1 /*
2 * Copyright 2012, Red Hat, Inc.
3 * Copyright 2012, Soren Sandmann
4 *
5 * Permission is hereby granted, free of charge, to any person obtaining a
6 * copy of this software and associated documentation files (the "Software"),
7 * to deal in the Software without restriction, including without limitation
8 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
9 * and/or sell copies of the Software, and to permit persons to whom the
10 * Software is furnished to do so, subject to the following conditions:
11 *
12 * The above copyright notice and this permission notice (including the next
13 * paragraph) shall be included in all copies or substantial portions of the
14 * Software.
15 *
16 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
17 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
18 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
19 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
20 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
21 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
22 * DEALINGS IN THE SOFTWARE.
23 *
24 * Author: Soren Sandmann <soren.sandmann@gmail.com>
25 */
26 #include <string.h>
27 #include <stdlib.h>
28 #include <stdio.h>
29 #include <math.h>
30 #include <assert.h>
31 #include <config.h>
32 #include "pixman-private.h"
33
34 typedef double (* kernel_func_t) (double x);
35
36 typedef struct
37 {
38 pixman_kernel_t kernel;
39 kernel_func_t func;
40 double width;
41 } filter_info_t;
42
43 static double
impulse_kernel(double x)44 impulse_kernel (double x)
45 {
46 return (x == 0.0)? 1.0 : 0.0;
47 }
48
49 static double
box_kernel(double x)50 box_kernel (double x)
51 {
52 return 1;
53 }
54
55 static double
linear_kernel(double x)56 linear_kernel (double x)
57 {
58 return 1 - fabs (x);
59 }
60
61 static double
gaussian_kernel(double x)62 gaussian_kernel (double x)
63 {
64 #define SQRT2 (1.4142135623730950488016887242096980785696718753769480)
65 #define SIGMA (SQRT2 / 2.0)
66
67 return exp (- x * x / (2 * SIGMA * SIGMA)) / (SIGMA * sqrt (2.0 * M_PI));
68 }
69
70 static double
sinc(double x)71 sinc (double x)
72 {
73 if (x == 0.0)
74 return 1.0;
75 else
76 return sin (M_PI * x) / (M_PI * x);
77 }
78
79 static double
lanczos(double x,int n)80 lanczos (double x, int n)
81 {
82 return sinc (x) * sinc (x * (1.0 / n));
83 }
84
85 static double
lanczos2_kernel(double x)86 lanczos2_kernel (double x)
87 {
88 return lanczos (x, 2);
89 }
90
91 static double
lanczos3_kernel(double x)92 lanczos3_kernel (double x)
93 {
94 return lanczos (x, 3);
95 }
96
97 static double
nice_kernel(double x)98 nice_kernel (double x)
99 {
100 return lanczos3_kernel (x * 0.75);
101 }
102
103 static double
general_cubic(double x,double B,double C)104 general_cubic (double x, double B, double C)
105 {
106 double ax = fabs(x);
107
108 if (ax < 1)
109 {
110 return ((12 - 9 * B - 6 * C) * ax * ax * ax +
111 (-18 + 12 * B + 6 * C) * ax * ax + (6 - 2 * B)) / 6;
112 }
113 else if (ax >= 1 && ax < 2)
114 {
115 return ((-B - 6 * C) * ax * ax * ax +
116 (6 * B + 30 * C) * ax * ax + (-12 * B - 48 * C) *
117 ax + (8 * B + 24 * C)) / 6;
118 }
119 else
120 {
121 return 0;
122 }
123 }
124
125 static double
cubic_kernel(double x)126 cubic_kernel (double x)
127 {
128 /* This is the Mitchell-Netravali filter.
129 *
130 * (0.0, 0.5) would give us the Catmull-Rom spline,
131 * but that one seems to be indistinguishable from Lanczos2.
