Area and Matrix

Data structures and functions to work with areas of interest and their transformations. More...

Data Structures
struct	TArea
	Describes an area of interest that is using three points (P0, P1 and P2). More...
struct	TDRect
	Double precision rectangle defined by its edges. More...
struct	TMatrix
	Defines a 2x2 transformation matrix. More...

Functions
double	Argument (double X, double Y)
	Calculates the argument (direction) of the vector X, Y. More...
cvbbool_t	CreateAffineTransformedImage (IMG ImageIn, const TCoordinateMap &CS, IMG &ImageOut)
	Creates an affine transformed image from the given ImageIn. More...
cvbbool_t	CreateAreaAffineTransformedImage (IMG ImageIn, const TCoordinateMap &CS, const TArea &Area, IMG &ImageOut)
	Creates an affine transformed, linear interpolated image of the given Area from the given ImageIn. More...
cvbbool_t	CreateMatrixTransformedImage (IMG ImageIn, TMatrix Matrix, IMG &ImageOut)
	Creates a matrix transformed image. More...
cvbbool_t	CreateMatrixTransformedImageEx (IMG ImageIn, TMatrix Matrix, IMG &ImageOut)
	Creates a matrix transformed image. More...
bool	InverseMatrix (TMatrix A, TMatrix &AInv)
	Computes the inverse of matrix A, if possible. More...
double	MatrixDeterminant (TMatrix A)
	Calculates the determinant of the given matrix A. More...
void	MatrixITransform (cvbval_t Xin, cvbval_t Yin, TMatrix A, cvbval_t &Xout, cvbval_t &Yout)
	Calculates the transformation for the input vector (Xin, Yin) based on the matrix A. More...
void	MatrixRTransform (double Xin, double Yin, TMatrix A, double &Xout, double &Yout)
	Calculates the transformation for the input vector (Xin, Yin) based on the matrix A. More...
void	MatrixTransformArea (TArea AreaIn, TMatrix A, TArea &AreaOut)
	Performs a matrix transformation on a given area. More...
void	MultiplyMatrices (TMatrix A, TMatrix B, TMatrix &R)
	Multiplies two matrices A and B. More...
void	RotationMatrix (double Angle, TMatrix &R)
	Calculates the rotation matrix coefficients for a given Angle. More...
void	SetArea (double X0, double Y0, double X1, double Y1, double X2, double Y2, TArea &Area)
	Sets the coordinates to the given Area. More...
void	SetMatrix (double A11, double A12, double A21, double A22, TMatrix &A)
	Sets the components to a 2x2 matrix A. More...
void	SetRectArea (double Left, double Top, double Right, double Bottom, TArea &Area)
	Sets the Area points P0, P1, and P2 based on the given rectangle borders. More...

Detailed Description

Data structures and functions to work with areas of interest and their transformations.

Function Documentation

Argument()

double Argument	(	double	X,
		double	Y
	)

Calculates the argument (direction) of the vector X, Y.

The angle is calculated clockwise form the positive x-axis.

Calculation

Parameters

[in]	X	X coordinate of the vector.
[in]	Y	Y coordinate of the vector.

Returns

Angle (in degrees) which is spanned between the vector and the positive x-axis.

CreateAffineTransformedImage()

cvbbool_t CreateAffineTransformedImage	(	IMG	ImageIn,
		const TCoordinateMap &	CS,
		IMG &	ImageOut
	)

Creates an affine transformed image from the given ImageIn.

The coordinate system is also transformed via ComposeCoordinateMaps to reflect the translatory changes. The resulting ImageOut width and height are as with CreateMatrixTransformedImage, but the image coordinates are also transformed regarding the origin of the given CS. This is where this function differs from CreateMatrixTransformedImage.

This is effectively a shorthand for

TArea area = { 0 };
if(!MaxImageArea(ImageIn))
  return false;
 
return CreateAreaAffineTransformedImage(ImageIn, CS, area, ImageOut);

The following BytesPerPixel for signed and unsigned integer cvbdatatype_t values are supported: 1, 2, 4, and 8. For floating point cvbdatatype_t values only 4 and 8 BytesPerPixel are supported.

Note

Call ReleaseObject on ImageOut, when it is no longer needed.

Parameters

[in]	ImageIn	Image object handle of the source image to be transformed.
[in]	CS	Affine matrix with which the image is transformed.
[out]	ImageOut	Variable to receive the handle of the output image.

