/*
* Copyright 2012, Red Hat, Inc.
* Copyright 2012, Soren Sandmann
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice (including the next
* paragraph) shall be included in all copies or substantial portions of the
* Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
* DEALINGS IN THE SOFTWARE.
*
* Author: Soren Sandmann <soren.sandmann@gmail.com>
*/
#include <string.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include "pixman-private.h"
typedef double (* kernel_func_t) (double x);
typedef struct
{
pixman_kernel_t kernel;
kernel_func_t func;
double width;
} filter_info_t;
static double
impulse_kernel (double x)
{
return (x == 0.0)? 1.0 : 0.0;
}
static double
box_kernel (double x)
{
return 1;
}
static double
linear_kernel (double x)
{
return 1 - fabs (x);
}
static double
gaussian_kernel (double x)
{
#define SQRT2 (1.4142135623730950488016887242096980785696718753769480)
#define SIGMA (SQRT2 / 2.0)
return exp (- x * x / (2 * SIGMA * SIGMA)) / (SIGMA * sqrt (2.0 * M_PI));
}
static double
sinc (double x)
{
if (x == 0.0)
return 1.0;
else
return sin (M_PI * x) / (M_PI * x);
}
static double
lanczos (double x, int n)
{
return sinc (x) * sinc (x * (1.0 / n));
}
static double
lanczos2_kernel (double x)
{
return lanczos (x, 2);
}
static double
lanczos3_kernel (double x)
{
return lanczos (x, 3);
}
static double
nice_kernel (double x)
{
return lanczos3_kernel (x * 0.75);
}
static double
general_cubic (double x, double B, double C)
{
double ax = fabs(x);
if (ax < 1)
{
return ((12 - 9 * B - 6 * C) * ax * ax * ax +
(-18 + 12 * B + 6 * C) * ax * ax + (6 - 2 * B)) / 6;
}
else if (ax >= 1 && ax < 2)
{
return ((-B - 6 * C) * ax * ax * ax +
(6 * B + 30 * C) * ax * ax + (-12 * B - 48 * C) *
ax + (8 * B + 24 * C)) / 6;
}
else
{
return 0;
}
}
static double
cubic_kernel (double x)
{
/* This is the Mitchell-Netravali filter.
*
* (0.0, 0.5) would give us the Catmull-Rom spline,
* but that one seems to be indistinguishable from Lanczos2.
*/
return general_cubic (x, 1/3.0, 1/3.0);
}
static const filter_info_t filters[] =
{
{ PIXMAN_KERNEL_IMPULSE, impulse_kernel, 0.0 },
{ PIXMAN_KERNEL_BOX, box_kernel, 1.0 },
{ PIXMAN_KERNEL_LINEAR, linear_kernel, 2.0 },
{ PIXMAN_KERNEL_CUBIC, cubic_kernel, 4.0 },
{ PIXMAN_KERNEL_GAUSSIAN, gaussian_kernel, 6 * SIGMA },
{ PIXMAN_KERNEL_LANCZOS2, lanczos2_kernel, 4.0 },
{ PIXMAN_KERNEL_LANCZOS3, lanczos3_kernel, 6.0 },
{ PIXMAN_KERNEL_LANCZOS3_STRETCHED, nice_kernel, 8.0 },
};
/* This function scales @kernel2 by @scale, then
* aligns @x1 in @kernel1 with @x2 in @kernel2 and
* and integrates the product of the kernels across @width.
*
* This function assumes that the intervals are within
* the kernels in question. E.g., the caller must not
* try to integrate a linear kernel ouside of [-1:1]
*/
static double
integral (pixman_kernel_t kernel1, double x1,
pixman_kernel_t kernel2, double scale, double x2,
double width)
{
/* If the integration interval crosses zero, break it into
* two separate integrals. This ensures that filters such
* as LINEAR that are not differentiable at 0 will still
* integrate properly.
