qt5base-lts/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp

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#include <QtTest/QtTest>
#include <QtCore/qmath.h>
#include <QtGui/qquaternion.h>

class tst_QQuaternion : public QObject
{
    Q_OBJECT
public:
    tst_QQuaternion() {}
    ~tst_QQuaternion() {}

private slots:
    void create();

    void length_data();
    void length();

    void normalized_data();
    void normalized();

    void normalize_data();
    void normalize();

    void compare();

    void add_data();
    void add();

    void subtract_data();
    void subtract();

    void multiply_data();
    void multiply();

    void multiplyFactor_data();
    void multiplyFactor();

    void divide_data();
    void divide();

    void negate_data();
    void negate();

    void conjugate_data();
    void conjugate();

    void fromAxisAndAngle_data();
    void fromAxisAndAngle();

    void slerp_data();
    void slerp();

    void nlerp_data();
    void nlerp();

    void properties();
    void metaTypes();
};

// QVector3D uses float internally, which can lead to some precision
// issues when using it with the qreal-based QQuaternion.
static bool fuzzyCompare(qreal x, qreal y)
{
    return qFuzzyIsNull(float(x - y));
}

// Test the creation of QQuaternion objects in various ways:
// construct, copy, and modify.
void tst_QQuaternion::create()
{
    QQuaternion identity;
    QCOMPARE(identity.x(), (qreal)0.0f);
    QCOMPARE(identity.y(), (qreal)0.0f);
    QCOMPARE(identity.z(), (qreal)0.0f);
    QCOMPARE(identity.scalar(), (qreal)1.0f);
    QVERIFY(identity.isIdentity());

    QQuaternion v1(34.0f, 1.0f, 2.5f, -89.25f);
    QCOMPARE(v1.x(), (qreal)1.0f);
    QCOMPARE(v1.y(), (qreal)2.5f);
    QCOMPARE(v1.z(), (qreal)-89.25f);
    QCOMPARE(v1.scalar(), (qreal)34.0f);
    QVERIFY(!v1.isNull());

    QQuaternion v1i(34, 1, 2, -89);
    QCOMPARE(v1i.x(), (qreal)1.0f);
    QCOMPARE(v1i.y(), (qreal)2.0f);
    QCOMPARE(v1i.z(), (qreal)-89.0f);
    QCOMPARE(v1i.scalar(), (qreal)34.0f);
    QVERIFY(!v1i.isNull());

    QQuaternion v2(v1);
    QCOMPARE(v2.x(), (qreal)1.0f);
    QCOMPARE(v2.y(), (qreal)2.5f);
    QCOMPARE(v2.z(), (qreal)-89.25f);
    QCOMPARE(v2.scalar(), (qreal)34.0f);
    QVERIFY(!v2.isNull());

    QQuaternion v4;
    QCOMPARE(v4.x(), (qreal)0.0f);
    QCOMPARE(v4.y(), (qreal)0.0f);
    QCOMPARE(v4.z(), (qreal)0.0f);
    QCOMPARE(v4.scalar(), (qreal)1.0f);
    QVERIFY(v4.isIdentity());
    v4 = v1;
    QCOMPARE(v4.x(), (qreal)1.0f);
    QCOMPARE(v4.y(), (qreal)2.5f);
    QCOMPARE(v4.z(), (qreal)-89.25f);
    QCOMPARE(v4.scalar(), (qreal)34.0f);
    QVERIFY(!v4.isNull());

    QQuaternion v9(34, QVector3D(1.0f, 2.5f, -89.25f));
    QCOMPARE(v9.x(), (qreal)1.0f);
    QCOMPARE(v9.y(), (qreal)2.5f);
    QCOMPARE(v9.z(), (qreal)-89.25f);
    QCOMPARE(v9.scalar(), (qreal)34.0f);
    QVERIFY(!v9.isNull());

    v1.setX(3.0f);
    QCOMPARE(v1.x(), (qreal)3.0f);
    QCOMPARE(v1.y(), (qreal)2.5f);
    QCOMPARE(v1.z(), (qreal)-89.25f);
    QCOMPARE(v1.scalar(), (qreal)34.0f);
    QVERIFY(!v1.isNull());

