qt 6.5.1 original

tests/auto/gui/painting/qtransform/CMakeLists.txt

@@ -0,0 +1,21 @@
+# Copyright (C) 2022 The Qt Company Ltd.
+# SPDX-License-Identifier: BSD-3-Clause
+
+#####################################################################
+## tst_qtransform Test:
+#####################################################################
+
+qt_internal_add_test(tst_qtransform
+    SOURCES
+        tst_qtransform.cpp
+    LIBRARIES
+        Qt::Gui
+)
+
+## Scopes:
+#####################################################################
+
+qt_internal_extend_target(tst_qtransform CONDITION UNIX AND NOT APPLE AND NOT HAIKU AND NOT INTEGRITY
+    LIBRARIES
+        m
+)

tests/auto/gui/painting/qtransform/tst_qtransform.cpp

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+// Copyright (C) 2016 The Qt Company Ltd.
+// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR GPL-3.0-only WITH Qt-GPL-exception-1.0
+
+
+#include <QTest>
+#include <qpainterpath.h>
+#include <qpolygon.h>
+#include <qtransform.h>
+#include <qdebug.h>
+
+class tst_QTransform : public QObject
+{
+    Q_OBJECT
+
+private slots:
+    void mapRect_data();
+    void mapToPolygon_data();
+    void mapRect();
+    void assignments();
+    void mapToPolygon();
+    void qhash();
+    void translate();
+    void scale();
+    void types();
+    void types2_data();
+    void types2();
+    void scalarOps();
+    void transform();
+    void mapEmptyPath();
+    void boundingRect();
+    void controlPointRect();
+    void inverted_data();
+    void inverted();
+    void projectivePathMapping();
+    void mapInt();
+    void mapPathWithPoint();
+
+private:
+    void mapping_data();
+};
+
+Q_DECLARE_METATYPE(QTransform)
+Q_DECLARE_METATYPE(QTransform::TransformationType)
+
+void tst_QTransform::mapRect_data()
+{
+    mapping_data();
+
+    // rotations that are not multiples of 90 degrees. mapRect returns the bounding rect here.
+    qreal deg = -45;
+    QTest::newRow( "rot 45 a" )
+        << QTransform().rotate(deg)
+        << QRect( 0, 0, 10, 10 )
+        << QPolygon( QRect( 0, -7, 14, 14 ) );
+    QTest::newRow( "rot 45 b" )
+        << QTransform().rotate(deg)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( 21, -14, 50, 49 ) );
+    QTest::newRow( "rot 45 c" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 0, 0, 10, 10 )
+        << QPolygon( QRect( 0, -71, 141, 142 ) );
+    QTest::newRow( "rot 45 d" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( 212, -141, 495, 495 ) );
+
+    deg = 45;
+    QTest::newRow( "rot -45 a" )
+        << QTransform().rotate(deg)
+        << QRect( 0, 0, 10, 10 )
+        << QPolygon( QRect( -7, 0, 14, 14 ) );
+    QTest::newRow( "rot -45 b" )
+        << QTransform().rotate(deg)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -35, 21, 49, 50 ) );
+    QTest::newRow( "rot -45 c" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 0, 0, 10, 10 )
+        << QPolygon( QRect( -71, 0, 142, 141 ) );
+    QTest::newRow( "rot -45 d" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -354, 212, 495, 495 ) );
+}
+
+void tst_QTransform::mapToPolygon_data()
+{
+    mapping_data();
+}
+
+void tst_QTransform::mapping_data()
+{
+    //create the testtable instance and define the elements
+    QTest::addColumn<QTransform>("matrix");
+    QTest::addColumn<QRect>("src");
+    QTest::addColumn<QPolygon>("res");
+
+    //next we fill it with data
+
+    // identity
+    QTest::newRow( "identity" )
+        << QTransform()
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( 10, 20, 30, 40 ) );
+    // scaling
+    QTest::newRow( "scale 0" )
+        << QTransform().scale(2, 2)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( 20, 40, 60, 80 ) );
+    QTest::newRow( "scale 1" )
