NAME
Image::Leptonica::Func::affinecompose
VERSION
version 0.04
affinecompose.c
affinecompose.c
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()FUNCTIONS
boxaAffineTransform
BOXA * boxaAffineTransform ( BOXA *boxas, l_float32 *mat )
boxaAffineTransform()
Input: boxas
mat (3x3 transform matrix; canonical form)
Return: boxad (transformed boxas), or null on errorboxaRotate
BOXA * boxaRotate ( BOXA *boxas, l_float32 xc, l_float32 yc, l_float32 angle )
boxaRotate()
Input: boxas
(xc, yc) (location of center of rotation)
angle (rotation in radians; clockwise is positive)
Return: boxad (scaled boxas), or null on error
Notes;
(1) See createMatrix2dRotate() for details of transform.boxaScale
BOXA * boxaScale ( BOXA *boxas, l_float32 scalex, l_float32 scaley )
boxaScale()
Input: boxas
scalex (horizontal scale factor)
scaley (vertical scale factor)
Return: boxad (scaled boxas), or null on error
Notes;
(1) See createMatrix2dScale() for details of transform.boxaTranslate
BOXA * boxaTranslate ( BOXA *boxas, l_float32 transx, l_float32 transy )
boxaTranslate()
Input: boxas
transx (x component of translation wrt. the origin)
transy (y component of translation wrt. the origin)
Return: boxad (translated boxas), or null on error
Notes;
(1) See createMatrix2dTranslate() for details of transform.createMatrix2dRotate
l_float32 * createMatrix2dRotate ( l_float32 xc, l_float32 yc, l_float32 angle )
createMatrix2dRotate()
Input: xc, yc (location of center of rotation)
angle (rotation in radians; clockwise is positive)
Return: 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: cos(a + b) = cosa * cosb - sina * sinb
sin(a + b) = sina * cosb + cosa * sinb ]
x' - xc = (x - xc) * cosa - (y - yc) * sina
y' - yc = (x - xc) * sina + (y - yc) * cosacreateMatrix2dScale
l_float32 * createMatrix2dScale ( l_float32 scalex, l_float32 scaley )
createMatrix2dScale()
Input: scalex (horizontal scale factor)
scaley (vertical scale factor)
Return: 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.createMatrix2dTranslate
l_float32 * createMatrix2dTranslate ( l_float32 transx, l_float32 transy )
createMatrix2dTranslate()
Input: transx (x component of translation wrt. the origin)
transy (y component of translation wrt. the origin)
Return: 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 tranlation 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.l_productMat2
l_int32 l_productMat2 ( l_float32 *mat1, l_float32 *mat2, l_float32 *matd, l_int32 size )
l_productMat2()
Input: mat1 (square matrix, as a 1-dimensional size^2 array)
mat2 (square matrix, as a 1-dimensional size^2 array)
matd (square matrix; product stored here)
size (of matrices)
Return: 0 if OK, 1 on errorl_productMat3
l_int32 l_productMat3 ( l_float32 *mat1, l_float32 *mat2, l_float32 *mat3, l_float32 *matd, l_int32 size )
l_productMat3()
Input: mat1 (square matrix, as a 1-dimensional size^2 array)
mat2 (square matrix, as a 1-dimensional size^2 array)
mat3 (square matrix, as a 1-dimensional size^2 array)
matd (square matrix; product stored here)
size (of matrices)
Return: 0 if OK, 1 on errorl_productMat4
l_int32 l_productMat4 ( l_float32 *mat1, l_float32 *mat2, l_float32 *mat3, l_float32 *mat4, l_float32 *matd, l_int32 size )
l_productMat4()
Input: mat1 (square matrix, as a 1-dimensional size^2 array)
mat2 (square matrix, as a 1-dimensional size^2 array)
mat3 (square matrix, as a 1-dimensional size^2 array)
mat4 (square matrix, as a 1-dimensional size^2 array)
matd (square matrix; product stored here)
size (of matrices)
Return: 0 if OK, 1 on errorl_productMatVec
l_int32 l_productMatVec ( l_float32 *mat, l_float32 *vecs, l_float32 *vecd, l_int32 size )
l_productMatVec()
Input: mat (square matrix, as a 1-dimensional @size^2 array)
vecs (input column vector of length @size)
vecd (result column vector)
size (matrix is @size x @size; vectors are length @size)
Return: 0 if OK, 1 on errorptaAffineTransform
PTA * ptaAffineTransform ( PTA *ptas, l_float32 *mat )
ptaAffineTransform()
Input: ptas (for initial points)
mat (3x3 transform matrix; canonical form)
Return: ptad (transformed points), or null on errorptaRotate
PTA * ptaRotate ( PTA *ptas, l_float32 xc, l_float32 yc, l_float32 angle )
ptaRotate()
Input: ptas (for initial points)
(xc, yc) (location of center of rotation)
angle (rotation in radians; clockwise is positive)
(&ptad) (<return> new locations)
Return: 0 if OK; 1 on error
Notes;
(1) See createMatrix2dScale() for details of transform.ptaScale
PTA * ptaScale ( PTA *ptas, l_float32 scalex, l_float32 scaley )
ptaScale()
Input: ptas (for initial points)
scalex (horizontal scale factor)
scaley (vertical scale factor)
Return: 0 if OK; 1 on error
Notes;
(1) See createMatrix2dScale() for details of transform.ptaTranslate
PTA * ptaTranslate ( PTA *ptas, l_float32 transx, l_float32 transy )
ptaTranslate()
Input: ptas (for initial points)
transx (x component of translation wrt. the origin)
transy (y component of translation wrt. the origin)
Return: ptad (translated points), or null on error
Notes;
(1) See createMatrix2dTranslate() for details of transform.AUTHOR
Zakariyya Mughal <zmughal@cpan.org>
COPYRIGHT AND LICENSE
This software is copyright (c) 2014 by Zakariyya Mughal.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.