Move math3d unit tests up one level to tests/auto

Some of the platform test infrastructure assumes that all unit
tests are sub-directories under tests/auto, and the tests/auto/math3d
sub-directory was confusing that infrastructure.

Reviewed-by: trustme

2 files changed, 2145 insertions, 0 deletions

diff --git a/tests/auto/qvectornd/qvectornd.pro b/tests/auto/qvectornd/qvectornd.pro
new file mode 100644
index 0000000..6346199
--- /dev/null
+++ b/tests/auto/qvectornd/qvectornd.pro
@@ -0,0 +1,2 @@
+load(qttest_p4)
+SOURCES += tst_qvectornd.cpp
diff --git a/tests/auto/qvectornd/tst_qvectornd.cpp b/tests/auto/qvectornd/tst_qvectornd.cpp
new file mode 100644
index 0000000..22f0ce1
--- /dev/null
+++ b/tests/auto/qvectornd/tst_qvectornd.cpp
@@ -0,0 +1,2143 @@
+/****************************************************************************
+**
+** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies).
+** Contact: Nokia Corporation (qt-info@nokia.com)
+**
+** This file is part of the test suite of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** No Commercial Usage
+** This file contains pre-release code and may not be distributed.
+** You may use this file in accordance with the terms and conditions
+** contained in the either Technology Preview License Agreement or the
+** Beta Release License Agreement.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 2.1 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL included in the
+** packaging of this file.  Please review the following information to
+** ensure the GNU Lesser General Public License version 2.1 requirements
+** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
+**
+** In addition, as a special exception, Nokia gives you certain
+** additional rights. These rights are described in the Nokia Qt LGPL
+** Exception version 1.0, included in the file LGPL_EXCEPTION.txt in this
+** package.
+**
+** GNU General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU
+** General Public License version 3.0 as published by the Free Software
+** Foundation and appearing in the file LICENSE.GPL included in the
+** packaging of this file.  Please review the following information to
+** ensure the GNU General Public License version 3.0 requirements will be
+** met: http://www.gnu.org/copyleft/gpl.html.
+**
+** If you are unsure which license is appropriate for your use, please
+** contact the sales department at http://qt.nokia.com/contact.
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+#include <QtTest/QtTest>
+#include <QtCore/qmath.h>
+#include <QtGui/qvector2d.h>
+#include <QtGui/qvector3d.h>
+#include <QtGui/qvector4d.h>
+
+class tst_QVector : public QObject
+{
+    Q_OBJECT
+public:
+    tst_QVector() {}
+    ~tst_QVector() {}
+
+private slots:
+    void create2();
+    void create3();
+    void create4();
+
+    void length2_data();
+    void length2();
+    void length3_data();
+    void length3();
+    void length4_data();
+    void length4();
+
+    void normalized2_data();
+    void normalized2();
+    void normalized3_data();
+    void normalized3();
+    void normalized4_data();
+    void normalized4();
+
+    void normalize2_data();
+    void normalize2();
+    void normalize3_data();
+    void normalize3();
+    void normalize4_data();
+    void normalize4();
+
+    void compare2();
+    void compare3();
+    void compare4();
+
+    void add2_data();
+    void add2();
+    void add3_data();
+    void add3();
+    void add4_data();
+    void add4();
+
+    void subtract2_data();
+    void subtract2();
+    void subtract3_data();
+    void subtract3();
+    void subtract4_data();
+    void subtract4();
+
+    void multiply2_data();
+    void multiply2();
+    void multiply3_data();
+    void multiply3();
+    void multiply4_data();
+    void multiply4();
+
+    void multiplyFactor2_data();
+    void multiplyFactor2();
+    void multiplyFactor3_data();
+    void multiplyFactor3();
+    void multiplyFactor4_data();
+    void multiplyFactor4();
+
+    void divide2_data();
+    void divide2();
+    void divide3_data();
+    void divide3();
+    void divide4_data();
+    void divide4();
+
+    void negate2_data();
+    void negate2();
+    void negate3_data();
+    void negate3();
+    void negate4_data();
+    void negate4();
+
+    void crossProduct_data();
+    void crossProduct();
+    void normal_data();
+    void normal();
+    void distanceToPlane_data();
+    void distanceToPlane();
+    void distanceToLine_data();
+    void distanceToLine();
+
+    void dotProduct2_data();
+    void dotProduct2();
+    void dotProduct3_data();
+    void dotProduct3();
+    void dotProduct4_data();
+    void dotProduct4();
+
+    void properties();
+    void metaTypes();
+};
+
+// qFuzzyCompare isn't always "fuzzy" enough to handle conversion
+// between float, double, and qreal.  So create "fuzzier" compares.
+static bool fuzzyCompare(float x, float y)
+{
+    float diff = x - y;
+    if (diff < 0.0f)
+        diff = -diff;
+    return (diff < 0.001);
+}
+
+// Test the creation of QVector2D objects in various ways:
+// construct, copy, and modify.
+void tst_QVector::create2()
+{
+    QVector2D null;
+    QCOMPARE(null.x(), (qreal)0.0f);
+    QCOMPARE(null.y(), (qreal)0.0f);
+    QVERIFY(null.isNull());
+
+    QVector2D v1(1.0f, 2.5f);
+    QCOMPARE(v1.x(), (qreal)1.0f);
+    QCOMPARE(v1.y(), (qreal)2.5f);
+    QVERIFY(!v1.isNull());
+
+    QVector2D v1i(1, 2);
+    QCOMPARE(v1i.x(), (qreal)1.0f);
+    QCOMPARE(v1i.y(), (qreal)2.0f);
+    QVERIFY(!v1i.isNull());
+
+    QVector2D v2(v1);
+    QCOMPARE(v2.x(), (qreal)1.0f);
+    QCOMPARE(v2.y(), (qreal)2.5f);
+    QVERIFY(!v2.isNull());
+
+    QVector2D v4;
+    QCOMPARE(v4.x(), (qreal)0.0f);
+    QCOMPARE(v4.y(), (qreal)0.0f);
+    QVERIFY(v4.isNull());
+    v4 = v1;
+    QCOMPARE(v4.x(), (qreal)1.0f);
+    QCOMPARE(v4.y(), (qreal)2.5f);
+    QVERIFY(!v4.isNull());
+
+    QVector2D v5(QPoint(1, 2));
+    QCOMPARE(v5.x(), (qreal)1.0f);
+    QCOMPARE(v5.y(), (qreal)2.0f);
+    QVERIFY(!v5.isNull());
+
+    QVector2D v6(QPointF(1, 2.5));
+    QCOMPARE(v6.x(), (qreal)1.0f);
+    QCOMPARE(v6.y(), (qreal)2.5f);
+    QVERIFY(!v6.isNull());
+
+    QVector2D v7(QVector3D(1.0f, 2.5f, 54.25f));
+    QCOMPARE(v7.x(), (qreal)1.0f);
+    QCOMPARE(v7.y(), (qreal)2.5f);
+    QVERIFY(!v6.isNull());
+
+    QVector2D v8(QVector4D(1.0f, 2.5f, 54.25f, 34.0f));
+    QCOMPARE(v8.x(), (qreal)1.0f);
+    QCOMPARE(v8.y(), (qreal)2.5f);
+    QVERIFY(!v6.isNull());
+
+    v1.setX(3.0f);
+    QCOMPARE(v1.x(), (qreal)3.0f);
+    QCOMPARE(v1.y(), (qreal)2.5f);
+    QVERIFY(!v1.isNull());
+
+    v1.setY(10.5f);
+    QCOMPARE(v1.x(), (qreal)3.0f);
+    QCOMPARE(v1.y(), (qreal)10.5f);
+    QVERIFY(!v1.isNull());
+
+    v1.setX(0.0f);
+    v1.setY(0.0f);
+    QCOMPARE(v1.x(), (qreal)0.0f);
+    QCOMPARE(v1.y(), (qreal)0.0f);
+    QVERIFY(v1.isNull());
+
+    QPoint p1 = v8.toPoint();
+    QCOMPARE(p1.x(), 1);
+    QCOMPARE(p1.y(), 3);
+
+    QPointF p2 = v8.toPointF();
+    QCOMPARE((qreal)p2.x(), (qreal)1.0f);
+    QCOMPARE((qreal)p2.y(), (qreal)2.5f);
+
+    QVector3D v9 = v8.toVector3D();
+    QCOMPARE(v9.x(), (qreal)1.0f);
+    QCOMPARE(v9.y(), (qreal)2.5f);
+    QCOMPARE(v9.z(), (qreal)0.0f);
+
+    QVector4D v10 = v8.toVector4D();
+    QCOMPARE(v10.x(), (qreal)1.0f);
+    QCOMPARE(v10.y(), (qreal)2.5f);
+    QCOMPARE(v10.z(), (qreal)0.0f);
+    QCOMPARE(v10.w(), (qreal)0.0f);
+}
+
+// Test the creation of QVector3D objects in various ways:
+// construct, copy, and modify.
