/*
* libpipi Pathetic image processing interface library
* Copyright (c) 2004-2008 Sam Hocevar <sam@zoy.org>
* All Rights Reserved
*
* $Id$
*
* This library is free software. It comes without any warranty, to
* the extent permitted by applicable law. You can redistribute it
* and/or modify it under the terms of the Do What The Fuck You Want
* To Public License, Version 2, as published by Sam Hocevar. See
* http://sam.zoy.org/wtfpl/COPYING for more details.
*/
/*
* reduce.c: palette reduction routines
*/
#include "config.h"
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#ifndef M_PI
# define M_PI 3.14159265358979323846
#endif
#include "pipi.h"
#include "pipi_internals.h"
#define R 0
#define G 1
#define B 2
#define X 3
#define Y 4
#define A 5
#define BRIGHT(x) (0.299*(x)[0] + 0.587*(x)[1] + 0.114*(x)[2])
#define MAXCOLORS 16
#define STEPS 1024
#define EPSILON (0.000001)
typedef struct
{
double pts[STEPS + 1][MAXCOLORS * (MAXCOLORS - 1) / 2][6];
int hullsize[STEPS + 1];
double bary[STEPS + 1][3];
}
hull_t;
static double const y[3] = { .299, .587, .114 };
static double u[3], v[3];
static int ylen;
/*
* Find two base vectors for the chrominance planes.
*/
static void init_uv(void)
{
double tmp;
ylen = sqrt(y[R] * y[R] + y[G] * y[G] + y[B] * y[B]);
u[R] = y[1];
u[G] = -y[0];
u[B] = 0;
tmp = sqrt(u[R] * u[R] + u[G] * u[G] + u[B] * u[B]);
u[R] /= tmp; u[G] /= tmp; u[B] /= tmp;
v[R] = y[G] * u[B] - y[B] * u[G];
v[G] = y[B] * u[R] - y[R] * u[B];
v[B] = y[R] * u[G] - y[G] * u[R];
tmp = sqrt(v[R] * v[R] + v[G] * v[G] + v[B] * v[B]);
v[R] /= tmp; v[G] /= tmp; v[B] /= tmp;
}
/*
* Compute the convex hull of a given palette.
*/
static hull_t *compute_hull(int ncolors, double const *palette)
{
double pal[MAXCOLORS][3];
double gray[3];
double *dark = NULL, *light = NULL;
double tmp, min = 1.0, max = 0.0;
hull_t *ret = malloc(sizeof(hull_t));
int i, j, n;
debug("");
debug("### NEW HULL ###");
debug("");
debug("Analysing %i colors", ncolors);
for(i = 0; i < ncolors; i++)
{
pal[i][R] = palette[i * 3];
pal[i][G] = palette[i * 3 + 1];
pal[i][B] = palette[i * 3 + 2];
debug(" [%i] (%g,%g,%g)", i, pal[i][R], pal[i][G], pal[i][B]);
}
/*
* 1. Find the darkest and lightest colours
*/
for(i = 0; i < ncolors; i++)
{
double p = BRIGHT(pal[i]);
if(p < min)
{
dark = pal[i];
min = p;
}
if(p > max)
{
light = pal[i];
max = p;
}
}
gray[R] = light[R] - dark[R];
gray[G] = light[G] - dark[G];
gray[B] = light[B] - dark[B];
debug(" gray axis (%g,%g,%g) - (%g,%g,%g)",
dark[R], dark[G], dark[B], light[R], light[G], light[B]);
/*
* 3. Browse the grey axis and do stuff
*/
for(n = 0; n <= STEPS; n++)
{
double pts[MAXCOLORS * (MAXCOLORS - 1) / 2][5];
double ptmp[5];
double p0[3];
#define SWAP(p1,p2) do { memcpy(ptmp, p1, sizeof(ptmp)); \
memcpy(p1, p2, sizeof(ptmp)); \
memcpy(p2, ptmp, sizeof(ptmp)); } while(0)
double ctx, cty, weight;
double t = n * 1.0 / STEPS;
int npts = 0, left;
debug("Slice %i/%i", n, STEPS);
p0[R] = dark[R] + t * gray[R];
p0[G] = dark[G] + t * gray[G];
p0[B] = dark[B] + t * gray[B];
debug(" 3D gray (%g,%g,%g)", p0[R], p0[G], p0[B]);
