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qt5base-lts/tests/auto/qmatrixnxn/tst_qmatrixnxn.cpp
Jyri Tahtela f9f395c28b Update licenseheader text in source files for qtbase Qt module 
Updated version of LGPL and FDL licenseheaders.
Apply release phase licenseheaders for all source files.

Reviewed-by: Trust Me
2011-05-24 12:34:08 +03:00

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/****************************************************************************
**
** Copyright (C) 2011 Nokia Corporation and/or its subsidiary(-ies).
** All rights reserved.
** Contact: Nokia Corporation (qt-info@nokia.com)
**
** This file is part of the test suite of the Qt Toolkit.
**
** $QT_BEGIN_LICENSE:LGPL$
** GNU Lesser General Public License Usage
** 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 1.1, 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.
**
** Other Usage
** Alternatively, this file may be used in accordance with the terms and
** conditions contained in a signed written agreement between you and Nokia.
**
**
**
**
**
** $QT_END_LICENSE$
**
****************************************************************************/
#include <QtTest/QtTest>
#include <QtCore/qmath.h>
#include <QtGui/qmatrix4x4.h>
class tst_QMatrixNxN : public QObject
{
Q_OBJECT
public:
tst_QMatrixNxN() {}
~tst_QMatrixNxN() {}
private slots:
void create2x2();
void create3x3();
void create4x4();
void create4x3();
void isIdentity2x2();
void isIdentity3x3();
void isIdentity4x4();
void isIdentity4x3();
void compare2x2();
void compare3x3();
void compare4x4();
void compare4x3();
void transposed2x2();
void transposed3x3();
void transposed4x4();
void transposed4x3();
void add2x2_data();
void add2x2();
void add3x3_data();
void add3x3();
void add4x4_data();
void add4x4();
void add4x3_data();
void add4x3();
void subtract2x2_data();
void subtract2x2();
void subtract3x3_data();
void subtract3x3();
void subtract4x4_data();
void subtract4x4();
void subtract4x3_data();
void subtract4x3();
void multiply2x2_data();
void multiply2x2();
void multiply3x3_data();
void multiply3x3();
void multiply4x4_data();
void multiply4x4();
void multiply4x3_data();
void multiply4x3();
void multiplyFactor2x2_data();
void multiplyFactor2x2();
void multiplyFactor3x3_data();
void multiplyFactor3x3();
void multiplyFactor4x4_data();
void multiplyFactor4x4();
void multiplyFactor4x3_data();
void multiplyFactor4x3();
void divideFactor2x2_data();
void divideFactor2x2();
void divideFactor3x3_data();
void divideFactor3x3();
void divideFactor4x4_data();
void divideFactor4x4();
void divideFactor4x3_data();
void divideFactor4x3();
void negate2x2_data();
void negate2x2();
void negate3x3_data();
void negate3x3();
void negate4x4_data();
void negate4x4();
void negate4x3_data();
void negate4x3();
void inverted4x4_data();
void inverted4x4();
void orthonormalInverse4x4();
void scale4x4_data();
void scale4x4();
void translate4x4_data();
void translate4x4();
void rotate4x4_data();
void rotate4x4();
void normalMatrix_data();
void normalMatrix();
void optimizedTransforms();
void ortho();
void frustum();
void perspective();
void flipCoordinates();
void convertGeneric();
void optimize_data();
void optimize();
void columnsAndRows();
void convertQMatrix();
void convertQTransform();
void fill();
void mapRect_data();
void mapRect();
void mapVector_data();
void mapVector();
void properties();
void metaTypes();
private:
static void setMatrix(QMatrix2x2& m, const qreal *values);
static void setMatrixDirect(QMatrix2x2& m, const qreal *values);
static bool isSame(const QMatrix2x2& m, const qreal *values);
static bool isIdentity(const QMatrix2x2& m);
static void setMatrix(QMatrix3x3& m, const qreal *values);
static void setMatrixDirect(QMatrix3x3& m, const qreal *values);
static bool isSame(const QMatrix3x3& m, const qreal *values);
static bool isIdentity(const QMatrix3x3& m);
static void setMatrix(QMatrix4x4& m, const qreal *values);
static void setMatrixDirect(QMatrix4x4& m, const qreal *values);
static bool isSame(const QMatrix4x4& m, const qreal *values);
static bool isIdentity(const QMatrix4x4& m);
static void setMatrix(QMatrix4x3& m, const qreal *values);
static void setMatrixDirect(QMatrix4x3& m, const qreal *values);
static bool isSame(const QMatrix4x3& m, const qreal *values);
static bool isIdentity(const QMatrix4x3& m);
};
static const qreal nullValues2[] =
{0.0f, 0.0f,
0.0f, 0.0f};
static qreal const identityValues2[16] =
{1.0f, 0.0f,
0.0f, 1.0f};
static const qreal doubleIdentity2[] =
{2.0f, 0.0f,
0.0f, 2.0f};
static qreal const uniqueValues2[16] =
{1.0f, 2.0f,
5.0f, 6.0f};
static qreal const transposedValues2[16] =
{1.0f, 5.0f,
2.0f, 6.0f};
static const qreal nullValues3[] =
{0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f};
static qreal const identityValues3[16] =
{1.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 1.0f};
static const qreal doubleIdentity3[] =
{2.0f, 0.0f, 0.0f,
0.0f, 2.0f, 0.0f,
0.0f, 0.0f, 2.0f};
static qreal const uniqueValues3[16] =
{1.0f, 2.0f, 3.0f,
5.0f, 6.0f, 7.0f,
9.0f, 10.0f, 11.0f};
static qreal const transposedValues3[16] =
{1.0f, 5.0f, 9.0f,
2.0f, 6.0f, 10.0f,
3.0f, 7.0f, 11.0f};
static const qreal nullValues4[] =
{0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f};
static qreal const identityValues4[16] =
{1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static const qreal doubleIdentity4[] =
{2.0f, 0.0f, 0.0f, 0.0f,
0.0f, 2.0f, 0.0f, 0.0f,
0.0f, 0.0f, 2.0f, 0.0f,
0.0f, 0.0f, 0.0f, 2.0f};
static qreal const uniqueValues4[16] =
{1.0f, 2.0f, 3.0f, 4.0f,
5.0f, 6.0f, 7.0f, 8.0f,
9.0f, 10.0f, 11.0f, 12.0f,
13.0f, 14.0f, 15.0f, 16.0f};
static qreal const transposedValues4[16] =
{1.0f, 5.0f, 9.0f, 13.0f,
2.0f, 6.0f, 10.0f, 14.0f,
3.0f, 7.0f, 11.0f, 15.0f,
4.0f, 8.0f, 12.0f, 16.0f};
static const qreal nullValues4x3[] =
{0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f};
static qreal const identityValues4x3[12] =
{1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f};
static qreal const doubleIdentity4x3[12] =
{2.0f, 0.0f, 0.0f, 0.0f,
0.0f, 2.0f, 0.0f, 0.0f,
0.0f, 0.0f, 2.0f, 0.0f};
static qreal const uniqueValues4x3[12] =
{1.0f, 2.0f, 3.0f, 4.0f,
5.0f, 6.0f, 7.0f, 8.0f,
9.0f, 10.0f, 11.0f, 12.0f};
static qreal const transposedValues3x4[12] =
{1.0f, 5.0f, 9.0f,
2.0f, 6.0f, 10.0f,
3.0f, 7.0f, 11.0f,
4.0f, 8.0f, 12.0f};
// Set a matrix to a specified array of values, which are assumed
// to be in row-major order. This sets the values using floating-point.
void tst_QMatrixNxN::setMatrix(QMatrix2x2& m, const qreal *values)
{
for (int row = 0; row < 2; ++row)
for (int col = 0; col < 2; ++col)
m(row, col) = values[row * 2 + col];
}
void tst_QMatrixNxN::setMatrix(QMatrix3x3& m, const qreal *values)
{
for (int row = 0; row < 3; ++row)
for (int col = 0; col < 3; ++col)
m(row, col) = values[row * 3 + col];
}
void tst_QMatrixNxN::setMatrix(QMatrix4x4& m, const qreal *values)
{
for (int row = 0; row < 4; ++row)
for (int col = 0; col < 4; ++col)
m(row, col) = values[row * 4 + col];
}
void tst_QMatrixNxN::setMatrix(QMatrix4x3& m, const qreal *values)
{
for (int row = 0; row < 3; ++row)
for (int col = 0; col < 4; ++col)
m(row, col) = values[row * 4 + col];
}
// Set a matrix to a specified array of values, which are assumed
// to be in row-major order. This sets the values directly into
// the internal data() array.
void tst_QMatrixNxN::setMatrixDirect(QMatrix2x2& m, const qreal *values)
{
qreal *data = m.data();
for (int row = 0; row < 2; ++row) {
for (int col = 0; col < 2; ++col) {
data[row + col * 2] = values[row * 2 + col];
}
}
}
void tst_QMatrixNxN::setMatrixDirect(QMatrix3x3& m, const qreal *values)
{
qreal *data = m.data();
for (int row = 0; row < 3; ++row) {
for (int col = 0; col < 3; ++col) {
data[row + col * 3] = values[row * 3 + col];
}
}
}
void tst_QMatrixNxN::setMatrixDirect(QMatrix4x4& m, const qreal *values)
{
qreal *data = m.data();
for (int row = 0; row < 4; ++row) {
for (int col = 0; col < 4; ++col) {
data[row + col * 4] = values[row * 4 + col];
}
}
}
void tst_QMatrixNxN::setMatrixDirect(QMatrix4x3& m, const qreal *values)
{
qreal *data = m.data();
for (int row = 0; row < 3; ++row) {
for (int col = 0; col < 4; ++col) {
data[row + col * 3] = values[row * 4 + col];
}
}
}
// QVector2/3/4D use float internally, which can sometimes lead
// to precision issues when converting to and from qreal during
// operations involving QMatrix4x4. This fuzzy compare is slightly
// "fuzzier" than the default qFuzzyCompare for qreal to compensate.
static bool fuzzyCompare(qreal x, qreal y)
{
return qFuzzyIsNull((float)(x - y));
}
static bool fuzzyCompare(const QVector3D &v1, const QVector3D &v2)
{
if (!fuzzyCompare(v1.x(), v2.x()))
return false;
if (!fuzzyCompare(v1.y(), v2.y()))
return false;
if (!fuzzyCompare(v1.z(), v2.z()))
return false;
return true;
}
// Determine if a matrix is the same as a specified array of values.
// The values are assumed to be specified in row-major order.
bool tst_QMatrixNxN::isSame(const QMatrix2x2& m, const qreal *values)
{
const qreal *mv = m.constData();
for (int row = 0; row < 2; ++row) {
for (int col = 0; col < 2; ++col) {
// Check the values using the operator() function.
if (!fuzzyCompare(m(row, col), values[row * 2 + col])) {
qDebug() << "floating-point failure at" << row << col << "actual =" << m(row, col) << "expected =" << values[row * 2 + col];
return false;
}
// Check the values using direct access, which verifies that the values
// are stored internally in column-major order.
if (!fuzzyCompare(mv[col * 2 + row], values[row * 2 + col])) {
qDebug() << "column floating-point failure at" << row << col << "actual =" << mv[col * 2 + row] << "expected =" << values[row * 2 + col];
return false;
}
}
}
return true;
}
bool tst_QMatrixNxN::isSame(const QMatrix3x3& m, const qreal *values)
{
const qreal *mv = m.constData();
for (int row = 0; row < 3; ++row) {
for (int col = 0; col < 3; ++col) {
// Check the values using the operator() access function.
if (!fuzzyCompare(m(row, col), values[row * 3 + col])) {
qDebug() << "floating-point failure at" << row << col << "actual =" << m(row, col) << "expected =" << values[row * 3 + col];
return false;
}
// Check the values using direct access, which verifies that the values
// are stored internally in column-major order.
if (!fuzzyCompare(mv[col * 3 + row], values[row * 3 + col])) {
qDebug() << "column floating-point failure at" << row << col << "actual =" << mv[col * 3 + row] << "expected =" << values[row * 3 + col];
return false;
}
}
}
return true;
}
bool tst_QMatrixNxN::isSame(const QMatrix4x4& m, const qreal *values)
{
const qreal *mv = m.constData();
for (int row = 0; row < 4; ++row) {
for (int col = 0; col < 4; ++col) {
// Check the values using the operator() access function.
if (!fuzzyCompare(m(row, col), values[row * 4 + col])) {
qDebug() << "floating-point failure at" << row << col << "actual =" << m(row, col) << "expected =" << values[row * 4 + col];
return false;
}
// Check the values using direct access, which verifies that the values
// are stored internally in column-major order.
if (!fuzzyCompare(mv[col * 4 + row], values[row * 4 + col])) {
qDebug() << "column floating-point failure at" << row << col << "actual =" << mv[col * 4 + row] << "expected =" << values[row * 4 + col];
return false;
}
}
}
return true;
}
bool tst_QMatrixNxN::isSame(const QMatrix4x3& m, const qreal *values)
{
const qreal *mv = m.constData();
for (int row = 0; row < 3; ++row) {
for (int col = 0; col < 4; ++col) {
// Check the values using the operator() access function.
if (!fuzzyCompare(m(row, col), values[row * 4 + col])) {
qDebug() << "floating-point failure at" << row << col << "actual =" << m(row, col) << "expected =" << values[row * 4 + col];
return false;
}
// Check the values using direct access, which verifies that the values
// are stored internally in column-major order.
if (!fuzzyCompare(mv[col * 3 + row], values[row * 4 + col])) {
qDebug() << "column floating-point failure at" << row << col << "actual =" << mv[col * 3 + row] << "expected =" << values[row * 4 + col];
return false;
}
}
}
return true;
}
// Determine if a matrix is the identity.
bool tst_QMatrixNxN::isIdentity(const QMatrix2x2& m)
{
return isSame(m, identityValues2);
}
bool tst_QMatrixNxN::isIdentity(const QMatrix3x3& m)
{
return isSame(m, identityValues3);
}
bool tst_QMatrixNxN::isIdentity(const QMatrix4x4& m)
{
return isSame(m, identityValues4);
}
bool tst_QMatrixNxN::isIdentity(const QMatrix4x3& m)
{
return isSame(m, identityValues4x3);
}
// Test the creation of QMatrix2x2 objects in various ways:
// construct, copy, and modify.