+void tst_QVector::create3()
+{
+    QVector3D null;
+    QCOMPARE(null.x(), (qreal)0.0f);
+    QCOMPARE(null.y(), (qreal)0.0f);
+    QCOMPARE(null.z(), (qreal)0.0f);
+    QVERIFY(null.isNull());
+
+    QVector3D v1(1.0f, 2.5f, -89.25f);
+    QCOMPARE(v1.x(), (qreal)1.0f);
+    QCOMPARE(v1.y(), (qreal)2.5f);
+    QCOMPARE(v1.z(), (qreal)-89.25f);
+    QVERIFY(!v1.isNull());
+
+    QVector3D v1i(1, 2, -89);
+    QCOMPARE(v1i.x(), (qreal)1.0f);
+    QCOMPARE(v1i.y(), (qreal)2.0f);
+    QCOMPARE(v1i.z(), (qreal)-89.0f);
+    QVERIFY(!v1i.isNull());
+
+    QVector3D v2(v1);
+    QCOMPARE(v2.x(), (qreal)1.0f);
+    QCOMPARE(v2.y(), (qreal)2.5f);
+    QCOMPARE(v2.z(), (qreal)-89.25f);
+    QVERIFY(!v2.isNull());
+
+    QVector3D v3(1.0f, 2.5f, 0.0f);
+    QCOMPARE(v3.x(), (qreal)1.0f);
+    QCOMPARE(v3.y(), (qreal)2.5f);
+    QCOMPARE(v3.z(), (qreal)0.0f);
+    QVERIFY(!v3.isNull());
+
+    QVector3D v3i(1, 2, 0);
+    QCOMPARE(v3i.x(), (qreal)1.0f);
+    QCOMPARE(v3i.y(), (qreal)2.0f);
+    QCOMPARE(v3i.z(), (qreal)0.0f);
+    QVERIFY(!v3i.isNull());
+
+    QVector3D v4;
+    QCOMPARE(v4.x(), (qreal)0.0f);
+    QCOMPARE(v4.y(), (qreal)0.0f);
+    QCOMPARE(v4.z(), (qreal)0.0f);
+    QVERIFY(v4.isNull());
+    v4 = v1;
+    QCOMPARE(v4.x(), (qreal)1.0f);
+    QCOMPARE(v4.y(), (qreal)2.5f);
+    QCOMPARE(v4.z(), (qreal)-89.25f);
+    QVERIFY(!v4.isNull());
+
+    QVector3D v5(QPoint(1, 2));
+    QCOMPARE(v5.x(), (qreal)1.0f);
+    QCOMPARE(v5.y(), (qreal)2.0f);
+    QCOMPARE(v5.z(), (qreal)0.0f);
+    QVERIFY(!v5.isNull());
+
+    QVector3D v6(QPointF(1, 2.5));
+    QCOMPARE(v6.x(), (qreal)1.0f);
+    QCOMPARE(v6.y(), (qreal)2.5f);
+    QCOMPARE(v6.z(), (qreal)0.0f);
+    QVERIFY(!v6.isNull());
+
+    QVector3D v7(QVector2D(1.0f, 2.5f));
+    QCOMPARE(v7.x(), (qreal)1.0f);
+    QCOMPARE(v7.y(), (qreal)2.5f);
+    QCOMPARE(v7.z(), (qreal)0.0f);
+    QVERIFY(!v7.isNull());
+
+    QVector3D v8(QVector2D(1.0f, 2.5f), 54.25f);
+    QCOMPARE(v8.x(), (qreal)1.0f);
+    QCOMPARE(v8.y(), (qreal)2.5f);
+    QCOMPARE(v8.z(), (qreal)54.25f);
+    QVERIFY(!v8.isNull());
+
+    QVector3D v9(QVector4D(1.0f, 2.5f, 54.25f, 34.0f));
+    QCOMPARE(v9.x(), (qreal)1.0f);
+    QCOMPARE(v9.y(), (qreal)2.5f);
+    QCOMPARE(v9.z(), (qreal)54.25f);
+    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);
+    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);
+    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);
+    QVERIFY(!v1.isNull());
+
+    v1.setX(0.0f);
+    v1.setY(0.0f);
+    v1.setZ(0.0f);
+    QCOMPARE(v1.x(), (qreal)0.0f);
+    QCOMPARE(v1.y(), (qreal)0.0f);
+    QCOMPARE(v1.z(), (qreal)0.0f);
+    QVERIFY(v1.isNull());
+
+    QPoint p1 = v8.toPoint();
+    QCOMPARE(p1.x(), 1);
+    QCOMPARE(p1.y(), 3);
+
+    QPointF p2 = v8.toPointF();
+    QCOMPARE((qreal)p2.x(), (qreal)1.0f);
+    QCOMPARE((qreal)p2.y(), (qreal)2.5f);
+
+    QVector2D v10 = v8.toVector2D();
+    QCOMPARE(v10.x(), (qreal)1.0f);
+    QCOMPARE(v10.y(), (qreal)2.5f);
+
+    QVector4D v11 = v8.toVector4D();
+    QCOMPARE(v11.x(), (qreal)1.0f);
+    QCOMPARE(v11.y(), (qreal)2.5f);
+    QCOMPARE(v11.z(), (qreal)54.25f);
+    QCOMPARE(v11.w(), (qreal)0.0f);
+}
+
+// Test the creation of QVector4D objects in various ways:
+// construct, copy, and modify.
