Add viewport transform to QMatrix4x4

This allows to easily create a matrix that performs the transformation
used by OpenGL fixed function to go from normalized device coordinates
to window coordinates.

This comes in useful if you need to perform the NDC->window coordinate
conversion inside a shader.

Change-Id: I183b3545bfb3eb1e8b13fc3172911b46926fcbb7
Reviewed-by: Paul Lemire <paul.lemire@kdab.com>
Reviewed-by: Laszlo Agocs <laszlo.agocs@digia.com>

src/gui/math3d/qmatrix4x4.cpp

@@ -1541,6 +1541,52 @@ void QMatrix4x4::lookAt(const QVector3D& eye, const QVector3D& center, const QVe
 
 #endif
 
+/*!
+    \fn void QMatrix4x4::viewport(const QRectF &rect)
+    \overload
+
+    Sets up viewport transform for viewport bounded by \a rect and with near and far set
+    to 0 and 1 respectively.
+*/
+
+/*!
+    Multiplies this matrix by another that performs the scale and bias
+    transformation used by OpenGL to transform from normalized device
+    coordinates (NDC) to viewport (window) coordinates. That is it maps
+    points from the cube ranging over [-1, 1] in each dimension to the
+    viewport with it's near-lower-left corner at (\a left, \a bottom, \a nearPlane)
+    and with size (\a width, \a height, \a farPlane - \a nearPlane).
+
+    This matches the transform used by the fixed function OpenGL viewport
+    transform controlled by the functions glViewport() and glDepthRange().
+ */
+void QMatrix4x4::viewport(float left, float bottom, float width, float height, float nearPlane, float farPlane)
+{
+    const float w2 = width / 2.0f;
+    const float h2 = height / 2.0f;
+
+    QMatrix4x4 m(1);
+    m.m[0][0] = w2;
+    m.m[1][0] = 0.0f;
+    m.m[2][0] = 0.0f;
+    m.m[3][0] = left + w2;
+    m.m[0][1] = 0.0f;
+    m.m[1][1] = h2;
+    m.m[2][1] = 0.0f;
+    m.m[3][1] = bottom + h2;
+    m.m[0][2] = 0.0f;
+    m.m[1][2] = 0.0f;
+    m.m[2][2] = (farPlane - nearPlane) / 2.0f;
+    m.m[3][2] = (nearPlane + farPlane) / 2.0f;
+    m.m[0][3] = 0.0f;
+    m.m[1][3] = 0.0f;
+    m.m[2][3] = 0.0f;
+    m.m[3][3] = 1.0f;
+    m.flagBits = General;
+
+    *this *= m;
+}
+
 /*!
     \deprecated
 

src/gui/math3d/qmatrix4x4.h

@@ -148,6 +148,8 @@ public:
 #ifndef QT_NO_VECTOR3D
     void lookAt(const QVector3D& eye, const QVector3D& center, const QVector3D& up);
 #endif
+    void viewport(const QRectF &rect);
+    void viewport(float left, float bottom, float width, float height, float nearPlane = 0.0f, float farPlane = 1.0f);
     void flipCoordinates();
 
     void copyDataTo(float *values) const;
@@ -1077,6 +1079,11 @@ inline float *QMatrix4x4::data()
     return *m;
 }
 
+inline void QMatrix4x4::viewport(const QRectF &rect)
+{
+    viewport(rect.x(), rect.y(), rect.width(), rect.height());
+}
+
 #ifndef QT_NO_DEBUG_STREAM
 Q_GUI_EXPORT QDebug operator<<(QDebug dbg, const QMatrix4x4 &m);
 #endif

tests/auto/gui/math3d/qmatrixnxn/tst_qmatrixnxn.cpp

@@ -147,6 +147,7 @@ private slots:
     void ortho();
     void frustum();
     void perspective();
+    void viewport();
     void flipCoordinates();
 
     void convertGeneric();
@@ -2794,6 +2795,40 @@ void tst_QMatrixNxN::perspective()
     QVERIFY(m5.isIdentity());
 }
 
+// Test viewport transformations
+void tst_QMatrixNxN::viewport()
+{
+    // Uses default depth range of 0->1
+    QMatrix4x4 m1;
+    m1.viewport(0.0f, 0.0f, 1024.0f, 768.0f);
+
+    // Lower left
+    QVector4D p1 = m1 * QVector4D(-1.0f, -1.0f, 0.0f, 1.0f);
+    QVERIFY(qFuzzyIsNull(p1.x()));
+    QVERIFY(qFuzzyIsNull(p1.y()));
+    QVERIFY(qFuzzyCompare(p1.z(), 0.5f));
+
+    // Lower right
+    QVector4D p2 = m1 * QVector4D(1.0f, -1.0f, 0.0f, 1.0f);
+    QVERIFY(qFuzzyCompare(p2.x(), 1024.0f));
+    QVERIFY(qFuzzyIsNull(p2.y()));
+
+    // Upper right
+    QVector4D p3 = m1 * QVector4D(1.0f, 1.0f, 0.0f, 1.0f);
+    QVERIFY(qFuzzyCompare(p3.x(), 1024.0f));
+    QVERIFY(qFuzzyCompare(p3.y(), 768.0f));
+
+    // Upper left
+    QVector4D p4 = m1 * QVector4D(-1.0f, 1.0f, 0.0f, 1.0f);
+    QVERIFY(qFuzzyIsNull(p4.x()));
+    QVERIFY(qFuzzyCompare(p4.y(), 768.0f));
+
+    // Center
+    QVector4D p5 = m1 * QVector4D(0.0f, 0.0f, 0.0f, 1.0f);
+    QVERIFY(qFuzzyCompare(p5.x(), 1024.0f / 2.0f));
+    QVERIFY(qFuzzyCompare(p5.y(), 768.0f / 2.0f));
+}
+
 // Test left-handed vs right-handed coordinate flipping.
 void tst_QMatrixNxN::flipCoordinates()
 {