Revert "Remove flagBits from QMatrix4x4"

This reverts commit 5ebb03c47604e0597502fbe1069de636987f33fc.

Reason for revert: Removing flagBits breaks the batchrenderer in declarative, which accesses them via QMatrix4x4_Accessor. If flagBits are still going to be removed, we need to first find a solution for the renderer.

Change-Id: Ib0a3fc7a327926f2245058c0e2ed30e8789aa75d
Reviewed-by: Simon Hausmann <simon.hausmann@qt.io>
Reviewed-by: Ulf Hermann <ulf.hermann@qt.io>
Reviewed-by: Laszlo Agocs <laszlo.agocs@qt.io>

2 files changed, 654 insertions, 181 deletions

diff --git a/src/gui/math3d/qmatrix4x4.cpp b/src/gui/math3d/qmatrix4x4.cpp
index 2297342be7..2adb94573b 100644
--- a/src/gui/math3d/qmatrix4x4.cpp
+++ b/src/gui/math3d/qmatrix4x4.cpp
@@ -105,6 +105,7 @@ QMatrix4x4::QMatrix4x4(const float *values)
     for (int row = 0; row < 4; ++row)
         for (int col = 0; col < 4; ++col)
             m[col][row] = values[row * 4 + col];
+    flagBits = General;
 }
 
 /*!
@@ -182,6 +183,7 @@ QMatrix4x4::QMatrix4x4(const float *values, int cols, int rows)
                 m[col][row] = 0.0f;
         }
     }
+    flagBits = General;
 }
 
 /*!
@@ -213,6 +215,7 @@ QMatrix4x4::QMatrix4x4(const QTransform& transform)
     m[3][1] = transform.dy();
     m[3][2] = 0.0f;
     m[3][3] = transform.m33();
+    flagBits = General;
 }
 
 /*!
@@ -346,11 +349,15 @@ static inline void copyToDoubles(const float m[4][4], double mm[4][4])
 */
 double QMatrix4x4::determinant() const
 {
-    if (isIdentity())
+    if ((flagBits & ~(Translation | Rotation2D | Rotation)) == Identity)
         return 1.0;
 
     double mm[4][4];
     copyToDoubles(m, mm);
+    if (flagBits < Rotation2D)
+        return mm[0][0] * mm[1][1] * mm[2][2]; // Translation | Scale
+    if (flagBits < Perspective)
+        return matrixDet3(mm, 0, 1, 2, 0, 1, 2);
     return matrixDet4(mm);
 }
 
@@ -369,10 +376,77 @@ double QMatrix4x4::determinant() const
 QMatrix4x4 QMatrix4x4::inverted(bool *invertible) const
 {
     // Handle some of the easy cases first.
-    if (isIdentity()) {
+    if (flagBits == Identity) {
         if (invertible)
             *invertible = true;
         return QMatrix4x4();
+    } else if (flagBits == Translation) {
+        QMatrix4x4 inv;
+        inv.m[3][0] = -m[3][0];
+        inv.m[3][1] = -m[3][1];
+        inv.m[3][2] = -m[3][2];
+        inv.flagBits = Translation;
+        if (invertible)
+            *invertible = true;
+        return inv;
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        if (m[0][0] == 0 || m[1][1] == 0 || m[2][2] == 0) {
+            if (invertible)
+                *invertible = false;
+            return QMatrix4x4();
+        }
+        QMatrix4x4 inv;
+        inv.m[0][0] = 1.0f / m[0][0];
+        inv.m[1][1] = 1.0f / m[1][1];
+        inv.m[2][2] = 1.0f / m[2][2];
+        inv.m[3][0] = -m[3][0] * inv.m[0][0];
+        inv.m[3][1] = -m[3][1] * inv.m[1][1];
+        inv.m[3][2] = -m[3][2] * inv.m[2][2];
+        inv.flagBits = flagBits;
+
+        if (invertible)
+            *invertible = true;
+        return inv;
+    } else if ((flagBits & ~(Translation | Rotation2D | Rotation)) == Identity) {
+        if (invertible)
+            *invertible = true;
+        return orthonormalInverse();
+    } else if (flagBits < Perspective) {
+        QMatrix4x4 inv(1); // The "1" says to not load the identity.
+
+        double mm[4][4];
+        copyToDoubles(m, mm);
+
+        double det = matrixDet3(mm, 0, 1, 2, 0, 1, 2);
+        if (det == 0.0f) {
+            if (invertible)
+                *invertible = false;
+            return QMatrix4x4();
+        }
+        det = 1.0f / det;
+
+        inv.m[0][0] =  matrixDet2(mm, 1, 2, 1, 2) * det;
+        inv.m[0][1] = -matrixDet2(mm, 0, 2, 1, 2) * det;
+        inv.m[0][2] =  matrixDet2(mm, 0, 1, 1, 2) * det;
+        inv.m[0][3] = 0;
+        inv.m[1][0] = -matrixDet2(mm, 1, 2, 0, 2) * det;
+        inv.m[1][1] =  matrixDet2(mm, 0, 2, 0, 2) * det;
+        inv.m[1][2] = -matrixDet2(mm, 0, 1, 0, 2) * det;
+        inv.m[1][3] = 0;
+        inv.m[2][0] =  matrixDet2(mm, 1, 2, 0, 1) * det;
+        inv.m[2][1] = -matrixDet2(mm, 0, 2, 0, 1) * det;
+        inv.m[2][2] =  matrixDet2(mm, 0, 1, 0, 1) * det;
+        inv.m[2][3] = 0;
+        inv.m[3][0] = -inv.m[0][0] * m[3][0] - inv.m[1][0] * m[3][1] - inv.m[2][0] * m[3][2];
+        inv.m[3][1] = -inv.m[0][1] * m[3][0] - inv.m[1][1] * m[3][1] - inv.m[2][1] * m[3][2];
+        inv.m[3][2] = -inv.m[0][2] * m[3][0] - inv.m[1][2] * m[3][1] - inv.m[2][2] * m[3][2];
+        inv.m[3][3] = 1;
+        inv.flagBits = flagBits;
+
+        if (invertible)
+            *invertible = true;
+        return inv;
     }
 
     QMatrix4x4 inv(1); // The "1" says to not load the identity.
@@ -404,6 +478,7 @@ QMatrix4x4 QMatrix4x4::inverted(bool *invertible) const
     inv.m[3][1] =  matrixDet3(mm, 0, 2, 3, 0, 1, 2) * det;
     inv.m[3][2] = -matrixDet3(mm, 0, 1, 3, 0, 1, 2) * det;
     inv.m[3][3] =  matrixDet3(mm, 0, 1, 2, 0, 1, 2) * det;
+    inv.flagBits = flagBits;
 
     if (invertible)
         *invertible = true;
@@ -422,6 +497,32 @@ QMatrix3x3 QMatrix4x4::normalMatrix() const
 {
     QMatrix3x3 inv;
 
+    // Handle the simple cases first.
+    if (flagBits < Scale) {
+        // Translation
+        return inv;
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        if (m[0][0] == 0.0f || m[1][1] == 0.0f || m[2][2] == 0.0f)
+            return inv;
+        inv.data()[0] = 1.0f / m[0][0];
+        inv.data()[4] = 1.0f / m[1][1];
+        inv.data()[8] = 1.0f / m[2][2];
+        return inv;
+    } else if ((flagBits & ~(Translation | Rotation2D | Rotation)) == Identity) {
+        float *invm = inv.data();
+        invm[0 + 0 * 3] = m[0][0];
+        invm[1 + 0 * 3] = m[0][1];
+        invm[2 + 0 * 3] = m[0][2];
+        invm[0 + 1 * 3] = m[1][0];
+        invm[1 + 1 * 3] = m[1][1];
+        invm[2 + 1 * 3] = m[1][2];
+        invm[0 + 2 * 3] = m[2][0];
+        invm[1 + 2 * 3] = m[2][1];
+        invm[2 + 2 * 3] = m[2][2];
+        return inv;
+    }
+
     double mm[4][4];
     copyToDoubles(m, mm);
     double det = matrixDet3(mm, 0, 1, 2, 0, 1, 2);
@@ -456,6 +557,8 @@ QMatrix4x4 QMatrix4x4::transposed() const
             result.m[col][row] = m[row][col];
         }
     }
+    // When a translation is transposed, it becomes a perspective transformation.
+    result.flagBits = (flagBits & Translation ? General : flagBits);
     return result;
 }
 