+void tst_QVector::create4()
+{
+    QVector4D null;
+    QCOMPARE(null.x(), (qreal)0.0f);
+    QCOMPARE(null.y(), (qreal)0.0f);
+    QCOMPARE(null.z(), (qreal)0.0f);
+    QCOMPARE(null.w(), (qreal)0.0f);
+    QVERIFY(null.isNull());
+
+    QVector4D v1(1.0f, 2.5f, -89.25f, 34.0f);
+    QCOMPARE(v1.x(), (qreal)1.0f);
+    QCOMPARE(v1.y(), (qreal)2.5f);
+    QCOMPARE(v1.z(), (qreal)-89.25f);
+    QCOMPARE(v1.w(), (qreal)34.0f);
+    QVERIFY(!v1.isNull());
+
+    QVector4D v1i(1, 2, -89, 34);
+    QCOMPARE(v1i.x(), (qreal)1.0f);
+    QCOMPARE(v1i.y(), (qreal)2.0f);
+    QCOMPARE(v1i.z(), (qreal)-89.0f);
+    QCOMPARE(v1i.w(), (qreal)34.0f);
+    QVERIFY(!v1i.isNull());
+
+    QVector4D v2(v1);
+    QCOMPARE(v2.x(), (qreal)1.0f);
+    QCOMPARE(v2.y(), (qreal)2.5f);
+    QCOMPARE(v2.z(), (qreal)-89.25f);
+    QCOMPARE(v2.w(), (qreal)34.0f);
+    QVERIFY(!v2.isNull());
+
+    QVector4D v3(1.0f, 2.5f, 0.0f, 0.0f);
+    QCOMPARE(v3.x(), (qreal)1.0f);
+    QCOMPARE(v3.y(), (qreal)2.5f);
+    QCOMPARE(v3.z(), (qreal)0.0f);
+    QCOMPARE(v3.w(), (qreal)0.0f);
+    QVERIFY(!v3.isNull());
+
+    QVector4D v3i(1, 2, 0, 0);
+    QCOMPARE(v3i.x(), (qreal)1.0f);
+    QCOMPARE(v3i.y(), (qreal)2.0f);
+    QCOMPARE(v3i.z(), (qreal)0.0f);
+    QCOMPARE(v3i.w(), (qreal)0.0f);
+    QVERIFY(!v3i.isNull());
+
+    QVector4D v3b(1.0f, 2.5f, -89.25f, 0.0f);
+    QCOMPARE(v3b.x(), (qreal)1.0f);
+    QCOMPARE(v3b.y(), (qreal)2.5f);
+    QCOMPARE(v3b.z(), (qreal)-89.25f);
+    QCOMPARE(v3b.w(), (qreal)0.0f);
+    QVERIFY(!v3b.isNull());
+
+    QVector4D v3bi(1, 2, -89, 0);
+    QCOMPARE(v3bi.x(), (qreal)1.0f);
+    QCOMPARE(v3bi.y(), (qreal)2.0f);
+    QCOMPARE(v3bi.z(), (qreal)-89.0f);
+    QCOMPARE(v3bi.w(), (qreal)0.0f);
+    QVERIFY(!v3bi.isNull());
+
+    QVector4D v4;
+    QCOMPARE(v4.x(), (qreal)0.0f);
+    QCOMPARE(v4.y(), (qreal)0.0f);
+    QCOMPARE(v4.z(), (qreal)0.0f);
+    QCOMPARE(v4.w(), (qreal)0.0f);
+    QVERIFY(v4.isNull());
+    v4 = v1;
+    QCOMPARE(v4.x(), (qreal)1.0f);
+    QCOMPARE(v4.y(), (qreal)2.5f);
+    QCOMPARE(v4.z(), (qreal)-89.25f);
+    QCOMPARE(v4.w(), (qreal)34.0f);
+    QVERIFY(!v4.isNull());
+
+    QVector4D v5(QPoint(1, 2));
+    QCOMPARE(v5.x(), (qreal)1.0f);
+    QCOMPARE(v5.y(), (qreal)2.0f);
+    QCOMPARE(v5.z(), (qreal)0.0f);
+    QCOMPARE(v5.w(), (qreal)0.0f);
+    QVERIFY(!v5.isNull());
+
+    QVector4D v6(QPointF(1, 2.5));
+    QCOMPARE(v6.x(), (qreal)1.0f);
+    QCOMPARE(v6.y(), (qreal)2.5f);
+    QCOMPARE(v6.z(), (qreal)0.0f);
+    QCOMPARE(v6.w(), (qreal)0.0f);
+    QVERIFY(!v6.isNull());
+
+    QVector4D v7(QVector2D(1.0f, 2.5f));
+    QCOMPARE(v7.x(), (qreal)1.0f);
+    QCOMPARE(v7.y(), (qreal)2.5f);
+    QCOMPARE(v7.z(), (qreal)0.0f);
+    QCOMPARE(v7.w(), (qreal)0.0f);
+    QVERIFY(!v7.isNull());
+
+    QVector4D v8(QVector3D(1.0f, 2.5f, -89.25f));
+    QCOMPARE(v8.x(), (qreal)1.0f);
+    QCOMPARE(v8.y(), (qreal)2.5f);
+    QCOMPARE(v8.z(), (qreal)-89.25f);
+    QCOMPARE(v8.w(), (qreal)0.0f);
+    QVERIFY(!v8.isNull());
+
+    QVector4D v9(QVector3D(1.0f, 2.5f, -89.25f), 34);
+    QCOMPARE(v9.x(), (qreal)1.0f);
+    QCOMPARE(v9.y(), (qreal)2.5f);
+    QCOMPARE(v9.z(), (qreal)-89.25f);
+    QCOMPARE(v9.w(), (qreal)34.0f);
+    QVERIFY(!v9.isNull());
+
+    QVector4D v10(QVector2D(1.0f, 2.5f), 23.5f, -8);
+    QCOMPARE(v10.x(), (qreal)1.0f);
+    QCOMPARE(v10.y(), (qreal)2.5f);
+    QCOMPARE(v10.z(), (qreal)23.5f);
+    QCOMPARE(v10.w(), (qreal)-8.0f);
+    QVERIFY(!v10.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.w(), (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.w(), (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.w(), (qreal)34.0f);
+    QVERIFY(!v1.isNull());
+
+    v1.setW(6.0f);
+    QCOMPARE(v1.x(), (qreal)3.0f);
+    QCOMPARE(v1.y(), (qreal)10.5f);
+    QCOMPARE(v1.z(), (qreal)15.5f);
+    QCOMPARE(v1.w(), (qreal)6.0f);
+    QVERIFY(!v1.isNull());
+
+    v1.setX(0.0f);
+    v1.setY(0.0f);
+    v1.setZ(0.0f);
+    v1.setW(0.0f);
+    QCOMPARE(v1.x(), (qreal)0.0f);
+    QCOMPARE(v1.y(), (qreal)0.0f);
+    QCOMPARE(v1.z(), (qreal)0.0f);
+    QCOMPARE(v1.w(), (qreal)0.0f);
+    QVERIFY(v1.isNull());
+
+    QPoint p1 = v8.toPoint();
+    QCOMPARE(p1.x(), 1);
+    QCOMPARE(p1.y(), 3);
+
+    QPointF p2 = v8.toPointF();
+    QCOMPARE((qreal)p2.x(), (qreal)1.0f);
+    QCOMPARE((qreal)p2.y(), (qreal)2.5f);
+
+    QVector2D v11 = v8.toVector2D();
+    QCOMPARE(v11.x(), (qreal)1.0f);
+    QCOMPARE(v11.y(), (qreal)2.5f);
+
+    QVector3D v12 = v8.toVector3D();
+    QCOMPARE(v12.x(), (qreal)1.0f);
+    QCOMPARE(v12.y(), (qreal)2.5f);
+    QCOMPARE(v12.z(), (qreal)-89.25f);
+
+    QVector2D v13 = v9.toVector2DAffine();
+    QVERIFY(fuzzyCompare(v13.x(), (qreal)(1.0f / 34.0f)));
+    QVERIFY(fuzzyCompare(v13.y(), (qreal)(2.5f / 34.0f)));
+
+    QVector4D zerow(1.0f, 2.0f, 3.0f, 0.0f);
+    v13 = zerow.toVector2DAffine();
+    QVERIFY(v13.isNull());
+
+    QVector3D v14 = v9.toVector3DAffine();
+    QVERIFY(fuzzyCompare(v14.x(), (qreal)(1.0f / 34.0f)));
+    QVERIFY(fuzzyCompare(v14.y(), (qreal)(2.5f / 34.0f)));
+    QVERIFY(fuzzyCompare(v14.z(), (qreal)(-89.25f / 34.0f)));
+
+    v14 = zerow.toVector3DAffine();
+    QVERIFY(v14.isNull());
+}
+
+// Test vector length computation for 2D vectors.