/*
* 3.1. Find all edges that intersect the t.y + (u,v) plane
*/
for(i = 0; i < ncolors; i++)
{
double k1[3];
double yk1;
k1[R] = pal[i][R] - p0[R];
k1[G] = pal[i][G] - p0[G];
k1[B] = pal[i][B] - p0[B];
tmp = sqrt(k1[R] * k1[R] + k1[G] * k1[G] + k1[B] * k1[B]);
/* If k1.y > t.y.y, we don't want this point */
yk1 = y[R] * k1[R] + y[G] * k1[G] + y[B] * k1[B];
if(yk1 > t * ylen * ylen + EPSILON)
continue;
for(j = 0; j < ncolors; j++)
{
double k2[3];
double yk2, s;
if(i == j)
continue;
k2[R] = pal[j][R] - p0[R];
k2[G] = pal[j][G] - p0[G];
k2[B] = pal[j][B] - p0[B];
tmp = sqrt(k2[R] * k2[R] + k2[G] * k2[G] + k2[B] * k2[B]);
/* If k2.y < t.y.y, we don't want this point */
yk2 = y[R] * k2[R] + y[G] * k2[G] + y[B] * k2[B];
if(yk2 < t * ylen * ylen - EPSILON)
continue;
if(yk2 < yk1)
continue;
s = yk1 == yk2 ? 0.5 : (t * ylen * ylen - yk1) / (yk2 - yk1);
pts[npts][R] = p0[R] + k1[R] + s * (k2[R] - k1[R]);
pts[npts][G] = p0[G] + k1[G] + s * (k2[G] - k1[G]);
pts[npts][B] = p0[B] + k1[B] + s * (k2[B] - k1[B]);
npts++;
}
}
/*
* 3.2. Find the barycentre of these points' convex hull. We use
* the Graham Scan technique.
*/
/* Make our problem a 2-D problem. */
for(i = 0; i < npts; i++)
{
pts[i][X] = (pts[i][R] - p0[R]) * u[R]
+ (pts[i][G] - p0[G]) * u[G]
+ (pts[i][B] - p0[B]) * u[B];
pts[i][Y] = (pts[i][R] - p0[R]) * v[R]
+ (pts[i][G] - p0[G]) * v[G]
+ (pts[i][B] - p0[B]) * v[B];
}
/* Find the leftmost point */
left = -1;
tmp = 10.;
for(i = 0; i < npts; i++)
if(pts[i][X] < tmp)
{
left = i;
tmp = pts[i][X];
}
SWAP(pts[0], pts[left]);
/* Sort the remaining points radially around pts[0]. Bubble sort
* is okay for small sizes, I don't care. */
for(i = 1; i < npts; i++)
for(j = 1; j < npts - i; j++)
{
double k1 = (pts[j][X] - pts[0][X])
* (pts[j + 1][Y] - pts[0][Y]);
double k2 = (pts[j + 1][X] - pts[0][X])
* (pts[j][Y] - pts[0][Y]);
if(k1 < k2 - EPSILON)
SWAP(pts[j], pts[j + 1]);
else if(k1 < k2 + EPSILON)
{
/* Aligned! keep the farthest point */
double ax = pts[j][X] - pts[0][X];
double ay = pts[j][Y] - pts[0][Y];
double bx = pts[j + 1][X] - pts[0][X];
double by = pts[j + 1][Y] - pts[0][Y];
if(ax * ax + ay * ay > bx * bx + by * by)
SWAP(pts[j], pts[j + 1]);
}
}
/* Remove points not in the convex hull */
for(i = 2; i < npts; /* */)
{
double k1, k2;
if(i < 2)
{
i++;
continue;
}
k1 = (pts[i - 1][X] - pts[i - 2][X])
* (pts[i][Y] - pts[i - 2][Y]);
k2 = (pts[i][X] - pts[i - 2][X])
* (pts[i - 1][Y] - pts[i - 2][Y]);
if(k1 <= k2 + EPSILON)
{
for(j = i - 1; j < npts - 1; j++)
SWAP(pts[j], pts[j + 1]);
npts--;
}
else
i++;
}
/* FIXME: check the last point */
for(i = 0; i < npts; i++)
debug(" 2D pt[%i] (%g,%g)", i, pts[i][X], pts[i][Y]);
/* Compute the barycentre coordinates */
ctx = 0.;
cty = 0.;
weight = 0.;
for(i = 2; i < npts; i++)
{
double abx = pts[i - 1][X] - pts[0][X];
double aby = pts[i - 1][Y] - pts[0][Y];
double acx = pts[i][X] - pts[0][X];
double acy = pts[i][Y] - pts[0][Y];
double area;
double sqarea = (abx * abx + aby * aby) * (acx * acx + acy * acy)
- (abx * acx + aby * acy) * (abx * acx + aby * acy);
if(sqarea <= 0.)