+        << QTransform().scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( 100, 200, 300, 400 ) );
+    // mirroring
+    QTest::newRow( "mirror 0" )
+        << QTransform().scale(-1, 1)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -40, 20, 30, 40 ) );
+    QTest::newRow( "mirror 1" )
+        << QTransform().scale(1, -1)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( 10, -60, 30, 40 ) );
+    QTest::newRow( "mirror 2" )
+        << QTransform().scale(-1, -1)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -40, -60, 30, 40 ) );
+    QTest::newRow( "mirror 3" )
+        << QTransform().scale(-2, -2)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -80, -120, 60, 80 ) );
+    QTest::newRow( "mirror 4" )
+        << QTransform().scale(-10, -10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -400, -600, 300, 400 ) );
+    QTest::newRow( "mirror 5" )
+        << QTransform().scale(-1, 1)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( -30, 0, 30, 40 ) );
+    QTest::newRow( "mirror 6" )
+        << QTransform().scale(1, -1)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( 0, -40, 30, 40 ) );
+    QTest::newRow( "mirror 7" )
+        << QTransform().scale(-1, -1)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( -30, -40, 30, 40 ) );
+    QTest::newRow( "mirror 8" )
+        << QTransform().scale(-2, -2)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( -60, -80, 60, 80 ) );
+    QTest::newRow( "mirror 9" )
+        << QTransform().scale(-10, -10) << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( -300, -400, 300, 400 ) );
+
+    // rotations
+    float deg = 0.;
+    QTest::newRow( "rot 0 a" )
+        << QTransform().rotate(deg)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon ( QRect( 0, 0, 30, 40 ) );
+    deg = 0.00001f;
+    QTest::newRow( "rot 0 b" )
+        << QTransform().rotate(deg)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon ( QRect( 0, 0, 30, 40 ) );
+    deg = 0.;
+    QTest::newRow( "rot 0 c" )
+        << QTransform().rotate(deg)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon ( QRect( 10, 20, 30, 40 ) );
+    deg = 0.00001f;
+    QTest::newRow( "rot 0 d" )
+        << QTransform().rotate(deg)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon ( QRect( 10, 20, 30, 40 ) );
+
+    // rotations
+    deg = -90.f;
+    QTest::newRow( "rotscale 90 a" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( 0, -300, 400, 300 ) );
+    deg = -90.00001f;
+    QTest::newRow( "rotscale 90 b" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( 0, -300, 400, 300 ) );
+    deg = -90.f;
+    QTest::newRow( "rotscale 90 c" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( 200, -400, 400, 300 ) );
+    deg = -90.00001f;
+    QTest::newRow( "rotscale 90 d" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( 200, -400, 400, 300 ) );
+
+    deg = 180.f;
+    QTest::newRow( "rotscale 180 a" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( -300, -400, 300, 400 ) );
+    deg = 180.000001f;
+    QTest::newRow( "rotscale 180 b" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( -300, -400, 300, 400 ) );
+    deg = 180.f;
+    QTest::newRow( "rotscale 180 c" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -400, -600, 300, 400 ) );
+    deg = 180.000001f;
+    QTest::newRow( "rotscale 180 d" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -400, -600, 300, 400 ) );
+
+    deg = -270.f;
+    QTest::newRow( "rotscale 270 a" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( -400, 0, 400, 300 ) );
+    deg = -270.0000001f;
+    QTest::newRow( "rotscale 270 b" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 0, 0, 30, 40 )
+        << QPolygon( QRect( -400, 0, 400, 300 ) );