+void tst_QVector::length2_data()
+{
+    QTest::addColumn<qreal>("x");
+    QTest::addColumn<qreal>("y");
+    QTest::addColumn<qreal>("len");
+
+    QTest::newRow("null") << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;
+    QTest::newRow("1x") << (qreal)1.0f << (qreal)0.0f << (qreal)1.0f;
+    QTest::newRow("1y") << (qreal)0.0f << (qreal)1.0f << (qreal)1.0f;
+    QTest::newRow("-1x") << (qreal)-1.0f << (qreal)0.0f << (qreal)1.0f;
+    QTest::newRow("-1y") << (qreal)0.0f << (qreal)-1.0f << (qreal)1.0f;
+    QTest::newRow("two") << (qreal)2.0f << (qreal)-2.0f << (qreal)qSqrt(8.0f);
+}
+void tst_QVector::length2()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+    QFETCH(qreal, len);
+
+    QVector2D v(x, y);
+    QCOMPARE((float)(v.length()), (float)len);
+    QCOMPARE((float)(v.lengthSquared()), (float)(x * x + y * y));
+}
+
+// Test vector length computation for 3D vectors.
+void tst_QVector::length3_data()
+{
+    QTest::addColumn<qreal>("x");
+    QTest::addColumn<qreal>("y");
+    QTest::addColumn<qreal>("z");
+    QTest::addColumn<qreal>("len");
+
+    QTest::newRow("null") << (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)1.0f;
+    QTest::newRow("1y") << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f << (qreal)1.0f;
+    QTest::newRow("1z") << (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)1.0f;
+    QTest::newRow("-1y") << (qreal)0.0f << (qreal)-1.0f << (qreal)0.0f << (qreal)1.0f;
+    QTest::newRow("-1z") << (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)qSqrt(12.0f);
+}
+void tst_QVector::length3()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+    QFETCH(qreal, z);
+    QFETCH(qreal, len);
+
+    QVector3D v(x, y, z);
+    QCOMPARE((float)(v.length()), (float)len);
+    QCOMPARE((float)(v.lengthSquared()), (float)(x * x + y * y + z * z));
+}
+
+// Test vector length computation for 4D vectors.
+void tst_QVector::length4_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_QVector::length4()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+    QFETCH(qreal, z);
+    QFETCH(qreal, w);
+    QFETCH(qreal, len);
+
+    QVector4D v(x, y, z, w);
+    QCOMPARE((float)(v.length()), (float)len);
+    QCOMPARE((float)(v.lengthSquared()), (float)(x * x + y * y + z * z + w * w));
+}
+
+// Test the unit vector conversion for 2D vectors.
+void tst_QVector::normalized2_data()
+{
+    // Use the same test data as the length test.
+    length2_data();
+}
+void tst_QVector::normalized2()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+    QFETCH(qreal, len);
+
+    QVector2D v(x, y);
+    QVector2D u = v.normalized();
+    if (v.isNull())
+        QVERIFY(u.isNull());
+    else
+        QCOMPARE((float)(u.length()), (float)1.0f);
+    QCOMPARE((float)(u.x() * len), (float)(v.x()));
+    QCOMPARE((float)(u.y() * len), (float)(v.y()));
+}
+
+// Test the unit vector conversion for 3D vectors.
+void tst_QVector::normalized3_data()
+{
+    // Use the same test data as the length test.
+    length3_data();
+}
+void tst_QVector::normalized3()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+    QFETCH(qreal, z);
+    QFETCH(qreal, len);
+
+    QVector3D v(x, y, z);
+    QVector3D u = v.normalized();
+    if (v.isNull())
+        QVERIFY(u.isNull());
+    else
+        QCOMPARE((float)(u.length()), (float)1.0f);
+    QCOMPARE((float)(u.x() * len), (float)(v.x()));
+    QCOMPARE((float)(u.y() * len), (float)(v.y()));
+    QCOMPARE((float)(u.z() * len), (float)(v.z()));
+}
+
+// Test the unit vector conversion for 4D vectors.
+void tst_QVector::normalized4_data()
+{
+    // Use the same test data as the length test.
+    length4_data();
+}
+void tst_QVector::normalized4()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+    QFETCH(qreal, z);
+    QFETCH(qreal, w);
+    QFETCH(qreal, len);
+
+    QVector4D v(x, y, z, w);
+    QVector4D u = v.normalized();
+    if (v.isNull())
+        QVERIFY(u.isNull());
+    else
+        QCOMPARE((float)(u.length()), (float)1.0f);
+    QCOMPARE((float)(u.x() * len), (float)(v.x()));
+    QCOMPARE((float)(u.y() * len), (float)(v.y()));
+    QCOMPARE((float)(u.z() * len), (float)(v.z()));
+    QCOMPARE((float)(u.w() * len), (float)(v.w()));
+}
+
+// Test the unit vector conversion for 2D vectors.
+void tst_QVector::normalize2_data()
+{
+    // Use the same test data as the length test.
+    length2_data();
+}
+void tst_QVector::normalize2()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+
+    QVector2D v(x, y);
+    bool isNull = v.isNull();
+    v.normalize();
+    if (isNull)
+        QVERIFY(v.isNull());
+    else
+        QCOMPARE((float)(v.length()), (float)1.0f);
+}
+
+// Test the unit vector conversion for 3D vectors.
+void tst_QVector::normalize3_data()
+{
+    // Use the same test data as the length test.
+    length3_data();
+}
+void tst_QVector::normalize3()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+    QFETCH(qreal, z);
+
+    QVector3D v(x, y, z);
+    bool isNull = v.isNull();
+    v.normalize();
+    if (isNull)
+        QVERIFY(v.isNull());
+    else
+        QCOMPARE((float)(v.length()), (float)1.0f);
+}
+
+// Test the unit vector conversion for 4D vectors.
+void tst_QVector::normalize4_data()
+{
+    // Use the same test data as the length test.
