fgl::FGMatrix

fgl::FGMatrix Class Reference

#include <fgmatrix.h>

List of all members.

Detailed Description

The FGMatrix class specifies 2D transformations of a coordinate system.

The standard coordinate system of a 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 FGDrawBuffer, which renders graphics in a paint device. A user-defined coordinate system can be specified by setting a FGMatrix for the FGDrawBuffer.

Example:

    MyWindow::OnPaint(void)
    {
            FGMatrix m;                      // our transformation matrix
            FGPoint position(30,20);
            m.translate( 100, 100 );                // rotated coordinate system
            m.scale( 3, 2);
            position = m.map(position);
            WindowText( position.x, position.y, "detator" );  // draw rotated text at 100+30*3, 100+20*2
    }

A matrix specifies how to translate, scale, shear or rotate the postitions.

The FGMatrix 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 FGMatrix::invert() 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 FGMatrix also has a function that sets rotate() directly.

FGMatrix lets you combine transformations like this:

    FGMatrix 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);
    FGMatrix m1(1, 0, 0, 1, 10, -20);  // translation matrix
    FGMatrix m2( cosa, sina,           // rotation matrix
            -sina, cosa, 0, 0 );
    FGMatrix m3(1.2, 0, 0, 0.7, 0, 0); // scaling matrix
    FGMatrix m;
    m = m3 * m2 * m1;                  // combine all transformations

QPainter has functions to translate, scale, shear and rotate the coordinate system without using a FGMatrix. Although these functions are very convenient, it can be more efficient to build a FGMatrix and call QPainter::setWorldMatrix() if you want to perform more than a single transform operation.

See also:: QPainter::setWorldMatrix(), QPixmap::xForm()

Public Types

enum TransformationMode { Points, Areas }

Public Member Functions

FGMatrix ()

FGMatrix (const FGMatrix &old)

FGMatrix (double m11, double m12, double m21, double m22, double dx, double dy)

void setMatrix (double m11, double m12, double m21, double m22, double dx, double dy)

double m11 () const

double m12 () const

double m21 () const

double m22 () const

double dx () const

double dy () const

void map (int x, int y, int *tx, int *ty) const

void map (double x, double y, double *tx, double *ty) const

FGRect mapRect (const FGRect &) const

FGPoint map (const FGPoint &p) const

FGCircle map (const FGCircle &c) const

FGSize map (const FGSize &sz) const

FGRect map (const FGRect &r) const

FGPointArray map (const FGPointArray &a) const

void map (FGPointArray &src, FGPointArray &dst)

void reset ()

bool isIdentity () const

FGMatrix & translate (double dx, double dy)

FGMatrix & scale (double sx, double sy)

FGMatrix & shear (double sh, double sv)

FGMatrix & rotate (double a)

void shift_x (double x)

void shift_y (double y)

void SetDxDy (double dx, double dy)

void zoom (double val)

FGMatrix & FGMatrix::scale_with_center (double sx, double sy, double center_x, double center_y)

bool isInvertible () const

double det () const

FGMatrix invert (bool *=0) const

bool operator== (const FGMatrix &) const

bool operator!= (const FGMatrix &) const

FGMatrix & operator *= (const FGMatrix &)

FGCircle operator * (const FGCircle &) const

FGPoint operator * (const FGPoint &) const

FGSize operator * (const FGSize &) const

FGPointArray operator * (const FGPointArray &a) const

Static Public Member Functions

static void setTransformationMode (FGMatrix::TransformationMode m)

static TransformationMode transformationMode ()

Related Functions

(Note that these are not member functions.)