    v1.setY(10.5f);
    QCOMPARE(v1.x(), (qreal)3.0f);
    QCOMPARE(v1.y(), (qreal)10.5f);
    QCOMPARE(v1.z(), (qreal)-89.25f);
    QCOMPARE(v1.scalar(), (qreal)34.0f);
    QVERIFY(!v1.isNull());

    v1.setZ(15.5f);
    QCOMPARE(v1.x(), (qreal)3.0f);
    QCOMPARE(v1.y(), (qreal)10.5f);
    QCOMPARE(v1.z(), (qreal)15.5f);
    QCOMPARE(v1.scalar(), (qreal)34.0f);
    QVERIFY(!v1.isNull());

    v1.setScalar(6.0f);
    QCOMPARE(v1.x(), (qreal)3.0f);
    QCOMPARE(v1.y(), (qreal)10.5f);
    QCOMPARE(v1.z(), (qreal)15.5f);
    QCOMPARE(v1.scalar(), (qreal)6.0f);
    QVERIFY(!v1.isNull());

    v1.setVector(2.0f, 6.5f, -1.25f);
    QCOMPARE(v1.x(), (qreal)2.0f);
    QCOMPARE(v1.y(), (qreal)6.5f);
    QCOMPARE(v1.z(), (qreal)-1.25f);
    QCOMPARE(v1.scalar(), (qreal)6.0f);
    QVERIFY(!v1.isNull());
    QVERIFY(v1.vector() == QVector3D(2.0f, 6.5f, -1.25f));

    v1.setVector(QVector3D(-2.0f, -6.5f, 1.25f));
    QCOMPARE(v1.x(), (qreal)-2.0f);
    QCOMPARE(v1.y(), (qreal)-6.5f);
    QCOMPARE(v1.z(), (qreal)1.25f);
    QCOMPARE(v1.scalar(), (qreal)6.0f);
    QVERIFY(!v1.isNull());
    QVERIFY(v1.vector() == QVector3D(-2.0f, -6.5f, 1.25f));

    v1.setX(0.0f);
    v1.setY(0.0f);
    v1.setZ(0.0f);
    v1.setScalar(0.0f);
    QCOMPARE(v1.x(), (qreal)0.0f);
    QCOMPARE(v1.y(), (qreal)0.0f);
    QCOMPARE(v1.z(), (qreal)0.0f);
    QCOMPARE(v1.scalar(), (qreal)0.0f);
    QVERIFY(v1.isNull());

    QVector4D v10 = v9.toVector4D();
    QCOMPARE(v10.x(), (qreal)1.0f);
    QCOMPARE(v10.y(), (qreal)2.5f);
    QCOMPARE(v10.z(), (qreal)-89.25f);
    QCOMPARE(v10.w(), (qreal)34.0f);
}

// Test length computation for quaternions.
void tst_QQuaternion::length_data()
{
    QTest::addColumn<qreal>("x");
    QTest::addColumn<qreal>("y");
    QTest::addColumn<qreal>("z");
    QTest::addColumn<qreal>("w");
    QTest::addColumn<qreal>("len");

    QTest::newRow("null") << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;
    QTest::newRow("1x") << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f;
    QTest::newRow("1y") << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f;
    QTest::newRow("1z") << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f << (qreal)1.0f;
    QTest::newRow("1w") << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f << (qreal)1.0f;
    QTest::newRow("-1x") << (qreal)-1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f;
    QTest::newRow("-1y") << (qreal)0.0f << (qreal)-1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f;
    QTest::newRow("-1z") << (qreal)0.0f << (qreal)0.0f << (qreal)-1.0f << (qreal)0.0f << (qreal)1.0f;
    QTest::newRow("-1w") << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)-1.0f << (qreal)1.0f;
    QTest::newRow("two") << (qreal)2.0f << (qreal)-2.0f << (qreal)2.0f << (qreal)2.0f << (qreal)qSqrt(16.0f);
}
void tst_QQuaternion::length()
{
    QFETCH(qreal, x);
    QFETCH(qreal, y);
    QFETCH(qreal, z);
    QFETCH(qreal, w);
    QFETCH(qreal, len);

