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// basisu_resampler_filters.cpp
// Copyright (C) 2019-2020 Binomial LLC. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "basisu_resampler_filters.h"
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
namespace basisu
{
#define BOX_FILTER_SUPPORT (0.5f)
static float box_filter(float t) /* pulse/Fourier window */
{
// make_clist() calls the filter function with t inverted (pos = left, neg = right)
if ((t >= -0.5f) && (t < 0.5f))
return 1.0f;
else
return 0.0f;
}
#define TENT_FILTER_SUPPORT (1.0f)
static float tent_filter(float t) /* box (*) box, bilinear/triangle */
{
if (t < 0.0f)
t = -t;
if (t < 1.0f)
return 1.0f - t;
else
return 0.0f;
}
#define BELL_SUPPORT (1.5f)
static float bell_filter(float t) /* box (*) box (*) box */
{
if (t < 0.0f)
t = -t;
if (t < .5f)
return (.75f - (t * t));
if (t < 1.5f)
{
t = (t - 1.5f);
return (.5f * (t * t));
}
return (0.0f);
}
#define B_SPLINE_SUPPORT (2.0f)
static float B_spline_filter(float t) /* box (*) box (*) box (*) box */
{
float tt;
if (t < 0.0f)
t = -t;
if (t < 1.0f)
{
tt = t * t;
return ((.5f * tt * t) - tt + (2.0f / 3.0f));
}
else if (t < 2.0f)
{
t = 2.0f - t;
return ((1.0f / 6.0f) * (t * t * t));
}
return (0.0f);
}
// Dodgson, N., "Quadratic Interpolation for Image Resampling"
#define QUADRATIC_SUPPORT 1.5f
static float quadratic(float t, const float R)
{
if (t < 0.0f)
t = -t;
if (t < QUADRATIC_SUPPORT)
{
float tt = t * t;
if (t <= .5f)
return (-2.0f * R) * tt + .5f * (R + 1.0f);
else
return (R * tt) + (-2.0f * R - .5f) * t + (3.0f / 4.0f) * (R + 1.0f);
}
else
return 0.0f;
}
static float quadratic_interp_filter(float t)
{
return quadratic(t, 1.0f);
}
static float quadratic_approx_filter(float t)
{
return quadratic(t, .5f);
}
static float quadratic_mix_filter(float t)
{
return quadratic(t, .8f);
}
// Mitchell, D. and A. Netravali, "Reconstruction Filters in Computer Graphics."
// Computer Graphics, Vol. 22, No. 4, pp. 221-228.
// (B, C)
// (1/3, 1/3) - Defaults recommended by Mitchell and Netravali
// (1, 0) - Equivalent to the Cubic B-Spline
// (0, 0.5) - Equivalent to the Catmull-Rom Spline
// (0, C) - The family of Cardinal Cubic Splines
// (B, 0) - Duff's tensioned B-Splines.
static float mitchell(float t, const float B, const float C)
{
float tt;
tt = t * t;
if (t < 0.0f)
t = -t;
if (t < 1.0f)
{
t = (((12.0f - 9.0f * B - 6.0f * C) * (t * tt)) + ((-18.0f + 12.0f * B + 6.0f * C) * tt) + (6.0f - 2.0f * B));
return (t / 6.0f);
}
else if (t < 2.0f)
{
t = (((-1.0f * B - 6.0f * C) * (t * tt)) + ((6.0f * B + 30.0f * C) * tt) + ((-12.0f * B - 48.0f * C) * t) + (8.0f * B + 24.0f * C));
return (t / 6.0f);
}
return (0.0f);
}
#define MITCHELL_SUPPORT (2.0f)
static float mitchell_filter(float t)
{
return mitchell(t, 1.0f / 3.0f, 1.0f / 3.0f);
}
#define CATMULL_ROM_SUPPORT (2.0f)
static float catmull_rom_filter(float t)
{
return mitchell(t, 0.0f, .5f);
}
static double sinc(double x)
{
x = (x * M_PI);
if ((x < 0.01f) && (x > -0.01f))
return 1.0f + x * x * (-1.0f / 6.0f + x * x * 1.0f / 120.0f);
return sin(x) / x;
}
static float clean(double t)
{
const float EPSILON = .0000125f;
if (fabs(t) < EPSILON)
return 0.0f;
return (float)t;
}
//static double blackman_window(double x)
//{
// return .42f + .50f * cos(M_PI*x) + .08f * cos(2.0f*M_PI*x);
//}
static double blackman_exact_window(double x)
{
return 0.42659071f + 0.49656062f * cos(M_PI * x) + 0.07684867f * cos(2.0f * M_PI * x);
}
#define BLACKMAN_SUPPORT (3.0f)
static float blackman_filter(float t)
{
if (t < 0.0f)
t = -t;
if (t < 3.0f)
//return clean(sinc(t) * blackman_window(t / 3.0f));
return clean(sinc(t) * blackman_exact_window(t / 3.0f));
else
return (0.0f);
}
#define GAUSSIAN_SUPPORT (1.25f)
static float gaussian_filter(float t) // with blackman window
{
if (t < 0)
t = -t;
if (t < GAUSSIAN_SUPPORT)
return clean(exp(-2.0f * t * t) * sqrt(2.0f / M_PI) * blackman_exact_window(t / GAUSSIAN_SUPPORT));
else
return 0.0f;
}
// Windowed sinc -- see "Jimm Blinn's Corner: Dirty Pixels" pg. 26.