void tst_QMatrixNxN::create2x2()
{
QMatrix2x2 m1;
QVERIFY(isIdentity(m1));
QVERIFY(m1.isIdentity());
QMatrix2x2 m2;
setMatrix(m2, uniqueValues2);
QVERIFY(isSame(m2, uniqueValues2));
QVERIFY(!m2.isIdentity());
QMatrix2x2 m3;
setMatrixDirect(m3, uniqueValues2);
QVERIFY(isSame(m3, uniqueValues2));
QMatrix2x2 m4(m3);
QVERIFY(isSame(m4, uniqueValues2));
QMatrix2x2 m5;
m5 = m3;
QVERIFY(isSame(m5, uniqueValues2));
m5.setToIdentity();
QVERIFY(isIdentity(m5));
QMatrix2x2 m6(uniqueValues2);
QVERIFY(isSame(m6, uniqueValues2));
qreal vals[4];
m6.copyDataTo(vals);
for (int index = 0; index < 4; ++index)
QCOMPARE(vals[index], uniqueValues2[index]);
}
// Test the creation of QMatrix3x3 objects in various ways:
// construct, copy, and modify.
void tst_QMatrixNxN::create3x3()
{
QMatrix3x3 m1;
QVERIFY(isIdentity(m1));
QVERIFY(m1.isIdentity());
QMatrix3x3 m2;
setMatrix(m2, uniqueValues3);
QVERIFY(isSame(m2, uniqueValues3));
QVERIFY(!m2.isIdentity());
QMatrix3x3 m3;
setMatrixDirect(m3, uniqueValues3);
QVERIFY(isSame(m3, uniqueValues3));
QMatrix3x3 m4(m3);
QVERIFY(isSame(m4, uniqueValues3));
QMatrix3x3 m5;
m5 = m3;
QVERIFY(isSame(m5, uniqueValues3));
m5.setToIdentity();
QVERIFY(isIdentity(m5));
QMatrix3x3 m6(uniqueValues3);
QVERIFY(isSame(m6, uniqueValues3));
qreal vals[9];
m6.copyDataTo(vals);
for (int index = 0; index < 9; ++index)
QCOMPARE(vals[index], uniqueValues3[index]);
}
// Test the creation of QMatrix4x4 objects in various ways:
// construct, copy, and modify.
void tst_QMatrixNxN::create4x4()
{
QMatrix4x4 m1;
QVERIFY(isIdentity(m1));
QVERIFY(m1.isIdentity());
QMatrix4x4 m2;
setMatrix(m2, uniqueValues4);
QVERIFY(isSame(m2, uniqueValues4));
QVERIFY(!m2.isIdentity());
QMatrix4x4 m3;
setMatrixDirect(m3, uniqueValues4);
QVERIFY(isSame(m3, uniqueValues4));
QMatrix4x4 m4(m3);
QVERIFY(isSame(m4, uniqueValues4));
QMatrix4x4 m5;
m5 = m3;
QVERIFY(isSame(m5, uniqueValues4));
m5.setToIdentity();
QVERIFY(isIdentity(m5));
QMatrix4x4 m6(uniqueValues4);
QVERIFY(isSame(m6, uniqueValues4));
qreal vals[16];
m6.copyDataTo(vals);
for (int index = 0; index < 16; ++index)
QCOMPARE(vals[index], uniqueValues4[index]);
QMatrix4x4 m8
(uniqueValues4[0], uniqueValues4[1], uniqueValues4[2], uniqueValues4[3],
uniqueValues4[4], uniqueValues4[5], uniqueValues4[6], uniqueValues4[7],
uniqueValues4[8], uniqueValues4[9], uniqueValues4[10], uniqueValues4[11],
uniqueValues4[12], uniqueValues4[13], uniqueValues4[14], uniqueValues4[15]);
QVERIFY(isSame(m8, uniqueValues4));
}
// Test the creation of QMatrix4x3 objects in various ways:
// construct, copy, and modify.
void tst_QMatrixNxN::create4x3()
{
QMatrix4x3 m1;
QVERIFY(isIdentity(m1));
QVERIFY(m1.isIdentity());
QMatrix4x3 m2;
setMatrix(m2, uniqueValues4x3);
QVERIFY(isSame(m2, uniqueValues4x3));
QVERIFY(!m2.isIdentity());
QMatrix4x3 m3;
setMatrixDirect(m3, uniqueValues4x3);
QVERIFY(isSame(m3, uniqueValues4x3));
QMatrix4x3 m4(m3);
QVERIFY(isSame(m4, uniqueValues4x3));
QMatrix4x3 m5;
m5 = m3;
QVERIFY(isSame(m5, uniqueValues4x3));
m5.setToIdentity();
QVERIFY(isIdentity(m5));
QMatrix4x3 m6(uniqueValues4x3);
QVERIFY(isSame(m6, uniqueValues4x3));
qreal vals[12];
m6.copyDataTo(vals);
for (int index = 0; index < 12; ++index)
QCOMPARE(vals[index], uniqueValues4x3[index]);
}
// Test isIdentity() for 2x2 matrices.
void tst_QMatrixNxN::isIdentity2x2()
{
for (int i = 0; i < 2 * 2; ++i) {
QMatrix2x2 m;
QVERIFY(m.isIdentity());
m.data()[i] = 42.0f;
QVERIFY(!m.isIdentity());
}
}
// Test isIdentity() for 3x3 matrices.
void tst_QMatrixNxN::isIdentity3x3()
{
for (int i = 0; i < 3 * 3; ++i) {
QMatrix3x3 m;
QVERIFY(m.isIdentity());
m.data()[i] = 42.0f;
QVERIFY(!m.isIdentity());
}
}
// Test isIdentity() for 4x4 matrices.
void tst_QMatrixNxN::isIdentity4x4()
{
for (int i = 0; i < 4 * 4; ++i) {
QMatrix4x4 m;
QVERIFY(m.isIdentity());
m.data()[i] = 42.0f;
QVERIFY(!m.isIdentity());
}
// Force the "Identity" flag bit to be lost and check again.
QMatrix4x4 m2;
m2.data()[0] = 1.0f;
QVERIFY(m2.isIdentity());
}
// Test isIdentity() for 4x3 matrices.
void tst_QMatrixNxN::isIdentity4x3()
{
for (int i = 0; i < 4 * 3; ++i) {
QMatrix4x3 m;
QVERIFY(m.isIdentity());
m.data()[i] = 42.0f;
QVERIFY(!m.isIdentity());
}
}
// Test 2x2 matrix comparisons.
void tst_QMatrixNxN::compare2x2()
{
QMatrix2x2 m1(uniqueValues2);
QMatrix2x2 m2(uniqueValues2);
QMatrix2x2 m3(transposedValues2);
QVERIFY(m1 == m2);
QVERIFY(!(m1 != m2));
QVERIFY(m1 != m3);
QVERIFY(!(m1 == m3));
}
// Test 3x3 matrix comparisons.
void tst_QMatrixNxN::compare3x3()
{
QMatrix3x3 m1(uniqueValues3);
QMatrix3x3 m2(uniqueValues3);
QMatrix3x3 m3(transposedValues3);
QVERIFY(m1 == m2);
QVERIFY(!(m1 != m2));
QVERIFY(m1 != m3);
QVERIFY(!(m1 == m3));
}
// Test 4x4 matrix comparisons.
void tst_QMatrixNxN::compare4x4()
{
QMatrix4x4 m1(uniqueValues4);
QMatrix4x4 m2(uniqueValues4);
QMatrix4x4 m3(transposedValues4);
QVERIFY(m1 == m2);
QVERIFY(!(m1 != m2));
QVERIFY(m1 != m3);
QVERIFY(!(m1 == m3));
}
// Test 4x3 matrix comparisons.
void tst_QMatrixNxN::compare4x3()
{
QMatrix4x3 m1(uniqueValues4x3);
QMatrix4x3 m2(uniqueValues4x3);
QMatrix4x3 m3(transposedValues3x4);
QVERIFY(m1 == m2);
QVERIFY(!(m1 != m2));
QVERIFY(m1 != m3);
QVERIFY(!(m1 == m3));
}
// Test matrix 2x2 transpose operations.
void tst_QMatrixNxN::transposed2x2()
{
// Transposing the identity should result in the identity.
QMatrix2x2 m1;
QMatrix2x2 m2 = m1.transposed();
QVERIFY(isIdentity(m2));
// Transpose a more interesting matrix that allows us to track
// exactly where each source element ends up.
QMatrix2x2 m3(uniqueValues2);
QMatrix2x2 m4 = m3.transposed();
QVERIFY(isSame(m4, transposedValues2));
// Transpose in-place, just to check that the compiler is sane.
m3 = m3.transposed();
QVERIFY(isSame(m3, transposedValues2));
}
// Test matrix 3x3 transpose operations.
void tst_QMatrixNxN::transposed3x3()
{
// Transposing the identity should result in the identity.
QMatrix3x3 m1;
QMatrix3x3 m2 = m1.transposed();
QVERIFY(isIdentity(m2));
// Transpose a more interesting matrix that allows us to track
// exactly where each source element ends up.
QMatrix3x3 m3(uniqueValues3);
QMatrix3x3 m4 = m3.transposed();
QVERIFY(isSame(m4, transposedValues3));
// Transpose in-place, just to check that the compiler is sane.
m3 = m3.transposed();
QVERIFY(isSame(m3, transposedValues3));
}
// Test matrix 4x4 transpose operations.
void tst_QMatrixNxN::transposed4x4()
{
// Transposing the identity should result in the identity.
QMatrix4x4 m1;
QMatrix4x4 m2 = m1.transposed();
QVERIFY(isIdentity(m2));
// Transpose a more interesting matrix that allows us to track
// exactly where each source element ends up.
QMatrix4x4 m3(uniqueValues4);
QMatrix4x4 m4 = m3.transposed();
QVERIFY(isSame(m4, transposedValues4));
// Transpose in-place, just to check that the compiler is sane.
m3 = m3.transposed();
QVERIFY(isSame(m3, transposedValues4));
}
// Test matrix 4x3 transpose operations.
void tst_QMatrixNxN::transposed4x3()
{
QMatrix4x3 m3(uniqueValues4x3);
QMatrix3x4 m4 = m3.transposed();
qreal values[12];
m4.copyDataTo(values);
for (int index = 0; index < 12; ++index)
QCOMPARE(values[index], transposedValues3x4[index]);
}
// Test matrix addition for 2x2 matrices.
void tst_QMatrixNxN::add2x2_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<void *>("m3Values");
QTest::newRow("null")
<< (void *)nullValues2 << (void *)nullValues2 << (void *)nullValues2;
QTest::newRow("identity/null")
<< (void *)identityValues2 << (void *)nullValues2 << (void *)identityValues2;
QTest::newRow("identity/identity")
<< (void *)identityValues2 << (void *)identityValues2 << (void *)doubleIdentity2;
static qreal const sumValues[16] =
{2.0f, 7.0f,
7.0f, 12.0f};
QTest::newRow("unique")
<< (void *)uniqueValues2 << (void *)transposedValues2 << (void *)sumValues;
}
void tst_QMatrixNxN::add2x2()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix2x2 m1((const qreal *)m1Values);
QMatrix2x2 m2((const qreal *)m2Values);
QMatrix2x2 m4(m1);
m4 += m2;
QVERIFY(isSame(m4, (const qreal *)m3Values));
QMatrix2x2 m5;
m5 = m1 + m2;
QVERIFY(isSame(m5, (const qreal *)m3Values));
}
// Test matrix addition for 3x3 matrices.
void tst_QMatrixNxN::add3x3_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<void *>("m3Values");
QTest::newRow("null")
<< (void *)nullValues3 << (void *)nullValues3 << (void *)nullValues3;
QTest::newRow("identity/null")
<< (void *)identityValues3 << (void *)nullValues3 << (void *)identityValues3;
QTest::newRow("identity/identity")
<< (void *)identityValues3 << (void *)identityValues3 << (void *)doubleIdentity3;
static qreal const sumValues[16] =
{2.0f, 7.0f, 12.0f,
7.0f, 12.0f, 17.0f,
12.0f, 17.0f, 22.0f};
QTest::newRow("unique")
<< (void *)uniqueValues3 << (void *)transposedValues3 << (void *)sumValues;
}
void tst_QMatrixNxN::add3x3()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix3x3 m1((const qreal *)m1Values);
QMatrix3x3 m2((const qreal *)m2Values);
QMatrix3x3 m4(m1);
m4 += m2;
QVERIFY(isSame(m4, (const qreal *)m3Values));
QMatrix3x3 m5;
m5 = m1 + m2;
QVERIFY(isSame(m5, (const qreal *)m3Values));
}
// Test matrix addition for 4x4 matrices.
void tst_QMatrixNxN::add4x4_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<void *>("m3Values");
QTest::newRow("null")
<< (void *)nullValues4 << (void *)nullValues4 << (void *)nullValues4;
QTest::newRow("identity/null")
<< (void *)identityValues4 << (void *)nullValues4 << (void *)identityValues4;
QTest::newRow("identity/identity")
<< (void *)identityValues4 << (void *)identityValues4 << (void *)doubleIdentity4;
static qreal const sumValues[16] =
{2.0f, 7.0f, 12.0f, 17.0f,
7.0f, 12.0f, 17.0f, 22.0f,
12.0f, 17.0f, 22.0f, 27.0f,
17.0f, 22.0f, 27.0f, 32.0f};
QTest::newRow("unique")
<< (void *)uniqueValues4 << (void *)transposedValues4 << (void *)sumValues;
}
void tst_QMatrixNxN::add4x4()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix4x4 m1((const qreal *)m1Values);
QMatrix4x4 m2((const qreal *)m2Values);
QMatrix4x4 m4(m1);
m4 += m2;
QVERIFY(isSame(m4, (const qreal *)m3Values));
QMatrix4x4 m5;
m5 = m1 + m2;
QVERIFY(isSame(m5, (const qreal *)m3Values));
}
// Test matrix addition for 4x3 matrices.
