341 lines
7.6 KiB
C++
341 lines
7.6 KiB
C++
// basisu_resampler_filters.cpp
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// Copyright (C) 2019-2021 Binomial LLC. All Rights Reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "basisu_resampler_filters.h"
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#ifndef M_PI
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#define M_PI 3.14159265358979323846
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#endif
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namespace basisu
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{
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#define BOX_FILTER_SUPPORT (0.5f)
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static float box_filter(float t) /* pulse/Fourier window */
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{
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// make_clist() calls the filter function with t inverted (pos = left, neg = right)
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if ((t >= -0.5f) && (t < 0.5f))
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return 1.0f;
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else
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return 0.0f;
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}
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#define TENT_FILTER_SUPPORT (1.0f)
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static float tent_filter(float t) /* box (*) box, bilinear/triangle */
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{
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if (t < 0.0f)
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t = -t;
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if (t < 1.0f)
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return 1.0f - t;
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else
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return 0.0f;
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}
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#define BELL_SUPPORT (1.5f)
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static float bell_filter(float t) /* box (*) box (*) box */
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{
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if (t < 0.0f)
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t = -t;
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if (t < .5f)
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return (.75f - (t * t));
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if (t < 1.5f)
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{
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t = (t - 1.5f);
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return (.5f * (t * t));
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}
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return (0.0f);
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}
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#define B_SPLINE_SUPPORT (2.0f)
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static float B_spline_filter(float t) /* box (*) box (*) box (*) box */
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{
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float tt;
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if (t < 0.0f)
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t = -t;
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if (t < 1.0f)
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{
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tt = t * t;
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return ((.5f * tt * t) - tt + (2.0f / 3.0f));
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}
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else if (t < 2.0f)
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{
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t = 2.0f - t;
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return ((1.0f / 6.0f) * (t * t * t));
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}
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return (0.0f);
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}
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// Dodgson, N., "Quadratic Interpolation for Image Resampling"
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#define QUADRATIC_SUPPORT 1.5f
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static float quadratic(float t, const float R)
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{
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if (t < 0.0f)
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t = -t;
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if (t < QUADRATIC_SUPPORT)
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{
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float tt = t * t;
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if (t <= .5f)
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return (-2.0f * R) * tt + .5f * (R + 1.0f);
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else
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return (R * tt) + (-2.0f * R - .5f) * t + (3.0f / 4.0f) * (R + 1.0f);
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}
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else
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return 0.0f;
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}
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static float quadratic_interp_filter(float t)
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{
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return quadratic(t, 1.0f);
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}
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static float quadratic_approx_filter(float t)
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{
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return quadratic(t, .5f);
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}
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static float quadratic_mix_filter(float t)
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{
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return quadratic(t, .8f);
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}
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// Mitchell, D. and A. Netravali, "Reconstruction Filters in Computer Graphics."
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// Computer Graphics, Vol. 22, No. 4, pp. 221-228.
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// (B, C)
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// (1/3, 1/3) - Defaults recommended by Mitchell and Netravali
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// (1, 0) - Equivalent to the Cubic B-Spline
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// (0, 0.5) - Equivalent to the Catmull-Rom Spline
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// (0, C) - The family of Cardinal Cubic Splines
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// (B, 0) - Duff's tensioned B-Splines.
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static float mitchell(float t, const float B, const float C)
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{
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float tt;
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tt = t * t;
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if (t < 0.0f)
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t = -t;
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if (t < 1.0f)
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{
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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));
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return (t / 6.0f);
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}
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else if (t < 2.0f)
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{
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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));
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return (t / 6.0f);
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}
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return (0.0f);
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}
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#define MITCHELL_SUPPORT (2.0f)
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static float mitchell_filter(float t)
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{
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return mitchell(t, 1.0f / 3.0f, 1.0f / 3.0f);
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}
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#define CATMULL_ROM_SUPPORT (2.0f)
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static float catmull_rom_filter(float t)
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{
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return mitchell(t, 0.0f, .5f);
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}
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static double sinc(double x)
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{
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x = (x * M_PI);
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if ((x < 0.01f) && (x > -0.01f))
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return 1.0f + x * x * (-1.0f / 6.0f + x * x * 1.0f / 120.0f);
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return sin(x) / x;
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}
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static float clean(double t)
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{
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const float EPSILON = .0000125f;
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if (fabs(t) < EPSILON)
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return 0.0f;
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return (float)t;
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}
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//static double blackman_window(double x)
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//{
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// return .42f + .50f * cos(M_PI*x) + .08f * cos(2.0f*M_PI*x);
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//}
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static double blackman_exact_window(double x)
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{
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return 0.42659071f + 0.49656062f * cos(M_PI * x) + 0.07684867f * cos(2.0f * M_PI * x);
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}
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#define BLACKMAN_SUPPORT (3.0f)
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static float blackman_filter(float t)
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{
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if (t < 0.0f)
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t = -t;
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if (t < 3.0f)
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//return clean(sinc(t) * blackman_window(t / 3.0f));
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return clean(sinc(t) * blackman_exact_window(t / 3.0f));
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else
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return (0.0f);
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}
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#define GAUSSIAN_SUPPORT (1.25f)
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static float gaussian_filter(float t) // with blackman window
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{
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if (t < 0)
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t = -t;
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if (t < GAUSSIAN_SUPPORT)
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return clean(exp(-2.0f * t * t) * sqrt(2.0f / M_PI) * blackman_exact_window(t / GAUSSIAN_SUPPORT));
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else
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return 0.0f;
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}
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// Windowed sinc -- see "Jimm Blinn's Corner: Dirty Pixels" pg. 26.
