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* Move the palette reduction algorithm into pipi_reduce(). 

git-svn-id: file:///srv/caca.zoy.org/var/lib/svn/libpipi/trunk@2736 92316355-f0b4-4df1-b90c-862c8a59935f
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sam 17 年之前
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共有 4 個文件被更改，包括 499 次插入 和 458 次删除
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  1. +1
    -458
      examples/img2rubik.c
  2. +4
    -0
      pipi/Makefile.am
  3. +2
    -0
      pipi/pipi.h
  4. +492
    -0
      pipi/quantize/reduce.c

+ 1
- 458
examples/img2rubik.c 查看文件

@@ -8,331 +8,8 @@

#include <pipi.h>

#define R 0
#define G 1
#define B 2
#define X 3
#define Y 4
#define A 5

//#define debug printf
#define debug(...) /* */

#define BRIGHT(x) (0.299*(x)[0] + 0.587*(x)[1] + 0.114*(x)[2])

#define MAXCOLORS 16
#define STEPS 256
#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)
{
hull_t *ret = malloc(sizeof(hull_t));
double tmp;
int i, j;

debug("\n### NEW HULL ###\n\n");

debug("Analysing %i colors\n", ncolors);

double pal[ncolors][3];
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)\n", i, pal[i][R], pal[i][G], pal[i][B]);
}

/*
* 1. Find the darkest and lightest colours
*/
double *dark = NULL, *light = NULL;
double min = 1.0, max = 0.0;
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;
}
}

double gray[3];

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)\n",
dark[R], dark[G], dark[B], light[R], light[G], light[B]);

/*
* 3. Browse the grey axis and do stuff
*/
int n;
for(n = 0; n <= STEPS; n++)
{
double pts[ncolors * (ncolors - 1) / 2][5];
double ptmp[5];
#define SWAP(p1,p2) do { memcpy(ptmp, p1, sizeof(ptmp)); \
memcpy(p1, p2, sizeof(ptmp)); \
memcpy(p2, ptmp, sizeof(ptmp)); } while(0)
double t = n * 1.0 / STEPS;
int npts = 0;

debug("Slice %i/%i\n", n, STEPS);

double p0[3];
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)\n", 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];
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 */
double 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++)
{
if(i == j)
continue;

double k2[3];
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 */
double yk2 = y[R] * k2[R] + y[G] * k2[G] + y[B] * k2[B];
if(yk2 < t * ylen * ylen - EPSILON)
continue;

if(yk2 < yk1)
continue;

double 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 */
int 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; /* */)
{
if(i < 2)
{
i++;
continue;
}

double k1 = (pts[i - 1][X] - pts[i - 2][X])
* (pts[i][Y] - pts[i - 2][Y]);
double 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)\n", i, pts[i][X], pts[i][Y]);

/* Compute the barycentre coordinates */
double 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 sqarea = (abx * abx + aby * aby) * (acx * acx + acy * acy)
- (abx * acx + aby * acy) * (abx * acx + aby * acy);
if(sqarea <= 0.)
continue;

double 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)\n", 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\n",
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)\n",
ret->bary[n][R], ret->bary[n][G], ret->bary[n][B]);
}

return ret;
}


int main(int argc, char *argv[])
{
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,
};

static double const mypal[] =
{
0.900, 0.001, 0.001, /* red */
@@ -343,142 +20,8 @@ int main(int argc, char *argv[])
0.800, 0.400, 0.001, /* orange */
};

int i, j;

init_uv();

hull_t *rgbhull = compute_hull(8, rgbpal);
hull_t *myhull = compute_hull(6, mypal);

/*
* 4. Load image and change its palette.
*/

debug("\n### PROCESSING IMAGE ###\n\n");

pipi_image_t *src = pipi_load(argv[1]);
pipi_pixels_t *srcp = pipi_getpixels(src, PIPI_PIXELS_RGBA_F);
float *srcdata = (float *)srcp->pixels;

int w = srcp->w, h = srcp->h;

pipi_image_t *dst = pipi_new(w, h);
pipi_pixels_t *dstp = pipi_getpixels(dst, PIPI_PIXELS_RGBA_F);
float *dstdata = (float *)dstp->pixels;

for(j = 0; j < h; j++)
for(i = 0; i < w; i++)
{
double p[3];
/* 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)\n", i, j, p[R], p[G], p[B]);

int slice = (int)(BRIGHT(p) * STEPS + 0.5);

debug(" slice %i\n", slice);

/* Convert to 2D. The origin is the slice's barycentre. */
double 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];
double 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)\n", 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. */
int n, count = rgbhull->hullsize[slice];
double 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) */
double xa = rgbhull->pts[slice][n % count][X];
double ya = rgbhull->pts[slice][n % count][Y];
double xb = rgbhull->pts[slice][(n + 1) % count][X];
double yb = rgbhull->pts[slice][(n + 1) % count][Y];
double 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)\n", 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];
double s = (xp * (yb - ya) - yp * (xb - xa)) / (xa * yb - xb * ya);

debug(" best custom %g (%g,%g) (%g,%g)\n", 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);

pipi_image_t *dst = pipi_reduce(src, 6, mypal);
pipi_save(dst, argv[2]);

return 0;