void tst_QMatrixNxN::add4x3_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<void *>("m3Values");
QTest::newRow("null")
<< (void *)nullValues4x3 << (void *)nullValues4x3 << (void *)nullValues4x3;
QTest::newRow("identity/null")
<< (void *)identityValues4x3 << (void *)nullValues4x3 << (void *)identityValues4x3;
QTest::newRow("identity/identity")
<< (void *)identityValues4x3 << (void *)identityValues4x3 << (void *)doubleIdentity4x3;
static qreal const sumValues[16] =
{2.0f, 7.0f, 12.0f, 6.0f,
11.0f, 16.0f, 10.0f, 15.0f,
20.0f, 14.0f, 19.0f, 24.0f};
QTest::newRow("unique")
<< (void *)uniqueValues4x3 << (void *)transposedValues3x4 << (void *)sumValues;
}
void tst_QMatrixNxN::add4x3()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix4x3 m1((const qreal *)m1Values);
QMatrix4x3 m2((const qreal *)m2Values);
QMatrix4x3 m4(m1);
m4 += m2;
QVERIFY(isSame(m4, (const qreal *)m3Values));
QMatrix4x3 m5;
m5 = m1 + m2;
QVERIFY(isSame(m5, (const qreal *)m3Values));
}
// Test matrix subtraction for 2x2 matrices.
void tst_QMatrixNxN::subtract2x2_data()
{
// Use the same test cases as the add test.
add2x2_data();
}
void tst_QMatrixNxN::subtract2x2()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix2x2 m1((const qreal *)m1Values);
QMatrix2x2 m2((const qreal *)m2Values);
QMatrix2x2 m3((const qreal *)m3Values);
QMatrix2x2 m4(m3);
m4 -= m1;
QVERIFY(isSame(m4, (const qreal *)m2Values));
QMatrix2x2 m5;
m5 = m3 - m1;
QVERIFY(isSame(m5, (const qreal *)m2Values));
QMatrix2x2 m6(m3);
m6 -= m2;
QVERIFY(isSame(m6, (const qreal *)m1Values));
QMatrix2x2 m7;
m7 = m3 - m2;
QVERIFY(isSame(m7, (const qreal *)m1Values));
}
// Test matrix subtraction for 3x3 matrices.
void tst_QMatrixNxN::subtract3x3_data()
{
// Use the same test cases as the add test.
add3x3_data();
}
void tst_QMatrixNxN::subtract3x3()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix3x3 m1((const qreal *)m1Values);
QMatrix3x3 m2((const qreal *)m2Values);
QMatrix3x3 m3((const qreal *)m3Values);
QMatrix3x3 m4(m3);
m4 -= m1;
QVERIFY(isSame(m4, (const qreal *)m2Values));
QMatrix3x3 m5;
m5 = m3 - m1;
QVERIFY(isSame(m5, (const qreal *)m2Values));
QMatrix3x3 m6(m3);
m6 -= m2;
QVERIFY(isSame(m6, (const qreal *)m1Values));
QMatrix3x3 m7;
m7 = m3 - m2;
QVERIFY(isSame(m7, (const qreal *)m1Values));
}
// Test matrix subtraction for 4x4 matrices.
void tst_QMatrixNxN::subtract4x4_data()
{
// Use the same test cases as the add test.
add4x4_data();
}
void tst_QMatrixNxN::subtract4x4()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix4x4 m1((const qreal *)m1Values);
QMatrix4x4 m2((const qreal *)m2Values);
QMatrix4x4 m3((const qreal *)m3Values);
QMatrix4x4 m4(m3);
m4 -= m1;
QVERIFY(isSame(m4, (const qreal *)m2Values));
QMatrix4x4 m5;
m5 = m3 - m1;
QVERIFY(isSame(m5, (const qreal *)m2Values));
QMatrix4x4 m6(m3);
m6 -= m2;
QVERIFY(isSame(m6, (const qreal *)m1Values));
QMatrix4x4 m7;
m7 = m3 - m2;
QVERIFY(isSame(m7, (const qreal *)m1Values));
}
// Test matrix subtraction for 4x3 matrices.
void tst_QMatrixNxN::subtract4x3_data()
{
// Use the same test cases as the add test.
add4x3_data();
}
void tst_QMatrixNxN::subtract4x3()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix4x3 m1((const qreal *)m1Values);
QMatrix4x3 m2((const qreal *)m2Values);
QMatrix4x3 m3((const qreal *)m3Values);
QMatrix4x3 m4(m3);
m4 -= m1;
QVERIFY(isSame(m4, (const qreal *)m2Values));
QMatrix4x3 m5;
m5 = m3 - m1;
QVERIFY(isSame(m5, (const qreal *)m2Values));
QMatrix4x3 m6(m3);
m6 -= m2;
QVERIFY(isSame(m6, (const qreal *)m1Values));
QMatrix4x3 m7;
m7 = m3 - m2;
QVERIFY(isSame(m7, (const qreal *)m1Values));
}
// Test matrix multiplication for 2x2 matrices.
void tst_QMatrixNxN::multiply2x2_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<void *>("m3Values");
QTest::newRow("null")
<< (void *)nullValues2 << (void *)nullValues2 << (void *)nullValues2;
QTest::newRow("null/unique")
<< (void *)nullValues2 << (void *)uniqueValues2 << (void *)nullValues2;
QTest::newRow("unique/null")
<< (void *)uniqueValues2 << (void *)nullValues2 << (void *)nullValues2;
QTest::newRow("unique/identity")
<< (void *)uniqueValues2 << (void *)identityValues2 << (void *)uniqueValues2;
QTest::newRow("identity/unique")
<< (void *)identityValues2 << (void *)uniqueValues2 << (void *)uniqueValues2;
static qreal uniqueResult[4];
for (int row = 0; row < 2; ++row) {
for (int col = 0; col < 2; ++col) {
qreal sum = 0.0f;
for (int j = 0; j < 2; ++j)
sum += uniqueValues2[row * 2 + j] * transposedValues2[j * 2 + col];
uniqueResult[row * 2 + col] = sum;
}
}
QTest::newRow("unique/transposed")
<< (void *)uniqueValues2 << (void *)transposedValues2 << (void *)uniqueResult;
}
void tst_QMatrixNxN::multiply2x2()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix2x2 m1((const qreal *)m1Values);
QMatrix2x2 m2((const qreal *)m2Values);
QMatrix2x2 m5;
m5 = m1 * m2;
QVERIFY(isSame(m5, (const qreal *)m3Values));
}
// Test matrix multiplication for 3x3 matrices.
void tst_QMatrixNxN::multiply3x3_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<void *>("m3Values");
QTest::newRow("null")
<< (void *)nullValues3 << (void *)nullValues3 << (void *)nullValues3;
QTest::newRow("null/unique")
<< (void *)nullValues3 << (void *)uniqueValues3 << (void *)nullValues3;
QTest::newRow("unique/null")
<< (void *)uniqueValues3 << (void *)nullValues3 << (void *)nullValues3;
QTest::newRow("unique/identity")
<< (void *)uniqueValues3 << (void *)identityValues3 << (void *)uniqueValues3;
QTest::newRow("identity/unique")
<< (void *)identityValues3 << (void *)uniqueValues3 << (void *)uniqueValues3;
static qreal uniqueResult[9];
for (int row = 0; row < 3; ++row) {
for (int col = 0; col < 3; ++col) {
qreal sum = 0.0f;
for (int j = 0; j < 3; ++j)
sum += uniqueValues3[row * 3 + j] * transposedValues3[j * 3 + col];
uniqueResult[row * 3 + col] = sum;
}
}
QTest::newRow("unique/transposed")
<< (void *)uniqueValues3 << (void *)transposedValues3 << (void *)uniqueResult;
}
void tst_QMatrixNxN::multiply3x3()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix3x3 m1((const qreal *)m1Values);
QMatrix3x3 m2((const qreal *)m2Values);
QMatrix3x3 m5;
m5 = m1 * m2;
QVERIFY(isSame(m5, (const qreal *)m3Values));
}
// Test matrix multiplication for 4x4 matrices.
void tst_QMatrixNxN::multiply4x4_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<void *>("m3Values");
QTest::newRow("null")
<< (void *)nullValues4 << (void *)nullValues4 << (void *)nullValues4;
QTest::newRow("null/unique")
<< (void *)nullValues4 << (void *)uniqueValues4 << (void *)nullValues4;
QTest::newRow("unique/null")
<< (void *)uniqueValues4 << (void *)nullValues4 << (void *)nullValues4;
QTest::newRow("unique/identity")
<< (void *)uniqueValues4 << (void *)identityValues4 << (void *)uniqueValues4;
QTest::newRow("identity/unique")
<< (void *)identityValues4 << (void *)uniqueValues4 << (void *)uniqueValues4;
static qreal uniqueResult[16];
for (int row = 0; row < 4; ++row) {
for (int col = 0; col < 4; ++col) {
qreal sum = 0.0f;
for (int j = 0; j < 4; ++j)
sum += uniqueValues4[row * 4 + j] * transposedValues4[j * 4 + col];
uniqueResult[row * 4 + col] = sum;
}
}
QTest::newRow("unique/transposed")
<< (void *)uniqueValues4 << (void *)transposedValues4 << (void *)uniqueResult;
}
void tst_QMatrixNxN::multiply4x4()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix4x4 m1((const qreal *)m1Values);
QMatrix4x4 m2((const qreal *)m2Values);
QMatrix4x4 m4;
m4 = m1;
m4 *= m2;
QVERIFY(isSame(m4, (const qreal *)m3Values));
QMatrix4x4 m5;
m5 = m1 * m2;
QVERIFY(isSame(m5, (const qreal *)m3Values));
}
// Test matrix multiplication for 4x3 matrices.
void tst_QMatrixNxN::multiply4x3_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<void *>("m3Values");
QTest::newRow("null")
<< (void *)nullValues4x3 << (void *)nullValues4x3 << (void *)nullValues3;
QTest::newRow("null/unique")
<< (void *)nullValues4x3 << (void *)uniqueValues4x3 << (void *)nullValues3;
QTest::newRow("unique/null")
<< (void *)uniqueValues4x3 << (void *)nullValues4x3 << (void *)nullValues3;
static qreal uniqueResult[9];
for (int row = 0; row < 3; ++row) {
for (int col = 0; col < 3; ++col) {
qreal sum = 0.0f;
for (int j = 0; j < 4; ++j)
sum += uniqueValues4x3[row * 4 + j] * transposedValues3x4[j * 3 + col];
uniqueResult[row * 3 + col] = sum;
}
}
QTest::newRow("unique/transposed")
<< (void *)uniqueValues4x3 << (void *)transposedValues3x4 << (void *)uniqueResult;
}
void tst_QMatrixNxN::multiply4x3()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(void *, m3Values);
QMatrix4x3 m1((const qreal *)m1Values);
QMatrix3x4 m2((const qreal *)m2Values);
QGenericMatrix<3, 3, qreal> m4;
m4 = m1 * m2;
qreal values[9];
m4.copyDataTo(values);
for (int index = 0; index < 9; ++index)
QCOMPARE(values[index], ((const qreal *)m3Values)[index]);
}
// Test matrix multiplication by a factor for 2x2 matrices.
void tst_QMatrixNxN::multiplyFactor2x2_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<qreal>("factor");
QTest::addColumn<void *>("m2Values");
QTest::newRow("null")
<< (void *)nullValues2 << (qreal)1.0f << (void *)nullValues2;
QTest::newRow("double identity")
<< (void *)identityValues2 << (qreal)2.0f << (void *)doubleIdentity2;
static qreal const values[16] =
{1.0f, 2.0f,
5.0f, 6.0f};
static qreal const doubleValues[16] =
{2.0f, 4.0f,
10.0f, 12.0f};
static qreal const negDoubleValues[16] =
{-2.0f, -4.0f,
-10.0f, -12.0f};
QTest::newRow("unique")
<< (void *)values << (qreal)2.0f << (void *)doubleValues;
QTest::newRow("neg")
<< (void *)values << (qreal)-2.0f << (void *)negDoubleValues;
QTest::newRow("zero")
<< (void *)values << (qreal)0.0f << (void *)nullValues4;
}
void tst_QMatrixNxN::multiplyFactor2x2()
{
QFETCH(void *, m1Values);
QFETCH(qreal, factor);
QFETCH(void *, m2Values);
QMatrix2x2 m1((const qreal *)m1Values);
QMatrix2x2 m3;
m3 = m1;
m3 *= factor;
QVERIFY(isSame(m3, (const qreal *)m2Values));
QMatrix2x2 m4;
m4 = m1 * factor;
QVERIFY(isSame(m4, (const qreal *)m2Values));
QMatrix2x2 m5;
m5 = factor * m1;
QVERIFY(isSame(m5, (const qreal *)m2Values));
}
// Test matrix multiplication by a factor for 3x3 matrices.
void tst_QMatrixNxN::multiplyFactor3x3_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<qreal>("factor");
QTest::addColumn<void *>("m2Values");
QTest::newRow("null")
<< (void *)nullValues3 << (qreal)1.0f << (void *)nullValues3;
QTest::newRow("double identity")
<< (void *)identityValues3 << (qreal)2.0f << (void *)doubleIdentity3;
static qreal const values[16] =
{1.0f, 2.0f, 3.0f,
5.0f, 6.0f, 7.0f,
9.0f, 10.0f, 11.0f};
static qreal const doubleValues[16] =
{2.0f, 4.0f, 6.0f,
10.0f, 12.0f, 14.0f,
18.0f, 20.0f, 22.0f};
static qreal const negDoubleValues[16] =
{-2.0f, -4.0f, -6.0f,
-10.0f, -12.0f, -14.0f,
-18.0f, -20.0f, -22.0f};
QTest::newRow("unique")
<< (void *)values << (qreal)2.0f << (void *)doubleValues;
QTest::newRow("neg")
<< (void *)values << (qreal)-2.0f << (void *)negDoubleValues;
QTest::newRow("zero")
<< (void *)values << (qreal)0.0f << (void *)nullValues4;
}
void tst_QMatrixNxN::multiplyFactor3x3()
{
QFETCH(void *, m1Values);
QFETCH(qreal, factor);
QFETCH(void *, m2Values);
QMatrix3x3 m1((const qreal *)m1Values);
QMatrix3x3 m3;
m3 = m1;
m3 *= factor;
QVERIFY(isSame(m3, (const qreal *)m2Values));
QMatrix3x3 m4;
m4 = m1 * factor;
QVERIFY(isSame(m4, (const qreal *)m2Values));
QMatrix3x3 m5;
m5 = factor * m1;
QVERIFY(isSame(m5, (const qreal *)m2Values));
}
// Test matrix multiplication by a factor for 4x4 matrices.