@@ -507,6 +610,7 @@ QMatrix4x4& QMatrix4x4::operator/=(float divisor)
     m[3][1] /= divisor;
     m[3][2] /= divisor;
     m[3][3] /= divisor;
+    flagBits = General;
     return *this;
 }
 
@@ -663,6 +767,7 @@ QMatrix4x4 operator/(const QMatrix4x4& matrix, float divisor)
     m.m[3][1] = matrix.m[3][1] / divisor;
     m.m[3][2] = matrix.m[3][2] / divisor;
     m.m[3][3] = matrix.m[3][3] / divisor;
+    m.flagBits = QMatrix4x4::General;
     return m;
 }
 
@@ -684,21 +789,38 @@ QMatrix4x4 operator/(const QMatrix4x4& matrix, float divisor)
 */
 void QMatrix4x4::scale(const QVector3D& vector)
 {
-    const float vx = vector.x();
-    const float vy = vector.y();
-    const float vz = vector.z();
-    m[0][0] *= vx;
-    m[0][1] *= vx;
-    m[0][2] *= vx;
-    m[0][3] *= vx;
-    m[1][0] *= vy;
-    m[1][1] *= vy;
-    m[1][2] *= vy;
-    m[1][3] *= vy;
-    m[2][0] *= vz;
-    m[2][1] *= vz;
-    m[2][2] *= vz;
-    m[2][3] *= vz;
+    float vx = vector.x();
+    float vy = vector.y();
+    float vz = vector.z();
+    if (flagBits < Scale) {
+        m[0][0] = vx;
+        m[1][1] = vy;
+        m[2][2] = vz;
+    } else if (flagBits < Rotation2D) {
+        m[0][0] *= vx;
+        m[1][1] *= vy;
+        m[2][2] *= vz;
+    } else if (flagBits < Rotation) {
+        m[0][0] *= vx;
+        m[0][1] *= vx;
+        m[1][0] *= vy;
+        m[1][1] *= vy;
+        m[2][2] *= vz;
+    } else {
+        m[0][0] *= vx;
+        m[0][1] *= vx;
+        m[0][2] *= vx;
+        m[0][3] *= vx;
+        m[1][0] *= vy;
+        m[1][1] *= vy;
+        m[1][2] *= vy;
+        m[1][3] *= vy;
+        m[2][0] *= vz;
+        m[2][1] *= vz;
+        m[2][2] *= vz;
+        m[2][3] *= vz;
+    }
+    flagBits |= Scale;
 }
 
 #endif
@@ -713,14 +835,28 @@ void QMatrix4x4::scale(const QVector3D& vector)
 */
 void QMatrix4x4::scale(float x, float y)
 {
-    m[0][0] *= x;
-    m[0][1] *= x;
-    m[0][2] *= x;
-    m[0][3] *= x;
-    m[1][0] *= y;
-    m[1][1] *= y;
-    m[1][2] *= y;
-    m[1][3] *= y;
+    if (flagBits < Scale) {
+        m[0][0] = x;
+        m[1][1] = y;
+    } else if (flagBits < Rotation2D) {
+        m[0][0] *= x;
+        m[1][1] *= y;
+    } else if (flagBits < Rotation) {
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+    } else {
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[0][2] *= x;
+        m[0][3] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+        m[1][2] *= y;
+        m[1][3] *= y;
+    }
+    flagBits |= Scale;
 }
 
 /*!
@@ -733,18 +869,35 @@ void QMatrix4x4::scale(float x, float y)
 */
 void QMatrix4x4::scale(float x, float y, float z)
 {
-    m[0][0] *= x;
-    m[0][1] *= x;
-    m[0][2] *= x;
-    m[0][3] *= x;
-    m[1][0] *= y;
-    m[1][1] *= y;
-    m[1][2] *= y;
-    m[1][3] *= y;
-    m[2][0] *= z;
-    m[2][1] *= z;
-    m[2][2] *= z;
-    m[2][3] *= z;
+    if (flagBits < Scale) {
+        m[0][0] = x;
+        m[1][1] = y;
+        m[2][2] = z;
+    } else if (flagBits < Rotation2D) {
+        m[0][0] *= x;
+        m[1][1] *= y;
+        m[2][2] *= z;
+    } else if (flagBits < Rotation) {
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+        m[2][2] *= z;
+    } else {
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[0][2] *= x;
+        m[0][3] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+        m[1][2] *= y;
+        m[1][3] *= y;
+        m[2][0] *= z;
+        m[2][1] *= z;
+        m[2][2] *= z;
+        m[2][3] *= z;
+    }
+    flagBits |= Scale;
 }
 
 /*!
@@ -757,18 +910,35 @@ void QMatrix4x4::scale(float x, float y, float z)
 */
 void QMatrix4x4::scale(float factor)
 {
-    m[0][0] *= factor;
-    m[0][1] *= factor;
-    m[0][2] *= factor;
-    m[0][3] *= factor;
-    m[1][0] *= factor;
-    m[1][1] *= factor;
-    m[1][2] *= factor;
-    m[1][3] *= factor;
-    m[2][0] *= factor;
-    m[2][1] *= factor;
-    m[2][2] *= factor;
-    m[2][3] *= factor;
+    if (flagBits < Scale) {
+        m[0][0] = factor;
+        m[1][1] = factor;
+        m[2][2] = factor;
+    } else if (flagBits < Rotation2D) {
+        m[0][0] *= factor;
+        m[1][1] *= factor;
+        m[2][2] *= factor;
+    } else if (flagBits < Rotation) {
+        m[0][0] *= factor;
+        m[0][1] *= factor;
+        m[1][0] *= factor;
+        m[1][1] *= factor;
+        m[2][2] *= factor;
+    } else {
+        m[0][0] *= factor;
+        m[0][1] *= factor;
+        m[0][2] *= factor;
+        m[0][3] *= factor;
+        m[1][0] *= factor;
+        m[1][1] *= factor;
+        m[1][2] *= factor;
+        m[1][3] *= factor;
+        m[2][0] *= factor;
+        m[2][1] *= factor;
+        m[2][2] *= factor;
+        m[2][3] *= factor;
+    }
+    flagBits |= Scale;
 }
 
