#include <math.h>
#include "allheaders.h"

Functions
l_float32 *	createMatrix2dTranslate (l_float32 transx, l_float32 transy)

l_float32 *	createMatrix2dScale (l_float32 scalex, l_float32 scaley)

l_float32 *	createMatrix2dRotate (l_float32 xc, l_float32 yc, l_float32 angle)

PTA *	ptaTranslate (PTA *ptas, l_float32 transx, l_float32 transy)

PTA *	ptaScale (PTA *ptas, l_float32 scalex, l_float32 scaley)

PTA *	ptaRotate (PTA *ptas, l_float32 xc, l_float32 yc, l_float32 angle)

BOXA *	boxaTranslate (BOXA *boxas, l_float32 transx, l_float32 transy)

BOXA *	boxaScale (BOXA *boxas, l_float32 scalex, l_float32 scaley)

BOXA *	boxaRotate (BOXA *boxas, l_float32 xc, l_float32 yc, l_float32 angle)

PTA *	ptaAffineTransform (PTA ptas, l_float32 mat)

BOXA *	boxaAffineTransform (BOXA boxas, l_float32 mat)

l_ok	l_productMatVec (l_float32 mat, l_float32 vecs, l_float32 *vecd, l_int32 size)

l_ok	l_productMat2 (l_float32 mat1, l_float32 mat2, l_float32 *matd, l_int32 size)

l_ok	l_productMat3 (l_float32 mat1, l_float32 mat2, l_float32 mat3, l_float32 matd, l_int32 size)

l_ok	l_productMat4 (l_float32 mat1, l_float32 mat2, l_float32 mat3, l_float32 mat4, l_float32 *matd, l_int32 size)

Detailed Description


     Composable coordinate transforms
          l_float32   *createMatrix2dTranslate()
          l_float32   *createMatrix2dScale()
          l_float32   *createMatrix2dRotate()

     Special coordinate transforms on pta
          PTA         *ptaTranslate()
          PTA         *ptaScale()
          PTA         *ptaRotate()

     Special coordinate transforms on boxa
          BOXA        *boxaTranslate()
          BOXA        *boxaScale()
          BOXA        *boxaRotate()

     General coordinate transform on pta and boxa
          PTA         *ptaAffineTransform()
          BOXA        *boxaAffineTransform()

     Matrix operations
          l_int32      l_productMatVec()
          l_int32      l_productMat2()
          l_int32      l_productMat3()
          l_int32      l_productMat4()

Definition in file affinecompose.c.

Function Documentation

◆ boxaAffineTransform()

BOXA * boxaAffineTransform	(	BOXA *	boxas,
		l_float32 *	mat )

boxaAffineTransform()

Parameters

[in]	boxas
[in]	mat	3x3 transform matrix; canonical form

Returns: boxad transformed boxas, or NULL on error

Definition at line 473 of file affinecompose.c.

References ptaAffineTransform().

◆ boxaRotate()

BOXA * boxaRotate	(	BOXA *	boxas,
		l_float32	xc,
		l_float32	yc,
		l_float32	angle )

boxaRotate()

Parameters

[in]	boxas
[in]	xc,yc	location of center of rotation
[in]	angle	rotation in radians; clockwise is positive

Returns: boxad rotated boxas, or NULL on error

Notes: (1) See createMatrix2dRotate() for details of transform.

Definition at line 408 of file affinecompose.c.

References ptaRotate().

◆ boxaScale()

BOXA * boxaScale	(	BOXA *	boxas,
		l_float32	scalex,
		l_float32	scaley )

boxaScale()

Parameters

[in]	boxas
[in]	scalex	horizontal scale factor
[in]	scaley	vertical scale factor

Returns: boxad scaled boxas, or NULL on error

Notes: (1) See createMatrix2dScale() for details of transform.

Definition at line 377 of file affinecompose.c.

References ptaScale().

◆ boxaTranslate()

BOXA * boxaTranslate	(	BOXA *	boxas,
		l_float32	transx,
		l_float32	transy )

boxaTranslate()

Parameters

[in]	boxas
[in]	transx	x component of translation wrt. the origin
[in]	transy	y component of translation wrt. the origin

Returns: boxad translated boxas, or NULL on error

Notes: (1) See createMatrix2dTranslate() for details of transform.

Definition at line 346 of file affinecompose.c.