Returns

true if successful; false otherwise.

See also

CreateMatrixTransformedImage, CreateAreaAffineTransformedImage

CreateAreaAffineTransformedImage()

cvbbool_t CreateAreaAffineTransformedImage	(	IMG	ImageIn,
		const TCoordinateMap &	CS,
		const TArea &	Area,
		IMG &	ImageOut
	)

Creates an affine transformed, linear interpolated image of the given Area from the given ImageIn.

The coordinate system is also transformed via ComposeCoordinateMaps to reflect the translatory changes. The resulting ImageOut has the dimensions of the smallest possible rectangle which encloses the given Area which has been transformed with TCoordinateMap::Matrix. The image coordinates are also transformed of ImageOut the given CS.

The following BytesPerPixel for signed and unsigned integer cvbdatatype_t values are supported: 1, 2, 4, and 8. For floating point cvbdatatype_t values only 4 and 8 BytesPerPixel are supported.

Note

Call ReleaseObject on ImageOut, when it is no longer needed.

Parameters

[in]	ImageIn	Image object handle of the source image to be transformed.
[in]	Area	Area of interest in image coordinates to be transformed.
[in]	CS	Affine matrix with which the image is transformed.
[out]	ImageOut	Variable to receive the handle of the output image.

Returns

true if successful; false otherwise.

See also

CreateMatrixTransformedImage, CreateAffineTransformedImage

CreateMatrixTransformedImage()

cvbbool_t CreateMatrixTransformedImage	(	IMG	ImageIn,
		TMatrix	Matrix,
		IMG &	ImageOut
	)

Creates a matrix transformed image.

The possible geometric transformations with the specified 2x2 Matrix include

• rotation
• scaling
• stretching.

The resulting ImageOut, which is created via CreateCompatibleImage, has the coordinate system being transformed regarding its origin. The resulting width and height is defined by the bounding box of the matrix transformed image area.

The following BytesPerPixel for signed and unsigned integer cvbdatatype_t values are supported: 1, 2, 4, and 8. For floating point cvbdatatype_t values only 4 and 8 BytesPerPixel are supported.

Note

Call ReleaseObject on ImageOut, when it is no longer needed.

Parameters

[in]	ImageIn	Image object handle of the source image to be transformed.
[in]	Matrix	Matrix with which the image is transformed.
[out]	ImageOut	Variable to receive the handle of the output image.

Returns

true if successful; false otherwise.

See also

CreateMatrixTransformedImageEx

CreateMatrixTransformedImageEx()

cvbbool_t CreateMatrixTransformedImageEx	(	IMG	ImageIn,
		TMatrix	Matrix,
		IMG &	ImageOut
	)

Creates a matrix transformed image.

The possible geometric transformations with the specified 2x2 Matrix include

• rotation
• scaling
• stretching.

The resulting ImageOut, which is created via CreateCompatibleImage, has the default coordinate system. The resulting width and height is defined by the bounding box of the matrix transformed image area.

The following BytesPerPixel for signed and unsigned integer cvbdatatype_t values are supported: 1, 2, 4, and 8. For floating point cvbdatatype_t values only 4 and 8 BytesPerPixel are supported.

Note

Call ReleaseObject on ImageOut, when it is no longer needed.

Parameters

[in]	ImageIn	Image object handle of the source image to be transformed.
[in]	Matrix	Matrix with which the image is transformed.
[out]	ImageOut	Variable to receive the handle of the output image.

Returns

true if successful; false otherwise.

See also

CreateMatrixTransformedImage

InverseMatrix()

bool InverseMatrix ( TMatrix  A, TMatrix &  AInv  )

related

Computes the inverse of matrix A, if possible.

Calculation

If the determinant is not zero

Parameters

[in]	A	Input matrix.
[out]	AInv	TMatrix object to be filled with the coefficients of the inverted matrix.

Returns

true if inversion succeeded; false otherwise (determinant is zero).

See also

MatrixDeterminant

MatrixDeterminant()

double MatrixDeterminant ( TMatrix  A )

related

Calculates the determinant of the given matrix A.

Calculation

Parameters

[in]

A

Matrix for which the determinant is calculated.

Returns

Determinant of given matrix A.

