0f});
    CORRADE_COMPARE(o.str(), "DualQuaternion({{1, 2, 3}, -4}, {{0.5, -3.1, 3.3}, 2})\n");
}

}}}

CORRADE_TEST_MAIN(Magnum::Math::Test::DualQuaternionTest)