void tst_QMatrixNxN::multiplyFactor4x4_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<qreal>("factor");
QTest::addColumn<void *>("m2Values");
QTest::newRow("null")
<< (void *)nullValues4 << (qreal)1.0f << (void *)nullValues4;
QTest::newRow("double identity")
<< (void *)identityValues4 << (qreal)2.0f << (void *)doubleIdentity4;
static qreal const values[16] =
{1.0f, 2.0f, 3.0f, 4.0f,
5.0f, 6.0f, 7.0f, 8.0f,
9.0f, 10.0f, 11.0f, 12.0f,
13.0f, 14.0f, 15.0f, 16.0f};
static qreal const doubleValues[16] =
{2.0f, 4.0f, 6.0f, 8.0f,
10.0f, 12.0f, 14.0f, 16.0f,
18.0f, 20.0f, 22.0f, 24.0f,
26.0f, 28.0f, 30.0f, 32.0f};
static qreal const negDoubleValues[16] =
{-2.0f, -4.0f, -6.0f, -8.0f,
-10.0f, -12.0f, -14.0f, -16.0f,
-18.0f, -20.0f, -22.0f, -24.0f,
-26.0f, -28.0f, -30.0f, -32.0f};
QTest::newRow("unique")
<< (void *)values << (qreal)2.0f << (void *)doubleValues;
QTest::newRow("neg")
<< (void *)values << (qreal)-2.0f << (void *)negDoubleValues;
QTest::newRow("zero")
<< (void *)values << (qreal)0.0f << (void *)nullValues4;
}
void tst_QMatrixNxN::multiplyFactor4x4()
{
QFETCH(void *, m1Values);
QFETCH(qreal, factor);
QFETCH(void *, m2Values);
QMatrix4x4 m1((const qreal *)m1Values);
QMatrix4x4 m3;
m3 = m1;
m3 *= factor;
QVERIFY(isSame(m3, (const qreal *)m2Values));
QMatrix4x4 m4;
m4 = m1 * factor;
QVERIFY(isSame(m4, (const qreal *)m2Values));
QMatrix4x4 m5;
m5 = factor * m1;
QVERIFY(isSame(m5, (const qreal *)m2Values));
}
// Test matrix multiplication by a factor for 4x3 matrices.
void tst_QMatrixNxN::multiplyFactor4x3_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<qreal>("factor");
QTest::addColumn<void *>("m2Values");
QTest::newRow("null")
<< (void *)nullValues4x3 << (qreal)1.0f << (void *)nullValues4x3;
QTest::newRow("double identity")
<< (void *)identityValues4x3 << (qreal)2.0f << (void *)doubleIdentity4x3;
static qreal const values[12] =
{1.0f, 2.0f, 3.0f, 4.0f,
5.0f, 6.0f, 7.0f, 8.0f,
9.0f, 10.0f, 11.0f, 12.0f};
static qreal const doubleValues[12] =
{2.0f, 4.0f, 6.0f, 8.0f,
10.0f, 12.0f, 14.0f, 16.0f,
18.0f, 20.0f, 22.0f, 24.0f};
static qreal const negDoubleValues[12] =
{-2.0f, -4.0f, -6.0f, -8.0f,
-10.0f, -12.0f, -14.0f, -16.0f,
-18.0f, -20.0f, -22.0f, -24.0f};
QTest::newRow("unique")
<< (void *)values << (qreal)2.0f << (void *)doubleValues;
QTest::newRow("neg")
<< (void *)values << (qreal)-2.0f << (void *)negDoubleValues;
QTest::newRow("zero")
<< (void *)values << (qreal)0.0f << (void *)nullValues4x3;
}
void tst_QMatrixNxN::multiplyFactor4x3()
{
QFETCH(void *, m1Values);
QFETCH(qreal, factor);
QFETCH(void *, m2Values);
QMatrix4x3 m1((const qreal *)m1Values);
QMatrix4x3 m3;
m3 = m1;
m3 *= factor;
QVERIFY(isSame(m3, (const qreal *)m2Values));
QMatrix4x3 m4;
m4 = m1 * factor;
QVERIFY(isSame(m4, (const qreal *)m2Values));
QMatrix4x3 m5;
m5 = factor * m1;
QVERIFY(isSame(m5, (const qreal *)m2Values));
}
// Test matrix division by a factor for 2x2 matrices.
void tst_QMatrixNxN::divideFactor2x2_data()
{
// Use the same test cases as the multiplyFactor test.
multiplyFactor2x2_data();
}
void tst_QMatrixNxN::divideFactor2x2()
{
QFETCH(void *, m1Values);
QFETCH(qreal, factor);
QFETCH(void *, m2Values);
if (factor == 0.0f)
return;
QMatrix2x2 m2((const qreal *)m2Values);
QMatrix2x2 m3;
m3 = m2;
m3 /= factor;
QVERIFY(isSame(m3, (const qreal *)m1Values));
QMatrix2x2 m4;
m4 = m2 / factor;
QVERIFY(isSame(m4, (const qreal *)m1Values));
}
// Test matrix division by a factor for 3x3 matrices.
void tst_QMatrixNxN::divideFactor3x3_data()
{
// Use the same test cases as the multiplyFactor test.
multiplyFactor3x3_data();
}
void tst_QMatrixNxN::divideFactor3x3()
{
QFETCH(void *, m1Values);
QFETCH(qreal, factor);
QFETCH(void *, m2Values);
if (factor == 0.0f)
return;
QMatrix3x3 m2((const qreal *)m2Values);
QMatrix3x3 m3;
m3 = m2;
m3 /= factor;
QVERIFY(isSame(m3, (const qreal *)m1Values));
QMatrix3x3 m4;
m4 = m2 / factor;
QVERIFY(isSame(m4, (const qreal *)m1Values));
}
// Test matrix division by a factor for 4x4 matrices.
void tst_QMatrixNxN::divideFactor4x4_data()
{
// Use the same test cases as the multiplyFactor test.
multiplyFactor4x4_data();
}
void tst_QMatrixNxN::divideFactor4x4()
{
QFETCH(void *, m1Values);
QFETCH(qreal, factor);
QFETCH(void *, m2Values);
if (factor == 0.0f)
return;
QMatrix4x4 m2((const qreal *)m2Values);
QMatrix4x4 m3;
m3 = m2;
m3 /= factor;
QVERIFY(isSame(m3, (const qreal *)m1Values));
QMatrix4x4 m4;
m4 = m2 / factor;
QVERIFY(isSame(m4, (const qreal *)m1Values));
}
// Test matrix division by a factor for 4x3 matrices.
void tst_QMatrixNxN::divideFactor4x3_data()
{
// Use the same test cases as the multiplyFactor test.
multiplyFactor4x3_data();
}
void tst_QMatrixNxN::divideFactor4x3()
{
QFETCH(void *, m1Values);
QFETCH(qreal, factor);
QFETCH(void *, m2Values);
if (factor == 0.0f)
return;
QMatrix4x3 m2((const qreal *)m2Values);
QMatrix4x3 m3;
m3 = m2;
m3 /= factor;
QVERIFY(isSame(m3, (const qreal *)m1Values));
QMatrix4x3 m4;
m4 = m2 / factor;
QVERIFY(isSame(m4, (const qreal *)m1Values));
}
// Test matrix negation for 2x2 matrices.
void tst_QMatrixNxN::negate2x2_data()
{
// Use the same test cases as the multiplyFactor test.
multiplyFactor2x2_data();
}
void tst_QMatrixNxN::negate2x2()
{
QFETCH(void *, m1Values);
const qreal *values = (const qreal *)m1Values;
QMatrix2x2 m1(values);
qreal negated[4];
for (int index = 0; index < 4; ++index)
negated[index] = -values[index];
QMatrix2x2 m2;
m2 = -m1;
QVERIFY(isSame(m2, negated));
}
// Test matrix negation for 3x3 matrices.
void tst_QMatrixNxN::negate3x3_data()
{
// Use the same test cases as the multiplyFactor test.
multiplyFactor3x3_data();
}
void tst_QMatrixNxN::negate3x3()
{
QFETCH(void *, m1Values);
const qreal *values = (const qreal *)m1Values;
QMatrix3x3 m1(values);
qreal negated[9];
for (int index = 0; index < 9; ++index)
negated[index] = -values[index];
QMatrix3x3 m2;
m2 = -m1;
QVERIFY(isSame(m2, negated));
}
// Test matrix negation for 4x4 matrices.
void tst_QMatrixNxN::negate4x4_data()
{
// Use the same test cases as the multiplyFactor test.
multiplyFactor4x4_data();
}
void tst_QMatrixNxN::negate4x4()
{
QFETCH(void *, m1Values);
const qreal *values = (const qreal *)m1Values;
QMatrix4x4 m1(values);
qreal negated[16];
for (int index = 0; index < 16; ++index)
negated[index] = -values[index];
QMatrix4x4 m2;
m2 = -m1;
QVERIFY(isSame(m2, negated));
}
// Test matrix negation for 4x3 matrices.
void tst_QMatrixNxN::negate4x3_data()
{
// Use the same test cases as the multiplyFactor test.
multiplyFactor4x3_data();
}
void tst_QMatrixNxN::negate4x3()
{
QFETCH(void *, m1Values);
const qreal *values = (const qreal *)m1Values;
QMatrix4x3 m1(values);
qreal negated[12];
for (int index = 0; index < 12; ++index)
negated[index] = -values[index];
QMatrix4x3 m2;
m2 = -m1;
QVERIFY(isSame(m2, negated));
}
// Matrix inverted. This is a more straight-forward implementation
// of the algorithm at http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q24
// than the optimized version in the QMatrix4x4 code. Hopefully it is
// easier to verify that this version is the same as the reference.
struct Matrix3
{
qreal v[9];
};
struct Matrix4
{
qreal v[16];
};
static qreal m3Determinant(const Matrix3& m)
{
return m.v[0] * (m.v[4] * m.v[8] - m.v[7] * m.v[5]) -
m.v[1] * (m.v[3] * m.v[8] - m.v[6] * m.v[5]) +
m.v[2] * (m.v[3] * m.v[7] - m.v[6] * m.v[4]);
}
static bool m3Inverse(const Matrix3& min, Matrix3& mout)
{
qreal det = m3Determinant(min);
if (det == 0.0f)
return false;
mout.v[0] = (min.v[4] * min.v[8] - min.v[5] * min.v[7]) / det;
mout.v[1] = -(min.v[1] * min.v[8] - min.v[2] * min.v[7]) / det;
mout.v[2] = (min.v[1] * min.v[5] - min.v[4] * min.v[2]) / det;
mout.v[3] = -(min.v[3] * min.v[8] - min.v[5] * min.v[6]) / det;
mout.v[4] = (min.v[0] * min.v[8] - min.v[6] * min.v[2]) / det;
mout.v[5] = -(min.v[0] * min.v[5] - min.v[3] * min.v[2]) / det;
mout.v[6] = (min.v[3] * min.v[7] - min.v[6] * min.v[4]) / det;
mout.v[7] = -(min.v[0] * min.v[7] - min.v[6] * min.v[1]) / det;
mout.v[8] = (min.v[0] * min.v[4] - min.v[1] * min.v[3]) / det;
return true;
}
static void m3Transpose(Matrix3& m)
{
qSwap(m.v[1], m.v[3]);
qSwap(m.v[2], m.v[6]);
qSwap(m.v[5], m.v[7]);
}
static void m4Submatrix(const Matrix4& min, Matrix3& mout, int i, int j)
{
for (int di = 0; di < 3; ++di) {
for (int dj = 0; dj < 3; ++dj) {
int si = di + ((di >= i) ? 1 : 0);
int sj = dj + ((dj >= j) ? 1 : 0);
mout.v[di * 3 + dj] = min.v[si * 4 + sj];
}
}
}
static qreal m4Determinant(const Matrix4& m)
{
qreal det;
qreal result = 0.0f;
qreal i = 1.0f;
Matrix3 msub;
for (int n = 0; n < 4; ++n, i *= -1.0f) {
m4Submatrix(m, msub, 0, n);
det = m3Determinant(msub);
result += m.v[n] * det * i;
}
return result;
}
static void m4Inverse(const Matrix4& min, Matrix4& mout)
{
qreal det = m4Determinant(min);
Matrix3 msub;
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
qreal sign = 1.0f - ((i + j) % 2) * 2.0f;
m4Submatrix(min, msub, i, j);
mout.v[i + j * 4] = (m3Determinant(msub) * sign) / det;
}
}
}
// Test matrix inverted for 4x4 matrices.
void tst_QMatrixNxN::inverted4x4_data()
{
QTest::addColumn<void *>("m1Values");
QTest::addColumn<void *>("m2Values");
QTest::addColumn<bool>("invertible");
QTest::newRow("null")
<< (void *)nullValues4 << (void *)identityValues4 << false;
QTest::newRow("identity")
<< (void *)identityValues4 << (void *)identityValues4 << true;
QTest::newRow("unique")
<< (void *)uniqueValues4 << (void *)identityValues4 << false;
static Matrix4 const invertible = {
{5.0f, 0.0f, 0.0f, 2.0f,
0.0f, 6.0f, 0.0f, 3.0f,
0.0f, 0.0f, 7.0f, 4.0f,
0.0f, 0.0f, 0.0f, 1.0f}
};
static Matrix4 inverted;
m4Inverse(invertible, inverted);
QTest::newRow("invertible")
<< (void *)invertible.v << (void *)inverted.v << true;
static Matrix4 const translate = {
{1.0f, 0.0f, 0.0f, 2.0f,
0.0f, 1.0f, 0.0f, 3.0f,
0.0f, 0.0f, 1.0f, 4.0f,
0.0f, 0.0f, 0.0f, 1.0f}
};
static Matrix4 const inverseTranslate = {
{1.0f, 0.0f, 0.0f, -2.0f,
0.0f, 1.0f, 0.0f, -3.0f,
0.0f, 0.0f, 1.0f, -4.0f,
0.0f, 0.0f, 0.0f, 1.0f}
};
QTest::newRow("translate")
<< (void *)translate.v << (void *)inverseTranslate.v << true;
}
void tst_QMatrixNxN::inverted4x4()
{
QFETCH(void *, m1Values);
QFETCH(void *, m2Values);
QFETCH(bool, invertible);
QMatrix4x4 m1((const qreal *)m1Values);
if (invertible)
QVERIFY(m1.determinant() != 0.0f);
else
QVERIFY(m1.determinant() == 0.0f);
Matrix4 m1alt;
memcpy(m1alt.v, (const qreal *)m1Values, sizeof(m1alt.v));
QCOMPARE(m1.determinant(), m4Determinant(m1alt));
QMatrix4x4 m2;
bool inv;
m2 = m1.inverted(&inv);
QVERIFY(isSame(m2, (const qreal *)m2Values));
if (invertible) {
QVERIFY(inv);
Matrix4 m2alt;
m4Inverse(m1alt, m2alt);
QVERIFY(isSame(m2, m2alt.v));
QMatrix4x4 m3;
m3 = m1 * m2;
QVERIFY(isIdentity(m3));
QMatrix4x4 m4;
m4 = m2 * m1;
QVERIFY(isIdentity(m4));
} else {
QVERIFY(!inv);
}
// Test again, after inferring the special matrix type.
m1.optimize();
m2 = m1.inverted(&inv);
QVERIFY(isSame(m2, (const qreal *)m2Values));
QCOMPARE(inv, invertible);
}
void tst_QMatrixNxN::orthonormalInverse4x4()
{
QMatrix4x4 m1;
QVERIFY(qFuzzyCompare(m1.inverted(), m1));
QMatrix4x4 m2;
m2.rotate(45.0, 1.0, 0.0, 0.0);
m2.translate(10.0, 0.0, 0.0);
// Use optimize() to drop the internal flags that
// mark the matrix as orthonormal. This will force inverted()
// to compute m3.inverted() the long way. We can then compare
// the result to what the faster algorithm produces on m2.