continue;
area = sqrt(sqarea);
ctx += area * (abx + acx) / 3;
cty += area * (aby + acy) / 3;
weight += area;
}
if(weight > EPSILON)
{
ctx = pts[0][X] + ctx / weight;
cty = pts[0][Y] + cty / weight;
}
else
{
int right = -1;
tmp = -10.;
for(i = 0; i < npts; i++)
if(pts[i][X] > tmp)
{
right = i;
tmp = pts[i][X];
}
ctx = 0.5 * (pts[0][X] + pts[right][X]);
cty = 0.5 * (pts[0][Y] + pts[right][Y]);
}
debug(" 2D bary (%g,%g)", ctx, cty);
/*
* 3.3. Store the barycentre and convex hull information.
*/
ret->bary[n][R] = p0[R] + ctx * u[R] + cty * v[R];
ret->bary[n][G] = p0[G] + ctx * u[G] + cty * v[G];
ret->bary[n][B] = p0[B] + ctx * u[B] + cty * v[B];
for(i = 0; i < npts; i++)
{
ret->pts[n][i][R] = pts[i][R];
ret->pts[n][i][G] = pts[i][G];
ret->pts[n][i][B] = pts[i][B];
ret->pts[n][i][X] = pts[i][X] - ctx;
ret->pts[n][i][Y] = pts[i][Y] - cty;
ret->pts[n][i][A] = atan2(pts[i][Y] - cty, pts[i][X] - ctx);
debug(" 3D pt[%i] (%g,%g,%g) angle %g",
i, pts[i][R], pts[i][G], pts[i][B], ret->pts[n][i][A]);
}
ret->hullsize[n] = npts;
debug(" 3D bary (%g,%g,%g)",
ret->bary[n][R], ret->bary[n][G], ret->bary[n][B]);
}
return ret;
}
pipi_image_t *pipi_reduce(pipi_image_t *src,
int ncolors, double const *palette)
{
static double const rgbpal[] =
{
0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1,
1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1,
};
pipi_image_t *dst;
pipi_pixels_t *srcp, *dstp;
float *srcdata, *dstdata;
hull_t *rgbhull, *myhull;
int i, j, w, h;
init_uv();
rgbhull = compute_hull(8, rgbpal);
myhull = compute_hull(ncolors, palette);
/*
* 4. Load image and change its palette.
