NAME

Image::Leptonica::Func::rotateamlow

version 0.04

rotateamlow.c

rotateamlow.c

Grayscale and color rotation (area mapped)

32 bpp grayscale rotation about image center
void    rotateAMColorLow()

8 bpp grayscale rotation about image center
void    rotateAMGrayLow()

32 bpp grayscale rotation about UL corner of image
void    rotateAMColorCornerLow()

8 bpp grayscale rotation about UL corner of image
void    rotateAMGrayCornerLow()

Fast RGB color rotation about center:
void    rotateAMColorFastLow()

FUNCTIONS

rotateAMColorFastLow

void rotateAMColorFastLow ( l_uint32 *datad, l_int32 w, l_int32 h, l_int32 wpld, l_uint32 *datas, l_int32 wpls, l_float32 angle, l_uint32 colorval )

rotateAMColorFastLow()

This is a special simplification of area mapping with division
of each pixel into 16 sub-pixels.  The exact coefficients that
should be used are the same as for the 4x linear interpolation
scaling case, and are given there.  I tried to approximate these
as weighted coefficients with a maximum sum of 4, which
allows us to do the arithmetic in parallel for the R, G and B
components in a 32 bit pixel.  However, there are three reasons
for not doing that:
(1) the loss of accuracy in the parallel implementation
is visually significant
(2) the parallel implementation (described below) is slower
(3) the parallel implementation requires allocation of
a temporary color image

There are 16 cases for the choice of the subpixel, and
for each, the mapping to the relevant source
pixels is as follows:

subpixel      src pixel weights
--------      -----------------
0          sp1
1          (3 * sp1 + sp2) / 4
2          (sp1 + sp2) / 2
3          (sp1 + 3 * sp2) / 4
4          (3 * sp1 + sp3) / 4
5          (9 * sp1 + 3 * sp2 + 3 * sp3 + sp4) / 16
6          (3 * sp1 + 3 * sp2 + sp3 + sp4) / 8
7          (3 * sp1 + 9 * sp2 + sp3 + 3 * sp4) / 16
8          (sp1 + sp3) / 2
9          (3 * sp1 + sp2 + 3 * sp3 + sp4) / 8
10         (sp1 + sp2 + sp3 + sp4) / 4
11         (sp1 + 3 * sp2 + sp3 + 3 * sp4) / 8
12         (sp1 + 3 * sp3) / 4
13         (3 * sp1 + sp2 + 9 * sp3 + 3 * sp4) / 16
14         (sp1 + sp2 + 3 * sp3 + 3 * sp4) / 8
15         (sp1 + 3 * sp2 + 3 * sp3 + 9 * sp4) / 16

Another way to visualize this is to consider the area mapping
(or linear interpolation) coefficients  for the pixel sp1.
Expressed in fourths, they can be written as asymmetric matrix:

4      3      2      1
3      2.25   1.5    0.75
2      1.5    1      0.5
1      0.75   0.5    0.25

The coefficients for the three neighboring pixels can be
similarly written.

This is implemented here, where, for each color component,
we inline its extraction from each participating word,
construct the linear combination, and combine the results
into the destination 32 bit RGB pixel, using the appropriate shifts.

It is interesting to note that an alternative method, where
we do the arithmetic on the 32 bit pixels directly (after
shifting the components so they won't overflow into each other)
is significantly inferior.  Because we have only 8 bits for
internal overflows, which can be distributed as 2, 3, 3, it
is impossible to add these with the correct linear
interpolation coefficients, which require a sum of up to 16.
Rounding off to a sum of 4 causes appreciable visual artifacts
in the rotated image.  The code for the inferior method
can be found in prog/rotatefastalt.c, for reference.

*** Warning: explicit assumption about RGB component ordering

AUTHOR

Zakariyya Mughal <zmughal@cpan.org>