References ptaTranslate().

◆ createMatrix2dRotate()

l_float32 * createMatrix2dRotate	(	l_float32	xc,
		l_float32	yc,
		l_float32	angle )

createMatrix2dRotate()

Parameters

[in]	xc,yc	location of center of rotation
[in]	angle	rotation in radians; clockwise is positive

Returns: 3x3 transform matrix, or NULL on error

Notes:
     (1) The rotation is equivalent to:
            v' = Av
         where v and v' are 1x3 column vectors in the form
            v = [x, y, 1]^    ^ denotes transpose
         and the affine rotation matrix is
            A = [ cosa   -sina    xc*1-cosa + yc*sina
                  sina    cosa    yc*1-cosa - xc*sina
                    0       0                 1         ]

         If the rotation is about the origin, xc, yc) = (0, 0 and
         this simplifies to
            A = [ cosa   -sina    0
                  sina    cosa    0
                    0       0     1 ]

         These relations follow from the following equations, which
         you can convince yourself are correct as follows.  Draw a
         circle centered on xc,yc) and passing through (x,y), with
         (x',y') on the arc at an angle 'a' clockwise from (x,y).
          [ Hint: cosa + b = cosa * cosb - sina * sinb
                  sina + b = sina * cosb + cosa * sinb ]

           x' - xc =  x - xc) * cosa - (y - yc * sina
           y' - yc =  x - xc) * sina + (y - yc * cosa

Definition at line 179 of file affinecompose.c.

◆ createMatrix2dScale()

l_float32 * createMatrix2dScale	(	l_float32	scalex,
		l_float32	scaley )

createMatrix2dScale()

Parameters

[in]	scalex	horizontal scale factor
[in]	scaley	vertical scale factor

Returns: 3x3 transform matrix, or NULL on error

Notes:
     (1) The scaling is equivalent to:
            v' = Av
        where v and v' are 1x3 column vectors in the form
             v = [x, y, 1]^    ^ denotes transpose
        and the affine scaling matrix is
            A = [ sx  0    0
                  0   sy   0
                  0   0    1  ]

     (2) We consider scaling as with respect to a fixed origin.
         In other words, the origin is the only point that doesn't
         move in the scaling transform.

Definition at line 130 of file affinecompose.c.

◆ createMatrix2dTranslate()

l_float32 * createMatrix2dTranslate	(	l_float32	transx,
		l_float32	transy )

createMatrix2dTranslate()

Parameters

[in]	transx	x component of translation wrt. the origin
[in]	transy	y component of translation wrt. the origin

Returns: 3x3 transform matrix, or NULL on error

Notes:
     (1) The translation is equivalent to:
            v' = Av
         where v and v' are 1x3 column vectors in the form
            v = [x, y, 1]^    ^ denotes transpose
         and the affine translation matrix is
            A = [ 1   0   tx
                  0   1   ty
                  0   0    1  ]

     (2) We consider translation as with respect to a fixed origin.
         In a clipping operation, the origin moves and the points
         are fixed, and you use (-tx, -ty) where (tx, ty) is the
         translation vector of the origin.

Definition at line 93 of file affinecompose.c.

◆ l_productMat2()

l_ok l_productMat2	(	l_float32 *	mat1,
		l_float32 *	mat2,
		l_float32 *	matd,
		l_int32	size )

l_productMat2()

Parameters

[in]	mat1	square matrix, as a 1-dimensional size^2 array
[in]	mat2	square matrix, as a 1-dimensional size^2 array
[in]	matd	square matrix; product stored here
[in]	size	of matrices

Returns: 0 if OK, 1 on error

Definition at line 540 of file affinecompose.c.

Referenced by l_productMat3(), and l_productMat4().

◆ l_productMat3()

l_ok l_productMat3	(	l_float32 *	mat1,
		l_float32 *	mat2,
		l_float32 *	mat3,
		l_float32 *	matd,
		l_int32	size )

l_productMat3()

Parameters

[in]	mat1	square matrix, as a 1-dimensional size^2 array
[in]	mat2	square matrix, as a 1-dimensional size^2 array
[in]	mat3	square matrix, as a 1-dimensional size^2 array
[in]	matd	square matrix; product stored here
[in]	size	of matrices

Returns: 0 if OK, 1 on error

Definition at line 577 of file affinecompose.c.