*/
debug("");
debug("### PROCESSING IMAGE ###");
debug("");
srcp = pipi_get_pixels(src, PIPI_PIXELS_RGBA_F32);
srcdata = (float *)srcp->pixels;
w = srcp->w;
h = srcp->h;
dst = pipi_new(w, h);
dstp = pipi_get_pixels(dst, PIPI_PIXELS_RGBA_F32);
dstdata = (float *)dstp->pixels;
for(j = 0; j < h; j++)
for(i = 0; i < w; i++)
{
double p[3];
double xp, yp, angle, xa, ya, xb, yb, t, s;
int slice, n, count;
/* FIXME: Imlib fucks up the RGB order. */
p[B] = srcdata[4 * (j * w + i)];
p[G] = srcdata[4 * (j * w + i) + 1];
p[R] = srcdata[4 * (j * w + i) + 2];
debug("Pixel +%i+%i (%g,%g,%g)", i, j, p[R], p[G], p[B]);
slice = (int)(BRIGHT(p) * STEPS + 0.5);
debug(" slice %i", slice);
/* Convert to 2D. The origin is the slice's barycentre. */
xp = (p[R] - rgbhull->bary[slice][R]) * u[R]
+ (p[G] - rgbhull->bary[slice][G]) * u[G]
+ (p[B] - rgbhull->bary[slice][B]) * u[B];
yp = (p[R] - rgbhull->bary[slice][R]) * v[R]
+ (p[G] - rgbhull->bary[slice][G]) * v[G]
+ (p[B] - rgbhull->bary[slice][B]) * v[B];
debug(" 2D pt (%g,%g)", xp, yp);
/* 1. find the excentricity in RGB space. There is an easier
* way to do this, which is to find the intersection of our
* line with the RGB cube itself, but we'd lose the possibility
* of having an original colour space other than RGB. */
/* First, find the relevant triangle. */
count = rgbhull->hullsize[slice];
angle = atan2(yp, xp);
for(n = 0; n < count; n++)
{
double a1 = rgbhull->pts[slice][n][A];
double a2 = rgbhull->pts[slice][(n + 1) % count][A];
if(a1 > a2)
{
if(angle >= a1)
a2 += 2 * M_PI;
else
a1 -= 2 * M_PI;
}
if(angle >= a1 && angle <= a2)
break;
}
/* Now compute the distance to the triangle's edge. If the edge
* intersection is M, then t is such as P = t.M (can be zero) */
xa = rgbhull->pts[slice][n % count][X];
ya = rgbhull->pts[slice][n % count][Y];
xb = rgbhull->pts[slice][(n + 1) % count][X];
yb = rgbhull->pts[slice][(n + 1) % count][Y];
t = (xp * (yb - ya) - yp * (xb - xa)) / (xa * yb - xb * ya);
if(t > 1.0)
t = 1.0;
debug(" best RGB %g (%g,%g) (%g,%g)", t, xa, ya, xb, yb);
/* 2. apply the excentricity in reduced space. */
count = myhull->hullsize[slice];
for(n = 0; n < count; n++)
{
double a1 = myhull->pts[slice][n][A];
double a2 = myhull->pts[slice][(n + 1) % count][A];
if(a1 > a2)
{
if(angle >= a1)
a2 += 2 * M_PI;
else
a1 -= 2 * M_PI;
}
if(angle >= a1 && angle <= a2)
break;
}
/* If the edge intersection is M', s is such as P = s.M'. We
* want P' = t.M' = t.P/s */
xa = myhull->pts[slice][n % count][X];
ya = myhull->pts[slice][n % count][Y];
xb = myhull->pts[slice][(n + 1) % count][X];
yb = myhull->pts[slice][(n + 1) % count][Y];
s = (xp * (yb - ya) - yp * (xb - xa)) / (xa * yb - xb * ya);
debug(" best custom %g (%g,%g) (%g,%g)", s, xa, ya, xb, yb);
if(s > 0)
{
xp *= t / s;
yp *= t / s;
}
p[R] = myhull->bary[slice][R] + xp * u[R] + yp * v[R];
p[G] = myhull->bary[slice][G] + xp * u[G] + yp * v[G];
p[B] = myhull->bary[slice][B] + xp * u[B] + yp * v[B];
/* Clipping should not be necessary, but the above code
* is unfortunately not perfect. */
if(p[R] < 0.0) p[R] = 0.0; else if(p[R] > 1.0) p[R] = 1.0;
if(p[G] < 0.0) p[G] = 0.0; else if(p[G] > 1.0) p[G] = 1.0;
if(p[B] < 0.0) p[B] = 0.0; else if(p[B] > 1.0) p[B] = 1.0;
dstdata[4 * (j * w + i)] = p[B];
dstdata[4 * (j * w + i) + 1] = p[G];
dstdata[4 * (j * w + i) + 2] = p[R];
}
free(rgbhull);
free(myhull);
return dst;
}