 #ifndef QT_NO_VECTOR3D
@@ -781,13 +951,36 @@ void QMatrix4x4::scale(float factor)
 
 void QMatrix4x4::translate(const QVector3D& vector)
 {
-    const float vx = vector.x();
-    const float vy = vector.y();
-    const float vz = vector.z();
-    m[3][0] += m[0][0] * vx + m[1][0] * vy + m[2][0] * vz;
-    m[3][1] += m[0][1] * vx + m[1][1] * vy + m[2][1] * vz;
-    m[3][2] += m[0][2] * vx + m[1][2] * vy + m[2][2] * vz;
-    m[3][3] += m[0][3] * vx + m[1][3] * vy + m[2][3] * vz;
+    float vx = vector.x();
+    float vy = vector.y();
+    float vz = vector.z();
+    if (flagBits == Identity) {
+        m[3][0] = vx;
+        m[3][1] = vy;
+        m[3][2] = vz;
+    } else if (flagBits == Translation) {
+        m[3][0] += vx;
+        m[3][1] += vy;
+        m[3][2] += vz;
+    } else if (flagBits == Scale) {
+        m[3][0] = m[0][0] * vx;
+        m[3][1] = m[1][1] * vy;
+        m[3][2] = m[2][2] * vz;
+    } else if (flagBits == (Translation | Scale)) {
+        m[3][0] += m[0][0] * vx;
+        m[3][1] += m[1][1] * vy;
+        m[3][2] += m[2][2] * vz;
+    } else if (flagBits < Rotation) {
+        m[3][0] += m[0][0] * vx + m[1][0] * vy;
+        m[3][1] += m[0][1] * vx + m[1][1] * vy;
+        m[3][2] += m[2][2] * vz;
+    } else {
+        m[3][0] += m[0][0] * vx + m[1][0] * vy + m[2][0] * vz;
+        m[3][1] += m[0][1] * vx + m[1][1] * vy + m[2][1] * vz;
+        m[3][2] += m[0][2] * vx + m[1][2] * vy + m[2][2] * vz;
+        m[3][3] += m[0][3] * vx + m[1][3] * vy + m[2][3] * vz;
+    }
+    flagBits |= Translation;
 }
 #endif
 
@@ -801,10 +994,28 @@ void QMatrix4x4::translate(const QVector3D& vector)
 */
 void QMatrix4x4::translate(float x, float y)
 {
-    m[3][0] += m[0][0] * x + m[1][0] * y;
-    m[3][1] += m[0][1] * x + m[1][1] * y;
-    m[3][2] += m[0][2] * x + m[1][2] * y;
-    m[3][3] += m[0][3] * x + m[1][3] * y;
+    if (flagBits == Identity) {
+        m[3][0] = x;
+        m[3][1] = y;
+    } else if (flagBits == Translation) {
+        m[3][0] += x;
+        m[3][1] += y;
+    } else if (flagBits == Scale) {
+        m[3][0] = m[0][0] * x;
+        m[3][1] = m[1][1] * y;
+    } else if (flagBits == (Translation | Scale)) {
+        m[3][0] += m[0][0] * x;
+        m[3][1] += m[1][1] * y;
+    } else if (flagBits < Rotation) {
+        m[3][0] += m[0][0] * x + m[1][0] * y;
+        m[3][1] += m[0][1] * x + m[1][1] * y;
+    } else {
+        m[3][0] += m[0][0] * x + m[1][0] * y;
+        m[3][1] += m[0][1] * x + m[1][1] * y;
+        m[3][2] += m[0][2] * x + m[1][2] * y;
+        m[3][3] += m[0][3] * x + m[1][3] * y;
+    }
+    flagBits |= Translation;
 }
 
 /*!
@@ -817,10 +1028,33 @@ void QMatrix4x4::translate(float x, float y)
 */
 void QMatrix4x4::translate(float x, float y, float z)
 {
-    m[3][0] += m[0][0] * x + m[1][0] * y + m[2][0] * z;
-    m[3][1] += m[0][1] * x + m[1][1] * y + m[2][1] * z;
-    m[3][2] += m[0][2] * x + m[1][2] * y + m[2][2] * z;
-    m[3][3] += m[0][3] * x + m[1][3] * y + m[2][3] * z;
+    if (flagBits == Identity) {
+        m[3][0] = x;
+        m[3][1] = y;
+        m[3][2] = z;
+    } else if (flagBits == Translation) {
+        m[3][0] += x;
+        m[3][1] += y;
+        m[3][2] += z;
+    } else if (flagBits == Scale) {
+        m[3][0] = m[0][0] * x;
+        m[3][1] = m[1][1] * y;
+        m[3][2] = m[2][2] * z;
+    } else if (flagBits == (Translation | Scale)) {
+        m[3][0] += m[0][0] * x;
+        m[3][1] += m[1][1] * y;
+        m[3][2] += m[2][2] * z;
+    } else if (flagBits < Rotation) {
+        m[3][0] += m[0][0] * x + m[1][0] * y;
+        m[3][1] += m[0][1] * x + m[1][1] * y;
+        m[3][2] += m[2][2] * z;
+    } else {
+        m[3][0] += m[0][0] * x + m[1][0] * y + m[2][0] * z;
+        m[3][1] += m[0][1] * x + m[1][1] * y + m[2][1] * z;
+        m[3][2] += m[0][2] * x + m[1][2] * y + m[2][2] * z;
+        m[3][3] += m[0][3] * x + m[1][3] * y + m[2][3] * z;
+    }
+    flagBits |= Translation;
 }
 
 #ifndef QT_NO_VECTOR3D
@@ -881,6 +1115,7 @@ void QMatrix4x4::rotate(float angle, float x, float y, float z)
                 m[0][3] = (tmp = m[0][3]) * c + m[1][3] * s;
                 m[1][3] = m[1][3] * c - tmp * s;
 
+                flagBits |= Rotation2D;
                 return;
             }
         } else if (z == 0.0f) {
@@ -897,6 +1132,7 @@ void QMatrix4x4::rotate(float angle, float x, float y, float z)
             m[2][3] = (tmp = m[2][3]) * c + m[0][3] * s;
             m[0][3] = m[0][3] * c - tmp * s;
 
+            flagBits |= Rotation;
             return;
         }
     } else if (y == 0.0f && z == 0.0f) {
@@ -913,6 +1149,7 @@ void QMatrix4x4::rotate(float angle, float x, float y, float z)
         m[1][3] = (tmp = m[1][3]) * c + m[2][3] * s;
         m[2][3] = m[2][3] * c - tmp * s;
 
+        flagBits |= Rotation;
         return;
     }
 
@@ -943,6 +1180,7 @@ void QMatrix4x4::rotate(float angle, float x, float y, float z)
     rot.m[1][3] = 0.0f;
     rot.m[2][3] = 0.0f;
     rot.m[3][3] = 1.0f;
+    rot.flagBits = Rotation;
     *this *= rot;
 }
 
@@ -966,7 +1204,7 @@ void QMatrix4x4::projectedRotate(float angle, float x, float y, float z)
         s = 0.0f;
         c = -1.0f;
     } else {
-        const float a = qDegreesToRadians(angle);
+        float a = qDegreesToRadians(angle);
         c = std::cos(a);
         s = std::sin(a);
     }
@@ -986,6 +1224,7 @@ void QMatrix4x4::projectedRotate(float angle, float x, float y, float z)
                 m[0][3] = (tmp = m[0][3]) * c + m[1][3] * s;
                 m[1][3] = m[1][3] * c - tmp * s;
 
+                flagBits |= Rotation2D;
                 return;
             }
         } else if (z == 0.0f) {
@@ -996,6 +1235,7 @@ void QMatrix4x4::projectedRotate(float angle, float x, float y, float z)
             m[0][1] = m[0][1] * c + m[3][1] * s * inv_dist_to_plane;
             m[0][2] = m[0][2] * c + m[3][2] * s * inv_dist_to_plane;
             m[0][3] = m[0][3] * c + m[3][3] * s * inv_dist_to_plane;
+            flagBits = General;
             return;
         }
     } else if (y == 0.0f && z == 0.0f) {
@@ -1006,6 +1246,7 @@ void QMatrix4x4::projectedRotate(float angle, float x, float y, float z)
         m[1][1] = m[1][1] * c - m[3][1] * s * inv_dist_to_plane;
         m[1][2] = m[1][2] * c - m[3][2] * s * inv_dist_to_plane;
         m[1][3] = m[1][3] * c - m[3][3] * s * inv_dist_to_plane;
+        flagBits = General;
         return;
     }
     double len = double(x) * double(x) +
@@ -1017,7 +1258,7 @@ void QMatrix4x4::projectedRotate(float angle, float x, float y, float z)
         y = float(double(y) / len);
         z = float(double(z) / len);
     }
-    const float ic = 1.0f - c;
+    float ic = 1.0f - c;
     QMatrix4x4 rot(1); // The "1" says to not load the identity.
     rot.m[0][0] = x * x * ic + c;
     rot.m[1][0] = x * y * ic - z * s;
@@ -1035,6 +1276,7 @@ void QMatrix4x4::projectedRotate(float angle, float x, float y, float z)
     rot.m[1][3] = (y * z * ic + x * s) * -inv_dist_to_plane;
     rot.m[2][3] = 0.0f;
     rot.m[3][3] = 1.0f;
+    rot.flagBits = General;
     *this *= rot;
 }
 
