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()
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
Zakariyya Mughal <email@example.com>
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.