+    length4_data();
+}
+void tst_QVector::normalize4()
+{
+    QFETCH(qreal, x);
+    QFETCH(qreal, y);
+    QFETCH(qreal, z);
+    QFETCH(qreal, w);
+
+    QVector4D v(x, y, z, w);
+    bool isNull = v.isNull();
+    v.normalize();
+    if (isNull)
+        QVERIFY(v.isNull());
+    else
+        QCOMPARE((float)(v.length()), (float)1.0f);
+}
+
+// Test the comparison operators for 2D vectors.
+void tst_QVector::compare2()
+{
+    QVector2D v1(1, 2);
+    QVector2D v2(1, 2);
+    QVector2D v3(3, 2);
+    QVector2D v4(1, 3);
+
+    QVERIFY(v1 == v2);
+    QVERIFY(v1 != v3);
+    QVERIFY(v1 != v4);
+}
+
+// Test the comparison operators for 3D vectors.
+void tst_QVector::compare3()
+{
+    QVector3D v1(1, 2, 4);
+    QVector3D v2(1, 2, 4);
+    QVector3D v3(3, 2, 4);
+    QVector3D v4(1, 3, 4);
+    QVector3D v5(1, 2, 3);
+
+    QVERIFY(v1 == v2);
+    QVERIFY(v1 != v3);
+    QVERIFY(v1 != v4);
+    QVERIFY(v1 != v5);
+}
+
+// Test the comparison operators for 4D vectors.
+void tst_QVector::compare4()
+{
+    QVector4D v1(1, 2, 4, 8);
+    QVector4D v2(1, 2, 4, 8);
+    QVector4D v3(3, 2, 4, 8);
+    QVector4D v4(1, 3, 4, 8);
+    QVector4D v5(1, 2, 3, 8);
+    QVector4D v6(1, 2, 4, 3);
+
+    QVERIFY(v1 == v2);
+    QVERIFY(v1 != v3);
+    QVERIFY(v1 != v4);
+    QVERIFY(v1 != v5);
+    QVERIFY(v1 != v6);
+}
+
+// Test vector addition for 2D vectors.
+void tst_QVector::add2_data()
+{
+    QTest::addColumn<qreal>("x1");
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("x2");
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("x3");
+    QTest::addColumn<qreal>("y3");
+
+    QTest::newRow("null")
+        << (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)2.0f << (qreal)0.0f
+        << (qreal)3.0f << (qreal)0.0f;
+
+    QTest::newRow("yonly")
+        << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f << (qreal)2.0f
+        << (qreal)0.0f << (qreal)3.0f;
+
+    QTest::newRow("all")
+        << (qreal)1.0f << (qreal)2.0f
+        << (qreal)4.0f << (qreal)5.0f
+        << (qreal)5.0f << (qreal)7.0f;
+}
+void tst_QVector::add2()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+
+    QVector2D v1(x1, y1);
+    QVector2D v2(x2, y2);
+    QVector2D v3(x3, y3);
+
+    QVERIFY((v1 + v2) == v3);
+
+    QVector2D v4(v1);
+    v4 += v2;
+    QVERIFY(v4 == v3);
+
+    QCOMPARE(v4.x(), v1.x() + v2.x());
+    QCOMPARE(v4.y(), v1.y() + v2.y());
+}
+
+// Test vector addition for 3D vectors.
+void tst_QVector::add3_data()
+{
+    QTest::addColumn<qreal>("x1");
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("z1");
+    QTest::addColumn<qreal>("x2");
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("z2");
+    QTest::addColumn<qreal>("x3");
+    QTest::addColumn<qreal>("y3");
+    QTest::addColumn<qreal>("z3");
+
+    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;
+
+    QTest::newRow("xonly")
+        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)2.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)3.0f << (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)0.0f << (qreal)3.0f << (qreal)0.0f;
+
+    QTest::newRow("zonly")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)2.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)3.0f;
+
+    QTest::newRow("all")
+        << (qreal)1.0f << (qreal)2.0f << (qreal)3.0f
+        << (qreal)4.0f << (qreal)5.0f << (qreal)-6.0f
+        << (qreal)5.0f << (qreal)7.0f << (qreal)-3.0f;
+}
+void tst_QVector::add3()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+    QFETCH(qreal, z3);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+    QVector3D v3(x3, y3, z3);
+
+    QVERIFY((v1 + v2) == v3);
+
+    QVector3D 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());
+}
+
+// Test vector addition for 4D vectors.
+void tst_QVector::add4_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_QVector::add4()
+{
+    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);
+
+    QVector4D v1(x1, y1, z1, w1);
+    QVector4D v2(x2, y2, z2, w2);
+    QVector4D v3(x3, y3, z3, w3);
+
+    QVERIFY((v1 + v2) == v3);
+
+    QVector4D 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.w(), v1.w() + v2.w());
+}
+
+// Test vector subtraction for 2D vectors.
+void tst_QVector::subtract2_data()
+{
+    // Use the same test data as the add test.
+    add2_data();
+}
+void tst_QVector::subtract2()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+
+    QVector2D v1(x1, y1);
+    QVector2D v2(x2, y2);
+    QVector2D v3(x3, y3);
+
+    QVERIFY((v3 - v1) == v2);
+    QVERIFY((v3 - v2) == v1);
+
+    QVector2D v4(v3);
+    v4 -= v1;
+    QVERIFY(v4 == v2);
+
+    QCOMPARE(v4.x(), v3.x() - v1.x());
+    QCOMPARE(v4.y(), v3.y() - v1.y());
+
+    QVector2D v5(v3);
+    v5 -= v2;
+    QVERIFY(v5 == v1);
+
+    QCOMPARE(v5.x(), v3.x() - v2.x());
+    QCOMPARE(v5.y(), v3.y() - v2.y());
+}
+
+// Test vector subtraction for 3D vectors.
+void tst_QVector::subtract3_data()
+{
+    // Use the same test data as the add test.
+    add3_data();
+}
+void tst_QVector::subtract3()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+    QFETCH(qreal, z3);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+    QVector3D v3(x3, y3, z3);
+
+    QVERIFY((v3 - v1) == v2);
+    QVERIFY((v3 - v2) == v1);
+
+    QVector3D 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());
+
+    QVector3D 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());
+}
+
+// Test vector subtraction for 4D vectors.
+void tst_QVector::subtract4_data()
+{
+    // Use the same test data as the add test.
+    add4_data();
+}
+void tst_QVector::subtract4()
+{
+    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);
+
+    QVector4D v1(x1, y1, z1, w1);
+    QVector4D v2(x2, y2, z2, w2);
+    QVector4D v3(x3, y3, z3, w3);
+
+    QVERIFY((v3 - v1) == v2);
+    QVERIFY((v3 - v2) == v1);
+
+    QVector4D 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.w(), v3.w() - v1.w());
+
+    QVector4D 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.w(), v3.w() - v2.w());
+}
+
+// Test component-wise vector multiplication for 2D vectors.
+void tst_QVector::multiply2_data()
+{
+    QTest::addColumn<qreal>("x1");
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("x2");
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("x3");
+    QTest::addColumn<qreal>("y3");
+
+    QTest::newRow("null")
+        << (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)2.0f << (qreal)0.0f
+        << (qreal)2.0f << (qreal)0.0f;
+
+    QTest::newRow("yonly")
+        << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f << (qreal)2.0f
+        << (qreal)0.0f << (qreal)2.0f;
+
+    QTest::newRow("all")
+        << (qreal)1.0f << (qreal)2.0f
+        << (qreal)4.0f << (qreal)5.0f
+        << (qreal)4.0f << (qreal)10.0f;
+}
+void tst_QVector::multiply2()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+
+    QVector2D v1(x1, y1);
+    QVector2D v2(x2, y2);
+    QVector2D v3(x3, y3);
+
+    QVERIFY((v1 * v2) == v3);
+
+    QVector2D v4(v1);
+    v4 *= v2;
+    QVERIFY(v4 == v3);
+
+    QCOMPARE(v4.x(), v1.x() * v2.x());
+    QCOMPARE(v4.y(), v1.y() * v2.y());
+}
+
+// Test component-wise vector multiplication for 3D vectors.