+    deg = -270.f;
+    QTest::newRow( "rotscale 270 c" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -600, 100, 400, 300 ) );
+    deg = -270.000001f;
+    QTest::newRow( "rotscale 270 d" )
+        << QTransform().rotate(deg).scale(10, 10)
+        << QRect( 10, 20, 30, 40 )
+        << QPolygon( QRect( -600, 100, 400, 300 ) );
+}
+
+void tst_QTransform::mapRect()
+{
+    QFETCH( QTransform, matrix );
+    QFETCH( QRect, src );
+    QFETCH( QPolygon, res );
+    QRect mapped = matrix.mapRect(src);
+    QCOMPARE( mapped, res.boundingRect().adjusted(0, 0, -1, -1) );
+
+    QRectF r = matrix.mapRect(QRectF(src));
+    QRect ir(r.topLeft().toPoint(), r.bottomRight().toPoint() - QPoint(1, 1));
+    QCOMPARE( mapped, ir );
+}
+
+void tst_QTransform::assignments()
+{
+    QTransform m;
+    m.scale(2, 3);
+    m.rotate(45);
+    m.shear(4, 5);
+
+    QTransform c1(m);
+
+    QCOMPARE(m.m11(), c1.m11());
+    QCOMPARE(m.m12(), c1.m12());
+    QCOMPARE(m.m21(), c1.m21());
+    QCOMPARE(m.m22(), c1.m22());
+    QCOMPARE(m.dx(), c1.dx());
+    QCOMPARE(m.dy(), c1.dy());
+
+    QTransform c2 = m;
+    QCOMPARE(m.m11(), c2.m11());
+    QCOMPARE(m.m12(), c2.m12());
+    QCOMPARE(m.m21(), c2.m21());
+    QCOMPARE(m.m22(), c2.m22());
+    QCOMPARE(m.dx(),  c2.dx());
+    QCOMPARE(m.dy(),  c2.dy());
+}
+
+
+void tst_QTransform::mapToPolygon()
+{
+    QFETCH( QTransform, matrix );
+    QFETCH( QRect, src );
+    QFETCH( QPolygon, res );
+
+    QPolygon poly = matrix.mapToPolygon(src);
+
+    // don't care about starting point
+    bool equal = false;
+    for (int i = 0; i < poly.size(); ++i) {
+        QPolygon rot;
+        for (int j = i; j < poly.size(); ++j)
+            rot << poly[j];
+        for (int j = 0; j < i; ++j)
+            rot << poly[j];
+        if (rot == res)
+            equal = true;
+    }
+
+    QVERIFY(equal);
+}
+
+void tst_QTransform::qhash()
+{
+    QTransform t1;
+    t1.shear(3.0, 2.0);
+    t1.rotate(44);
+
+    QTransform t2 = t1;
+
+    // not really much to test here, so just the bare minimum:
+    QCOMPARE(qHash(t1), qHash(t2));
+}
+
+
+void tst_QTransform::translate()
+{
+    QTransform m( 1, 2, 3, 4, 5, 6 );
+    QTransform res2( m );
+    QTransform res( 1, 2, 3, 4, 75, 106 );
+    m.translate( 10,  20 );
+    QVERIFY( m == res );
+    m.translate( -10,  -20 );
+    QVERIFY( m == res2 );
+    QVERIFY( QTransform::fromTranslate( 0, 0 ).type() == QTransform::TxNone );
+    QVERIFY( QTransform::fromTranslate( 10, 0 ).type() == QTransform::TxTranslate );
+    QVERIFY( QTransform::fromTranslate( -1, 5 ) == QTransform().translate( -1, 5 ));
+    QVERIFY( QTransform::fromTranslate( 0, 0 ) == QTransform());
+}
+
+void tst_QTransform::scale()
+{
+    QTransform m( 1, 2, 3, 4, 5, 6 );
+    QTransform res2( m );
+    QTransform res( 10, 20, 60, 80, 5, 6 );
+    m.scale( 10,  20 );
+    QVERIFY( m == res );
+    m.scale( 1./10.,  1./20. );
+    QVERIFY( m == res2 );
+    QVERIFY( QTransform::fromScale( 1, 1 ).type() == QTransform::TxNone );
+    QVERIFY( QTransform::fromScale( 2, 4 ).type() == QTransform::TxScale );
+    QVERIFY( QTransform::fromScale( 2, 4 ) == QTransform().scale( 2, 4 ));
+    QVERIFY( QTransform::fromScale( 1, 1 ) == QTransform());
+}
+
+void tst_QTransform::types()
+{
+    QTransform m1;
+    QCOMPARE(m1.type(), QTransform::TxNone);
+
+    m1.translate(1.0f, 0.0f);
+    QCOMPARE(m1.type(), QTransform::TxTranslate);
+    QCOMPARE(m1.inverted().type(), QTransform::TxTranslate);
+
+    m1.scale(1.0f, 2.0f);
+    QCOMPARE(m1.type(), QTransform::TxScale);
+    QCOMPARE(m1.inverted().type(), QTransform::TxScale);
+
+    m1.rotate(45.0f);
+    // Rotation after non-uniform scaling -> shearing. Uniform scale + rotate tested below.