@@ -1083,6 +1325,7 @@ void QMatrix4x4::rotate(const QQuaternion& quaternion)
     m.m[1][3] = 0.0f;
     m.m[2][3] = 0.0f;
     m.m[3][3] = 1.0f;
+    m.flagBits = Rotation;
     *this *= m;
 }
 
@@ -1135,9 +1378,9 @@ void QMatrix4x4::ortho(float left, float right, float bottom, float top, float n
         return;
 
     // Construct the projection.
-    const float width = right - left;
-    const float invheight = top - bottom;
-    const float clip = farPlane - nearPlane;
+    float width = right - left;
+    float invheight = top - bottom;
+    float clip = farPlane - nearPlane;
     QMatrix4x4 m(1);
     m.m[0][0] = 2.0f / width;
     m.m[1][0] = 0.0f;
@@ -1155,6 +1398,7 @@ void QMatrix4x4::ortho(float left, float right, float bottom, float top, float n
     m.m[1][3] = 0.0f;
     m.m[2][3] = 0.0f;
     m.m[3][3] = 1.0f;
+    m.flagBits = Translation | Scale;
 
     // Apply the projection.
     *this *= m;
@@ -1176,9 +1420,9 @@ void QMatrix4x4::frustum(float left, float right, float bottom, float top, float
 
     // Construct the projection.
     QMatrix4x4 m(1);
-    const float width = right - left;
-    const float invheight = top - bottom;
-    const float clip = farPlane - nearPlane;
+    float width = right - left;
+    float invheight = top - bottom;
+    float clip = farPlane - nearPlane;
     m.m[0][0] = 2.0f * nearPlane / width;
     m.m[1][0] = 0.0f;
     m.m[2][0] = (left + right) / width;
@@ -1195,6 +1439,7 @@ void QMatrix4x4::frustum(float left, float right, float bottom, float top, float
     m.m[1][3] = 0.0f;
     m.m[2][3] = -1.0f;
     m.m[3][3] = 0.0f;
+    m.flagBits = General;
 
     // Apply the projection.
     *this *= m;
@@ -1218,12 +1463,12 @@ void QMatrix4x4::perspective(float verticalAngle, float aspectRatio, float nearP
 
     // Construct the projection.
     QMatrix4x4 m(1);
-    const float radians = qDegreesToRadians(verticalAngle / 2.0f);
-    const float sine = std::sin(radians);
+    float radians = qDegreesToRadians(verticalAngle / 2.0f);
+    float sine = std::sin(radians);
     if (sine == 0.0f)
         return;
-    const float cotan = std::cos(radians) / sine;
-    const float clip = farPlane - nearPlane;
+    float cotan = std::cos(radians) / sine;
+    float clip = farPlane - nearPlane;
     m.m[0][0] = cotan / aspectRatio;
     m.m[1][0] = 0.0f;
     m.m[2][0] = 0.0f;
@@ -1240,6 +1485,7 @@ void QMatrix4x4::perspective(float verticalAngle, float aspectRatio, float nearP
     m.m[1][3] = 0.0f;
     m.m[2][3] = -1.0f;
     m.m[3][3] = 0.0f;
+    m.flagBits = General;
 
     // Apply the projection.
     *this *= m;
@@ -1283,6 +1529,7 @@ void QMatrix4x4::lookAt(const QVector3D& eye, const QVector3D& center, const QVe
     m.m[1][3] = 0.0f;
     m.m[2][3] = 0.0f;
     m.m[3][3] = 1.0f;
+    m.flagBits = Rotation;
 
     *this *= m;
     translate(-eye);
@@ -1331,6 +1578,7 @@ void QMatrix4x4::viewport(float left, float bottom, float width, float height, f
     m.m[1][3] = 0.0f;
     m.m[2][3] = 0.0f;
     m.m[3][3] = 1.0f;
+    m.flagBits = General;
 
     *this *= m;
 }
@@ -1350,14 +1598,21 @@ void QMatrix4x4::flipCoordinates()
     // Multiplying the y and z coordinates with -1 does NOT flip between right-handed and
     // left-handed coordinate systems, it just rotates 180 degrees around the x axis, so
     // I'm deprecating this function.
-    m[1][0] = -m[1][0];
-    m[1][1] = -m[1][1];
-    m[1][2] = -m[1][2];
-    m[1][3] = -m[1][3];
-    m[2][0] = -m[2][0];
-    m[2][1] = -m[2][1];
-    m[2][2] = -m[2][2];
-    m[2][3] = -m[2][3];
+    if (flagBits < Rotation2D) {
+        // Translation | Scale
+        m[1][1] = -m[1][1];
+        m[2][2] = -m[2][2];
+    } else {
+        m[1][0] = -m[1][0];
+        m[1][1] = -m[1][1];
+        m[1][2] = -m[1][2];
+        m[1][3] = -m[1][3];
+        m[2][0] = -m[2][0];
+        m[2][1] = -m[2][1];
+        m[2][2] = -m[2][2];
+        m[2][3] = -m[2][3];
+    }
+    flagBits |= Scale;
 }
 
 /*!
@@ -1421,7 +1676,7 @@ QTransform QMatrix4x4::toTransform(float distanceToPlane) const
         //      | 0 0 d 1 |
         // where d = -1 / distanceToPlane.  After projection, row 3 and
         // column 3 are dropped to form the final QTransform.
-        const float d = 1.0f / distanceToPlane;
+        float d = 1.0f / distanceToPlane;
         return QTransform(m[0][0], m[0][1], m[0][3] - m[0][2] * d,
                           m[1][0], m[1][1], m[1][3] - m[1][2] * d,
                           m[3][0], m[3][1], m[3][3] - m[3][2] * d);
@@ -1493,16 +1748,38 @@ QTransform QMatrix4x4::toTransform(float distanceToPlane) const
 */
 QRect QMatrix4x4::mapRect(const QRect& rect) const
 {
-    const QPoint tl = map(rect.topLeft());
-    const QPoint tr = map(QPoint(rect.x() + rect.width(), rect.y()));
-    const QPoint bl = map(QPoint(rect.x(), rect.y() + rect.height()));
-    const QPoint br = map(QPoint(rect.x() + rect.width(),
-                                 rect.y() + rect.height()));
+    if (flagBits < Scale) {
+        // Translation
+        return QRect(qRound(rect.x() + m[3][0]),
+                     qRound(rect.y() + m[3][1]),
+                     rect.width(), rect.height());
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        float x = rect.x() * m[0][0] + m[3][0];
+        float y = rect.y() * m[1][1] + m[3][1];
+        float w = rect.width() * m[0][0];
+        float h = rect.height() * m[1][1];
+        if (w < 0) {
+            w = -w;
+            x -= w;
+        }
+        if (h < 0) {
+            h = -h;
+            y -= h;
+        }
+        return QRect(qRound(x), qRound(y), qRound(w), qRound(h));
+    }
+
+    QPoint tl = map(rect.topLeft());
+    QPoint tr = map(QPoint(rect.x() + rect.width(), rect.y()));
+    QPoint bl = map(QPoint(rect.x(), rect.y() + rect.height()));
+    QPoint br = map(QPoint(rect.x() + rect.width(),
+                           rect.y() + rect.height()));
 