*/
if (x1 < 0 && x1 + width > 0)
{
return
integral (kernel1, x1, kernel2, scale, x2, - x1) +
integral (kernel1, 0, kernel2, scale, x2 - x1, width + x1);
}
else if (x2 < 0 && x2 + width > 0)
{
return
integral (kernel1, x1, kernel2, scale, x2, - x2) +
integral (kernel1, x1 - x2, kernel2, scale, 0, width + x2);
}
else if (kernel1 == PIXMAN_KERNEL_IMPULSE)
{
assert (width == 0.0);
return filters[kernel2].func (x2 * scale);
}
else if (kernel2 == PIXMAN_KERNEL_IMPULSE)
{
assert (width == 0.0);
return filters[kernel1].func (x1);
}
else
{
/* Integration via Simpson's rule */
#define N_SEGMENTS 128
#define SAMPLE(a1, a2) \
(filters[kernel1].func ((a1)) * filters[kernel2].func ((a2) * scale))
double s = 0.0;
double h = width / (double)N_SEGMENTS;
int i;
s = SAMPLE (x1, x2);
for (i = 1; i < N_SEGMENTS; i += 2)
{
double a1 = x1 + h * i;
double a2 = x2 + h * i;
s += 2 * SAMPLE (a1, a2);
if (i >= 2 && i < N_SEGMENTS - 1)
s += 4 * SAMPLE (a1, a2);
}
s += SAMPLE (x1 + width, x2 + width);
return h * s * (1.0 / 3.0);
}
}
static pixman_fixed_t *
create_1d_filter (int *width,
pixman_kernel_t reconstruct,
pixman_kernel_t sample,
double scale,
int n_phases)
{
pixman_fixed_t *params, *p;
double step;
double size;
int i;
size = scale * filters[sample].width + filters[reconstruct].width;
*width = ceil (size);
p = params = malloc (*width * n_phases * sizeof (pixman_fixed_t));
if (!params)
return NULL;
step = 1.0 / n_phases;
for (i = 0; i < n_phases; ++i)
{
double frac = step / 2.0 + i * step;
pixman_fixed_t new_total;
int x, x1, x2;
double total;
/* Sample convolution of reconstruction and sampling
* filter. See rounding.txt regarding the rounding
* and sample positions.
*/
x1 = ceil (frac - *width / 2.0 - 0.5);
x2 = x1 + *width;
total = 0;
for (x = x1; x < x2; ++x)
{
double pos = x + 0.5 - frac;
double rlow = - filters[reconstruct].width / 2.0;
double rhigh = rlow + filters[reconstruct].width;
double slow = pos - scale * filters[sample].width / 2.0;
double shigh = slow + scale * filters[sample].width;
double c = 0.0;
double ilow, ihigh;
if (rhigh >= slow && rlow <= shigh)
{
ilow = MAX (slow, rlow);
ihigh = MIN (shigh, rhigh);
c = integral (reconstruct, ilow,
sample, 1.0 / scale, ilow - pos,
ihigh - ilow);
}
total += c;
*p++ = (pixman_fixed_t)(c * 65536.0 + 0.5);
}
/* Normalize */
p -= *width;
total = 1 / total;
new_total = 0;
for (x = x1; x < x2; ++x)
{
pixman_fixed_t t = (*p) * total + 0.5;
new_total += t;
*p++ = t;
}
if (new_total != pixman_fixed_1)
*(p - *width / 2) += (pixman_fixed_1 - new_total);
}
return params;
}
/* Create the parameter list for a SEPARABLE_CONVOLUTION filter
* with the given kernels and scale parameters
*/
PIXMAN_EXPORT pixman_fixed_t *
pixman_filter_create_separable_convolution (int *n_values,
pixman_fixed_t scale_x,
pixman_fixed_t scale_y,
pixman_kernel_t reconstruct_x,
pixman_kernel_t reconstruct_y,
pixman_kernel_t sample_x,
pixman_kernel_t sample_y,
int subsample_bits_x,
int subsample_bits_y)
{
double sx = fabs (pixman_fixed_to_double (scale_x));
double sy = fabs (pixman_fixed_to_double (scale_y));
pixman_fixed_t *horz = NULL, *vert = NULL, *params = NULL;
int subsample_x, subsample_y;
int width, height;
subsample_x = (1 << subsample_bits_x);
subsample_y = (1 << subsample_bits_y);
horz = create_1d_filter (&width, reconstruct_x, sample_x, sx, subsample_x);
vert = create_1d_filter (&height, reconstruct_y, sample_y, sy, subsample_y);
if (!horz || !vert)
goto out;
*n_values = 4 + width * subsample_x + height * subsample_y;
params = malloc (*n_values * sizeof (pixman_fixed_t));
if (!params)
goto out;
params[0] = pixman_int_to_fixed (width);
params[1] = pixman_int_to_fixed (height);
params[2] = pixman_int_to_fixed (subsample_bits_x);
params[3] = pixman_int_to_fixed (subsample_bits_y);
memcpy (params + 4, horz,
width * subsample_x * sizeof (pixman_fixed_t));
memcpy (params + 4 + width * subsample_x, vert,
height * subsample_y * sizeof (pixman_fixed_t));
out:
free (horz);
free (vert);
return params;
}