    QQuaternion v(w, x, y, z);
    QCOMPARE(v.length(), len);
    QCOMPARE(v.lengthSquared(), x * x + y * y + z * z + w * w);
}

// Test the unit vector conversion for quaternions.
void tst_QQuaternion::normalized_data()
{
    // Use the same test data as the length test.
    length_data();
}
void tst_QQuaternion::normalized()
{
    QFETCH(qreal, x);
    QFETCH(qreal, y);
    QFETCH(qreal, z);
    QFETCH(qreal, w);
    QFETCH(qreal, len);

    QQuaternion v(w, x, y, z);
    QQuaternion u = v.normalized();
    if (v.isNull())
        QVERIFY(u.isNull());
    else
        QCOMPARE(u.length(), qreal(1.0f));
    QCOMPARE(u.x() * len, v.x());
    QCOMPARE(u.y() * len, v.y());
    QCOMPARE(u.z() * len, v.z());
    QCOMPARE(u.scalar() * len, v.scalar());
}

// Test the unit vector conversion for quaternions.
void tst_QQuaternion::normalize_data()
{
    // Use the same test data as the length test.
    length_data();
}
void tst_QQuaternion::normalize()
{
    QFETCH(qreal, x);
    QFETCH(qreal, y);
    QFETCH(qreal, z);
    QFETCH(qreal, w);

    QQuaternion v(w, x, y, z);
    bool isNull = v.isNull();
    v.normalize();
    if (isNull)
        QVERIFY(v.isNull());
    else
        QCOMPARE(v.length(), qreal(1.0f));
}

// Test the comparison operators for quaternions.
void tst_QQuaternion::compare()
{
    QQuaternion v1(8, 1, 2, 4);
    QQuaternion v2(8, 1, 2, 4);
    QQuaternion v3(8, 3, 2, 4);
    QQuaternion v4(8, 1, 3, 4);
    QQuaternion v5(8, 1, 2, 3);
    QQuaternion v6(3, 1, 2, 4);

    QVERIFY(v1 == v2);
    QVERIFY(v1 != v3);
    QVERIFY(v1 != v4);
    QVERIFY(v1 != v5);
    QVERIFY(v1 != v6);
}

// Test addition for quaternions.
void tst_QQuaternion::add_data()
{
    QTest::addColumn<qreal>("x1");
    QTest::addColumn<qreal>("y1");
    QTest::addColumn<qreal>("z1");
    QTest::addColumn<qreal>("w1");
    QTest::addColumn<qreal>("x2");
    QTest::addColumn<qreal>("y2");
    QTest::addColumn<qreal>("z2");
    QTest::addColumn<qreal>("w2");
    QTest::addColumn<qreal>("x3");
    QTest::addColumn<qreal>("y3");
    QTest::addColumn<qreal>("z3");
    QTest::addColumn<qreal>("w3");

    QTest::newRow("null")
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;

    QTest::newRow("xonly")
        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)2.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)3.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;

    QTest::newRow("yonly")
        << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)0.0f << (qreal)2.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)0.0f << (qreal)3.0f << (qreal)0.0f << (qreal)0.0f;

    QTest::newRow("zonly")
        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)2.0f << (qreal)0.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)3.0f << (qreal)0.0f;

    QTest::newRow("wonly")
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)2.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)3.0f;

    QTest::newRow("all")
        << (qreal)1.0f << (qreal)2.0f << (qreal)3.0f << (qreal)8.0f
        << (qreal)4.0f << (qreal)5.0f << (qreal)-6.0f << (qreal)9.0f
        << (qreal)5.0f << (qreal)7.0f << (qreal)-3.0f << (qreal)17.0f;
}
void tst_QQuaternion::add()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, w1);
    QFETCH(qreal, x2);
    QFETCH(qreal, y2);
    QFETCH(qreal, z2);
    QFETCH(qreal, w2);
    QFETCH(qreal, x3);
    QFETCH(qreal, y3);
    QFETCH(qreal, z3);
    QFETCH(qreal, w3);

    QQuaternion v1(w1, x1, y1, z1);
    QQuaternion v2(w2, x2, y2, z2);
    QQuaternion v3(w3, x3, y3, z3);

    QVERIFY((v1 + v2) == v3);

    QQuaternion v4(v1);
    v4 += v2;
    QVERIFY(v4 == v3);