-    const int xmin = qMin(qMin(tl.x(), tr.x()), qMin(bl.x(), br.x()));
-    const int xmax = qMax(qMax(tl.x(), tr.x()), qMax(bl.x(), br.x()));
-    const int ymin = qMin(qMin(tl.y(), tr.y()), qMin(bl.y(), br.y()));
-    const int ymax = qMax(qMax(tl.y(), tr.y()), qMax(bl.y(), br.y()));
+    int xmin = qMin(qMin(tl.x(), tr.x()), qMin(bl.x(), br.x()));
+    int xmax = qMax(qMax(tl.x(), tr.x()), qMax(bl.x(), br.x()));
+    int ymin = qMin(qMin(tl.y(), tr.y()), qMin(bl.y(), br.y()));
+    int ymax = qMax(qMax(tl.y(), tr.y()), qMax(bl.y(), br.y()));
 
     return QRect(xmin, ymin, xmax - xmin, ymax - ymin);
 }
@@ -1517,13 +1794,33 @@ QRect QMatrix4x4::mapRect(const QRect& rect) const
 */
 QRectF QMatrix4x4::mapRect(const QRectF& rect) const
 {
-    const QPointF tl = map(rect.topLeft()); QPointF tr = map(rect.topRight());
-    const QPointF bl = map(rect.bottomLeft()); QPointF br = map(rect.bottomRight());
+    if (flagBits < Scale) {
+        // Translation
+        return rect.translated(m[3][0], m[3][1]);
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        float x = rect.x() * m[0][0] + m[3][0];
+        float y = rect.y() * m[1][1] + m[3][1];
+        float w = rect.width() * m[0][0];
+        float h = rect.height() * m[1][1];
+        if (w < 0) {
+            w = -w;
+            x -= w;
+        }
+        if (h < 0) {
+            h = -h;
+            y -= h;
+        }
+        return QRectF(x, y, w, h);
+    }
+
+    QPointF tl = map(rect.topLeft()); QPointF tr = map(rect.topRight());
+    QPointF bl = map(rect.bottomLeft()); QPointF br = map(rect.bottomRight());
 
-    const float xmin = qMin(qMin(tl.x(), tr.x()), qMin(bl.x(), br.x()));
-    const float xmax = qMax(qMax(tl.x(), tr.x()), qMax(bl.x(), br.x()));
-    const float ymin = qMin(qMin(tl.y(), tr.y()), qMin(bl.y(), br.y()));
-    const float ymax = qMax(qMax(tl.y(), tr.y()), qMax(bl.y(), br.y()));
+    float xmin = qMin(qMin(tl.x(), tr.x()), qMin(bl.x(), br.x()));
+    float xmax = qMax(qMax(tl.x(), tr.x()), qMax(bl.x(), br.x()));
+    float ymin = qMin(qMin(tl.y(), tr.y()), qMin(bl.y(), br.y()));
+    float ymax = qMax(qMax(tl.y(), tr.y()), qMax(bl.y(), br.y()));
 
     return QRectF(QPointF(xmin, ymin), QPointF(xmax, ymax));
 }
@@ -1581,6 +1878,8 @@ QMatrix4x4 QMatrix4x4::orthonormalInverse() const
     result.m[3][2] = -(result.m[0][2] * m[3][0] + result.m[1][2] * m[3][1] + result.m[2][2] * m[3][2]);
     result.m[3][3] = 1.0f;
 
+    result.flagBits = flagBits;
+
     return result;
 }
 
@@ -1606,6 +1905,54 @@ QMatrix4x4 QMatrix4x4::orthonormalInverse() const
 */
 void QMatrix4x4::optimize()
 {
+    // If the last row is not (0, 0, 0, 1), the matrix is not a special type.
+    flagBits = General;
+    if (m[0][3] != 0 || m[1][3] != 0 || m[2][3] != 0 || m[3][3] != 1)
+        return;
+
+    flagBits &= ~Perspective;
+
+    // If the last column is (0, 0, 0, 1), then there is no translation.
+    if (m[3][0] == 0 && m[3][1] == 0 && m[3][2] == 0)
+        flagBits &= ~Translation;
+
+    // If the two first elements of row 3 and column 3 are 0, then any rotation must be about Z.
+    if (!m[0][2] && !m[1][2] && !m[2][0] && !m[2][1]) {
+        flagBits &= ~Rotation;
+        // If the six non-diagonal elements in the top left 3x3 matrix are 0, there is no rotation.
+        if (!m[0][1] && !m[1][0]) {
+            flagBits &= ~Rotation2D;
+            // Check for identity.
+            if (m[0][0] == 1 && m[1][1] == 1 && m[2][2] == 1)
+                flagBits &= ~Scale;
+        } else {
+            // If the columns are orthonormal and form a right-handed system, then there is no scale.
+            double mm[4][4];
+            copyToDoubles(m, mm);
+            double det = matrixDet2(mm, 0, 1, 0, 1);
+            double lenX = mm[0][0] * mm[0][0] + mm[0][1] * mm[0][1];
+            double lenY = mm[1][0] * mm[1][0] + mm[1][1] * mm[1][1];
+            double lenZ = mm[2][2];
+            if (qFuzzyCompare(det, 1.0) && qFuzzyCompare(lenX, 1.0)
+                    && qFuzzyCompare(lenY, 1.0) && qFuzzyCompare(lenZ, 1.0))
+            {
+                flagBits &= ~Scale;
+            }
+        }
+    } else {
+        // If the columns are orthonormal and form a right-handed system, then there is no scale.
+        double mm[4][4];
+        copyToDoubles(m, mm);
+        double det = matrixDet3(mm, 0, 1, 2, 0, 1, 2);
+        double lenX = mm[0][0] * mm[0][0] + mm[0][1] * mm[0][1] + mm[0][2] * mm[0][2];
+        double lenY = mm[1][0] * mm[1][0] + mm[1][1] * mm[1][1] + mm[1][2] * mm[1][2];
+        double lenZ = mm[2][0] * mm[2][0] + mm[2][1] * mm[2][1] + mm[2][2] * mm[2][2];
+        if (qFuzzyCompare(det, 1.0) && qFuzzyCompare(lenX, 1.0)
+                && qFuzzyCompare(lenY, 1.0) && qFuzzyCompare(lenZ, 1.0))
+        {
+            flagBits &= ~Scale;
+        }
+    }
 }
 
 /*!
@@ -1623,10 +1970,23 @@ QDebug operator<<(QDebug dbg, const QMatrix4x4 &m)
     QDebugStateSaver saver(dbg);
     // Create a string that represents the matrix type.
     QByteArray bits;
-    if (m.isIdentity()) {
+    if (m.flagBits == QMatrix4x4::Identity) {
         bits = "Identity";
-    } else {
+    } else if (m.flagBits == QMatrix4x4::General) {
         bits = "General";
+    } else {
+        if ((m.flagBits & QMatrix4x4::Translation) != 0)
+            bits += "Translation,";
+        if ((m.flagBits & QMatrix4x4::Scale) != 0)
+            bits += "Scale,";
+        if ((m.flagBits & QMatrix4x4::Rotation2D) != 0)
+            bits += "Rotation2D,";
+        if ((m.flagBits & QMatrix4x4::Rotation) != 0)
+            bits += "Rotation,";
+        if ((m.flagBits & QMatrix4x4::Perspective) != 0)
+            bits += "Perspective,";
+        if (bits.size() > 0)
+            bits = bits.left(bits.size() - 1);
     }
 