QMatrix4x4 m3 = m2;
m3.optimize();
bool invertible;
QVERIFY(qFuzzyCompare(m2.inverted(&invertible), m3.inverted()));
QVERIFY(invertible);
QMatrix4x4 m4;
m4.rotate(45.0, 0.0, 1.0, 0.0);
QMatrix4x4 m5 = m4;
m5.optimize();
QVERIFY(qFuzzyCompare(m4.inverted(), m5.inverted()));
QMatrix4x4 m6;
m1.rotate(88, 0.0, 0.0, 1.0);
m1.translate(-20.0, 20.0, 15.0);
m1.rotate(25, 1.0, 0.0, 0.0);
QMatrix4x4 m7 = m6;
m7.optimize();
QVERIFY(qFuzzyCompare(m6.inverted(), m7.inverted()));
}
// Test the generation and use of 4x4 scale matrices.
void tst_QMatrixNxN::scale4x4_data()
{
QTest::addColumn<qreal>("x");
QTest::addColumn<qreal>("y");
QTest::addColumn<qreal>("z");
QTest::addColumn<void *>("resultValues");
static const qreal nullScale[] =
{0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("null")
<< (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (void *)nullScale;
QTest::newRow("identity")
<< (qreal)1.0f << (qreal)1.0f << (qreal)1.0f << (void *)identityValues4;
static const qreal doubleScale[] =
{2.0f, 0.0f, 0.0f, 0.0f,
0.0f, 2.0f, 0.0f, 0.0f,
0.0f, 0.0f, 2.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("double")
<< (qreal)2.0f << (qreal)2.0f << (qreal)2.0f << (void *)doubleScale;
static const qreal complexScale[] =
{2.0f, 0.0f, 0.0f, 0.0f,
0.0f, 11.0f, 0.0f, 0.0f,
0.0f, 0.0f, -6.5f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("complex")
<< (qreal)2.0f << (qreal)11.0f << (qreal)-6.5f << (void *)complexScale;
static const qreal complexScale2D[] =
{2.0f, 0.0f, 0.0f, 0.0f,
0.0f, -11.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("complex2D")
<< (qreal)2.0f << (qreal)-11.0f << (qreal)1.0f << (void *)complexScale2D;
}
void tst_QMatrixNxN::scale4x4()
{
QFETCH(qreal, x);
QFETCH(qreal, y);
QFETCH(qreal, z);
QFETCH(void *, resultValues);
QMatrix4x4 result((const qreal *)resultValues);
QMatrix4x4 m1;
m1.scale(QVector3D(x, y, z));
QVERIFY(isSame(m1, (const qreal *)resultValues));
QMatrix4x4 m2;
m2.scale(x, y, z);
QVERIFY(isSame(m2, (const qreal *)resultValues));
if (z == 1.0f) {
QMatrix4x4 m2b;
m2b.scale(x, y);
QVERIFY(m2b == m2);
}
QVector3D v1(2.0f, 3.0f, -4.0f);
QVector3D v2 = m1 * v1;
QCOMPARE(v2.x(), (qreal)(2.0f * x));
QCOMPARE(v2.y(), (qreal)(3.0f * y));
QCOMPARE(v2.z(), (qreal)(-4.0f * z));
v2 = v1 * m1;
QCOMPARE(v2.x(), (qreal)(2.0f * x));
QCOMPARE(v2.y(), (qreal)(3.0f * y));
QCOMPARE(v2.z(), (qreal)(-4.0f * z));
QVector4D v3(2.0f, 3.0f, -4.0f, 34.0f);
QVector4D v4 = m1 * v3;
QCOMPARE(v4.x(), (qreal)(2.0f * x));
QCOMPARE(v4.y(), (qreal)(3.0f * y));
QCOMPARE(v4.z(), (qreal)(-4.0f * z));
QCOMPARE(v4.w(), (qreal)34.0f);
v4 = v3 * m1;
QCOMPARE(v4.x(), (qreal)(2.0f * x));
QCOMPARE(v4.y(), (qreal)(3.0f * y));
QCOMPARE(v4.z(), (qreal)(-4.0f * z));
QCOMPARE(v4.w(), (qreal)34.0f);
QPoint p1(2, 3);
QPoint p2 = m1 * p1;
QCOMPARE(p2.x(), (int)(2.0f * x));
QCOMPARE(p2.y(), (int)(3.0f * y));
p2 = p1 * m1;
QCOMPARE(p2.x(), (int)(2.0f * x));
QCOMPARE(p2.y(), (int)(3.0f * y));
QPointF p3(2.0f, 3.0f);
QPointF p4 = m1 * p3;
QCOMPARE(p4.x(), (qreal)(2.0f * x));
QCOMPARE(p4.y(), (qreal)(3.0f * y));
p4 = p3 * m1;
QCOMPARE(p4.x(), (qreal)(2.0f * x));
QCOMPARE(p4.y(), (qreal)(3.0f * y));
QMatrix4x4 m3(uniqueValues4);
QMatrix4x4 m4(m3);
m4.scale(x, y, z);
QVERIFY(m4 == m3 * m1);
if (x == y && y == z) {
QMatrix4x4 m5;
m5.scale(x);
QVERIFY(isSame(m5, (const qreal *)resultValues));
}
if (z == 1.0f) {
QMatrix4x4 m4b(m3);
m4b.scale(x, y);
QVERIFY(m4b == m4);
}
// Test coverage when the special matrix type is unknown.
QMatrix4x4 m6;
m6(0, 0) = 1.0f;
m6.scale(QVector3D(x, y, z));
QVERIFY(isSame(m6, (const qreal *)resultValues));
QMatrix4x4 m7;
m7(0, 0) = 1.0f;
m7.scale(x, y, z);
QVERIFY(isSame(m7, (const qreal *)resultValues));
if (x == y && y == z) {
QMatrix4x4 m8;
m8(0, 0) = 1.0f;
m8.scale(x);
QVERIFY(isSame(m8, (const qreal *)resultValues));
m8.optimize();
m8.scale(1.0f);
QVERIFY(isSame(m8, (const qreal *)resultValues));
QMatrix4x4 m9;
m9.translate(0.0f, 0.0f, 0.0f);
m9.scale(x);
QVERIFY(isSame(m9, (const qreal *)resultValues));
}
}
// Test the generation and use of 4x4 translation matrices.
void tst_QMatrixNxN::translate4x4_data()
{
QTest::addColumn<qreal>("x");
QTest::addColumn<qreal>("y");
QTest::addColumn<qreal>("z");
QTest::addColumn<void *>("resultValues");
QTest::newRow("null")
<< (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (void *)identityValues4;
static const qreal identityTranslate[] =
{1.0f, 0.0f, 0.0f, 1.0f,
0.0f, 1.0f, 0.0f, 1.0f,
0.0f, 0.0f, 1.0f, 1.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("identity")
<< (qreal)1.0f << (qreal)1.0f << (qreal)1.0f << (void *)identityTranslate;
static const qreal complexTranslate[] =
{1.0f, 0.0f, 0.0f, 2.0f,
0.0f, 1.0f, 0.0f, 11.0f,
0.0f, 0.0f, 1.0f, -6.5f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("complex")
<< (qreal)2.0f << (qreal)11.0f << (qreal)-6.5f << (void *)complexTranslate;
static const qreal complexTranslate2D[] =
{1.0f, 0.0f, 0.0f, 2.0f,
0.0f, 1.0f, 0.0f, -11.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("complex2D")
<< (qreal)2.0f << (qreal)-11.0f << (qreal)0.0f << (void *)complexTranslate2D;
}
void tst_QMatrixNxN::translate4x4()
{
QFETCH(qreal, x);
QFETCH(qreal, y);
QFETCH(qreal, z);
QFETCH(void *, resultValues);
QMatrix4x4 result((const qreal *)resultValues);
QMatrix4x4 m1;
m1.translate(QVector3D(x, y, z));
QVERIFY(isSame(m1, (const qreal *)resultValues));
QMatrix4x4 m2;
m2.translate(x, y, z);
QVERIFY(isSame(m2, (const qreal *)resultValues));
if (z == 0.0f) {
QMatrix4x4 m2b;
m2b.translate(x, y);
QVERIFY(m2b == m2);
}
QVector3D v1(2.0f, 3.0f, -4.0f);
QVector3D v2 = m1 * v1;
QCOMPARE(v2.x(), (qreal)(2.0f + x));
QCOMPARE(v2.y(), (qreal)(3.0f + y));
QCOMPARE(v2.z(), (qreal)(-4.0f + z));
QVector4D v3(2.0f, 3.0f, -4.0f, 1.0f);
QVector4D v4 = m1 * v3;
QCOMPARE(v4.x(), (qreal)(2.0f + x));
QCOMPARE(v4.y(), (qreal)(3.0f + y));
QCOMPARE(v4.z(), (qreal)(-4.0f + z));
QCOMPARE(v4.w(), (qreal)1.0f);
QVector4D v5(2.0f, 3.0f, -4.0f, 34.0f);
QVector4D v6 = m1 * v5;
QCOMPARE(v6.x(), (qreal)(2.0f + x * 34.0f));
QCOMPARE(v6.y(), (qreal)(3.0f + y * 34.0f));
QCOMPARE(v6.z(), (qreal)(-4.0f + z * 34.0f));
QCOMPARE(v6.w(), (qreal)34.0f);
QPoint p1(2, 3);
QPoint p2 = m1 * p1;
QCOMPARE(p2.x(), (int)(2.0f + x));
QCOMPARE(p2.y(), (int)(3.0f + y));
QPointF p3(2.0f, 3.0f);
QPointF p4 = m1 * p3;
QCOMPARE(p4.x(), (qreal)(2.0f + x));
QCOMPARE(p4.y(), (qreal)(3.0f + y));
QMatrix4x4 m3(uniqueValues4);
QMatrix4x4 m4(m3);
m4.translate(x, y, z);
QVERIFY(m4 == m3 * m1);
if (z == 0.0f) {
QMatrix4x4 m4b(m3);
m4b.translate(x, y);
QVERIFY(m4b == m4);
}
}
// Test the generation and use of 4x4 rotation matrices.
void tst_QMatrixNxN::rotate4x4_data()
{
QTest::addColumn<qreal>("angle");
QTest::addColumn<qreal>("x");
QTest::addColumn<qreal>("y");
QTest::addColumn<qreal>("z");
QTest::addColumn<void *>("resultValues");
static const qreal nullRotate[] =
{0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("null")
<< (qreal)90.0f
<< (qreal)0.0f << (qreal)0.0f << (qreal)0.0f
<< (void *)nullRotate;
static const qreal noRotate[] =
{1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("zerodegrees")
<< (qreal)0.0f
<< (qreal)2.0f << (qreal)3.0f << (qreal)-4.0f
<< (void *)noRotate;
static const qreal xRotate[] =
{1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, -1.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("xrotate")
<< (qreal)90.0f
<< (qreal)1.0f << (qreal)0.0f << (qreal)0.0f
<< (void *)xRotate;
static const qreal xRotateNeg[] =
{1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, -1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("-xrotate")
<< (qreal)90.0f
<< (qreal)-1.0f << (qreal)0.0f << (qreal)0.0f
<< (void *)xRotateNeg;
static const qreal yRotate[] =
{0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
-1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("yrotate")
<< (qreal)90.0f
<< (qreal)0.0f << (qreal)1.0f << (qreal)0.0f
<< (void *)yRotate;
static const qreal yRotateNeg[] =
{0.0f, 0.0f, -1.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("-yrotate")
<< (qreal)90.0f
<< (qreal)0.0f << (qreal)-1.0f << (qreal)0.0f
<< (void *)yRotateNeg;
static const qreal zRotate[] =
{0.0f, -1.0f, 0.0f, 0.0f,
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("zrotate")
<< (qreal)90.0f
<< (qreal)0.0f << (qreal)0.0f << (qreal)1.0f
<< (void *)zRotate;
static const qreal zRotateNeg[] =
{0.0f, 1.0f, 0.0f, 0.0f,
-1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("-zrotate")
<< (qreal)90.0f
<< (qreal)0.0f << (qreal)0.0f << (qreal)-1.0f
<< (void *)zRotateNeg;
// Algorithm from http://en.wikipedia.org/wiki/Rotation_matrix.