132 */
133 return general_cubic (x, 1/3.0, 1/3.0);
134 }
135
136 static const filter_info_t filters[] =
137 {
138 { PIXMAN_KERNEL_IMPULSE, impulse_kernel, 0.0 },
139 { PIXMAN_KERNEL_BOX, box_kernel, 1.0 },
140 { PIXMAN_KERNEL_LINEAR, linear_kernel, 2.0 },
141 { PIXMAN_KERNEL_CUBIC, cubic_kernel, 4.0 },
142 { PIXMAN_KERNEL_GAUSSIAN, gaussian_kernel, 6 * SIGMA },
143 { PIXMAN_KERNEL_LANCZOS2, lanczos2_kernel, 4.0 },
144 { PIXMAN_KERNEL_LANCZOS3, lanczos3_kernel, 6.0 },
145 { PIXMAN_KERNEL_LANCZOS3_STRETCHED, nice_kernel, 8.0 },
146 };
147
148 /* This function scales @kernel2 by @scale, then
149 * aligns @x1 in @kernel1 with @x2 in @kernel2 and
150 * and integrates the product of the kernels across @width.
151 *
152 * This function assumes that the intervals are within
153 * the kernels in question. E.g., the caller must not
154 * try to integrate a linear kernel ouside of [-1:1]
155 */
156 static double
integral(pixman_kernel_t kernel1,double x1,pixman_kernel_t kernel2,double scale,double x2,double width)157 integral (pixman_kernel_t kernel1, double x1,
158 pixman_kernel_t kernel2, double scale, double x2,
159 double width)
160 {
161 /* If the integration interval crosses zero, break it into
162 * two separate integrals. This ensures that filters such
163 * as LINEAR that are not differentiable at 0 will still
164 * integrate properly.
165 */
166 if (x1 < 0 && x1 + width > 0)
167 {
168 return
169 integral (kernel1, x1, kernel2, scale, x2, - x1) +
170 integral (kernel1, 0, kernel2, scale, x2 - x1, width + x1);
171 }
172 else if (x2 < 0 && x2 + width > 0)
173 {
174 return
175 integral (kernel1, x1, kernel2, scale, x2, - x2) +
176 integral (kernel1, x1 - x2, kernel2, scale, 0, width + x2);
177 }
178 else if (kernel1 == PIXMAN_KERNEL_IMPULSE)
179 {
180 assert (width == 0.0);
181 return filters[kernel2].func (x2 * scale);
182 }
183 else if (kernel2 == PIXMAN_KERNEL_IMPULSE)
184 {
185 assert (width == 0.0);
186 return filters[kernel1].func (x1);
187 }
188 else
189 {
190 /* Integration via Simpson's rule */
191 #define N_SEGMENTS 128
192 #define SAMPLE(a1, a2) \
193 (filters[kernel1].func ((a1)) * filters[kernel2].func ((a2) * scale))
194
195 double s = 0.0;
196 double h = width / (double)N_SEGMENTS;
197 int i;
198
199 s = SAMPLE (x1, x2);
200
201 for (i = 1; i < N_SEGMENTS; i += 2)
202 {
203 double a1 = x1 + h * i;
204 double a2 = x2 + h * i;
205
206 s += 2 * SAMPLE (a1, a2);
207
208 if (i >= 2 && i < N_SEGMENTS - 1)
209 s += 4 * SAMPLE (a1, a2);
210 }
211
212 s += SAMPLE (x1 + width, x2 + width);
213
214 return h * s * (1.0 / 3.0);
215 }
216 }
217
218 static pixman_fixed_t *
create_1d_filter(int * width,pixman_kernel_t reconstruct,pixman_kernel_t sample,double scale,int n_phases)219 create_1d_filter (int *width,
220 pixman_kernel_t reconstruct,
221 pixman_kernel_t sample,
222 double scale,
223 int n_phases)
224 {
225 pixman_fixed_t *params, *p;
226 double step;
227 double size;
228 int i;
229
230 size = scale * filters[sample].width + filters[reconstruct].width;
231 *width = ceil (size);
232
233 p = params = malloc (*width * n_phases * sizeof (pixman_fixed_t));
234 if (!params)
235 return NULL;
236
237 step = 1.0 / n_phases;
238
239 for (i = 0; i < n_phases; ++i)
240 {
241 double frac = step / 2.0 + i * step;
242 pixman_fixed_t new_total;
243 int x, x1, x2;
244 double total;
245
246 /* Sample convolution of reconstruction and sampling
247 * filter. See rounding.txt regarding the rounding
248 * and sample positions.