     // Output in row-major order because it is more human-readable.
diff --git a/src/gui/math3d/qmatrix4x4.h b/src/gui/math3d/qmatrix4x4.h
index 198a47c51b..95f4db92ec 100644
--- a/src/gui/math3d/qmatrix4x4.h
+++ b/src/gui/math3d/qmatrix4x4.h
@@ -59,7 +59,7 @@ class Q_GUI_EXPORT QMatrix4x4
 {
 public:
     inline QMatrix4x4() { setToIdentity(); }
-    explicit QMatrix4x4(Qt::Initialization) {}
+    explicit QMatrix4x4(Qt::Initialization) : flagBits(General) {}
     explicit QMatrix4x4(const float *values);
     inline QMatrix4x4(float m11, float m12, float m13, float m14,
                       float m21, float m22, float m23, float m24,
@@ -186,9 +186,19 @@ public:
 
     void projectedRotate(float angle, float x, float y, float z);
 private:
-
-    // No other members are allowed in order to ensure a size of 16 * sizeof(float)
-    float m[4][4]; // Column-major order to match OpenGL.
+    float m[4][4];          // Column-major order to match OpenGL.
+    int flagBits;           // Flag bits from the enum below.
+
+    // When matrices are multiplied, the flag bits are or-ed together.
+    enum {
+        Identity        = 0x0000, // Identity matrix
+        Translation     = 0x0001, // Contains a translation
+        Scale           = 0x0002, // Contains a scale
+        Rotation2D      = 0x0004, // Contains a rotation about the Z axis
+        Rotation        = 0x0008, // Contains an arbitrary rotation
+        Perspective     = 0x0010, // Last row is different from (0, 0, 0, 1)
+        General         = 0x001f  // General matrix, unknown contents
+    };
 
     // Construct without initializing identity matrix.
     explicit QMatrix4x4(int) { }
@@ -212,6 +222,7 @@ inline QMatrix4x4::QMatrix4x4
     m[1][0] = m12; m[1][1] = m22; m[1][2] = m32; m[1][3] = m42;
     m[2][0] = m13; m[2][1] = m23; m[2][2] = m33; m[2][3] = m43;
     m[3][0] = m14; m[3][1] = m24; m[3][2] = m34; m[3][3] = m44;
+    flagBits = General;
 }
 
 template <int N, int M>
@@ -229,6 +240,7 @@ Q_INLINE_TEMPLATE QMatrix4x4::QMatrix4x4
                 m[matrixCol][matrixRow] = 0.0f;
         }
     }
+    flagBits = General;
 }
 
 template <int N, int M>
@@ -258,6 +270,7 @@ inline const float& QMatrix4x4::operator()(int aRow, int aColumn) const
 inline float& QMatrix4x4::operator()(int aRow, int aColumn)
 {
     Q_ASSERT(aRow >= 0 && aRow < 4 && aColumn >= 0 && aColumn < 4);
+    flagBits = General;
     return m[aColumn][aRow];
 }
 
@@ -275,6 +288,7 @@ inline void QMatrix4x4::setColumn(int index, const QVector4D& value)
     m[index][1] = value.y();
     m[index][2] = value.z();
     m[index][3] = value.w();
+    flagBits = General;
 }
 
 inline QVector4D QMatrix4x4::row(int index) const
@@ -290,6 +304,7 @@ inline void QMatrix4x4::setRow(int index, const QVector4D& value)
     m[1][index] = value.y();
     m[2][index] = value.z();
     m[3][index] = value.w();
+    flagBits = General;
 }
 #endif
 
@@ -302,6 +317,8 @@ inline bool QMatrix4x4::isAffine() const
 
 inline bool QMatrix4x4::isIdentity() const
 {
+    if (flagBits == Identity)
+        return true;
     if (m[0][0] != 1.0f || m[0][1] != 0.0f || m[0][2] != 0.0f)
         return false;
     if (m[0][3] != 0.0f || m[1][0] != 0.0f || m[1][1] != 1.0f)
@@ -333,6 +350,7 @@ inline void QMatrix4x4::setToIdentity()
     m[3][1] = 0.0f;
     m[3][2] = 0.0f;
     m[3][3] = 1.0f;
+    flagBits = Identity;
 }
 
 inline void QMatrix4x4::fill(float value)
@@ -353,6 +371,7 @@ inline void QMatrix4x4::fill(float value)
     m[3][1] = value;
     m[3][2] = value;
     m[3][3] = value;
+    flagBits = General;
 }
 
 inline QMatrix4x4& QMatrix4x4::operator+=(const QMatrix4x4& other)
@@ -373,6 +392,7 @@ inline QMatrix4x4& QMatrix4x4::operator+=(const QMatrix4x4& other)
     m[3][1] += other.m[3][1];
     m[3][2] += other.m[3][2];
     m[3][3] += other.m[3][3];
+    flagBits = General;
     return *this;
 }
 
@@ -394,12 +414,25 @@ inline QMatrix4x4& QMatrix4x4::operator-=(const QMatrix4x4& other)
     m[3][1] -= other.m[3][1];
     m[3][2] -= other.m[3][2];
     m[3][3] -= other.m[3][3];
+    flagBits = General;
     return *this;
 }
 
 inline QMatrix4x4& QMatrix4x4::operator*=(const QMatrix4x4& o)
 {
     const QMatrix4x4 other = o; // prevent aliasing when &o == this ### Qt 6: take o by value
+    flagBits |= other.flagBits;
+
+    if (flagBits < Rotation2D) {
+        m[3][0] += m[0][0] * other.m[3][0];
+        m[3][1] += m[1][1] * other.m[3][1];
+        m[3][2] += m[2][2] * other.m[3][2];
+
+        m[0][0] *= other.m[0][0];
+        m[1][1] *= other.m[1][1];
+        m[2][2] *= other.m[2][2];
+        return *this;
+    }
 
     float m0, m1, m2;
     m0 = m[0][0] * other.m[0][0]
@@ -502,6 +535,7 @@ inline QMatrix4x4& QMatrix4x4::operator*=(float factor)
     m[3][1] *= factor;
     m[3][2] *= factor;
     m[3][3] *= factor;
+    flagBits = General;
     return *this;
 }
 
@@ -564,6 +598,7 @@ inline QMatrix4x4 operator+(const QMatrix4x4& m1, const QMatrix4x4& m2)
     m.m[3][1] = m1.m[3][1] + m2.m[3][1];
     m.m[3][2] = m1.m[3][2] + m2.m[3][2];
     m.m[3][3] = m1.m[3][3] + m2.m[3][3];
+    m.flagBits = QMatrix4x4::General;
     return m;
 }
 
@@ -586,11 +621,26 @@ inline QMatrix4x4 operator-(const QMatrix4x4& m1, const QMatrix4x4& m2)
     m.m[3][1] = m1.m[3][1] - m2.m[3][1];
     m.m[3][2] = m1.m[3][2] - m2.m[3][2];
     m.m[3][3] = m1.m[3][3] - m2.m[3][3];
+    m.flagBits = QMatrix4x4::General;
     return m;
 }
 
 inline QMatrix4x4 operator*(const QMatrix4x4& m1, const QMatrix4x4& m2)
 {
+    int flagBits = m1.flagBits | m2.flagBits;
+    if (flagBits < QMatrix4x4::Rotation2D) {
+        QMatrix4x4 m = m1;
+        m.m[3][0] += m.m[0][0] * m2.m[3][0];
+        m.m[3][1] += m.m[1][1] * m2.m[3][1];
+        m.m[3][2] += m.m[2][2] * m2.m[3][2];
+
+        m.m[0][0] *= m2.m[0][0];
+        m.m[1][1] *= m2.m[1][1];
+        m.m[2][2] *= m2.m[2][2];
+        m.flagBits = flagBits;
+        return m;
+    }
+
     QMatrix4x4 m(1);
     m.m[0][0] = m1.m[0][0] * m2.m[0][0]
               + m1.m[1][0] * m2.m[0][1]
@@ -659,6 +709,7 @@ inline QMatrix4x4 operator*(const QMatrix4x4& m1, const QMatrix4x4& m2)
               + m1.m[1][3] * m2.m[3][1]
               + m1.m[2][3] * m2.m[3][2]
               + m1.m[3][3] * m2.m[3][3];
+    m.flagBits = flagBits;
     return m;
 }
 