#define LANCZOS3_SUPPORT (3.0f)
static float lanczos3_filter(float t)
{
if (t < 0.0f)
t = -t;
if (t < 3.0f)
return clean(sinc(t) * sinc(t / 3.0f));
else
return (0.0f);
}
#define LANCZOS4_SUPPORT (4.0f)
static float lanczos4_filter(float t)
{
if (t < 0.0f)
t = -t;
if (t < 4.0f)
return clean(sinc(t) * sinc(t / 4.0f));
else
return (0.0f);
}
#define LANCZOS6_SUPPORT (6.0f)
static float lanczos6_filter(float t)
{
if (t < 0.0f)
t = -t;
if (t < 6.0f)
return clean(sinc(t) * sinc(t / 6.0f));
else
return (0.0f);
}
#define LANCZOS12_SUPPORT (12.0f)
static float lanczos12_filter(float t)
{
if (t < 0.0f)
t = -t;
if (t < 12.0f)
return clean(sinc(t) * sinc(t / 12.0f));
else
return (0.0f);
}
static double bessel0(double x)
{
const double EPSILON_RATIO = 1E-16;
double xh, sum, pow, ds;
int k;
xh = 0.5 * x;
sum = 1.0;
pow = 1.0;
k = 0;
ds = 1.0;
while (ds > sum * EPSILON_RATIO) // FIXME: Shouldn't this stop after X iterations for max. safety?
{
++k;
pow = pow * (xh / k);
ds = pow * pow;
sum = sum + ds;
}
return sum;
}
//static const float KAISER_ALPHA = 4.0;
static double kaiser(double alpha, double half_width, double x)
{
const double ratio = (x / half_width);
return bessel0(alpha * sqrt(1 - ratio * ratio)) / bessel0(alpha);
}
#define KAISER_SUPPORT 3
static float kaiser_filter(float t)
{
if (t < 0.0f)
t = -t;
if (t < KAISER_SUPPORT)
{
// db atten
const float att = 40.0f;
const float alpha = (float)(exp(log((double)0.58417 * (att - 20.96)) * 0.4) + 0.07886 * (att - 20.96));
//const float alpha = KAISER_ALPHA;
return (float)clean(sinc(t) * kaiser(alpha, KAISER_SUPPORT, t));
}
return 0.0f;
}
const resample_filter g_resample_filters[] =
{
{ "box", box_filter, BOX_FILTER_SUPPORT },
{ "tent", tent_filter, TENT_FILTER_SUPPORT },
{ "bell", bell_filter, BELL_SUPPORT },
{ "b-spline", B_spline_filter, B_SPLINE_SUPPORT },
{ "mitchell", mitchell_filter, MITCHELL_SUPPORT },
{ "blackman", blackman_filter, BLACKMAN_SUPPORT },
{ "lanczos3", lanczos3_filter, LANCZOS3_SUPPORT },
{ "lanczos4", lanczos4_filter, LANCZOS4_SUPPORT },
{ "lanczos6", lanczos6_filter, LANCZOS6_SUPPORT },
{ "lanczos12", lanczos12_filter, LANCZOS12_SUPPORT },
{ "kaiser", kaiser_filter, KAISER_SUPPORT },
{ "gaussian", gaussian_filter, GAUSSIAN_SUPPORT },
{ "catmullrom", catmull_rom_filter, CATMULL_ROM_SUPPORT },
{ "quadratic_interp", quadratic_interp_filter, QUADRATIC_SUPPORT },
{ "quadratic_approx", quadratic_approx_filter, QUADRATIC_SUPPORT },
{ "quadratic_mix", quadratic_mix_filter, QUADRATIC_SUPPORT },
};
const int g_num_resample_filters = BASISU_ARRAY_SIZE(g_resample_filters);
int find_resample_filter(const char *pName)
{
for (int i = 0; i < g_num_resample_filters; i++)
if (strcmp(pName, g_resample_filters[i].name) == 0)
return i;
return -1;
}
} // namespace basisu