    QCOMPARE(v4.x(), v1.x() + v2.x());
    QCOMPARE(v4.y(), v1.y() + v2.y());
    QCOMPARE(v4.z(), v1.z() + v2.z());
    QCOMPARE(v4.scalar(), v1.scalar() + v2.scalar());
}

// Test subtraction for quaternions.
void tst_QQuaternion::subtract_data()
{
    // Use the same test data as the add test.
    add_data();
}
void tst_QQuaternion::subtract()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, w1);
    QFETCH(qreal, x2);
    QFETCH(qreal, y2);
    QFETCH(qreal, z2);
    QFETCH(qreal, w2);
    QFETCH(qreal, x3);
    QFETCH(qreal, y3);
    QFETCH(qreal, z3);
    QFETCH(qreal, w3);

    QQuaternion v1(w1, x1, y1, z1);
    QQuaternion v2(w2, x2, y2, z2);
    QQuaternion v3(w3, x3, y3, z3);

    QVERIFY((v3 - v1) == v2);
    QVERIFY((v3 - v2) == v1);

    QQuaternion v4(v3);
    v4 -= v1;
    QVERIFY(v4 == v2);

    QCOMPARE(v4.x(), v3.x() - v1.x());
    QCOMPARE(v4.y(), v3.y() - v1.y());
    QCOMPARE(v4.z(), v3.z() - v1.z());
    QCOMPARE(v4.scalar(), v3.scalar() - v1.scalar());

    QQuaternion v5(v3);
    v5 -= v2;
    QVERIFY(v5 == v1);

    QCOMPARE(v5.x(), v3.x() - v2.x());
    QCOMPARE(v5.y(), v3.y() - v2.y());
    QCOMPARE(v5.z(), v3.z() - v2.z());
    QCOMPARE(v5.scalar(), v3.scalar() - v2.scalar());
}

// Test quaternion multiplication.
void tst_QQuaternion::multiply_data()
{
    QTest::addColumn<qreal>("x1");
    QTest::addColumn<qreal>("y1");
    QTest::addColumn<qreal>("z1");
    QTest::addColumn<qreal>("w1");
    QTest::addColumn<qreal>("x2");
    QTest::addColumn<qreal>("y2");
    QTest::addColumn<qreal>("z2");
    QTest::addColumn<qreal>("w2");

    QTest::newRow("null")
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;

    QTest::newRow("unitvec")
        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
        << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f << (qreal)1.0f;

    QTest::newRow("complex")
        << (qreal)1.0f << (qreal)2.0f << (qreal)3.0f << (qreal)7.0f
        << (qreal)4.0f << (qreal)5.0f << (qreal)6.0f << (qreal)8.0f;

    for (qreal w = -1.0f; w <= 1.0f; w += 0.5f)
        for (qreal x = -1.0f; x <= 1.0f; x += 0.5f)
            for (qreal y = -1.0f; y <= 1.0f; y += 0.5f)
                for (qreal z = -1.0f; z <= 1.0f; z += 0.5f) {
                    QTest::newRow("exhaustive")
                        << x << y << z << w
                        << z << w << y << x;
                }
}
void tst_QQuaternion::multiply()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, w1);
    QFETCH(qreal, x2);
    QFETCH(qreal, y2);
    QFETCH(qreal, z2);
    QFETCH(qreal, w2);

    QQuaternion q1(w1, x1, y1, z1);
    QQuaternion q2(w2, x2, y2, z2);

    // Use the simple algorithm at:
    // http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q53
    // to calculate the answer we expect to get.
    QVector3D v1(x1, y1, z1);
    QVector3D v2(x2, y2, z2);
    qreal scalar = w1 * w2 - QVector3D::dotProduct(v1, v2);
    QVector3D vector = w1 * v2 + w2 * v1 + QVector3D::crossProduct(v1, v2);
    QQuaternion result(scalar, vector);

    QVERIFY((q1 * q2) == result);
}

// Test multiplication by a factor for quaternions.
void tst_QQuaternion::multiplyFactor_data()
{
    QTest::addColumn<qreal>("x1");
    QTest::addColumn<qreal>("y1");
    QTest::addColumn<qreal>("z1");
    QTest::addColumn<qreal>("w1");
    QTest::addColumn<qreal>("factor");
    QTest::addColumn<qreal>("x2");
    QTest::addColumn<qreal>("y2");
    QTest::addColumn<qreal>("z2");
    QTest::addColumn<qreal>("w2");