@@ -666,19 +717,20 @@ inline QMatrix4x4 operator*(const QMatrix4x4& m1, const QMatrix4x4& m2)
 
 inline QVector3D operator*(const QVector3D& vector, const QMatrix4x4& matrix)
 {
-    const float x = vector.x() * matrix.m[0][0] +
+    float x, y, z, w;
+    x = vector.x() * matrix.m[0][0] +
         vector.y() * matrix.m[0][1] +
         vector.z() * matrix.m[0][2] +
         matrix.m[0][3];
-    const float y = vector.x() * matrix.m[1][0] +
+    y = vector.x() * matrix.m[1][0] +
         vector.y() * matrix.m[1][1] +
         vector.z() * matrix.m[1][2] +
         matrix.m[1][3];
-    const float z = vector.x() * matrix.m[2][0] +
+    z = vector.x() * matrix.m[2][0] +
         vector.y() * matrix.m[2][1] +
         vector.z() * matrix.m[2][2] +
         matrix.m[2][3];
-    const float w = vector.x() * matrix.m[3][0] +
+    w = vector.x() * matrix.m[3][0] +
         vector.y() * matrix.m[3][1] +
         vector.z() * matrix.m[3][2] +
         matrix.m[3][3];
@@ -690,29 +742,41 @@ inline QVector3D operator*(const QVector3D& vector, const QMatrix4x4& matrix)
 
 inline QVector3D operator*(const QMatrix4x4& matrix, const QVector3D& vector)
 {
-    if (matrix.isIdentity())
+    float x, y, z, w;
+    if (matrix.flagBits == QMatrix4x4::Identity) {
         return vector;
-
-    const float x = vector.x() * matrix.m[0][0] +
-        vector.y() * matrix.m[1][0] +
-        vector.z() * matrix.m[2][0] +
-        matrix.m[3][0];
-    const float y = vector.x() * matrix.m[0][1] +
-        vector.y() * matrix.m[1][1] +
-        vector.z() * matrix.m[2][1] +
-        matrix.m[3][1];
-    const float z = vector.x() * matrix.m[0][2] +
-        vector.y() * matrix.m[1][2] +
-        vector.z() * matrix.m[2][2] +
-        matrix.m[3][2];
-    const float w = vector.x() * matrix.m[0][3] +
-        vector.y() * matrix.m[1][3] +
-        vector.z() * matrix.m[2][3] +
-        matrix.m[3][3];
-    if (w == 1.0f)
-        return QVector3D(x, y, z);
-    else
-        return QVector3D(x / w, y / w, z / w);
+    } else if (matrix.flagBits < QMatrix4x4::Rotation2D) {
+        // Translation | Scale
+        return QVector3D(vector.x() * matrix.m[0][0] + matrix.m[3][0],
+                         vector.y() * matrix.m[1][1] + matrix.m[3][1],
+                         vector.z() * matrix.m[2][2] + matrix.m[3][2]);
+    } else if (matrix.flagBits < QMatrix4x4::Rotation) {
+        // Translation | Scale | Rotation2D
+        return QVector3D(vector.x() * matrix.m[0][0] + vector.y() * matrix.m[1][0] + matrix.m[3][0],
+                         vector.x() * matrix.m[0][1] + vector.y() * matrix.m[1][1] + matrix.m[3][1],
+                         vector.z() * matrix.m[2][2] + matrix.m[3][2]);
+    } else {
+        x = vector.x() * matrix.m[0][0] +
+            vector.y() * matrix.m[1][0] +
+            vector.z() * matrix.m[2][0] +
+            matrix.m[3][0];
+        y = vector.x() * matrix.m[0][1] +
+            vector.y() * matrix.m[1][1] +
+            vector.z() * matrix.m[2][1] +
+            matrix.m[3][1];
+        z = vector.x() * matrix.m[0][2] +
+            vector.y() * matrix.m[1][2] +
+            vector.z() * matrix.m[2][2] +
+            matrix.m[3][2];
+        w = vector.x() * matrix.m[0][3] +
+            vector.y() * matrix.m[1][3] +
+            vector.z() * matrix.m[2][3] +
+            matrix.m[3][3];
+        if (w == 1.0f)
+            return QVector3D(x, y, z);
+        else
+            return QVector3D(x / w, y / w, z / w);
+    }
 }
 
 #endif
@@ -721,19 +785,20 @@ inline QVector3D operator*(const QMatrix4x4& matrix, const QVector3D& vector)
 
 inline QVector4D operator*(const QVector4D& vector, const QMatrix4x4& matrix)
 {
-    const float x = vector.x() * matrix.m[0][0] +
+    float x, y, z, w;
+    x = vector.x() * matrix.m[0][0] +
         vector.y() * matrix.m[0][1] +
         vector.z() * matrix.m[0][2] +
         vector.w() * matrix.m[0][3];
-    const float y = vector.x() * matrix.m[1][0] +
+    y = vector.x() * matrix.m[1][0] +
         vector.y() * matrix.m[1][1] +
         vector.z() * matrix.m[1][2] +
         vector.w() * matrix.m[1][3];
-    const float z = vector.x() * matrix.m[2][0] +
+    z = vector.x() * matrix.m[2][0] +
         vector.y() * matrix.m[2][1] +
         vector.z() * matrix.m[2][2] +
         vector.w() * matrix.m[2][3];
-    const float w = vector.x() * matrix.m[3][0] +
+    w = vector.x() * matrix.m[3][0] +
         vector.y() * matrix.m[3][1] +
         vector.z() * matrix.m[3][2] +
         vector.w() * matrix.m[3][3];
@@ -742,19 +807,20 @@ inline QVector4D operator*(const QVector4D& vector, const QMatrix4x4& matrix)
 
 inline QVector4D operator*(const QMatrix4x4& matrix, const QVector4D& vector)
 {
-    const float x = vector.x() * matrix.m[0][0] +
+    float x, y, z, w;
+    x = vector.x() * matrix.m[0][0] +
         vector.y() * matrix.m[1][0] +
         vector.z() * matrix.m[2][0] +
         vector.w() * matrix.m[3][0];
-    const float y = vector.x() * matrix.m[0][1] +
+    y = vector.x() * matrix.m[0][1] +
         vector.y() * matrix.m[1][1] +
         vector.z() * matrix.m[2][1] +
         vector.w() * matrix.m[3][1];
-    const float z = vector.x() * matrix.m[0][2] +
+    z = vector.x() * matrix.m[0][2] +
         vector.y() * matrix.m[1][2] +
         vector.z() * matrix.m[2][2] +
         vector.w() * matrix.m[3][2];
-    const float w = vector.x() * matrix.m[0][3] +
+    w = vector.x() * matrix.m[0][3] +
         vector.y() * matrix.m[1][3] +
         vector.z() * matrix.m[2][3] +
         vector.w() * matrix.m[3][3];
@@ -765,15 +831,17 @@ inline QVector4D operator*(const QMatrix4x4& matrix, const QVector4D& vector)
 
 inline QPoint operator*(const QPoint& point, const QMatrix4x4& matrix)
 {
-    const float xin = point.x();
-    const float yin = point.y();
-    const float x = xin * matrix.m[0][0] +
+    float xin, yin;
+    float x, y, w;
+    xin = point.x();
+    yin = point.y();
+    x = xin * matrix.m[0][0] +
         yin * matrix.m[0][1] +
         matrix.m[0][3];
-    const float y = xin * matrix.m[1][0] +
+    y = xin * matrix.m[1][0] +
         yin * matrix.m[1][1] +
         matrix.m[1][3];
-    const float w = xin * matrix.m[3][0] +
+    w = xin * matrix.m[3][0] +
         yin * matrix.m[3][1] +
         matrix.m[3][3];
     if (w == 1.0f)
@@ -784,15 +852,17 @@ inline QPoint operator*(const QPoint& point, const QMatrix4x4& matrix)
 