// Deliberately different from the one in the code for cross-checking.
static qreal complexRotate[16];
qreal x = 1.0f;
qreal y = 2.0f;
qreal z = -6.0f;
qreal angle = -45.0f;
qreal c = qCos(angle * M_PI / 180.0f);
qreal s = qSin(angle * M_PI / 180.0f);
qreal len = qSqrt(x * x + y * y + z * z);
qreal xu = x / len;
qreal yu = y / len;
qreal zu = z / len;
complexRotate[0] = (qreal)((1 - xu * xu) * c + xu * xu);
complexRotate[1] = (qreal)(-zu * s - xu * yu * c + xu * yu);
complexRotate[2] = (qreal)(yu * s - xu * zu * c + xu * zu);
complexRotate[3] = 0;
complexRotate[4] = (qreal)(zu * s - xu * yu * c + xu * yu);
complexRotate[5] = (qreal)((1 - yu * yu) * c + yu * yu);
complexRotate[6] = (qreal)(-xu * s - yu * zu * c + yu * zu);
complexRotate[7] = 0;
complexRotate[8] = (qreal)(-yu * s - xu * zu * c + xu * zu);
complexRotate[9] = (qreal)(xu * s - yu * zu * c + yu * zu);
complexRotate[10] = (qreal)((1 - zu * zu) * c + zu * zu);
complexRotate[11] = 0;
complexRotate[12] = 0;
complexRotate[13] = 0;
complexRotate[14] = 0;
complexRotate[15] = 1;
QTest::newRow("complex")
<< (qreal)angle
<< (qreal)x << (qreal)y << (qreal)z
<< (void *)complexRotate;
}
void tst_QMatrixNxN::rotate4x4()
{
QFETCH(qreal, angle);
QFETCH(qreal, x);
QFETCH(qreal, y);
QFETCH(qreal, z);
QFETCH(void *, resultValues);
QMatrix4x4 m1;
m1.rotate(angle, QVector3D(x, y, z));
QVERIFY(isSame(m1, (const qreal *)resultValues));
QMatrix4x4 m2;
m2.rotate(angle, x, y, z);
QVERIFY(isSame(m2, (const qreal *)resultValues));
QMatrix4x4 m3(uniqueValues4);
QMatrix4x4 m4(m3);
m4.rotate(angle, x, y, z);
QVERIFY(qFuzzyCompare(m4, m3 * m1));
// Null vectors don't make sense for quaternion rotations.
if (x != 0 || y != 0 || z != 0) {
QMatrix4x4 m5;
m5.rotate(QQuaternion::fromAxisAndAngle(QVector3D(x, y, z), angle));
QVERIFY(isSame(m5, (const qreal *)resultValues));
}
#define ROTATE4(xin,yin,zin,win,xout,yout,zout,wout) \
do { \
xout = ((const qreal *)resultValues)[0] * xin + \
((const qreal *)resultValues)[1] * yin + \
((const qreal *)resultValues)[2] * zin + \
((const qreal *)resultValues)[3] * win; \
yout = ((const qreal *)resultValues)[4] * xin + \
((const qreal *)resultValues)[5] * yin + \
((const qreal *)resultValues)[6] * zin + \
((const qreal *)resultValues)[7] * win; \
zout = ((const qreal *)resultValues)[8] * xin + \
((const qreal *)resultValues)[9] * yin + \
((const qreal *)resultValues)[10] * zin + \
((const qreal *)resultValues)[11] * win; \
wout = ((const qreal *)resultValues)[12] * xin + \
((const qreal *)resultValues)[13] * yin + \
((const qreal *)resultValues)[14] * zin + \
((const qreal *)resultValues)[15] * win; \
} while (0)
// Rotate various test vectors using the straight-forward approach.
qreal v1x, v1y, v1z, v1w;
ROTATE4(2.0f, 3.0f, -4.0f, 1.0f, v1x, v1y, v1z, v1w);
v1x /= v1w;
v1y /= v1w;
v1z /= v1w;
qreal v3x, v3y, v3z, v3w;
ROTATE4(2.0f, 3.0f, -4.0f, 1.0f, v3x, v3y, v3z, v3w);
qreal v5x, v5y, v5z, v5w;
ROTATE4(2.0f, 3.0f, -4.0f, 34.0f, v5x, v5y, v5z, v5w);
qreal p1x, p1y, p1z, p1w;
ROTATE4(2.0f, 3.0f, 0.0f, 1.0f, p1x, p1y, p1z, p1w);
p1x /= p1w;
p1y /= p1w;
p1z /= p1w;
QVector3D v1(2.0f, 3.0f, -4.0f);
QVector3D v2 = m1 * v1;
QVERIFY(fuzzyCompare(v2.x(), v1x));
QVERIFY(fuzzyCompare(v2.y(), v1y));
QVERIFY(fuzzyCompare(v2.z(), v1z));
QVector4D v3(2.0f, 3.0f, -4.0f, 1.0f);
QVector4D v4 = m1 * v3;
QVERIFY(fuzzyCompare(v4.x(), v3x));
QVERIFY(fuzzyCompare(v4.y(), v3y));
QVERIFY(fuzzyCompare(v4.z(), v3z));
QVERIFY(fuzzyCompare(v4.w(), v3w));
QVector4D v5(2.0f, 3.0f, -4.0f, 34.0f);
QVector4D v6 = m1 * v5;
QVERIFY(fuzzyCompare(v6.x(), v5x));
QVERIFY(fuzzyCompare(v6.y(), v5y));
QVERIFY(fuzzyCompare(v6.z(), v5z));
QVERIFY(fuzzyCompare(v6.w(), v5w));
QPoint p1(2, 3);
QPoint p2 = m1 * p1;
QCOMPARE(p2.x(), qRound(p1x));
QCOMPARE(p2.y(), qRound(p1y));
QPointF p3(2.0f, 3.0f);
QPointF p4 = m1 * p3;
QVERIFY(fuzzyCompare(p4.x(), p1x));
QVERIFY(fuzzyCompare(p4.y(), p1y));
if (x != 0 || y != 0 || z != 0) {
QQuaternion q = QQuaternion::fromAxisAndAngle(QVector3D(x, y, z), angle);
QVector3D vq = q.rotatedVector(v1);
QVERIFY(fuzzyCompare(vq.x(), v1x));
QVERIFY(fuzzyCompare(vq.y(), v1y));
QVERIFY(fuzzyCompare(vq.z(), v1z));
}
}
static bool isSame(const QMatrix3x3& m1, const Matrix3& m2)
{
for (int row = 0; row < 3; ++row) {
for (int col = 0; col < 3; ++col) {
if (!fuzzyCompare(m1(row, col), m2.v[row * 3 + col]))
return false;
}
}
return true;
}
// Test the computation of normal matrices from 4x4 transformation matrices.
void tst_QMatrixNxN::normalMatrix_data()
{
QTest::addColumn<void *>("mValues");
QTest::newRow("identity")
<< (void *)identityValues4;
QTest::newRow("unique")
<< (void *)uniqueValues4; // Not invertible because determinant == 0.
static qreal const translateValues[16] =
{1.0f, 0.0f, 0.0f, 4.0f,
0.0f, 1.0f, 0.0f, 5.0f,
0.0f, 0.0f, 1.0f, -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const scaleValues[16] =
{2.0f, 0.0f, 0.0f, 0.0f,
0.0f, 7.0f, 0.0f, 0.0f,
0.0f, 0.0f, 9.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const bothValues[16] =
{2.0f, 0.0f, 0.0f, 4.0f,
0.0f, 7.0f, 0.0f, 5.0f,
0.0f, 0.0f, 9.0f, -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const nullScaleValues1[16] =
{0.0f, 0.0f, 0.0f, 4.0f,
0.0f, 7.0f, 0.0f, 5.0f,
0.0f, 0.0f, 9.0f, -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const nullScaleValues2[16] =
{2.0f, 0.0f, 0.0f, 4.0f,
0.0f, 0.0f, 0.0f, 5.0f,
0.0f, 0.0f, 9.0f, -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const nullScaleValues3[16] =
{2.0f, 0.0f, 0.0f, 4.0f,
0.0f, 7.0f, 0.0f, 5.0f,
0.0f, 0.0f, 0.0f, -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("translate") << (void *)translateValues;
QTest::newRow("scale") << (void *)scaleValues;
QTest::newRow("both") << (void *)bothValues;
QTest::newRow("null scale 1") << (void *)nullScaleValues1;
QTest::newRow("null scale 2") << (void *)nullScaleValues2;
QTest::newRow("null scale 3") << (void *)nullScaleValues3;
}
void tst_QMatrixNxN::normalMatrix()
{
QFETCH(void *, mValues);
const qreal *values = (const qreal *)mValues;
// Compute the expected answer the long way.
Matrix3 min;
Matrix3 answer;
min.v[0] = values[0];
min.v[1] = values[1];
min.v[2] = values[2];
min.v[3] = values[4];
min.v[4] = values[5];
min.v[5] = values[6];
min.v[6] = values[8];
min.v[7] = values[9];
min.v[8] = values[10];
bool invertible = m3Inverse(min, answer);
m3Transpose(answer);
// Perform the test.
QMatrix4x4 m1(values);
QMatrix3x3 n1 = m1.normalMatrix();
if (invertible)
QVERIFY(::isSame(n1, answer));
else
QVERIFY(isIdentity(n1));
// Perform the test again, after inferring special matrix types.
// This tests the optimized paths in the normalMatrix() function.
m1.optimize();
n1 = m1.normalMatrix();
if (invertible)
QVERIFY(::isSame(n1, answer));
else
QVERIFY(isIdentity(n1));
}
// Test optimized transformations on 4x4 matrices.
void tst_QMatrixNxN::optimizedTransforms()
{
static qreal const translateValues[16] =
{1.0f, 0.0f, 0.0f, 4.0f,
0.0f, 1.0f, 0.0f, 5.0f,
0.0f, 0.0f, 1.0f, -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const translateDoubleValues[16] =
{1.0f, 0.0f, 0.0f, 8.0f,
0.0f, 1.0f, 0.0f, 10.0f,
0.0f, 0.0f, 1.0f, -6.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const scaleValues[16] =
{2.0f, 0.0f, 0.0f, 0.0f,
0.0f, 7.0f, 0.0f, 0.0f,
0.0f, 0.0f, 9.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const scaleDoubleValues[16] =
{4.0f, 0.0f, 0.0f, 0.0f,
0.0f, 49.0f, 0.0f, 0.0f,
0.0f, 0.0f, 81.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const bothValues[16] =
{2.0f, 0.0f, 0.0f, 4.0f,
0.0f, 7.0f, 0.0f, 5.0f,
0.0f, 0.0f, 9.0f, -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const bothReverseValues[16] =
{2.0f, 0.0f, 0.0f, 4.0f * 2.0f,
0.0f, 7.0f, 0.0f, 5.0f * 7.0f,
0.0f, 0.0f, 9.0f, -3.0f * 9.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const bothThenTranslateValues[16] =
{2.0f, 0.0f, 0.0f, 4.0f + 2.0f * 4.0f,
0.0f, 7.0f, 0.0f, 5.0f + 7.0f * 5.0f,
0.0f, 0.0f, 9.0f, -3.0f + 9.0f * -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
static qreal const bothThenScaleValues[16] =
{4.0f, 0.0f, 0.0f, 4.0f,
0.0f, 49.0f, 0.0f, 5.0f,
0.0f, 0.0f, 81.0f, -3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QMatrix4x4 translate(translateValues);
QMatrix4x4 scale(scaleValues);
QMatrix4x4 both(bothValues);
QMatrix4x4 m1;
m1.translate(4.0f, 5.0f, -3.0f);
QVERIFY(isSame(m1, translateValues));
m1.translate(4.0f, 5.0f, -3.0f);
QVERIFY(isSame(m1, translateDoubleValues));
QMatrix4x4 m2;
m2.translate(QVector3D(4.0f, 5.0f, -3.0f));
QVERIFY(isSame(m2, translateValues));
m2.translate(QVector3D(4.0f, 5.0f, -3.0f));
QVERIFY(isSame(m2, translateDoubleValues));
QMatrix4x4 m3;
m3.scale(2.0f, 7.0f, 9.0f);
QVERIFY(isSame(m3, scaleValues));
m3.scale(2.0f, 7.0f, 9.0f);
QVERIFY(isSame(m3, scaleDoubleValues));
QMatrix4x4 m4;
m4.scale(QVector3D(2.0f, 7.0f, 9.0f));
QVERIFY(isSame(m4, scaleValues));
m4.scale(QVector3D(2.0f, 7.0f, 9.0f));
QVERIFY(isSame(m4, scaleDoubleValues));
QMatrix4x4 m5;
m5.translate(4.0f, 5.0f, -3.0f);
m5.scale(2.0f, 7.0f, 9.0f);
QVERIFY(isSame(m5, bothValues));
m5.translate(4.0f, 5.0f, -3.0f);
QVERIFY(isSame(m5, bothThenTranslateValues));
QMatrix4x4 m6;
m6.translate(QVector3D(4.0f, 5.0f, -3.0f));
m6.scale(QVector3D(2.0f, 7.0f, 9.0f));
QVERIFY(isSame(m6, bothValues));
m6.translate(QVector3D(4.0f, 5.0f, -3.0f));
QVERIFY(isSame(m6, bothThenTranslateValues));
QMatrix4x4 m7;
m7.scale(2.0f, 7.0f, 9.0f);
m7.translate(4.0f, 5.0f, -3.0f);
QVERIFY(isSame(m7, bothReverseValues));
QMatrix4x4 m8;
m8.scale(QVector3D(2.0f, 7.0f, 9.0f));
m8.translate(QVector3D(4.0f, 5.0f, -3.0f));
QVERIFY(isSame(m8, bothReverseValues));
QMatrix4x4 m9;
m9.translate(4.0f, 5.0f, -3.0f);
m9.scale(2.0f, 7.0f, 9.0f);
QVERIFY(isSame(m9, bothValues));
m9.scale(2.0f, 7.0f, 9.0f);
QVERIFY(isSame(m9, bothThenScaleValues));
QMatrix4x4 m10;
m10.translate(QVector3D(4.0f, 5.0f, -3.0f));
m10.scale(QVector3D(2.0f, 7.0f, 9.0f));
QVERIFY(isSame(m10, bothValues));
m10.scale(QVector3D(2.0f, 7.0f, 9.0f));
QVERIFY(isSame(m10, bothThenScaleValues));
}
// Test orthographic projections.