    QTest::newRow("null")
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)100.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;

    QTest::newRow("xonly")
        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)2.0f
        << (qreal)2.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;

    QTest::newRow("yonly")
        << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
        << (qreal)2.0f
        << (qreal)0.0f << (qreal)2.0f << (qreal)0.0f << (qreal)0.0f;

    QTest::newRow("zonly")
        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f
        << (qreal)2.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)2.0f << (qreal)0.0f;

    QTest::newRow("wonly")
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
        << (qreal)2.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)2.0f;

    QTest::newRow("all")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)4.0f
        << (qreal)2.0f
        << (qreal)2.0f << (qreal)4.0f << (qreal)-6.0f << (qreal)8.0f;

    QTest::newRow("allzero")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)4.0f
        << (qreal)0.0f
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;
}
void tst_QQuaternion::multiplyFactor()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, w1);
    QFETCH(qreal, factor);
    QFETCH(qreal, x2);
    QFETCH(qreal, y2);
    QFETCH(qreal, z2);
    QFETCH(qreal, w2);

    QQuaternion v1(w1, x1, y1, z1);
    QQuaternion v2(w2, x2, y2, z2);

    QVERIFY((v1 * factor) == v2);
    QVERIFY((factor * v1) == v2);

    QQuaternion v3(v1);
    v3 *= factor;
    QVERIFY(v3 == v2);

    QCOMPARE(v3.x(), v1.x() * factor);
    QCOMPARE(v3.y(), v1.y() * factor);
    QCOMPARE(v3.z(), v1.z() * factor);
    QCOMPARE(v3.scalar(), v1.scalar() * factor);
}

// Test division by a factor for quaternions.
void tst_QQuaternion::divide_data()
{
    // Use the same test data as the multiply test.
    multiplyFactor_data();
}
void tst_QQuaternion::divide()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, w1);
    QFETCH(qreal, factor);
    QFETCH(qreal, x2);
    QFETCH(qreal, y2);
    QFETCH(qreal, z2);
    QFETCH(qreal, w2);

    QQuaternion v1(w1, x1, y1, z1);
    QQuaternion v2(w2, x2, y2, z2);

    if (factor == (qreal)0.0f)
        return;

    QVERIFY((v2 / factor) == v1);

    QQuaternion v3(v2);
    v3 /= factor;
    QVERIFY(v3 == v1);

    QCOMPARE(v3.x(), v2.x() / factor);
    QCOMPARE(v3.y(), v2.y() / factor);
    QCOMPARE(v3.z(), v2.z() / factor);
    QCOMPARE(v3.scalar(), v2.scalar() / factor);
}

// Test negation for quaternions.
void tst_QQuaternion::negate_data()
{
    // Use the same test data as the add test.
    add_data();
}
void tst_QQuaternion::negate()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, w1);

    QQuaternion v1(w1, x1, y1, z1);
    QQuaternion v2(-w1, -x1, -y1, -z1);

    QVERIFY(-v1 == v2);
}

// Test quaternion conjugate calculations.
void tst_QQuaternion::conjugate_data()
{
    // Use the same test data as the add test.
    add_data();
}
void tst_QQuaternion::conjugate()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, w1);

    QQuaternion v1(w1, x1, y1, z1);
    QQuaternion v2(w1, -x1, -y1, -z1);

    QVERIFY(v1.conjugate() == v2);
}

// Test quaternion creation from an axis and an angle.
void tst_QQuaternion::fromAxisAndAngle_data()
{
    QTest::addColumn<qreal>("x1");
    QTest::addColumn<qreal>("y1");
    QTest::addColumn<qreal>("z1");
    QTest::addColumn<qreal>("angle");

    QTest::newRow("null")
        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;

    QTest::newRow("xonly")
        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)90.0f;

    QTest::newRow("yonly")
        << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f << (qreal)180.0f;

    QTest::newRow("zonly")
        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f << (qreal)270.0f;