249 */
250
251 x1 = ceil (frac - *width / 2.0 - 0.5);
252 x2 = x1 + *width;
253
254 total = 0;
255 for (x = x1; x < x2; ++x)
256 {
257 double pos = x + 0.5 - frac;
258 double rlow = - filters[reconstruct].width / 2.0;
259 double rhigh = rlow + filters[reconstruct].width;
260 double slow = pos - scale * filters[sample].width / 2.0;
261 double shigh = slow + scale * filters[sample].width;
262 double c = 0.0;
263 double ilow, ihigh;
264
265 if (rhigh >= slow && rlow <= shigh)
266 {
267 ilow = MAX (slow, rlow);
268 ihigh = MIN (shigh, rhigh);
269
270 c = integral (reconstruct, ilow,
271 sample, 1.0 / scale, ilow - pos,
272 ihigh - ilow);
273 }
274
275 total += c;
276 *p++ = (pixman_fixed_t)(c * 65535.0 + 0.5);
277 }
278
279 /* Normalize */
280 p -= *width;
281 total = 1 / total;
282 new_total = 0;
283 for (x = x1; x < x2; ++x)
284 {
285 pixman_fixed_t t = (*p) * total + 0.5;
286
287 new_total += t;
288 *p++ = t;
289 }
290
291 if (new_total != pixman_fixed_1)
292 *(p - *width / 2) += (pixman_fixed_1 - new_total);
293 }
294
295 return params;
296 }
297
298 /* Create the parameter list for a SEPARABLE_CONVOLUTION filter
299 * with the given kernels and scale parameters
300 */
301 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)302 pixman_filter_create_separable_convolution (int *n_values,
303 pixman_fixed_t scale_x,
304 pixman_fixed_t scale_y,
305 pixman_kernel_t reconstruct_x,
306 pixman_kernel_t reconstruct_y,
307 pixman_kernel_t sample_x,
308 pixman_kernel_t sample_y,
309 int subsample_bits_x,
310 int subsample_bits_y)
311 {
312 double sx = fabs (pixman_fixed_to_double (scale_x));
313 double sy = fabs (pixman_fixed_to_double (scale_y));
314 pixman_fixed_t *horz = NULL, *vert = NULL, *params = NULL;
315 int subsample_x, subsample_y;
316 int width, height;
317
318 subsample_x = (1 << subsample_bits_x);
319 subsample_y = (1 << subsample_bits_y);
320
321 horz = create_1d_filter (&width, reconstruct_x, sample_x, sx, subsample_x);
322 vert = create_1d_filter (&height, reconstruct_y, sample_y, sy, subsample_y);
323
324 if (!horz || !vert)
325 goto out;
326
327 *n_values = 4 + width * subsample_x + height * subsample_y;
328
329 params = malloc (*n_values * sizeof (pixman_fixed_t));
330 if (!params)
331 goto out;
332
333 params[0] = pixman_int_to_fixed (width);
334 params[1] = pixman_int_to_fixed (height);
335 params[2] = pixman_int_to_fixed (subsample_bits_x);
336 params[3] = pixman_int_to_fixed (subsample_bits_y);
337
338 memcpy (params + 4, horz,
339 width * subsample_x * sizeof (pixman_fixed_t));
340 memcpy (params + 4 + width * subsample_x, vert,
341 height * subsample_y * sizeof (pixman_fixed_t));
342
343 out:
344 free (horz);
345 free (vert);
346
347 return params;
348 }
349