 inline QPointF operator*(const QPointF& point, const QMatrix4x4& matrix)
 {
-    const float xin = float(point.x());
-    const float yin = float(point.y());
-    const float x = xin * matrix.m[0][0] +
+    float xin, yin;
+    float x, y, w;
+    xin = float(point.x());
+    yin = float(point.y());
+    x = xin * matrix.m[0][0] +
         yin * matrix.m[0][1] +
         matrix.m[0][3];
-    const float y = xin * matrix.m[1][0] +
+    y = xin * matrix.m[1][0] +
         yin * matrix.m[1][1] +
         matrix.m[1][3];
-    const float w = xin * matrix.m[3][0] +
+    w = xin * matrix.m[3][0] +
         yin * matrix.m[3][1] +
         matrix.m[3][3];
     if (w == 1.0f) {
@@ -804,46 +874,69 @@ inline QPointF operator*(const QPointF& point, const QMatrix4x4& matrix)
 
 inline QPoint operator*(const QMatrix4x4& matrix, const QPoint& point)
 {
-    if (matrix.isIdentity())
+    float xin, yin;
+    float x, y, w;
+    xin = point.x();
+    yin = point.y();
+    if (matrix.flagBits == QMatrix4x4::Identity) {
         return point;
-
-    const float xin = point.x();
-    const float yin = point.y();
-    const float x = xin * matrix.m[0][0] +
-                    yin * matrix.m[1][0] +
-                    matrix.m[3][0];
-    const float y = xin * matrix.m[0][1] +
-                    yin * matrix.m[1][1] +
-                    matrix.m[3][1];
-    const float w = xin * matrix.m[0][3] +
-                    yin * matrix.m[1][3] +
-                    matrix.m[3][3];
-    if (w == 1.0f)
-        return QPoint(qRound(x), qRound(y));
-
-    return QPoint(qRound(x / w), qRound(y / w));
+    } else if (matrix.flagBits < QMatrix4x4::Rotation2D) {
+        // Translation | Scale
+        return QPoint(qRound(xin * matrix.m[0][0] + matrix.m[3][0]),
+                      qRound(yin * matrix.m[1][1] + matrix.m[3][1]));
+    } else if (matrix.flagBits < QMatrix4x4::Perspective) {
+        return QPoint(qRound(xin * matrix.m[0][0] + yin * matrix.m[1][0] + matrix.m[3][0]),
+                      qRound(xin * matrix.m[0][1] + yin * matrix.m[1][1] + matrix.m[3][1]));
+    } else {
+        x = xin * matrix.m[0][0] +
+            yin * matrix.m[1][0] +
+            matrix.m[3][0];
+        y = xin * matrix.m[0][1] +
+            yin * matrix.m[1][1] +
+            matrix.m[3][1];
+        w = xin * matrix.m[0][3] +
+            yin * matrix.m[1][3] +
+            matrix.m[3][3];
+        if (w == 1.0f)
+            return QPoint(qRound(x), qRound(y));
+        else
+            return QPoint(qRound(x / w), qRound(y / w));
+    }
 }
 
 inline QPointF operator*(const QMatrix4x4& matrix, const QPointF& point)
 {
-    if (matrix.isIdentity())
+    qreal xin, yin;
+    qreal x, y, w;
+    xin = point.x();
+    yin = point.y();
+    if (matrix.flagBits == QMatrix4x4::Identity) {
         return point;
-
-    const qreal xin = point.x();
-    const qreal yin = point.y();
-    const qreal x = xin * qreal(matrix.m[0][0]) +
+    } else if (matrix.flagBits < QMatrix4x4::Rotation2D) {
+        // Translation | Scale
+        return QPointF(xin * qreal(matrix.m[0][0]) + qreal(matrix.m[3][0]),
+                       yin * qreal(matrix.m[1][1]) + qreal(matrix.m[3][1]));
+    } else if (matrix.flagBits < QMatrix4x4::Perspective) {
+        return QPointF(xin * qreal(matrix.m[0][0]) + yin * qreal(matrix.m[1][0]) +
+                       qreal(matrix.m[3][0]),
+                       xin * qreal(matrix.m[0][1]) + yin * qreal(matrix.m[1][1]) +
+                       qreal(matrix.m[3][1]));
+    } else {
+        x = xin * qreal(matrix.m[0][0]) +
             yin * qreal(matrix.m[1][0]) +
             qreal(matrix.m[3][0]);
-    const qreal y = xin * qreal(matrix.m[0][1]) +
+        y = xin * qreal(matrix.m[0][1]) +
             yin * qreal(matrix.m[1][1]) +
             qreal(matrix.m[3][1]);
-    const qreal w = xin * qreal(matrix.m[0][3]) +
+        w = xin * qreal(matrix.m[0][3]) +
             yin * qreal(matrix.m[1][3]) +
             qreal(matrix.m[3][3]);
-    if (w == 1.0)
-        return QPointF(qreal(x), qreal(y));
-
-    return QPointF(qreal(x / w), qreal(y / w));
+        if (w == 1.0) {
+            return QPointF(qreal(x), qreal(y));
+        } else {
+            return QPointF(qreal(x / w), qreal(y / w));
+        }
+    }
 }
 
 inline QMatrix4x4 operator-(const QMatrix4x4& matrix)
@@ -865,6 +958,7 @@ inline QMatrix4x4 operator-(const QMatrix4x4& matrix)
     m.m[3][1] = -matrix.m[3][1];
     m.m[3][2] = -matrix.m[3][2];
     m.m[3][3] = -matrix.m[3][3];
+    m.flagBits = QMatrix4x4::General;
     return m;
 }
 
@@ -887,6 +981,7 @@ inline QMatrix4x4 operator*(float factor, const QMatrix4x4& matrix)
     m.m[3][1] = matrix.m[3][1] * factor;
     m.m[3][2] = matrix.m[3][2] * factor;
     m.m[3][3] = matrix.m[3][3] * factor;
+    m.flagBits = QMatrix4x4::General;
     return m;
 }
 
@@ -909,6 +1004,7 @@ inline QMatrix4x4 operator*(const QMatrix4x4& matrix, float factor)
     m.m[3][1] = matrix.m[3][1] * factor;
     m.m[3][2] = matrix.m[3][2] * factor;
     m.m[3][3] = matrix.m[3][3] * factor;
+    m.flagBits = QMatrix4x4::General;
     return m;
 }
 
@@ -951,9 +1047,25 @@ inline QVector3D QMatrix4x4::map(const QVector3D& point) const
 
 inline QVector3D QMatrix4x4::mapVector(const QVector3D& vector) const
 {
-    return QVector3D(vector.x() * m[0][0] + vector.y() * m[1][0] + vector.z() * m[2][0],
-                     vector.x() * m[0][1] + vector.y() * m[1][1] + vector.z() * m[2][1],
-                     vector.x() * m[0][2] + vector.y() * m[1][2] + vector.z() * m[2][2]);
+    if (flagBits < Scale) {
+        // Translation
+        return vector;
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        return QVector3D(vector.x() * m[0][0],
+                         vector.y() * m[1][1],
+                         vector.z() * m[2][2]);
+    } else {
+        return QVector3D(vector.x() * m[0][0] +
+                         vector.y() * m[1][0] +
+                         vector.z() * m[2][0],
+                         vector.x() * m[0][1] +
+                         vector.y() * m[1][1] +
+                         vector.z() * m[2][1],
+                         vector.x() * m[0][2] +
+                         vector.y() * m[1][2] +
+                         vector.z() * m[2][2]);
+    }
 }
 
 #endif
@@ -971,6 +1083,7 @@ inline float *QMatrix4x4::data()
 {
     // We have to assume that the caller will modify the matrix elements,
     // so we flip it over to "General" mode.
+    flagBits = General;
     return *m;
 }