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#define LANCZOS3_SUPPORT (3.0f)
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static float lanczos3_filter(float t)
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{
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if (t < 0.0f)
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t = -t;
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if (t < 3.0f)
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return clean(sinc(t) * sinc(t / 3.0f));
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else
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return (0.0f);
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}
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#define LANCZOS4_SUPPORT (4.0f)
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static float lanczos4_filter(float t)
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{
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if (t < 0.0f)
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t = -t;
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if (t < 4.0f)
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return clean(sinc(t) * sinc(t / 4.0f));
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else
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return (0.0f);
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}
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#define LANCZOS6_SUPPORT (6.0f)
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static float lanczos6_filter(float t)
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{
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if (t < 0.0f)
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t = -t;
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if (t < 6.0f)
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return clean(sinc(t) * sinc(t / 6.0f));
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else
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return (0.0f);
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}
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#define LANCZOS12_SUPPORT (12.0f)
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static float lanczos12_filter(float t)
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{
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if (t < 0.0f)
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t = -t;
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if (t < 12.0f)
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return clean(sinc(t) * sinc(t / 12.0f));
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else
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return (0.0f);
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}
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static double bessel0(double x)
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{
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const double EPSILON_RATIO = 1E-16;
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double xh, sum, pow, ds;
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int k;
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xh = 0.5 * x;
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sum = 1.0;
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pow = 1.0;
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k = 0;
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ds = 1.0;
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while (ds > sum * EPSILON_RATIO) // FIXME: Shouldn't this stop after X iterations for max. safety?
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{
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++k;
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pow = pow * (xh / k);
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ds = pow * pow;
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sum = sum + ds;
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}
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return sum;
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}
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//static const float KAISER_ALPHA = 4.0;
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static double kaiser(double alpha, double half_width, double x)
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{
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const double ratio = (x / half_width);
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return bessel0(alpha * sqrt(1 - ratio * ratio)) / bessel0(alpha);
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}
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#define KAISER_SUPPORT 3
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static float kaiser_filter(float t)
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{
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if (t < 0.0f)
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t = -t;
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if (t < KAISER_SUPPORT)
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{
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// db atten
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const float att = 40.0f;
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const float alpha = (float)(exp(log((double)0.58417 * (att - 20.96)) * 0.4) + 0.07886 * (att - 20.96));
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//const float alpha = KAISER_ALPHA;
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return (float)clean(sinc(t) * kaiser(alpha, KAISER_SUPPORT, t));
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}
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return 0.0f;
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}
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const resample_filter g_resample_filters[] =
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{
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{ "box", box_filter, BOX_FILTER_SUPPORT },
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{ "tent", tent_filter, TENT_FILTER_SUPPORT },
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{ "bell", bell_filter, BELL_SUPPORT },
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{ "b-spline", B_spline_filter, B_SPLINE_SUPPORT },
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{ "mitchell", mitchell_filter, MITCHELL_SUPPORT },
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{ "blackman", blackman_filter, BLACKMAN_SUPPORT },
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{ "lanczos3", lanczos3_filter, LANCZOS3_SUPPORT },
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{ "lanczos4", lanczos4_filter, LANCZOS4_SUPPORT },
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{ "lanczos6", lanczos6_filter, LANCZOS6_SUPPORT },
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{ "lanczos12", lanczos12_filter, LANCZOS12_SUPPORT },
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{ "kaiser", kaiser_filter, KAISER_SUPPORT },
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{ "gaussian", gaussian_filter, GAUSSIAN_SUPPORT },
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{ "catmullrom", catmull_rom_filter, CATMULL_ROM_SUPPORT },
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{ "quadratic_interp", quadratic_interp_filter, QUADRATIC_SUPPORT },
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{ "quadratic_approx", quadratic_approx_filter, QUADRATIC_SUPPORT },
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{ "quadratic_mix", quadratic_mix_filter, QUADRATIC_SUPPORT },
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};
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const int g_num_resample_filters = BASISU_ARRAY_SIZE(g_resample_filters);
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int find_resample_filter(const char *pName)
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{
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for (int i = 0; i < g_num_resample_filters; i++)
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if (strcmp(pName, g_resample_filters[i].name) == 0)
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return i;
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return -1;
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}
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} // namespace basisu
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