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The QMatrix class specifies 2D transformations of a coordinate system. More...
#include <QMatrix>
The QMatrix class specifies 2D transformations of a coordinate system.
The standard coordinate system of a paint device has the origin located at the top-left position. x values increase to the right; y values increase downward.
This coordinate system is the default for the QPainter, which renders graphics in a paint device. A user-defined coordinate system can be specified by setting a QMatrix for the painter.
Example:
void MyWidget::paintEvent(QPaintEvent *)
{
QPainter p; // our painter
QMatrix m; // our transformation matrix
m.rotate(22.5); // rotated coordinate system
p.begin(this); // start painting
p.setMatrix(m); // use rotated coordinate system
p.drawText(30,20, "detator"); // draw rotated text at 30,20
p.end(); // painting done
}
A matrix specifies how to translate, scale, shear or rotate the graphics; the actual transformation is performed by the drawing routines in QPainter and by QPixmap::xForm().
The QMatrix class contains a 3x3 matrix of the form:
| m11 | m12 | 0 |
| m21 | m22 | 0 |
| dx | dy | 1 |
A matrix transforms a point in the plane to another point:
x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy
The point (x, y) is the original point, and (x', y') is the transformed point. (x', y') can be transformed back to (x, y) by performing the same operation on the inverted matrix.
The elements dx and dy specify horizontal and vertical translation. The elements m11 and m22 specify horizontal and vertical scaling. The elements m12 and m21 specify horizontal and vertical shearing.
The identity matrix has m11 and m22 set to 1; all others are set to 0. This matrix maps a point to itself.
Translation is the simplest transformation. Setting dx and dy will move the coordinate system dx units along the X axis and dy units along the Y axis.
Scaling can be done by setting m11 and m22. For example, setting m11 to 2 and m22 to 1.5 will double the height and increase the width by 50%.
Shearing is controlled by m12 and m21. Setting these elements to values different from zero will twist the coordinate system.
Rotation is achieved by carefully setting both the shearing factors and the scaling factors. The QMatrix also has a function that sets rotation directly.
QMatrix lets you combine transformations like this:
QMatrix m; // identity matrix
m.translate(10, -20); // first translate (10,-20)
m.rotate(25); // then rotate 25 degrees
m.scale(1.2, 0.7); // finally scale it
Here's the same example using basic matrix operations:
double a = pi/180 * 25; // convert 25 to radians
double sina = sin(a);
double cosa = cos(a);
QMatrix m1(1, 0, 0, 1, 10, -20); // translation matrix
QMatrix m2(cosa, sina, // rotation matrix
-sina, cosa, 0, 0);
QMatrix m3(1.2, 0, 0, 0.7, 0, 0); // scaling matrix
QMatrix m;
m = m3 * m2 * m1; // combine all transformations
The matrix can also be transformed using the map() functions, and transformed points, rectangles, etc., can be obtained using map(), mapRect(), mapToRegion(), and mapToPolygon() functions.
QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QMatrix. Although these functions are very convenient, it can be more efficient to build a QMatrix and call QPainter::setMatrix() if you want to perform more than a single transform operation.
See also QPainter::setMatrix() and QPixmap::xForm().
Constructs an identity matrix. All elements are set to zero except m11 and m22 (scaling), which are set to 1.
Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy.
Constructs a matrix with the elements from the matrix matrix
Returns the X scaling factor.
Returns the vertical shearing factor.
Returns the horizontal shearing factor.
Returns the Y scaling factor.
Returns the matrix's determinant.
Returns the horizontal translation.
Returns the vertical translation.
Returns the inverted matrix.
If the matrix is singular (not invertible), the identity matrix is returned.
If invertible is not 0: the value of *invertible is set to true if the matrix is invertible; otherwise *invertible is set to false.
See also isInvertible().
Returns true if the matrix is the identity matrix; otherwise returns false.
See also reset().
Returns true if the matrix is invertible; otherwise returns false.
See also inverted().
Transforms (x, y) to (*tx, *ty) using the following formulas:
*tx = m11*x + m21*y + dx
*ty = m22*y + m12*x + dy
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms (x, y) to (*tx, *ty) using the formulas:
*tx = m11*x + m21*y + dx (rounded to the nearest integer)
*ty = m22*y + m12*x + dy (rounded to the nearest integer)
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms p to using these formulas:
retx = m11*px + m21*py + dx (rounded to the nearest integer)
rety = m22*py + m12*px + dy (rounded to the nearest integer)
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms point using these formulas:
retx = m11*px + m21*py + dx
rety = m22*py + m12*px + dy
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms both ends of line using these formulas:
retx = m11 * px + m21 * py + dx
rety = m22 * py + m12 * px + dy
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms both ends of line using these formulas:
retx = m11 * px + m21 * py + dx (rounded to the nearest integer)
rety = m22 * py + m12 * px + dy (rounded to the nearest integer)
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Returns the point array a transformed by calling map for each point.
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Returns the point array a transformed by calling map for each point.
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms the region r.
Calling this method can be rather expensive, if rotations or shearing are used.
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Transforms the painter path path.
Returns the transformed rectangle rect rounded to the neares integer.
The bounding rectangle is returned if rotation or shearing has been specified.
If you need to know the exact region rect maps to use operator*().
See also operator*().
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Returns the transformed rectangle rect.
The bounding rectangle is returned if rotation or shearing has been specified.
If you need to know the exact region rect maps to use operator*().
See also operator*().
Returns the transformed rectangle rect as a polygon.
Polygons and rectangles behave slightly differently when transformed (due to integer rounding), so matrix.map(QPolygon(rect)) is not always the same as matrix.mapToPolygon(rect).
Resets the matrix to an identity matrix.
All elements are set to zero, except m11 and m22 (scaling) which are set to 1.
See also isIdentity().
Rotates the coordinate system a degrees counterclockwise.
Note that if you apply a QMatrix to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards.
Returns a reference to the matrix.
See also translate(), scale(), and shear().
Scales the coordinate system unit by sx horizontally and sy vertically.
Returns a reference to the matrix.
See also translate(), shear(), and rotate().
Sets the matrix elements to the specified values, m11, m12, m21, m22, dx and dy.
Shears the coordinate system by sh horizontally and sv vertically.
Returns a reference to the matrix.
See also translate(), scale(), and rotate().
Moves the coordinate system dx along the x axis and dy along the y axis.
Returns a reference to the matrix.
See also scale(), shear(), and rotate().
Returns true if this matrix is not equal to m; otherwise returns false.
Returns the product of this * m.
Note that matrix multiplication is not commutative, i.e. a*b != b*a.
Returns the result of multiplying this matrix by matrix m.
Assigns matrix matrix's values to this matrix.
Returns true if this matrix is equal to m; otherwise returns false.
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
This is the same as m.mapRect(p).
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Same as m.map(p).
See also QMatrix::map().
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
This is the same as m.mapRect(a).
See also QMatrix::mapRect().
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
This is the same as m.mapRect(r).
See also QMatrix::mapRect().
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Writes the matrix m to the stream s and returns a reference to the stream.
See also Format of the QDataStream operators.
This is an overloaded member function, provided for convenience. It behaves essentially like the above function.
Reads the matrix m from the stream s and returns a reference to the stream.
See also Format of the QDataStream operators.
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