void tst_QMatrixNxN::ortho()
{
QMatrix4x4 m1;
m1.ortho(QRect(0, 0, 300, 150));
QPointF p1 = m1 * QPointF(0, 0);
QPointF p2 = m1 * QPointF(300, 0);
QPointF p3 = m1 * QPointF(0, 150);
QPointF p4 = m1 * QPointF(300, 150);
QVector3D p5 = m1 * QVector3D(300, 150, 1);
QVERIFY(fuzzyCompare(p1.x(), -1.0));
QVERIFY(fuzzyCompare(p1.y(), 1.0));
QVERIFY(fuzzyCompare(p2.x(), 1.0));
QVERIFY(fuzzyCompare(p2.y(), 1.0));
QVERIFY(fuzzyCompare(p3.x(), -1.0));
QVERIFY(fuzzyCompare(p3.y(), -1.0));
QVERIFY(fuzzyCompare(p4.x(), 1.0));
QVERIFY(fuzzyCompare(p4.y(), -1.0));
QVERIFY(fuzzyCompare(p5.x(), (qreal)1.0));
QVERIFY(fuzzyCompare(p5.y(), (qreal)-1.0));
QVERIFY(fuzzyCompare(p5.z(), (qreal)-1.0));
QMatrix4x4 m2;
m2.ortho(QRectF(0, 0, 300, 150));
p1 = m2 * QPointF(0, 0);
p2 = m2 * QPointF(300, 0);
p3 = m2 * QPointF(0, 150);
p4 = m2 * QPointF(300, 150);
p5 = m2 * QVector3D(300, 150, 1);
QVERIFY(fuzzyCompare(p1.x(), -1.0));
QVERIFY(fuzzyCompare(p1.y(), 1.0));
QVERIFY(fuzzyCompare(p2.x(), 1.0));
QVERIFY(fuzzyCompare(p2.y(), 1.0));
QVERIFY(fuzzyCompare(p3.x(), -1.0));
QVERIFY(fuzzyCompare(p3.y(), -1.0));
QVERIFY(fuzzyCompare(p4.x(), 1.0));
QVERIFY(fuzzyCompare(p4.y(), -1.0));
QVERIFY(fuzzyCompare(p5.x(), (qreal)1.0));
QVERIFY(fuzzyCompare(p5.y(), (qreal)-1.0));
QVERIFY(fuzzyCompare(p5.z(), (qreal)-1.0));
QMatrix4x4 m3;
m3.ortho(0, 300, 150, 0, -1, 1);
p1 = m3 * QPointF(0, 0);
p2 = m3 * QPointF(300, 0);
p3 = m3 * QPointF(0, 150);
p4 = m3 * QPointF(300, 150);
p5 = m3 * QVector3D(300, 150, 1);
QVERIFY(fuzzyCompare(p1.x(), -1.0));
QVERIFY(fuzzyCompare(p1.y(), 1.0));
QVERIFY(fuzzyCompare(p2.x(), 1.0));
QVERIFY(fuzzyCompare(p2.y(), 1.0));
QVERIFY(fuzzyCompare(p3.x(), -1.0));
QVERIFY(fuzzyCompare(p3.y(), -1.0));
QVERIFY(fuzzyCompare(p4.x(), 1.0));
QVERIFY(fuzzyCompare(p4.y(), -1.0));
QVERIFY(fuzzyCompare(p5.x(), (qreal)1.0));
QVERIFY(fuzzyCompare(p5.y(), (qreal)-1.0));
QVERIFY(fuzzyCompare(p5.z(), (qreal)-1.0));
QMatrix4x4 m4;
m4.ortho(0, 300, 150, 0, -2, 3);
p1 = m4 * QPointF(0, 0);
p2 = m4 * QPointF(300, 0);
p3 = m4 * QPointF(0, 150);
p4 = m4 * QPointF(300, 150);
p5 = m4 * QVector3D(300, 150, 1);
QVERIFY(fuzzyCompare(p1.x(), -1.0));
QVERIFY(fuzzyCompare(p1.y(), 1.0));
QVERIFY(fuzzyCompare(p2.x(), 1.0));
QVERIFY(fuzzyCompare(p2.y(), 1.0));
QVERIFY(fuzzyCompare(p3.x(), -1.0));
QVERIFY(fuzzyCompare(p3.y(), -1.0));
QVERIFY(fuzzyCompare(p4.x(), 1.0));
QVERIFY(fuzzyCompare(p4.y(), -1.0));
QVERIFY(fuzzyCompare(p5.x(), (qreal)1.0));
QVERIFY(fuzzyCompare(p5.y(), (qreal)-1.0));
QVERIFY(fuzzyCompare(p5.z(), (qreal)-0.6));
// An empty view volume should leave the matrix alone.
QMatrix4x4 m5;
m5.ortho(0, 0, 150, 0, -2, 3);
QVERIFY(m5.isIdentity());
m5.ortho(0, 300, 150, 150, -2, 3);
QVERIFY(m5.isIdentity());
m5.ortho(0, 300, 150, 0, 2, 2);
QVERIFY(m5.isIdentity());
}
// Test perspective frustum projections.
void tst_QMatrixNxN::frustum()
{
QMatrix4x4 m1;
m1.frustum(-1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f);
QVector3D p1 = m1 * QVector3D(-1.0f, -1.0f, 1.0f);
QVector3D p2 = m1 * QVector3D(1.0f, -1.0f, 1.0f);
QVector3D p3 = m1 * QVector3D(-1.0f, 1.0f, 1.0f);
QVector3D p4 = m1 * QVector3D(1.0f, 1.0f, 1.0f);
QVector3D p5 = m1 * QVector3D(0.0f, 0.0f, 2.0f);
QVERIFY(fuzzyCompare(p1.x(), -1.0f));
QVERIFY(fuzzyCompare(p1.y(), -1.0f));
QVERIFY(fuzzyCompare(p1.z(), -1.0f));
QVERIFY(fuzzyCompare(p2.x(), 1.0f));
QVERIFY(fuzzyCompare(p2.y(), -1.0f));
QVERIFY(fuzzyCompare(p2.z(), -1.0f));
QVERIFY(fuzzyCompare(p3.x(), -1.0f));
QVERIFY(fuzzyCompare(p3.y(), 1.0f));
QVERIFY(fuzzyCompare(p3.z(), -1.0f));
QVERIFY(fuzzyCompare(p4.x(), 1.0f));
QVERIFY(fuzzyCompare(p4.y(), 1.0f));
QVERIFY(fuzzyCompare(p4.z(), -1.0f));
QVERIFY(fuzzyCompare(p5.x(), 0.0f));
QVERIFY(fuzzyCompare(p5.y(), 0.0f));
QVERIFY(fuzzyCompare(p5.z(), -0.5f));
// An empty view volume should leave the matrix alone.
QMatrix4x4 m5;
m5.frustum(0, 0, 150, 0, -2, 3);
QVERIFY(m5.isIdentity());
m5.frustum(0, 300, 150, 150, -2, 3);
QVERIFY(m5.isIdentity());
m5.frustum(0, 300, 150, 0, 2, 2);
QVERIFY(m5.isIdentity());
}
// Test perspective field-of-view projections.
void tst_QMatrixNxN::perspective()
{
QMatrix4x4 m1;
m1.perspective(45.0f, 1.0f, -1.0f, 1.0f);
QVector3D p1 = m1 * QVector3D(-1.0f, -1.0f, 1.0f);
QVector3D p2 = m1 * QVector3D(1.0f, -1.0f, 1.0f);
QVector3D p3 = m1 * QVector3D(-1.0f, 1.0f, 1.0f);
QVector3D p4 = m1 * QVector3D(1.0f, 1.0f, 1.0f);
QVector3D p5 = m1 * QVector3D(0.0f, 0.0f, 2.0f);
QVERIFY(fuzzyCompare(p1.x(), 2.41421));
QVERIFY(fuzzyCompare(p1.y(), 2.41421));
QVERIFY(fuzzyCompare(p1.z(), -1));
QVERIFY(fuzzyCompare(p2.x(), -2.41421));
QVERIFY(fuzzyCompare(p2.y(), 2.41421));
QVERIFY(fuzzyCompare(p2.z(), -1.0f));
QVERIFY(fuzzyCompare(p3.x(), 2.41421));
QVERIFY(fuzzyCompare(p3.y(), -2.41421));
QVERIFY(fuzzyCompare(p3.z(), -1.0f));
QVERIFY(fuzzyCompare(p4.x(), -2.41421));
QVERIFY(fuzzyCompare(p4.y(), -2.41421));
QVERIFY(fuzzyCompare(p4.z(), -1.0f));
QVERIFY(fuzzyCompare(p5.x(), 0.0f));
QVERIFY(fuzzyCompare(p5.y(), 0.0f));
QVERIFY(fuzzyCompare(p5.z(), -0.5f));
// An empty view volume should leave the matrix alone.
QMatrix4x4 m5;
m5.perspective(45.0f, 1.0f, 0.0f, 0.0f);
QVERIFY(m5.isIdentity());
m5.perspective(45.0f, 0.0f, -1.0f, 1.0f);
QVERIFY(m5.isIdentity());
m5.perspective(0.0f, 1.0f, -1.0f, 1.0f);
QVERIFY(m5.isIdentity());
}
// Test left-handed vs right-handed coordinate flipping.
void tst_QMatrixNxN::flipCoordinates()
{
QMatrix4x4 m1;
m1.flipCoordinates();
QVector3D p1 = m1 * QVector3D(2, 3, 4);
QVERIFY(p1 == QVector3D(2, -3, -4));
QMatrix4x4 m2;
m2.scale(2.0f, 3.0f, 1.0f);
m2.flipCoordinates();
QVector3D p2 = m2 * QVector3D(2, 3, 4);
QVERIFY(p2 == QVector3D(4, -9, -4));
QMatrix4x4 m3;
m3.translate(2.0f, 3.0f, 1.0f);
m3.flipCoordinates();
QVector3D p3 = m3 * QVector3D(2, 3, 4);
QVERIFY(p3 == QVector3D(4, 0, -3));
QMatrix4x4 m4;
m4.rotate(90.0f, 0.0f, 0.0f, 1.0f);
m4.flipCoordinates();
QVector3D p4 = m4 * QVector3D(2, 3, 4);
QVERIFY(p4 == QVector3D(3, 2, -4));
}
// Test conversion of generic matrices to and from the non-generic types.
void tst_QMatrixNxN::convertGeneric()
{
QMatrix4x3 m1(uniqueValues4x3);
static qreal const unique4x4[16] = {
1.0f, 2.0f, 3.0f, 4.0f,
5.0f, 6.0f, 7.0f, 8.0f,
9.0f, 10.0f, 11.0f, 12.0f,
0.0f, 0.0f, 0.0f, 1.0f
};
QMatrix4x4 m4(m1);
QVERIFY(isSame(m4, unique4x4));
QMatrix4x4 m5 = qGenericMatrixToMatrix4x4(m1);
QVERIFY(isSame(m5, unique4x4));
static qreal const conv4x4[12] = {
1.0f, 2.0f, 3.0f, 4.0f,
5.0f, 6.0f, 7.0f, 8.0f,
9.0f, 10.0f, 11.0f, 12.0f
};
QMatrix4x4 m9(uniqueValues4);
QMatrix4x3 m10 = m9.toGenericMatrix<4, 3>();
QVERIFY(isSame(m10, conv4x4));
QMatrix4x3 m11 = qGenericMatrixFromMatrix4x4<4, 3>(m9);
QVERIFY(isSame(m11, conv4x4));
}
// Copy of "flagBits" in qmatrix4x4.h.
enum {
Identity = 0x0001, // Identity matrix
General = 0x0002, // General matrix, unknown contents
Translation = 0x0004, // Contains a simple translation
Scale = 0x0008, // Contains a simple scale
Rotation = 0x0010 // Contains a simple rotation
};
// Structure that allows direct access to "flagBits" for testing.
struct Matrix4x4
{
qreal m[4][4];
int flagBits;
};
// Test the inferring of special matrix types.
void tst_QMatrixNxN::optimize_data()
{
QTest::addColumn<void *>("mValues");
QTest::addColumn<int>("flagBits");
QTest::newRow("null")
<< (void *)nullValues4 << (int)General;
QTest::newRow("identity")
<< (void *)identityValues4 << (int)Identity;
QTest::newRow("unique")
<< (void *)uniqueValues4 << (int)General;
static qreal scaleValues[16] = {
2.0f, 0.0f, 0.0f, 0.0f,
0.0f, 3.0f, 0.0f, 0.0f,
0.0f, 0.0f, 4.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f
};
QTest::newRow("scale")
<< (void *)scaleValues << (int)Scale;
static qreal translateValues[16] = {
1.0f, 0.0f, 0.0f, 2.0f,
0.0f, 1.0f, 0.0f, 3.0f,
0.0f, 0.0f, 1.0f, 4.0f,
0.0f, 0.0f, 0.0f, 1.0f
};
QTest::newRow("scale")
<< (void *)translateValues << (int)Translation;
static qreal bothValues[16] = {
1.0f, 0.0f, 0.0f, 2.0f,
0.0f, 2.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 4.0f,
0.0f, 0.0f, 0.0f, 1.0f
};
QTest::newRow("both")
<< (void *)bothValues << (int)(Scale | Translation);
static qreal belowValues[16] = {
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
4.0f, 0.0f, 0.0f, 1.0f
};
QTest::newRow("below")
<< (void *)belowValues << (int)General;
}
void tst_QMatrixNxN::optimize()
{
QFETCH(void *, mValues);
QFETCH(int, flagBits);
QMatrix4x4 m((const qreal *)mValues);
m.optimize();
QCOMPARE(reinterpret_cast<Matrix4x4 *>(&m)->flagBits, flagBits);
}
void tst_QMatrixNxN::columnsAndRows()
{
QMatrix4x4 m1(uniqueValues4);
QVERIFY(m1.column(0) == QVector4D(1, 5, 9, 13));
QVERIFY(m1.column(1) == QVector4D(2, 6, 10, 14));
QVERIFY(m1.column(2) == QVector4D(3, 7, 11, 15));
QVERIFY(m1.column(3) == QVector4D(4, 8, 12, 16));
QVERIFY(m1.row(0) == QVector4D(1, 2, 3, 4));
QVERIFY(m1.row(1) == QVector4D(5, 6, 7, 8));
QVERIFY(m1.row(2) == QVector4D(9, 10, 11, 12));
QVERIFY(m1.row(3) == QVector4D(13, 14, 15, 16));
m1.setColumn(0, QVector4D(-1, -5, -9, -13));
m1.setColumn(1, QVector4D(-2, -6, -10, -14));
m1.setColumn(2, QVector4D(-3, -7, -11, -15));
m1.setColumn(3, QVector4D(-4, -8, -12, -16));
QVERIFY(m1.column(0) == QVector4D(-1, -5, -9, -13));
QVERIFY(m1.column(1) == QVector4D(-2, -6, -10, -14));
QVERIFY(m1.column(2) == QVector4D(-3, -7, -11, -15));
QVERIFY(m1.column(3) == QVector4D(-4, -8, -12, -16));
QVERIFY(m1.row(0) == QVector4D(-1, -2, -3, -4));
QVERIFY(m1.row(1) == QVector4D(-5, -6, -7, -8));
QVERIFY(m1.row(2) == QVector4D(-9, -10, -11, -12));
QVERIFY(m1.row(3) == QVector4D(-13, -14, -15, -16));
m1.setRow(0, QVector4D(1, 5, 9, 13));
m1.setRow(1, QVector4D(2, 6, 10, 14));
m1.setRow(2, QVector4D(3, 7, 11, 15));
m1.setRow(3, QVector4D(4, 8, 12, 16));
QVERIFY(m1.column(0) == QVector4D(1, 2, 3, 4));
QVERIFY(m1.column(1) == QVector4D(5, 6, 7, 8));
QVERIFY(m1.column(2) == QVector4D(9, 10, 11, 12));
QVERIFY(m1.column(3) == QVector4D(13, 14, 15, 16));
QVERIFY(m1.row(0) == QVector4D(1, 5, 9, 13));
QVERIFY(m1.row(1) == QVector4D(2, 6, 10, 14));
QVERIFY(m1.row(2) == QVector4D(3, 7, 11, 15));
QVERIFY(m1.row(3) == QVector4D(4, 8, 12, 16));
}
// Test converting QMatrix objects into QMatrix4x4 and then
// checking that transformations in the original perform the
// equivalent transformations in the new matrix.