    QTest::newRow("complex")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)45.0f;
}
void tst_QQuaternion::fromAxisAndAngle()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, angle);

    // Use a straight-forward implementation of the algorithm at:
    // http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56
    // to calculate the answer we expect to get.
    QVector3D vector = QVector3D(x1, y1, z1).normalized();
    qreal sin_a = qSin((angle * M_PI / 180.0) / 2.0);
    qreal cos_a = qCos((angle * M_PI / 180.0) / 2.0);
    QQuaternion result((qreal)cos_a,
                       (qreal)(vector.x() * sin_a),
                       (qreal)(vector.y() * sin_a),
                       (qreal)(vector.z() * sin_a));
    result = result.normalized();

    QQuaternion answer = QQuaternion::fromAxisAndAngle(QVector3D(x1, y1, z1), angle);
    QVERIFY(fuzzyCompare(answer.x(), result.x()));
    QVERIFY(fuzzyCompare(answer.y(), result.y()));
    QVERIFY(fuzzyCompare(answer.z(), result.z()));
    QVERIFY(fuzzyCompare(answer.scalar(), result.scalar()));

    answer = QQuaternion::fromAxisAndAngle(x1, y1, z1, angle);
    QVERIFY(fuzzyCompare(answer.x(), result.x()));
    QVERIFY(fuzzyCompare(answer.y(), result.y()));
    QVERIFY(fuzzyCompare(answer.z(), result.z()));
    QVERIFY(fuzzyCompare(answer.scalar(), result.scalar()));
}

// Test spherical interpolation of quaternions.
void tst_QQuaternion::slerp_data()
{
    QTest::addColumn<qreal>("x1");
    QTest::addColumn<qreal>("y1");
    QTest::addColumn<qreal>("z1");
    QTest::addColumn<qreal>("angle1");
    QTest::addColumn<qreal>("x2");
    QTest::addColumn<qreal>("y2");
    QTest::addColumn<qreal>("z2");
    QTest::addColumn<qreal>("angle2");
    QTest::addColumn<qreal>("t");
    QTest::addColumn<qreal>("x3");
    QTest::addColumn<qreal>("y3");
    QTest::addColumn<qreal>("z3");
    QTest::addColumn<qreal>("angle3");

    QTest::newRow("first")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)90.0f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)180.0f
        << (qreal)0.0f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)90.0f;
    QTest::newRow("first2")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)90.0f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)180.0f
        << (qreal)-0.5f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)90.0f;
    QTest::newRow("second")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)90.0f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)180.0f
        << (qreal)1.0f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)180.0f;
    QTest::newRow("second2")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)90.0f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)180.0f
        << (qreal)1.5f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)180.0f;
    QTest::newRow("middle")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)90.0f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)180.0f
        << (qreal)0.5f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)135.0f;
    QTest::newRow("wide angle")
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)0.0f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)270.0f
        << (qreal)0.5f
        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f << (qreal)-45.0f;
}
void tst_QQuaternion::slerp()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, angle1);
    QFETCH(qreal, x2);
    QFETCH(qreal, y2);
    QFETCH(qreal, z2);
    QFETCH(qreal, angle2);
    QFETCH(qreal, t);
    QFETCH(qreal, x3);
    QFETCH(qreal, y3);
    QFETCH(qreal, z3);
    QFETCH(qreal, angle3);

    QQuaternion q1 = QQuaternion::fromAxisAndAngle(x1, y1, z1, angle1);
    QQuaternion q2 = QQuaternion::fromAxisAndAngle(x2, y2, z2, angle2);
    QQuaternion q3 = QQuaternion::fromAxisAndAngle(x3, y3, z3, angle3);

    QQuaternion result = QQuaternion::slerp(q1, q2, t);

    QVERIFY(fuzzyCompare(result.x(), q3.x()));
    QVERIFY(fuzzyCompare(result.y(), q3.y()));
    QVERIFY(fuzzyCompare(result.z(), q3.z()));
    QVERIFY(fuzzyCompare(result.scalar(), q3.scalar()));
}

