/* * 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 */ #include #include #include #include #include #ifdef HAVE_CONFIG_H #include #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 + (-18 + 12 * B + 6 * C)) * ax * ax + (6 - 2 * B)) / 6; } else if (ax < 2) { return ((((-B - 6 * C) * ax + (6 * B + 30 * C)) * 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, 5.0 }, { 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 (kernel1 == PIXMAN_KERNEL_BOX && kernel2 == PIXMAN_KERNEL_BOX) { return width; } /* The LINEAR filter is not differentiable at 0, so if the * integration interval crosses zero, break it into two * separate integrals. */ else if (kernel1 == PIXMAN_KERNEL_LINEAR && x1 < 0 && x1 + width > 0) { return integral (kernel1, x1, kernel2, scale, x2, - x1) + integral (kernel1, 0, kernel2, scale, x2 - x1, width + x1); } else if (kernel2 == PIXMAN_KERNEL_LINEAR && 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 * See http://www.intmath.com/integration/6-simpsons-rule.php * 12 segments (6 cubic approximations) seems to produce best * result for lanczos3.linear, which was the combination that * showed the most errors. This makes sense as the lanczos3 * filter is 6 wide. */ #define N_SEGMENTS 12 #define SAMPLE(a1, a2) \ (filters[kernel1].func ((a1)) * filters[kernel2].func ((a2) * scale)) double s = 0.0; double h = width / 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 += 4 * SAMPLE (a1, a2); } for (i = 2; i < N_SEGMENTS; i += 2) { double a1 = x1 + h * i; double a2 = x2 + h * i; s += 2 * SAMPLE (a1, a2); } s += SAMPLE (x1 + width, x2 + width); return h * s * (1.0 / 3.0); } } static void create_1d_filter (int width, pixman_kernel_t reconstruct, pixman_kernel_t sample, double scale, int n_phases, pixman_fixed_t *p) { double step; int i; 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, e; /* 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); } *p = (pixman_fixed_t)floor (c * 65536.0 + 0.5); total += *p; p++; } /* Normalize, with error diffusion */ p -= width; total = 65536.0 / total; new_total = 0; e = 0.0; for (x = x1; x < x2; ++x) { double v = (*p) * total + e; pixman_fixed_t t = floor (v + 0.5); e = v - t; new_total += t; *p++ = t; } /* pixman_fixed_e's worth of error may remain; put it * at the first sample, since that is the only one that * hasn't had any error diffused into it. */ *(p - width) += pixman_fixed_1 - new_total; } } static int filter_width (pixman_kernel_t reconstruct, pixman_kernel_t sample, double size) { return ceil (filters[reconstruct].width + size * filters[sample].width); } #ifdef PIXMAN_GNUPLOT /* If enable-gnuplot is configured, then you can pipe the output of a * pixman-using program to gnuplot and get a continuously-updated plot * of the horizontal filter. This works well with demos/scale to test * the filter generation. * * The plot is all the different subposition filters shuffled * together. This is misleading in a few cases: * * IMPULSE.BOX - goes up and down as the subfilters have different * numbers of non-zero samples * IMPULSE.TRIANGLE - somewhat crooked for the same reason * 1-wide filters - looks triangular, but a 1-wide box would be more * accurate */ static void gnuplot_filter (int width, int n_phases, const pixman_fixed_t* p) { double step; int i, j; int first; step = 1.0 / n_phases; printf ("set style line 1 lc rgb '#0060ad' lt 1 lw 0.5 pt 7 pi 1 ps 0.5\n"); printf ("plot [x=%g:%g] '-' with linespoints ls 1\n", -width*0.5, width*0.5); /* Print a point at the origin so that y==0 line is included: */ printf ("0 0\n\n"); /* The position of the first sample of the phase corresponding to * frac is given by: * * ceil (frac - width / 2.0 - 0.5) + 0.5 - frac * * We have to find the frac that minimizes this expression. * * For odd widths, we have * * ceil (frac - width / 2.0 - 0.5) + 0.5 - frac * = ceil (frac) + K - frac * = 1 + K - frac * * for some K, so this is minimized when frac is maximized and * strictly growing with frac. So for odd widths, we can simply * start at the last phase and go backwards. * * For even widths, we have * * ceil (frac - width / 2.0 - 0.5) + 0.5 - frac * = ceil (frac - 0.5) + K - frac * * The graph for this function (ignoring K) looks like this: * * 0.5 * | |\ * | | \ * | | \ * 0 | | \ * |\ | * | \ | * | \ | * -0.5 | \| * --------------------------------- * 0 0.5 1 * * So in this case we need to start with the phase whose frac is * less than, but as close as possible to 0.5, then go backwards * until we hit the first phase, then wrap around to the last * phase and continue backwards. * * Which phase is as close as possible 0.5? The locations of the * sampling point corresponding to the kth phase is given by * 1/(2 * n_phases) + k / n_phases: * * 1/(2 * n_phases) + k / n_phases = 0.5 * * from which it follows that * * k = (n_phases - 1) / 2 * * rounded down is the phase in question. */ if (width & 1) first = n_phases - 1; else first = (n_phases - 1) / 2; for (j = 0; j < width; ++j) { for (i = 0; i < n_phases; ++i) { int phase = first - i; double frac, pos; if (phase < 0) phase = n_phases + phase; frac = step / 2.0 + phase * step; pos = ceil (frac - width / 2.0 - 0.5) + 0.5 - frac + j; printf ("%g %g\n", pos, pixman_fixed_to_double (*(p + phase * width + j))); } } printf ("e\n"); fflush (stdout); } #endif /* 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 *params; int subsample_x, subsample_y; int width, height; width = filter_width (reconstruct_x, sample_x, sx); subsample_x = (1 << subsample_bits_x); height = filter_width (reconstruct_y, sample_y, sy); subsample_y = (1 << subsample_bits_y); *n_values = 4 + width * subsample_x + height * subsample_y; params = malloc (*n_values * sizeof (pixman_fixed_t)); if (!params) return NULL; 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); create_1d_filter (width, reconstruct_x, sample_x, sx, subsample_x, params + 4); create_1d_filter (height, reconstruct_y, sample_y, sy, subsample_y, params + 4 + width * subsample_x); #ifdef PIXMAN_GNUPLOT gnuplot_filter(width, subsample_x, params + 4); #endif return params; }