+void tst_QVector::multiply3_data()
+{
+    QTest::addColumn<qreal>("x1");
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("z1");
+    QTest::addColumn<qreal>("x2");
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("z2");
+    QTest::addColumn<qreal>("x3");
+    QTest::addColumn<qreal>("y3");
+    QTest::addColumn<qreal>("z3");
+
+    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;
+
+    QTest::newRow("xonly")
+        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)2.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)2.0f << (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)0.0f << (qreal)2.0f << (qreal)0.0f;
+
+    QTest::newRow("zonly")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)2.0f
+        << (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)5.0f << (qreal)-6.0f
+        << (qreal)4.0f << (qreal)10.0f << (qreal)-18.0f;
+}
+void tst_QVector::multiply3()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+    QFETCH(qreal, z3);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+    QVector3D v3(x3, y3, z3);
+
+    QVERIFY((v1 * v2) == v3);
+
+    QVector3D 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());
+}
+
+// Test component-wise vector multiplication for 4D vectors.
+void tst_QVector::multiply4_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)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)0.0f << (qreal)2.0f << (qreal)0.0f << (qreal)0.0f
+        << (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)0.0f << (qreal)0.0f << (qreal)2.0f << (qreal)0.0f
+        << (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)0.0f << (qreal)0.0f << (qreal)0.0f << (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)8.0f
+        << (qreal)4.0f << (qreal)5.0f << (qreal)-6.0f << (qreal)9.0f
+        << (qreal)4.0f << (qreal)10.0f << (qreal)-18.0f << (qreal)72.0f;
+}
+void tst_QVector::multiply4()
+{
+    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);
+
+    QVector4D v1(x1, y1, z1, w1);
+    QVector4D v2(x2, y2, z2, w2);
+    QVector4D v3(x3, y3, z3, w3);
+
+    QVERIFY((v1 * v2) == v3);
+
+    QVector4D 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.w(), v1.w() * v2.w());
+}
+
+// Test vector multiplication by a factor for 2D vectors.
+void tst_QVector::multiplyFactor2_data()
+{
+    QTest::addColumn<qreal>("x1");
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("factor");
+    QTest::addColumn<qreal>("x2");
+    QTest::addColumn<qreal>("y2");
+
+    QTest::newRow("null")
+        << (qreal)0.0f << (qreal)0.0f
+        << (qreal)100.0f
+        << (qreal)0.0f << (qreal)0.0f;
+
+    QTest::newRow("xonly")
+        << (qreal)1.0f << (qreal)0.0f
+        << (qreal)2.0f
+        << (qreal)2.0f << (qreal)0.0f;
+
+    QTest::newRow("yonly")
+        << (qreal)0.0f << (qreal)1.0f
+        << (qreal)2.0f
+        << (qreal)0.0f << (qreal)2.0f;
+
+    QTest::newRow("all")
+        << (qreal)1.0f << (qreal)2.0f
+        << (qreal)2.0f
+        << (qreal)2.0f << (qreal)4.0f;
+
+    QTest::newRow("allzero")
+        << (qreal)1.0f << (qreal)2.0f
+        << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f;
+}
+void tst_QVector::multiplyFactor2()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, factor);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+
+    QVector2D v1(x1, y1);
+    QVector2D v2(x2, y2);
+
+    QVERIFY((v1 * factor) == v2);
+    QVERIFY((factor * v1) == v2);
+
+    QVector2D v3(v1);
+    v3 *= factor;
+    QVERIFY(v3 == v2);
+
+    QCOMPARE(v3.x(), v1.x() * factor);
+    QCOMPARE(v3.y(), v1.y() * factor);
+}
+
+// Test vector multiplication by a factor for 3D vectors.
+void tst_QVector::multiplyFactor3_data()
+{
+    QTest::addColumn<qreal>("x1");
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("z1");
+    QTest::addColumn<qreal>("factor");
+    QTest::addColumn<qreal>("x2");
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("z2");
+
+    QTest::newRow("null")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)100.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;
+
+    QTest::newRow("xonly")
+        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)2.0f
+        << (qreal)2.0f << (qreal)0.0f << (qreal)0.0f;
+
+    QTest::newRow("yonly")
+        << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f
+        << (qreal)2.0f
+        << (qreal)0.0f << (qreal)2.0f << (qreal)0.0f;
+
+    QTest::newRow("zonly")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)2.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)2.0f;
+
+    QTest::newRow("all")
+        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f
+        << (qreal)2.0f
+        << (qreal)2.0f << (qreal)4.0f << (qreal)-6.0f;
+
+    QTest::newRow("allzero")
+        << (qreal)1.0f << (qreal)2.0f << (qreal)-3.0f
+        << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;
+}
+void tst_QVector::multiplyFactor3()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, factor);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+
+    QVERIFY((v1 * factor) == v2);
+    QVERIFY((factor * v1) == v2);
+
+    QVector3D 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);
+}
+
+// Test vector multiplication by a factor for 4D vectors.
+void tst_QVector::multiplyFactor4_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_QVector::multiplyFactor4()
+{
+    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);
+
+    QVector4D v1(x1, y1, z1, w1);
+    QVector4D v2(x2, y2, z2, w2);
+
+    QVERIFY((v1 * factor) == v2);
+    QVERIFY((factor * v1) == v2);
+
+    QVector4D 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.w(), v1.w() * factor);
+}
+
+// Test vector division by a factor for 2D vectors.
+void tst_QVector::divide2_data()
+{
+    // Use the same test data as the multiply test.
+    multiplyFactor2_data();
+}
+void tst_QVector::divide2()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, factor);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+
+    QVector2D v1(x1, y1);
+    QVector2D v2(x2, y2);
+
+    if (factor == (qreal)0.0f)
+        return;
+
+    QVERIFY((v2 / factor) == v1);
+
+    QVector2D v3(v2);
+    v3 /= factor;
+    QVERIFY(v3 == v1);
+
+    QCOMPARE(v3.x(), v2.x() / factor);
+    QCOMPARE(v3.y(), v2.y() / factor);
+}
+
+// Test vector division by a factor for 3D vectors.
+void tst_QVector::divide3_data()
+{
+    // Use the same test data as the multiply test.
+    multiplyFactor3_data();
+}
+void tst_QVector::divide3()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, factor);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+
+    if (factor == (qreal)0.0f)
+        return;
+
+    QVERIFY((v2 / factor) == v1);
+
+    QVector3D 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);
+}
+
+// Test vector division by a factor for 4D vectors.
+void tst_QVector::divide4_data()
+{
+    // Use the same test data as the multiply test.