FGMatrix operator * (const FGMatrix &m1, const FGMatrix &m2)

Member Enumeration Documentation

enum fgl::FGMatrix::TransformationMode

FGMatrix offers two transformation modes. Calculations can either be done in terms of points (Points mode, the default), or in terms of area (Area mode).
In Points mode the transformation is applied to the points that mark out the shape's bounding line. In Areas mode the transformation is applied in such a way that the area of the contained region is correctly transformed under the matrix.
Points transformations are applied to the shape's points. Areas transformations are applied (e.g. to the width and height) so that the area is transformed.
Example:
Suppose we have a rectangle, {FGRect( 10, 20, 30, 40 )} and a transformation matrix {FGMatrix( 2, 0, 0, 2, 0, 0 )} to double the rectangle's size.
In Points mode, the matrix will transform the top-left (10,20) and the bottom-right (39,59) points producing a rectangle with its top-left point at (20,40) and its bottom-right point at (78,118), i.e. with a width of 59 and a height of 79.
In Areas mode, the matrix will transform the top-left point in the same way as in Points mode to (20/40), and double the width and height, so the bottom-right will become (69,99), i.e. a width of 60 and a height of 80.
Because integer arithmetic is used (for speed), FGrounding differences mean that the modes will produce slightly different results given the same shape and the same transformation, especially when scaling up. This also means that some operations are not commutative.
Under Points mode, {matrix * ( region1 | region2 )} is not equal to {matrix * region1 | matrix * region2}. Under Area mode, {matrix * (pointarray[i])} is not neccesarily equal to {(matrix * pointarry)[i]}.

Comparison of Points and Areas TransformationModes

Constructor & Destructor Documentation

fgl::FGMatrix::FGMatrix ( )

Constructs an identity matrix. All elements are set to zero except m11 and m22 (scaling), which are set to 1.

fgl::FGMatrix::FGMatrix ( double m11,

double m12,

double m21,

double m22,

double dx,

double dy

)

Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy.

Member Function Documentation

double fgl::FGMatrix::det ( ) const [inline]

Returns the matrix's determinant.

double fgl::FGMatrix::dx ( ) const [inline]

Returns the horizontal translation.

double fgl::FGMatrix::dy ( ) const [inline]

Returns the vertical translation.

FGMatrix fgl::FGMatrix::invert ( bool * invertible = 0 ) const

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()

bool fgl::FGMatrix::isIdentity ( ) const

Returns TRUE if the matrix is the identity matrix; otherwise returns FALSE.

See also:
reset()

bool fgl::FGMatrix::isInvertible ( ) const [inline]

Returns TRUE if the matrix is invertible; otherwise returns FALSE.

See also:
invert()

double fgl::FGMatrix::m11 ( ) const [inline]

Returns the X scaling factor.

double fgl::FGMatrix::m12 ( ) const [inline]

Returns the vertical shearing factor.

double fgl::FGMatrix::m21 ( ) const [inline]

Returns the horizontal shearing factor.

double fgl::FGMatrix::m22 ( ) const [inline]

Returns the Y scaling factor.

FGPointArray fgl::FGMatrix::map ( const FGPointArray & a ) const [inline]

Returns the point array a transformed by calling map for each point.

FGRect fgl::FGMatrix::map ( const FGRect & r ) const [inline]

Deprecated:
Please use FGMatrix::mapRect() instead.
Note that this method does return the bounding rectangle of the r, when shearing or rotations are used.

FGPoint fgl::FGMatrix::map ( const FGPoint & p ) const [inline]

Transforms p to using the formulae:

retx = m11*px + m21*py + dx (FGrounded to the nearest integer) rety = m22*py + m12*px + dy (FGrounded to the nearest integer)

void fgl::FGMatrix::map ( double x,

double y,

double * tx,

double * ty

) const

Transforms ( x, y ) to ( *tx, *ty ) using the following formulae:

*tx = m11*x + m21*y + dx *ty = m22*y + m12*x + dy

void fgl::FGMatrix::map ( int x,

int y,

int * tx,

int * ty

) const

Transforms ( x, y ) to ( *tx, *ty ) using the formulae:

*tx = m11*x + m21*y + dx (FGrounded to the nearest integer) *ty = m22*y + m12*x + dy (FGrounded to the nearest integer)

FGRect fgl::FGMatrix::mapRect ( const FGRect & rect ) const

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*()

FGMatrix & fgl::FGMatrix::operator *= ( const FGMatrix & m )

Returns the result of multiplying this matrix by matrix m.

bool fgl::FGMatrix::operator!= ( const FGMatrix & m ) const

Returns TRUE if this matrix is not equal to m; otherwise returns FALSE.

bool fgl::FGMatrix::operator== ( const FGMatrix & m ) const

Returns TRUE if this matrix is equal to m; otherwise returns FALSE.

void fgl::FGMatrix::reset ( )

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()

FGMatrix & fgl::FGMatrix::rotate ( double a )

Rotates the coordinate system a degrees counterclockwise.
Returns a reference to the matrix.