// Test normalized linear interpolation of quaternions.
void tst_QQuaternion::nlerp_data()
{
    slerp_data();
}
void tst_QQuaternion::nlerp()
{
    QFETCH(qreal, x1);
    QFETCH(qreal, y1);
    QFETCH(qreal, z1);
    QFETCH(qreal, angle1);
    QFETCH(qreal, x2);
    QFETCH(qreal, y2);
    QFETCH(qreal, z2);
    QFETCH(qreal, angle2);
    QFETCH(qreal, t);

    QQuaternion q1 = QQuaternion::fromAxisAndAngle(x1, y1, z1, angle1);
    QQuaternion q2 = QQuaternion::fromAxisAndAngle(x2, y2, z2, angle2);

    QQuaternion result = QQuaternion::nlerp(q1, q2, t);

    qreal resultx, resulty, resultz, resultscalar;
    if (t <= 0.0f) {
        resultx = q1.x();
        resulty = q1.y();
        resultz = q1.z();
        resultscalar = q1.scalar();
    } else if (t >= 1.0f) {
        resultx = q2.x();
        resulty = q2.y();
        resultz = q2.z();
        resultscalar = q2.scalar();
    } else if (qAbs(angle1 - angle2) <= 180.f) {
        resultx = q1.x() * (1 - t) + q2.x() * t;
        resulty = q1.y() * (1 - t) + q2.y() * t;
        resultz = q1.z() * (1 - t) + q2.z() * t;
        resultscalar = q1.scalar() * (1 - t) + q2.scalar() * t;
    } else {
        // Angle greater than 180 degrees: negate q2.
        resultx = q1.x() * (1 - t) - q2.x() * t;
        resulty = q1.y() * (1 - t) - q2.y() * t;
        resultz = q1.z() * (1 - t) - q2.z() * t;
        resultscalar = q1.scalar() * (1 - t) - q2.scalar() * t;
    }

    QQuaternion q3 = QQuaternion(resultscalar, resultx, resulty, resultz).normalized();

    QVERIFY(fuzzyCompare(result.x(), q3.x()));
    QVERIFY(fuzzyCompare(result.y(), q3.y()));
    QVERIFY(fuzzyCompare(result.z(), q3.z()));
    QVERIFY(fuzzyCompare(result.scalar(), q3.scalar()));
}

class tst_QQuaternionProperties : public QObject
{
    Q_OBJECT
    Q_PROPERTY(QQuaternion quaternion READ quaternion WRITE setQuaternion)
public:
    tst_QQuaternionProperties(QObject *parent = 0) : QObject(parent) {}

    QQuaternion quaternion() const { return q; }
    void setQuaternion(const QQuaternion& value) { q = value; }

private:
    QQuaternion q;
};

// Test getting and setting quaternion properties via the metaobject system.
void tst_QQuaternion::properties()
{
    tst_QQuaternionProperties obj;

    obj.setQuaternion(QQuaternion(6.0f, 7.0f, 8.0f, 9.0f));

    QQuaternion q = qVariantValue<QQuaternion>(obj.property("quaternion"));
    QCOMPARE(q.scalar(), (qreal)6.0f);
    QCOMPARE(q.x(), (qreal)7.0f);
    QCOMPARE(q.y(), (qreal)8.0f);
    QCOMPARE(q.z(), (qreal)9.0f);

    obj.setProperty("quaternion",
                    qVariantFromValue(QQuaternion(-6.0f, -7.0f, -8.0f, -9.0f)));

    q = qVariantValue<QQuaternion>(obj.property("quaternion"));
    QCOMPARE(q.scalar(), (qreal)-6.0f);
    QCOMPARE(q.x(), (qreal)-7.0f);
    QCOMPARE(q.y(), (qreal)-8.0f);
    QCOMPARE(q.z(), (qreal)-9.0f);
}

void tst_QQuaternion::metaTypes()
{
    QVERIFY(QMetaType::type("QQuaternion") == QMetaType::QQuaternion);

    QCOMPARE(QByteArray(QMetaType::typeName(QMetaType::QQuaternion)),
             QByteArray("QQuaternion"));

    QVERIFY(QMetaType::isRegistered(QMetaType::QQuaternion));

    QVERIFY(qMetaTypeId<QQuaternion>() == QMetaType::QQuaternion);
}

QTEST_APPLESS_MAIN(tst_QQuaternion)

#include "tst_qquaternion.moc"