+    multiplyFactor4_data();
+}
+void tst_QVector::divide4()
+{
+    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);
+
+    QVector4D v1(x1, y1, z1, w1);
+    QVector4D v2(x2, y2, z2, w2);
+
+    if (factor == (qreal)0.0f)
+        return;
+
+    QVERIFY((v2 / factor) == v1);
+
+    QVector4D 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.w(), v2.w() / factor);
+}
+
+// Test vector negation for 2D vectors.
+void tst_QVector::negate2_data()
+{
+    // Use the same test data as the add test.
+    add2_data();
+}
+void tst_QVector::negate2()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+
+    QVector2D v1(x1, y1);
+    QVector2D v2(-x1, -y1);
+
+    QVERIFY(-v1 == v2);
+}
+
+// Test vector negation for 3D vectors.
+void tst_QVector::negate3_data()
+{
+    // Use the same test data as the add test.
+    add3_data();
+}
+void tst_QVector::negate3()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(-x1, -y1, -z1);
+
+    QVERIFY(-v1 == v2);
+}
+
+// Test vector negation for 4D vectors.
+void tst_QVector::negate4_data()
+{
+    // Use the same test data as the add test.
+    add4_data();
+}
+void tst_QVector::negate4()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, w1);
+
+    QVector4D v1(x1, y1, z1, w1);
+    QVector4D v2(-x1, -y1, -z1, -w1);
+
+    QVERIFY(-v1 == v2);
+}
+
+// Test the computation of vector cross-products.
+void tst_QVector::crossProduct_data()
+{
+    QTest::addColumn<qreal>("x1");
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("z1");
+    QTest::addColumn<qreal>("x2");
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("z2");
+    QTest::addColumn<qreal>("x3");
+    QTest::addColumn<qreal>("y3");
+    QTest::addColumn<qreal>("z3");
+    QTest::addColumn<qreal>("dot");
+
+    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;
+
+    QTest::newRow("unitvec")
+        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f;
+
+    QTest::newRow("complex")
+        << (qreal)1.0f << (qreal)2.0f << (qreal)3.0f
+        << (qreal)4.0f << (qreal)5.0f << (qreal)6.0f
+        << (qreal)-3.0f << (qreal)6.0f << (qreal)-3.0f
+        << (qreal)32.0f;
+}
+void tst_QVector::crossProduct()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+    QFETCH(qreal, z3);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+    QVector3D v3(x3, y3, z3);
+
+    QVector3D v4 = QVector3D::crossProduct(v1, v2);
+    QVERIFY(v4 == v3);
+
+    // Compute the cross-product long-hand and check again.
+    qreal xres = y1 * z2 - z1 * y2;
+    qreal yres = z1 * x2 - x1 * z2;
+    qreal zres = x1 * y2 - y1 * x2;
+
+    QCOMPARE(v4.x(), xres);
+    QCOMPARE(v4.y(), yres);
+    QCOMPARE(v4.z(), zres);
+}
+
+// Test the computation of normals.
+void tst_QVector::normal_data()
+{
+    // Use the same test data as the crossProduct test.
+    crossProduct_data();
+}
+void tst_QVector::normal()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+    QFETCH(qreal, z3);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+    QVector3D v3(x3, y3, z3);
+
+    QVERIFY(QVector3D::normal(v1, v2) == v3.normalized());
+    QVERIFY(QVector3D::normal(QVector3D(), v1, v2) == v3.normalized());
+
+    QVector3D point(1.0f, 2.0f, 3.0f);
+    QVERIFY(QVector3D::normal(point, v1 + point, v2 + point) == v3.normalized());
+}
+
+// Test distance to plane calculations.
+void tst_QVector::distanceToPlane_data()
+{
+    QTest::addColumn<qreal>("x1");  // Point on plane
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("z1");
+    QTest::addColumn<qreal>("x2");  // Normal to plane
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("z2");
+    QTest::addColumn<qreal>("x3");  // Point to test for distance
+    QTest::addColumn<qreal>("y3");
+    QTest::addColumn<qreal>("z3");
+    QTest::addColumn<qreal>("x4");  // Second point on plane
+    QTest::addColumn<qreal>("y4");
+    QTest::addColumn<qreal>("z4");
+    QTest::addColumn<qreal>("x5");  // Third point on plane
+    QTest::addColumn<qreal>("y5");
+    QTest::addColumn<qreal>("z5");
+    QTest::addColumn<qreal>("distance");
+
+    QTest::newRow("null")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (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;
+
+    QTest::newRow("above")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)2.0f
+        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)2.0f << (qreal)0.0f
+        << (qreal)2.0f;
+
+    QTest::newRow("below")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)-1.0f << (qreal)1.0f << (qreal)-2.0f
+        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)2.0f << (qreal)0.0f
+        << (qreal)-2.0f;
+}
+void tst_QVector::distanceToPlane()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+    QFETCH(qreal, z3);
+    QFETCH(qreal, x4);
+    QFETCH(qreal, y4);
+    QFETCH(qreal, z4);
+    QFETCH(qreal, x5);
+    QFETCH(qreal, y5);
+    QFETCH(qreal, z5);
+    QFETCH(qreal, distance);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+    QVector3D v3(x3, y3, z3);
+    QVector3D v4(x4, y4, z4);
+    QVector3D v5(x5, y5, z5);
+
+    QCOMPARE(v3.distanceToPlane(v1, v2), distance);
+    QCOMPARE(v3.distanceToPlane(v1, v4, v5), distance);
+}
+
+// Test distance to line calculations.
+void tst_QVector::distanceToLine_data()
+{
+    QTest::addColumn<qreal>("x1");  // Point on line
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("z1");
+    QTest::addColumn<qreal>("x2");  // Direction of the line
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("z2");
+    QTest::addColumn<qreal>("x3");  // Point to test for distance
+    QTest::addColumn<qreal>("y3");
+    QTest::addColumn<qreal>("z3");
+    QTest::addColumn<qreal>("distance");
+
+    QTest::newRow("null")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f;
+
+    QTest::newRow("on line")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)5.0f
+        << (qreal)0.0f;
+
+    QTest::newRow("off line")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)1.0f;
+
+    QTest::newRow("off line 2")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
+        << (qreal)0.0f << (qreal)-2.0f << (qreal)0.0f
+        << (qreal)2.0f;
+
+    QTest::newRow("points")
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)5.0f << (qreal)0.0f
+        << (qreal)5.0f;
+}
+void tst_QVector::distanceToLine()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+    QFETCH(qreal, z3);
+    QFETCH(qreal, distance);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+    QVector3D v3(x3, y3, z3);
+
+    QCOMPARE(v3.distanceToLine(v1, v2), distance);
+}
+
+// Test the computation of dot products for 2D vectors.
+void tst_QVector::dotProduct2_data()
+{
+    QTest::addColumn<qreal>("x1");
+    QTest::addColumn<qreal>("y1");
+    QTest::addColumn<qreal>("x2");
+    QTest::addColumn<qreal>("y2");
+    QTest::addColumn<qreal>("dot");
+
+    QTest::newRow("null")
+        << (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;
+
+    QTest::newRow("complex")
+        << (qreal)1.0f << (qreal)2.0f
+        << (qreal)4.0f << (qreal)5.0f
+        << (qreal)14.0f;
+}
+void tst_QVector::dotProduct2()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, dot);
+
+    QVector2D v1(x1, y1);
+    QVector2D v2(x2, y2);
+
+    QVERIFY(QVector2D::dotProduct(v1, v2) == dot);
+
+    // Compute the dot-product long-hand and check again.