MatrixITransform()

void MatrixITransform ( cvbval_t  Xin, cvbval_t  Yin, TMatrix  A, cvbval_t &  Xout, cvbval_t &  Yout  )

related

Calculates the transformation for the input vector (Xin, Yin) based on the matrix A.

The transformation is calculated with double precision floating point arithmetic and then rounded (mathematically) to the next integer.

Calculation

Attention

The rounding used in this function is not mathematical for negative values:

double round(double v) { return floor(v + 0.5); }

Parameters

[in]	Xin	X coordinate of input vector.
[in]	Yin	Y coordinate of input vector.
[in]	A	Matrix with which the vector is multiplied.
[out]	Xout	Variable to be filled with X coordinate of the output vector.
[out]	Yout	Variable to be filled with Y coordinate of the output vector.

See also

MatrixRTransform

MatrixRTransform()

void MatrixRTransform ( double  Xin, double  Yin, TMatrix  A, double &  Xout, double &  Yout  )

related

Calculates the transformation for the input vector (Xin, Yin) based on the matrix A.

Calculation

Parameters

[in]	Xin	X coordinate of input vector.
[in]	Yin	Y coordinate of input vector.
[in]	A	Matrix with which the vector is multiplied.
[out]	Xout	Variable to be filled with X coordinate of the output vector.
[out]	Yout	Variable to be filled with Y coordinate of the output vector.

See also

MatrixITransform

MatrixTransformArea()

void MatrixTransformArea ( TArea  AreaIn, TMatrix  A, TArea &  AreaOut  )

related

Performs a matrix transformation on a given area.

Calculation

Transforms each point of the AreaIn with the given matrix A.

MatrixRTransform(AreaIn.X0, AreaIn.Y0, A, AreaOut.X0, AreaOut.Y0);
MatrixRTransform(AreaIn.X1, AreaIn.Y1, A, AreaOut.X1, AreaOut.Y1);
MatrixRTransform(AreaIn.X2, AreaIn.Y2, A, AreaOut.X2, AreaOut.Y2);

Parameters

[in]	AreaIn	Input area.
[in]	A	Transformation matrix.
[out]	AreaOut	Area to receive the transformed point coordinates.

MultiplyMatrices()

void MultiplyMatrices ( TMatrix  A, TMatrix  B, TMatrix &  R  )

related

Multiplies two matrices A and B.

Calculation

Parameters

[in]	A	A on the left side of the multiplication.
[in]	B	A on the right side of the multiplication.
[out]	R	TMatrix object to be filled with the result of the multiplication.

RotationMatrix()

void RotationMatrix ( double  Angle, TMatrix &  R  )

related

Calculates the rotation matrix coefficients for a given Angle.

Calculation

Parameters

[in]	Angle	Rotation angle (in degrees).
[out]	R	TMatrix object to be filled with rotation matrix coefficients.

SetArea()

void SetArea ( double  X0, double  Y0, double  X1, double  Y1, double  X2, double  Y2, TArea &  Area  )

related

Sets the coordinates to the given Area.

This simply assigns the values to the Area.

Parameters

[in]	X0	X coordinate of point 0.
[in]	Y0	Y coordinate of point 0.
[in]	X1	X coordinate of point 1.
[in]	Y1	Y coordinate of point 1.
[in]	X2	X coordinate of point 2.
[in]	Y2	Y coordinate of point 2.
[out]	Area	TArea object to be filled with given coordinates.

SetMatrix()

void SetMatrix ( double  A11, double  A12, double  A21, double  A22, TMatrix &  A  )

related

Sets the components to a 2x2 matrix A.

This simply assigns the values to the matrix A as defined in TMatrix.

Parameters

[in]	A11	Top left element of matrix.
[in]	A12	Top right element of matrix.
[in]	A21	Bottom left element of matrix.
[in]	A22	Bottom right element of matrix.
[out]	A	TMatrix object to be filled with given coefficients.

SetRectArea()

void SetRectArea ( double  Left, double  Top, double  Right, double  Bottom, TArea &  Area  )

related

Sets the Area points P0, P1, and P2 based on the given rectangle borders.

P0: (Left, Top)
P1: (Right, Top)
P2: (Left, Bottom)

Parameters

[in]	Left	Left border coordinate of area.
[in]	Top	Top border coordinate of area.
[in]	Right	Right border coordinate of area (inclusive).
[in]	Bottom	Bottom border coordinate of area (inclusive).
[out]	Area	TArea object which points are set based on the given borders.