+    QCOMPARE(m1.type(), QTransform::TxShear);
+    QCOMPARE(m1.inverted().type(), QTransform::TxShear);
+
+    m1.shear(0.5f, 0.25f);
+    QCOMPARE(m1.type(), QTransform::TxShear);
+    QCOMPARE(m1.inverted().type(), QTransform::TxShear);
+
+    m1.rotate(45.0f, Qt::XAxis);
+    QCOMPARE(m1.type(), QTransform::TxProject);
+    m1.shear(0.5f, 0.25f);
+    QCOMPARE(m1.type(), QTransform::TxProject);
+    m1.rotate(45.0f);
+    QCOMPARE(m1.type(), QTransform::TxProject);
+    m1.scale(1.0f, 2.0f);
+    QCOMPARE(m1.type(), QTransform::TxProject);
+    m1.translate(1.0f, 0.0f);
+    QCOMPARE(m1.type(), QTransform::TxProject);
+
+    QTransform m2(1.0f, 0.0f, 0.0f,
+                  0.0f, 1.0f, 0.0f,
+                  -1.0f, -1.0f, 1.0f);
+
+    QCOMPARE(m2.type(), QTransform::TxTranslate);
+    QCOMPARE((m1 * m2).type(), QTransform::TxProject);
+
+    m1 *= QTransform();
+    QCOMPARE(m1.type(), QTransform::TxProject);
+
+    m1 *= QTransform(1.0f, 0.0f, 0.0f,
+                     0.0f, 1.0f, 0.0f,
+                     1.0f, 0.0f, 1.0f);
+    QCOMPARE(m1.type(), QTransform::TxProject);
+
+    m2.reset();
+    QCOMPARE(m2.type(), QTransform::TxNone);
+
+    m2.setMatrix(1.0f, 0.0f, 0.0f,
+                 0.0f, 1.0f, 0.0f,
+                 0.0f, 0.0f, 1.0f);
+    QCOMPARE(m2.type(), QTransform::TxNone);
+
+    m2 *= QTransform();
+    QCOMPARE(m2.type(), QTransform::TxNone);
+
+    m2.setMatrix(2.0f, 0.0f, 0.0f,
+                 0.0f, 1.0f, 0.0f,
+                 0.0f, 0.0f, 1.0f);
+    QCOMPARE(m2.type(), QTransform::TxScale);
+    m2 *= QTransform();
+    QCOMPARE(m2.type(), QTransform::TxScale);
+
+    m2.setMatrix(0.0f, 1.0f, 0.0f,
+                 1.0f, 0.0f, 0.0f,
+                 0.0f, 1.0f, 1.0f);
+    QCOMPARE(m2.type(), QTransform::TxRotate);
+    m2 *= QTransform();
+    QCOMPARE(m2.type(), QTransform::TxRotate);
+
+    m2.setMatrix(1.0f, 0.0f, 0.5f,
+                 0.0f, 1.0f, 0.0f,
+                 0.0f, 0.0f, 1.0f);
+    QCOMPARE(m2.type(), QTransform::TxProject);
+    m2 *= QTransform();
+    QCOMPARE(m2.type(), QTransform::TxProject);
+
+    m2.setMatrix(1.0f, 1.0f, 0.0f,
+                 1.0f, 0.0f, 0.0f,
+                 0.0f, 1.0f, 1.0f);
+    QCOMPARE(m2.type(), QTransform::TxShear);
+
+    m2 *= m2.inverted();
+    QCOMPARE(m2.type(), QTransform::TxNone);
+
+    m2.translate(5.0f, 5.0f);
+    m2.rotate(45.0f);
+    m2.rotate(-45.0f);
+    QCOMPARE(m2.type(), QTransform::TxTranslate);
+
+    m2.scale(2.0f, 3.0f);
+    m2.shear(1.0f, 0.0f);
+    m2.shear(-1.0f, 0.0f);
+    QCOMPARE(m2.type(), QTransform::TxScale);
+
+    m2 *= QTransform(1.0f, 1.0f, 0.0f,
+                     0.0f, 1.0f, 0.0f,
+                     0.0f, 0.0f, 1.0f);
+    QCOMPARE(m2.type(), QTransform::TxShear);
+
+    m2 *= QTransform(1.0f, 0.0f, 0.0f,
+                     0.0f, 1.0f, 0.0f,
+                     1.0f, 0.0f, 1.0f);
+    QCOMPARE(m2.type(), QTransform::TxShear);
+
+    QTransform m3(1.8f, 0.0f, 0.0f,
+                  0.0f, 1.8f, 0.0f,
+                  0.0f, 0.0f, 1.0f);
+
+    QCOMPARE(m3.type(), QTransform::TxScale);
+    m3.translate(5.0f, 5.0f);
+    QCOMPARE(m3.type(), QTransform::TxScale);
+    QCOMPARE(m3.inverted().type(), QTransform::TxScale);
+
+    m3.setMatrix(1.0f, 0.0f, 0.0f,