+    qreal d = x1 * x2 + y1 * y2;
+
+    QCOMPARE(QVector2D::dotProduct(v1, v2), d);
+}
+
+// Test the computation of dot products for 3D vectors.
+void tst_QVector::dotProduct3_data()
+{
+    // Use the same test data as the crossProduct test.
+    crossProduct_data();
+}
+void tst_QVector::dotProduct3()
+{
+    QFETCH(qreal, x1);
+    QFETCH(qreal, y1);
+    QFETCH(qreal, z1);
+    QFETCH(qreal, x2);
+    QFETCH(qreal, y2);
+    QFETCH(qreal, z2);
+    QFETCH(qreal, x3);
+    QFETCH(qreal, y3);
+    QFETCH(qreal, z3);
+    QFETCH(qreal, dot);
+
+    Q_UNUSED(x3);
+    Q_UNUSED(y3);
+    Q_UNUSED(z3);
+
+    QVector3D v1(x1, y1, z1);
+    QVector3D v2(x2, y2, z2);
+
+    QVERIFY(QVector3D::dotProduct(v1, v2) == dot);
+
+    // Compute the dot-product long-hand and check again.
+    qreal d = x1 * x2 + y1 * y2 + z1 * z2;
+
+    QCOMPARE(QVector3D::dotProduct(v1, v2), d);
+}
+
+// Test the computation of dot products for 4D vectors.
+void tst_QVector::dotProduct4_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>("dot");
+
+    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;
+
+    QTest::newRow("unitvec")
+        << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f << (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
+        << (qreal)0.0f;
+
+    QTest::newRow("complex")
+        << (qreal)1.0f << (qreal)2.0f << (qreal)3.0f << (qreal)4.0f
+        << (qreal)4.0f << (qreal)5.0f << (qreal)6.0f << (qreal)7.0f
+        << (qreal)60.0f;
+}
+void tst_QVector::dotProduct4()
+{
+    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, dot);
+
+    QVector4D v1(x1, y1, z1, w1);
+    QVector4D v2(x2, y2, z2, w2);
+
+    QVERIFY(QVector4D::dotProduct(v1, v2) == dot);
+
+    // Compute the dot-product long-hand and check again.
+    qreal d = x1 * x2 + y1 * y2 + z1 * z2 + w1 * w2;
+
+    QCOMPARE(QVector4D::dotProduct(v1, v2), d);
+}
+
+class tst_QVectorProperties : public QObject
+{
+    Q_OBJECT
+    Q_PROPERTY(QVector2D vector2D READ vector2D WRITE setVector2D)
+    Q_PROPERTY(QVector3D vector3D READ vector3D WRITE setVector3D)
+    Q_PROPERTY(QVector4D vector4D READ vector4D WRITE setVector4D)
+public:
+    tst_QVectorProperties(QObject *parent = 0) : QObject(parent) {}
+
+    QVector2D vector2D() const { return v2; }
+    void setVector2D(const QVector2D& value) { v2 = value; }
+
+    QVector3D vector3D() const { return v3; }
+    void setVector3D(const QVector3D& value) { v3 = value; }
+
+    QVector4D vector4D() const { return v4; }
+    void setVector4D(const QVector4D& value) { v4 = value; }
+
+private:
+    QVector2D v2;
+    QVector3D v3;
+    QVector4D v4;
+};
+
+// Test getting and setting vector properties via the metaobject system.
+void tst_QVector::properties()
+{
+    tst_QVectorProperties obj;
+
+    obj.setVector2D(QVector2D(1.0f, 2.0f));
+    obj.setVector3D(QVector3D(3.0f, 4.0f, 5.0f));
+    obj.setVector4D(QVector4D(6.0f, 7.0f, 8.0f, 9.0f));
+
+    QVector2D v2 = qVariantValue<QVector2D>(obj.property("vector2D"));
+    QCOMPARE(v2.x(), (qreal)1.0f);
+    QCOMPARE(v2.y(), (qreal)2.0f);
+
+    QVector3D v3 = qVariantValue<QVector3D>(obj.property("vector3D"));
+    QCOMPARE(v3.x(), (qreal)3.0f);
+    QCOMPARE(v3.y(), (qreal)4.0f);
+    QCOMPARE(v3.z(), (qreal)5.0f);
+
+    QVector4D v4 = qVariantValue<QVector4D>(obj.property("vector4D"));
+    QCOMPARE(v4.x(), (qreal)6.0f);
+    QCOMPARE(v4.y(), (qreal)7.0f);
+    QCOMPARE(v4.z(), (qreal)8.0f);
+    QCOMPARE(v4.w(), (qreal)9.0f);
+
+    obj.setProperty("vector2D",
+                    qVariantFromValue(QVector2D(-1.0f, -2.0f)));
+    obj.setProperty("vector3D",
+                    qVariantFromValue(QVector3D(-3.0f, -4.0f, -5.0f)));
+    obj.setProperty("vector4D",
+                    qVariantFromValue(QVector4D(-6.0f, -7.0f, -8.0f, -9.0f)));
+
+    v2 = qVariantValue<QVector2D>(obj.property("vector2D"));
+    QCOMPARE(v2.x(), (qreal)-1.0f);
+    QCOMPARE(v2.y(), (qreal)-2.0f);
+
+    v3 = qVariantValue<QVector3D>(obj.property("vector3D"));
+    QCOMPARE(v3.x(), (qreal)-3.0f);
+    QCOMPARE(v3.y(), (qreal)-4.0f);
+    QCOMPARE(v3.z(), (qreal)-5.0f);
+
+    v4 = qVariantValue<QVector4D>(obj.property("vector4D"));
+    QCOMPARE(v4.x(), (qreal)-6.0f);
+    QCOMPARE(v4.y(), (qreal)-7.0f);
+    QCOMPARE(v4.z(), (qreal)-8.0f);
+    QCOMPARE(v4.w(), (qreal)-9.0f);
+}
+
+void tst_QVector::metaTypes()
+{
+    QVERIFY(QMetaType::type("QVector2D") == QMetaType::QVector2D);
+    QVERIFY(QMetaType::type("QVector3D") == QMetaType::QVector3D);
+    QVERIFY(QMetaType::type("QVector4D") == QMetaType::QVector4D);
+
+    QCOMPARE(QByteArray(QMetaType::typeName(QMetaType::QVector2D)),
+             QByteArray("QVector2D"));
+    QCOMPARE(QByteArray(QMetaType::typeName(QMetaType::QVector3D)),
+             QByteArray("QVector3D"));
+    QCOMPARE(QByteArray(QMetaType::typeName(QMetaType::QVector4D)),
+             QByteArray("QVector4D"));
+
+    QVERIFY(QMetaType::isRegistered(QMetaType::QVector2D));
+    QVERIFY(QMetaType::isRegistered(QMetaType::QVector3D));
+    QVERIFY(QMetaType::isRegistered(QMetaType::QVector4D));
+
+    QVERIFY(qMetaTypeId<QVector2D>() == QMetaType::QVector2D);
+    QVERIFY(qMetaTypeId<QVector3D>() == QMetaType::QVector3D);
+    QVERIFY(qMetaTypeId<QVector4D>() == QMetaType::QVector4D);
+}
+
+QTEST_APPLESS_MAIN(tst_QVector)
+
+#include "tst_qvectornd.moc"