+ 4
- 0
pipi/Makefile.am 查看文件

@@ -27,6 +27,7 @@ libpipi_la_SOURCES = \
$(paint_sources) \
$(combine_sources) \
$(filter_sources) \
$(quantize_sources) \
$(dither_sources) \
$(NULL)
libpipi_la_CFLAGS = $(codec_cflags)
@@ -55,6 +56,9 @@ filter_sources = \
filter/convolution.c filter/convolution_template.h \
filter/color.c

quantize_sources = \
quantize/reduce.c

dither_sources = \
dither/floydsteinberg.c \
dither/jajuni.c \


+ 2
- 0
pipi/pipi.h 查看文件

@@ -131,6 +131,8 @@ extern pipi_image_t *pipi_tile(pipi_image_t *, int, int);
extern int pipi_flood_fill(pipi_image_t *,
int, int, float, float, float, float);

extern pipi_image_t *pipi_reduce(pipi_image_t *, int, double const *);

extern pipi_image_t *pipi_dither_floydsteinberg(pipi_image_t *, pipi_scan_t);
extern pipi_image_t *pipi_dither_jajuni(pipi_image_t *, pipi_scan_t);
extern pipi_image_t *pipi_dither_ordered(pipi_image_t *, pipi_image_t *);


+ 492
- 0
pipi/quantize/reduce.c 查看文件

@@ -0,0 +1,492 @@
/*
* libpipi Proper image processing implementation 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 "common.h"

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

#include <pipi.h>

#define R 0
#define G 1
#define B 2
#define X 3
#define Y 4
#define A 5

//#define debug printf
#define debug(...) /* */

#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)
{
hull_t *ret = malloc(sizeof(hull_t));
double tmp;
int i, j;

debug("\n### NEW HULL ###\n\n");

debug("Analysing %i colors\n", ncolors);

double pal[ncolors][3];
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)\n", i, pal[i][R], pal[i][G], pal[i][B]);
}

/*
* 1. Find the darkest and lightest colours
*/
double *dark = NULL, *light = NULL;
double min = 1.0, max = 0.0;
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;
}
}

double gray[3];

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)\n",
dark[R], dark[G], dark[B], light[R], light[G], light[B]);

/*
* 3. Browse the grey axis and do stuff
*/
int n;
for(n = 0; n <= STEPS; n++)
{
double pts[ncolors * (ncolors - 1) / 2][5];
double ptmp[5];
#define SWAP(p1,p2) do { memcpy(ptmp, p1, sizeof(ptmp)); \
memcpy(p1, p2, sizeof(ptmp)); \
memcpy(p2, ptmp, sizeof(ptmp)); } while(0)
double t = n * 1.0 / STEPS;
int npts = 0;

debug("Slice %i/%i\n", n, STEPS);

double p0[3];
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)\n", 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];
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 */
double 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++)
{
if(i == j)
continue;

double k2[3];
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 */
double yk2 = y[R] * k2[R] + y[G] * k2[G] + y[B] * k2[B];
if(yk2 < t * ylen * ylen - EPSILON)
continue;

if(yk2 < yk1)
continue;

double 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 */
int 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; /* */)
{
if(i < 2)
{
i++;
continue;
}

double k1 = (pts[i - 1][X] - pts[i - 2][X])
* (pts[i][Y] - pts[i - 2][Y]);
double 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)\n", i, pts[i][X], pts[i][Y]);

/* Compute the barycentre coordinates */
double 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 sqarea = (abx * abx + aby * aby) * (acx * acx + acy * acy)
- (abx * acx + aby * acy) * (abx * acx + aby * acy);
if(sqarea <= 0.)
continue;

double 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)\n", 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\n",
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)\n",
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,
};

int i, j;

init_uv();

hull_t *rgbhull = compute_hull(8, rgbpal);
hull_t *myhull = compute_hull(ncolors, palette);

/*
* 4. Load image and change its palette.
*/

debug("\n### PROCESSING IMAGE ###\n\n");

pipi_pixels_t *srcp = pipi_getpixels(src, PIPI_PIXELS_RGBA_F);
float *srcdata = (float *)srcp->pixels;

int w = srcp->w, h = srcp->h;

pipi_image_t *dst = pipi_new(w, h);
pipi_pixels_t *dstp = pipi_getpixels(dst, PIPI_PIXELS_RGBA_F);
float *dstdata = (float *)dstp->pixels;

for(j = 0; j < h; j++)
for(i = 0; i < w; i++)
{
double p[3];
/* 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)\n", i, j, p[R], p[G], p[B]);

int slice = (int)(BRIGHT(p) * STEPS + 0.5);

debug(" slice %i\n", slice);

/* Convert to 2D. The origin is the slice's barycentre. */
double 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];
double 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)\n", 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. */
int n, count = rgbhull->hullsize[slice];
double 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) */
double xa = rgbhull->pts[slice][n % count][X];
double ya = rgbhull->pts[slice][n % count][Y];
double xb = rgbhull->pts[slice][(n + 1) % count][X];
double yb = rgbhull->pts[slice][(n + 1) % count][Y];
double 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)\n", 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];
double s = (xp * (yb - ya) - yp * (xb - xa)) / (xa * yb - xb * ya);

debug(" best custom %g (%g,%g) (%g,%g)\n", 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;
}


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