+                 0.0f, 1.0f, 0.0f,
+                 0.0f, 0.0f, 2.0f);
+    QCOMPARE(m3.type(), QTransform::TxProject);
+
+    m3.setMatrix(0.0f, 2.0f, 0.0f,
+                 1.0f, 0.0f, 0.0f,
+                 0.0f, 0.0f, 2.0f);
+    QCOMPARE(m3.type(), QTransform::TxProject);
+
+    QTransform m4;
+    m4.scale(5, 5);
+    m4.translate(4, 2);
+    m4.rotate(45);
+
+    QCOMPARE(m4.type(), QTransform::TxRotate);
+
+    QTransform m5;
+    m5.scale(5, 5);
+    m5 = m5.adjoint() / m5.determinant();
+    QCOMPARE(m5.type(), QTransform::TxScale);
+}
+
+void tst_QTransform::types2_data()
+{
+    QTest::addColumn<QTransform>("t1");
+    QTest::addColumn<QTransform::TransformationType>("type");
+
+    QTest::newRow( "identity" ) << QTransform() << QTransform::TxNone;
+    QTest::newRow( "translate" ) << QTransform().translate(10, -0.1) << QTransform::TxTranslate;
+    QTest::newRow( "scale" ) << QTransform().scale(10, -0.1) << QTransform::TxScale;
+    QTest::newRow( "rotate" ) << QTransform().rotate(10) << QTransform::TxRotate;
+    QTest::newRow( "shear" ) << QTransform().shear(10, -0.1) << QTransform::TxShear;
+    QTest::newRow( "project" ) << QTransform().rotate(10, Qt::XAxis) << QTransform::TxProject;
+    QTest::newRow( "combined" ) << QTransform().translate(10, -0.1).scale(10, -0.1).rotate(10, Qt::YAxis) << QTransform::TxProject;
+}
+
+void tst_QTransform::types2()
+{
+#define CHECKTXTYPE(func) { QTransform t2(func); \
+                            QTransform t3(t2.m11(), t2.m12(), t2.m13(), t2.m21(), t2.m22(), t2.m23(), t2.m31(), t2.m32(), t2.m33()); \
+                            QVERIFY2(t3.type() == t2.type(), #func); \
+                          }
+
+    QFETCH( QTransform, t1 );
+    QFETCH( QTransform::TransformationType, type );
+
+    Q_ASSERT(t1.type() == type);
+
+    CHECKTXTYPE(t1.adjoint());
+    CHECKTXTYPE(t1.inverted());
+    CHECKTXTYPE(t1.transposed());
+
+#undef CHECKTXTYPE
+}
+
+void tst_QTransform::scalarOps()
+{
+    QTransform t;
+    QCOMPARE(t.m11(), 1.);
+    QCOMPARE(t.m33(), 1.);
+    QCOMPARE(t.m21(), 0.);
+
+    t = QTransform() + 3;
+    QCOMPARE(t.m11(), 4.);
+    QCOMPARE(t.m33(), 4.);
+    QCOMPARE(t.m21(), 3.);
+
+    t = t - 3;
+    QCOMPARE(t.m11(), 1.);
+    QCOMPARE(t.m33(), 1.);
+    QCOMPARE(t.m21(), 0.);
+    QCOMPARE(t.isIdentity(), true);
+
+    t += 3;
+    t = t * 2;
+    QCOMPARE(t.m11(), 8.);
+    QCOMPARE(t.m33(), 8.);
+    QCOMPARE(t.m21(), 6.);
+}
+
+void tst_QTransform::transform()
+{
+    QTransform t;
+    t.rotate(30, Qt::YAxis);
+    t.translate(15, 10);
+    t.scale(2, 2);
+    t.rotate(30);
+    t.shear(0.5, 0.5);
+
+    QTransform a, b, c, d, e;
+    a.rotate(30, Qt::YAxis);
+    b.translate(15, 10);
+    c.scale(2, 2);
+    d.rotate(30);
+    e.shear(0.5, 0.5);
+
+    QVERIFY(qFuzzyCompare(t, e * d * c * b * a));
+}
+
+void tst_QTransform::mapEmptyPath()
+{
+    QPainterPath path;
+    path.moveTo(10, 10);
+    path.lineTo(10, 10);
+    QCOMPARE(QTransform().map(path), path);
+}
+
+void tst_QTransform::boundingRect()
+{
+    QPainterPath path;
+    path.moveTo(10, 10);
+    path.lineTo(10, 10);
+    QCOMPARE(path.boundingRect(), QRectF(10, 10, 0, 0));
+}
+
+void tst_QTransform::controlPointRect()
+{
+    QPainterPath path;
+    path.moveTo(10, 10);
+    path.lineTo(10, 10);