See also:
translate(), scale(), shear()

FGMatrix & fgl::FGMatrix::scale ( double sx,

double sy

)

Scales the coordinate system unit by sx horizontally and sy vertically.
Returns a reference to the matrix.

See also:
translate(), shear(), rotate()

void fgl::FGMatrix::setMatrix ( double m11,

double m12,

double m21,

double m22,

double dx,

double dy

)

Sets the matrix elements to the specified values, m11, m12, m21, m22, dx and dy.

void fgl::FGMatrix::setTransformationMode ( FGMatrix::TransformationMode m ) [static]

Sets the transformation mode that FGMatrix and painter transformations use to m.

See also:
FGMatrix::TransformationMode

FGMatrix & fgl::FGMatrix::shear ( double sh,

double sv

)

Shears the coordinate system by sh horizontally and sv vertically.
Returns a reference to the matrix.

See also:
translate(), scale(), rotate()

FGMatrix::TransformationMode fgl::FGMatrix::transformationMode ( ) [static]

Returns the current transformation mode.

See also:
FGMatrix::TransformationMode

FGMatrix & fgl::FGMatrix::translate ( double dx,

double dy

)

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(), rotate()

Friends And Related Function Documentation

FGMatrix operator * ( const FGMatrix & m1,

const FGMatrix & m2

) [related]

Returns the product of m1 * m2.
Note that matrix multiplication is not commutative, i.e. a*b != b*a.

Generated on Wed Feb 9 11:31:49 2005 for OpenGUI by

1.4.0


Public Types
enum	TransformationMode { Points, Areas }
Public Member Functions
	FGMatrix ()
	FGMatrix (const FGMatrix &old)
	FGMatrix (double m11, double m12, double m21, double m22, double dx, double dy)
void	setMatrix (double m11, double m12, double m21, double m22, double dx, double dy)
double	m11 () const
double	m12 () const
double	m21 () const
double	m22 () const
double	dx () const
double	dy () const
void	map (int x, int y, int tx, int ty) const
void	map (double x, double y, double tx, double ty) const
FGRect	mapRect (const FGRect &) const
FGPoint	map (const FGPoint &p) const
FGCircle	map (const FGCircle &c) const
FGSize	map (const FGSize &sz) const
FGRect	map (const FGRect &r) const
FGPointArray	map (const FGPointArray &a) const
void	map (FGPointArray &src, FGPointArray &dst)
void	reset ()
bool	isIdentity () const
FGMatrix &	translate (double dx, double dy)
FGMatrix &	scale (double sx, double sy)
FGMatrix &	shear (double sh, double sv)
FGMatrix &	rotate (double a)
void	shift_x (double x)
void	shift_y (double y)
void	SetDxDy (double dx, double dy)
void	zoom (double val)
FGMatrix &	FGMatrix::scale_with_center (double sx, double sy, double center_x, double center_y)
bool	isInvertible () const
double	det () const
FGMatrix	invert (bool *=0) const
bool	operator== (const FGMatrix &) const
bool	operator!= (const FGMatrix &) const
FGMatrix &	operator *= (const FGMatrix &)
FGCircle	operator * (const FGCircle &) const
FGPoint	operator * (const FGPoint &) const
FGSize	operator * (const FGSize &) const
FGPointArray	operator * (const FGPointArray &a) const
Static Public Member Functions
static void	setTransformationMode (FGMatrix::TransformationMode m)
static TransformationMode	transformationMode ()
Related Functions
(Note that these are not member functions.)
FGMatrix	operator * (const FGMatrix &m1, const FGMatrix &m2)