References l_productMat2().

Referenced by l_productMat4().

◆ l_productMat4()

l_ok l_productMat4	(	l_float32 *	mat1,
		l_float32 *	mat2,
		l_float32 *	mat3,
		l_float32 *	mat4,
		l_float32 *	matd,
		l_int32	size )

l_productMat4()

Parameters

[in]	mat1	square matrix, as a 1-dimensional size^2 array
[in]	mat2	square matrix, as a 1-dimensional size^2 array
[in]	mat3	square matrix, as a 1-dimensional size^2 array
[in]	mat4	square matrix, as a 1-dimensional size^2 array
[in]	matd	square matrix; product stored here
[in]	size	of matrices

Returns: 0 if OK, 1 on error

Definition at line 616 of file affinecompose.c.

References l_productMat2(), and l_productMat3().

◆ l_productMatVec()

l_ok l_productMatVec	(	l_float32 *	mat,
		l_float32 *	vecs,
		l_float32 *	vecd,
		l_int32	size )

l_productMatVec()

Parameters

[in]	mat	square matrix, as a 1-dimensional size^2 array
[in]	vecs	input column vector of length size
[in]	vecd	result column vector
[in]	size	matrix is size x size; vectors are length size

Returns: 0 if OK, 1 on error

Definition at line 506 of file affinecompose.c.

Referenced by ptaAffineTransform().

◆ ptaAffineTransform()

PTA * ptaAffineTransform	(	PTA *	ptas,
		l_float32 *	mat )

ptaAffineTransform()

Parameters

[in]	ptas	for initial points
[in]	mat	3x3 transform matrix; canonical form

Returns: ptad transformed points, or NULL on error

Definition at line 439 of file affinecompose.c.

References l_productMatVec().

Referenced by boxaAffineTransform().

◆ ptaRotate()

PTA * ptaRotate	(	PTA *	ptas,
		l_float32	xc,
		l_float32	yc,
		l_float32	angle )

ptaRotate()

Parameters

[in]	ptas	for initial points
[in]	xc,yc	location of center of rotation
[in]	angle	rotation in radians; clockwise is positive

Returns: ptad rotated pta, or NULL on error

Notes;
     (1) See createMatrix2dRotate() for details of transform.
     (2) This transform can be thought of as composed of the
         sum of two parts:
          a) an (x,y)-dependent rotation about the origin:
             xr = x * cosa - y * sina
             yr = x * sina + y * cosa
          b) an (x,y)-independent translation that depends on the
             rotation center and the angle:
             xt = xc - xc * cosa + yc * sina
             yt = yc - xc * sina - yc * cosa
         The translation part (xt,yt) is equal to the difference
         between the center (xc,yc) and the location of the
         center after it is rotated about the origin.

Definition at line 303 of file affinecompose.c.

Referenced by boxaRotate().

◆ ptaScale()

PTA * ptaScale	(	PTA *	ptas,
		l_float32	scalex,
		l_float32	scaley )

ptaScale()

Parameters

[in]	ptas	for initial points
[in]	scalex	horizontal scale factor
[in]	scaley	vertical scale factor

Returns: 0 if OK; 1 on error

Notes:
     (1) See createMatrix2dScale() for details of transform.

Definition at line 254 of file affinecompose.c.

Referenced by boxaScale().

◆ ptaTranslate()

PTA * ptaTranslate	(	PTA *	ptas,
		l_float32	transx,
		l_float32	transy )

ptaTranslate()

Parameters

[in]	ptas	for initial points
[in]	transx	x component of translation wrt. the origin
[in]	transy	y component of translation wrt. the origin

Returns: ptad translated points, or NULL on error

Notes:
     (1) See createMatrix2dTranslate() for details of transform.

Definition at line 217 of file affinecompose.c.

Referenced by boxaTranslate().

Functions

Detailed Description

Function Documentation

◆ boxaAffineTransform()

◆ boxaRotate()

◆ boxaScale()

◆ boxaTranslate()

◆ createMatrix2dRotate()

◆ createMatrix2dScale()

◆ createMatrix2dTranslate()

◆ l_productMat2()

◆ l_productMat3()

◆ l_productMat4()

◆ l_productMatVec()

◆ ptaAffineTransform()

◆ ptaRotate()

◆ ptaScale()

◆ ptaTranslate()