+    QCOMPARE(path.controlPointRect(), QRectF(10, 10, 0, 0));
+}
+
+void tst_QTransform::inverted_data()
+{
+    QTest::addColumn<QTransform>("matrix");
+
+    QTest::newRow("identity")
+        << QTransform();
+
+    QTest::newRow("TxTranslate")
+        << QTransform().translate(200, 10);
+
+    QTest::newRow("TxScale")
+        << QTransform().scale(5, 2);
+
+    QTest::newRow("TxTranslate TxScale")
+        << QTransform().translate(100, -10).scale(40, 2);
+
+    QTest::newRow("TxScale TxTranslate")
+        << QTransform().scale(40, 2).translate(100, -10);
+
+    QTest::newRow("TxRotate")
+        << QTransform().rotate(40, Qt::ZAxis);
+
+    QTest::newRow("TxRotate TxScale")
+        << QTransform().rotate(60, Qt::ZAxis).scale(2, 0.25);
+
+    QTest::newRow("TxScale TxRotate")
+        << QTransform().scale(2, 0.25).rotate(30, Qt::ZAxis);
+
+    QTest::newRow("TxRotate TxScale TxTranslate")
+        << QTransform().rotate(60, Qt::ZAxis).scale(2, 0.25).translate(200, -3000);
+
+    QTest::newRow("TxRotate TxTranslate TxScale")
+        << QTransform().rotate(60, Qt::ZAxis).translate(200, -3000).scale(19, 77);
+
+    QTest::newRow("TxShear")
+        << QTransform().shear(10, 10);
+
+    QTest::newRow("TxShear TxRotate")
+        << QTransform().shear(10, 10).rotate(45, Qt::ZAxis);
+
+    QTest::newRow("TxShear TxRotate TxScale")
+        << QTransform().shear(10, 10).rotate(45, Qt::ZAxis).scale(19, 81);
+
+    QTest::newRow("TxTranslate TxShear TxRotate TxScale")
+        << QTransform().translate(150, -1).shear(10, 10).rotate(45, Qt::ZAxis).scale(19, 81);
+
+    const qreal s = 500000;
+
+    QTransform big;
+    big.scale(s, s);
+
+    QTest::newRow("big") << big;
+
+    QTransform smallTransform;
+    smallTransform.scale(1/s, 1/s);
+
+    QTest::newRow("small") << smallTransform;
+}
+
+void tst_QTransform::inverted()
+{
+    if (sizeof(qreal) != sizeof(double))
+        QSKIP("precision error if qreal is not double");
+
+    QFETCH(QTransform, matrix);
+
+    const QTransform inverted = matrix.inverted();
+
+    QCOMPARE(matrix.isIdentity(), inverted.isIdentity());
+    QCOMPARE(matrix.type(), inverted.type());
+
+    QVERIFY((matrix * inverted).isIdentity());
+    QVERIFY((inverted * matrix).isIdentity());
+}
+
+void tst_QTransform::projectivePathMapping()
+{
+    QPainterPath path;
+    path.addRect(-50, -50, 100, 100);
+
+    const QRectF view(0, 0, 1024, 1024);
+
+    QVERIFY(view.intersects(path.boundingRect()));
+
+    for (int i = 0; i < 85; i += 5) {
+        QTransform transform;
+        transform.translate(512, 512);
+        transform.rotate(i, Qt::YAxis);
+
+        const QPainterPath mapped = transform.map(path);
+
+        QVERIFY(view.intersects(mapped.boundingRect()));
+        QVERIFY(transform.inverted().mapRect(view).intersects(path.boundingRect()));
+    }
+}
+
+void tst_QTransform::mapInt()
+{
+    int x = 0;
+    int y = 0;
+
+    QTransform::fromTranslate(10, 10).map(x, y, &x, &y);
+
+    QCOMPARE(x, 10);
+    QCOMPARE(y, 10);
+}
+
+void tst_QTransform::mapPathWithPoint()
+{
+    QPainterPath p(QPointF(10, 10));
+    p = QTransform::fromTranslate(10, 10).map(p);
+    QCOMPARE(p.currentPosition(), QPointF(20, 20));
+}
+
+QTEST_APPLESS_MAIN(tst_QTransform)
+
+
+#include "tst_qtransform.moc"