void tst_QMatrixNxN::convertQMatrix()
{
QMatrix m1;
m1.translate(-3.5, 2.0);
QPointF p1 = m1.map(QPointF(100.0, 150.0));
QCOMPARE(p1.x(), 100.0 - 3.5);
QCOMPARE(p1.y(), 150.0 + 2.0);
QMatrix4x4 m2(m1);
QPointF p2 = m2 * QPointF(100.0, 150.0);
QCOMPARE((double)p2.x(), 100.0 - 3.5);
QCOMPARE((double)p2.y(), 150.0 + 2.0);
QVERIFY(m1 == m2.toAffine());
QMatrix m3;
m3.scale(1.5, -2.0);
QPointF p3 = m3.map(QPointF(100.0, 150.0));
QCOMPARE(p3.x(), 1.5 * 100.0);
QCOMPARE(p3.y(), -2.0 * 150.0);
QMatrix4x4 m4(m3);
QPointF p4 = m4 * QPointF(100.0, 150.0);
QCOMPARE((double)p4.x(), 1.5 * 100.0);
QCOMPARE((double)p4.y(), -2.0 * 150.0);
QVERIFY(m3 == m4.toAffine());
QMatrix m5;
m5.rotate(45.0);
QPointF p5 = m5.map(QPointF(100.0, 150.0));
QMatrix4x4 m6(m5);
QPointF p6 = m6 * QPointF(100.0, 150.0);
QVERIFY(fuzzyCompare(p5.x(), p6.x()));
QVERIFY(fuzzyCompare(p5.y(), p6.y()));
QMatrix m7 = m6.toAffine();
QVERIFY(fuzzyCompare(m5.m11(), m7.m11()));
QVERIFY(fuzzyCompare(m5.m12(), m7.m12()));
QVERIFY(fuzzyCompare(m5.m21(), m7.m21()));
QVERIFY(fuzzyCompare(m5.m22(), m7.m22()));
QVERIFY(fuzzyCompare(m5.dx(), m7.dx()));
QVERIFY(fuzzyCompare(m5.dy(), m7.dy()));
}
// Test converting QTransform objects into QMatrix4x4 and then
// checking that transformations in the original perform the
// equivalent transformations in the new matrix.
void tst_QMatrixNxN::convertQTransform()
{
QTransform m1;
m1.translate(-3.5, 2.0);
QPointF p1 = m1.map(QPointF(100.0, 150.0));
QCOMPARE(p1.x(), 100.0 - 3.5);
QCOMPARE(p1.y(), 150.0 + 2.0);
QMatrix4x4 m2(m1);
QPointF p2 = m2 * QPointF(100.0, 150.0);
QCOMPARE((double)p2.x(), 100.0 - 3.5);
QCOMPARE((double)p2.y(), 150.0 + 2.0);
QVERIFY(m1 == m2.toTransform());
QTransform m3;
m3.scale(1.5, -2.0);
QPointF p3 = m3.map(QPointF(100.0, 150.0));
QCOMPARE(p3.x(), 1.5 * 100.0);
QCOMPARE(p3.y(), -2.0 * 150.0);
QMatrix4x4 m4(m3);
QPointF p4 = m4 * QPointF(100.0, 150.0);
QCOMPARE((double)p4.x(), 1.5 * 100.0);
QCOMPARE((double)p4.y(), -2.0 * 150.0);
QVERIFY(m3 == m4.toTransform());
QTransform m5;
m5.rotate(45.0);
QPointF p5 = m5.map(QPointF(100.0, 150.0));
QMatrix4x4 m6(m5);
QPointF p6 = m6 * QPointF(100.0, 150.0);
QVERIFY(fuzzyCompare(p5.x(), p6.x()));
QVERIFY(fuzzyCompare(p5.y(), p6.y()));
QTransform m7 = m6.toTransform();
QVERIFY(fuzzyCompare(m5.m11(), m7.m11()));
QVERIFY(fuzzyCompare(m5.m12(), m7.m12()));
QVERIFY(fuzzyCompare(m5.m21(), m7.m21()));
QVERIFY(fuzzyCompare(m5.m22(), m7.m22()));
QVERIFY(fuzzyCompare(m5.dx(), m7.dx()));
QVERIFY(fuzzyCompare(m5.dy(), m7.dy()));
QVERIFY(fuzzyCompare(m5.m13(), m7.m13()));
QVERIFY(fuzzyCompare(m5.m23(), m7.m23()));
QVERIFY(fuzzyCompare(m5.m33(), m7.m33()));
}
// Test filling matrices with specific values.
void tst_QMatrixNxN::fill()
{
QMatrix4x4 m1;
m1.fill(0.0f);
QVERIFY(isSame(m1, nullValues4));
static const qreal fillValues4[] =
{2.5f, 2.5f, 2.5f, 2.5f,
2.5f, 2.5f, 2.5f, 2.5f,
2.5f, 2.5f, 2.5f, 2.5f,
2.5f, 2.5f, 2.5f, 2.5f};
m1.fill(2.5f);
QVERIFY(isSame(m1, fillValues4));
QMatrix4x3 m2;
m2.fill(0.0f);
QVERIFY(isSame(m2, nullValues4x3));
static const qreal fillValues4x3[] =
{2.5f, 2.5f, 2.5f, 2.5f,
2.5f, 2.5f, 2.5f, 2.5f,
2.5f, 2.5f, 2.5f, 2.5f};
m2.fill(2.5f);
QVERIFY(isSame(m2, fillValues4x3));
}
// Test the mapRect() function for QRect and QRectF.
void tst_QMatrixNxN::mapRect_data()
{
QTest::addColumn<qreal>("x");
QTest::addColumn<qreal>("y");
QTest::addColumn<qreal>("width");
QTest::addColumn<qreal>("height");
QTest::newRow("null")
<< (qreal)0.0f << (qreal)0.0f << (qreal)0.0f << (qreal)0.0f;
QTest::newRow("rect")
<< (qreal)1.0f << (qreal)-20.5f << (qreal)100.0f << (qreal)63.75f;
}
void tst_QMatrixNxN::mapRect()
{
QFETCH(qreal, x);
QFETCH(qreal, y);
QFETCH(qreal, width);
QFETCH(qreal, height);
QRectF rect(x, y, width, height);
QRect recti(qRound(x), qRound(y), qRound(width), qRound(height));
QMatrix4x4 m1;
QVERIFY(m1.mapRect(rect) == rect);
QVERIFY(m1.mapRect(recti) == recti);
QMatrix4x4 m2;
m2.translate(-100.5f, 64.0f);
QRectF translated = rect.translated(-100.5f, 64.0f);
QRect translatedi = QRect(qRound(recti.x() - 100.5f), recti.y() + 64,
recti.width(), recti.height());
QVERIFY(m2.mapRect(rect) == translated);
QVERIFY(m2.mapRect(recti) == translatedi);
QMatrix4x4 m3;
m3.scale(-100.5f, 64.0f);
qreal scalex = x * -100.5f;
qreal scaley = y * 64.0f;
qreal scalewid = width * -100.5f;
qreal scaleht = height * 64.0f;
if (scalewid < 0.0f) {
scalewid = -scalewid;
scalex -= scalewid;
}
if (scaleht < 0.0f) {
scaleht = -scaleht;
scaley -= scaleht;
}
QRectF scaled(scalex, scaley, scalewid, scaleht);
QVERIFY(m3.mapRect(rect) == scaled);
scalex = recti.x() * -100.5f;
scaley = recti.y() * 64.0f;
scalewid = recti.width() * -100.5f;
scaleht = recti.height() * 64.0f;
if (scalewid < 0.0f) {
scalewid = -scalewid;
scalex -= scalewid;
}
if (scaleht < 0.0f) {
scaleht = -scaleht;
scaley -= scaleht;
}
QRect scaledi(qRound(scalex), qRound(scaley),
qRound(scalewid), qRound(scaleht));
QVERIFY(m3.mapRect(recti) == scaledi);
QMatrix4x4 m4;
m4.translate(-100.5f, 64.0f);
m4.scale(-2.5f, 4.0f);
qreal transx1 = x * -2.5f - 100.5f;
qreal transy1 = y * 4.0f + 64.0f;
qreal transx2 = (x + width) * -2.5f - 100.5f;
qreal transy2 = (y + height) * 4.0f + 64.0f;
if (transx1 > transx2)
qSwap(transx1, transx2);
if (transy1 > transy2)
qSwap(transy1, transy2);
QRectF trans(transx1, transy1, transx2 - transx1, transy2 - transy1);
QVERIFY(m4.mapRect(rect) == trans);
transx1 = recti.x() * -2.5f - 100.5f;
transy1 = recti.y() * 4.0f + 64.0f;
transx2 = (recti.x() + recti.width()) * -2.5f - 100.5f;
transy2 = (recti.y() + recti.height()) * 4.0f + 64.0f;
if (transx1 > transx2)
qSwap(transx1, transx2);
if (transy1 > transy2)
qSwap(transy1, transy2);
QRect transi(qRound(transx1), qRound(transy1),
qRound(transx2) - qRound(transx1),
qRound(transy2) - qRound(transy1));
QVERIFY(m4.mapRect(recti) == transi);
m4.rotate(45.0f, 0.0f, 0.0f, 1.0f);
QTransform t4;
t4.translate(-100.5f, 64.0f);
t4.scale(-2.5f, 4.0f);
t4.rotate(45.0f);
QRectF mr = m4.mapRect(rect);
QRectF tr = t4.mapRect(rect);
QVERIFY(fuzzyCompare(mr.x(), tr.x()));
QVERIFY(fuzzyCompare(mr.y(), tr.y()));
QVERIFY(fuzzyCompare(mr.width(), tr.width()));
QVERIFY(fuzzyCompare(mr.height(), tr.height()));
QRect mri = m4.mapRect(recti);
QRect tri = t4.mapRect(recti);
QVERIFY(mri == tri);
}
void tst_QMatrixNxN::mapVector_data()
{
QTest::addColumn<void *>("mValues");
QTest::newRow("null")
<< (void *)nullValues4;
QTest::newRow("identity")
<< (void *)identityValues4;
QTest::newRow("unique")
<< (void *)uniqueValues4;
static const qreal scale[] =
{2.0f, 0.0f, 0.0f, 0.0f,
0.0f, 11.0f, 0.0f, 0.0f,
0.0f, 0.0f, -6.5f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("scale")
<< (void *)scale;
static const qreal scaleTranslate[] =
{2.0f, 0.0f, 0.0f, 1.0f,
0.0f, 11.0f, 0.0f, 2.0f,
0.0f, 0.0f, -6.5f, 3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("scaleTranslate")
<< (void *)scaleTranslate;
static const qreal translate[] =
{1.0f, 0.0f, 0.0f, 1.0f,
0.0f, 1.0f, 0.0f, 2.0f,
0.0f, 0.0f, 1.0f, 3.0f,
0.0f, 0.0f, 0.0f, 1.0f};
QTest::newRow("translate")
<< (void *)translate;
}
void tst_QMatrixNxN::mapVector()
{
QFETCH(void *, mValues);
QMatrix4x4 m1((const qreal *)mValues);
m1.optimize();
QVector3D v(3.5f, -1.0f, 2.5f);
QVector3D expected
(v.x() * m1(0, 0) + v.y() * m1(0, 1) + v.z() * m1(0, 2),
v.x() * m1(1, 0) + v.y() * m1(1, 1) + v.z() * m1(1, 2),
v.x() * m1(2, 0) + v.y() * m1(2, 1) + v.z() * m1(2, 2));
QVector3D actual = m1.mapVector(v);
QVERIFY(fuzzyCompare(actual.x(), expected.x()));
QVERIFY(fuzzyCompare(actual.y(), expected.y()));
QVERIFY(fuzzyCompare(actual.z(), expected.z()));
}
class tst_QMatrixNxN4x4Properties : public QObject
{
Q_OBJECT
Q_PROPERTY(QMatrix4x4 matrix READ matrix WRITE setMatrix)
public:
tst_QMatrixNxN4x4Properties(QObject *parent = 0) : QObject(parent) {}
QMatrix4x4 matrix() const { return m; }
void setMatrix(const QMatrix4x4& value) { m = value; }
private:
QMatrix4x4 m;
};
// Test getting and setting matrix properties via the metaobject system.
void tst_QMatrixNxN::properties()
{
tst_QMatrixNxN4x4Properties obj;
QMatrix4x4 m1(uniqueValues4);
obj.setMatrix(m1);
QMatrix4x4 m2 = qVariantValue<QMatrix4x4>(obj.property("matrix"));
QVERIFY(isSame(m2, uniqueValues4));
QMatrix4x4 m3(transposedValues4);
obj.setProperty("matrix", qVariantFromValue(m3));
m2 = qVariantValue<QMatrix4x4>(obj.property("matrix"));
QVERIFY(isSame(m2, transposedValues4));
}
void tst_QMatrixNxN::metaTypes()
{
QVERIFY(QMetaType::type("QMatrix4x4") == QMetaType::QMatrix4x4);
QCOMPARE(QByteArray(QMetaType::typeName(QMetaType::QMatrix4x4)),
QByteArray("QMatrix4x4"));
QVERIFY(QMetaType::isRegistered(QMetaType::QMatrix4x4));
QVERIFY(qMetaTypeId<QMatrix4x4>() == QMetaType::QMatrix4x4);
}
QTEST_APPLESS_MAIN(tst_QMatrixNxN)
#include "tst_qmatrixnxn.moc"
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