[cairo] [PATCH pixman 2/3] New pixman_filter_create_separable_convolution
Bill Spitzak
spitzak at gmail.com
Mon Aug 18 19:51:08 PDT 2014
Uses filter evaluators that know the size of a pixel, and thus can integrate
with reconstruction filters directly. The result is equivalent to having the
box and impulse sampling filters use a box reconstruction, and all others use
box for sizes smaller than their Nyquist rate and impulse for larger sizes.
For back-compatibility the "reconstruction" filter argument is used at a size
of 1 if it is not box or impulse and the filter size is less than 1.
IMHO this preserves all the useful results of the previous code, is a good
deal simpler, and the caller no longer has to alter the arguments depending on
whether the size is less than one or not.
---
pixman/pixman-filter.c | 392 ++++++++++++++++++++++++------------------------
1 file changed, 194 insertions(+), 198 deletions(-)
diff --git a/pixman/pixman-filter.c b/pixman/pixman-filter.c
index b2bf53f..1087f6d 100644
--- a/pixman/pixman-filter.c
+++ b/pixman/pixman-filter.c
@@ -33,42 +33,83 @@
#endif
#include "pixman-private.h"
-typedef double (* kernel_func_t) (double x);
+/* Produce contribution of a filter of size r for pixel centered on x.
+ * For a typical low-pass function this evaluates the function at x/r.
+ * If the frequency is higher than 1/2, such as when r is less than 1,
+ * this may need to integrate several samples, see cubic for examples.
+ */
+typedef double (* kernel_func_t) (double x, double r);
typedef struct
{
pixman_kernel_t kernel;
kernel_func_t func;
- double width;
+ double width; /* note special handling if <= 1 */
} filter_info_t;
+/* PIXMAN_KERNEL_IMPULSE: Returns pixel nearest the center. This
+ * matches PIXMAN_FILTER_NEAREST. This is useful if you wish to
+ * combine the result of nearest in one direction with another filter
+ * in the other.
+ */
static double
-impulse_kernel (double x)
+impulse_kernel (double x, double r)
{
- return (x == 0.0)? 1.0 : 0.0;
+ return 1;
}
+/* PIXMAN_KERNEL_BOX: Intersection of a box of width r with square
+ * pixels. This is the smallest possible filter such that the output
+ * image contains an equal contribution from all the input
+ * pixels. Lots of software uses this. The function is a trapazoid of
+ * width r+1, not a box.
+ *
+ * When r == 1.0, PIXMAN_KERNEL_BOX and PIXMAN_KERNEL_LINEAR produce
+ * the same filter, allowing them to be exchanged at this point.
+ */
static double
-box_kernel (double x)
+box_kernel (double x, double r)
{
- return 1;
+ return MAX (0.0, MIN (MIN (r, 1.0),
+ MIN ((r + 1) / 2 - x, (r + 1) / 2 + x)));
}
+/* PIXMAN_KERNEL_LINEAR: Triangle of width 2r. Lots of software uses
+ * this as a "better" filter, twice the size of a box but smaller than
+ * a cubic.
+ *
+ * When r == 1.0, PIXMAN_KERNEL_BOX and PIXMAN_KERNEL_LINEAR produce
+ * the same filter, allowing them to be exchanged at this point.
+ */
static double
-linear_kernel (double x)
+linear_kernel (double x, double r)
{
- return 1 - fabs (x);
+ if (r < 1.0)
+ return box_kernel(x, r);
+ else
+ return MAX (1.0 - fabs(x / r), 0.0);
}
+/* PIXMAN_KERNEL_GAUSSIAN: Gaussian function, cut off somewhere near
+ +/-2.5. Output looks like it has been blurred by a gaussian filter
+ of size 1. This may be useful if the output is to be blurred
+ further as that blur can be reduced by 1.
+*/
static double
-gaussian_kernel (double x)
+gaussian_kernel (double x, double r)
{
-#define SQRT2 (1.4142135623730950488016887242096980785696718753769480)
-#define SIGMA (SQRT2 / 2.0)
-
- return exp (- x * x / (2 * SIGMA * SIGMA)) / (SIGMA * sqrt (2.0 * M_PI));
+ if (r < 0.5)
+ return
+ gaussian_kernel (x * 2 - .5, r * 2) +
+ gaussian_kernel (x * 2 + .5, r * 2);
+ return exp (- x * x) / sqrt (M_PI);
}
+/* PIXMAN_KERNEL_LANCZOS2: lanczos windowed sinc function from -2 to
+ * +2. This is very close to the cubic filter that is often used
+ * by other software. Should be slightly higher quality.
+ */
+
static double
sinc (double x)
{
@@ -79,60 +120,91 @@ sinc (double x)
}
static double
-lanczos (double x, int n)
+lanczos (double x, double r, double n)
{
- return sinc (x) * sinc (x * (1.0 / n));
+ if (r < 1.0)
+ return
+ lanczos (x * 2 - .5, r * 2, n) +
+ lanczos (x * 2 + .5, r * 2, n);
+ x /= r;
+ return fabs (x) < n ? sinc (x) * sinc (x * (1.0 / n)) : 0.0;
}
static double
-lanczos2_kernel (double x)
+lanczos2_kernel (double x, double r)
{
- return lanczos (x, 2);
+ return lanczos (x, r, 2.0);
}
+/* PIXMAN_KERNEL_LANCZOS3: lanczos windowed sinc function from -3 to
+ * +3. Very popular with high-end software though I think any
+ * advantage over cubics is hidden by quantization and programming
+ * mistakes. You will see LANCZOS5 or even 7 sometimes.
+ */
static double
-lanczos3_kernel (double x)
+lanczos3_kernel (double x, double r)
{
- return lanczos (x, 3);
+ return lanczos (x, r, 3.0);
}
+/* PIXMAN_KERNEL_LANCZOS3_STRETCHED - The LANCZOS3 kernel widened by
+ * 4/3. Recommended by Jim Blinn
+ * http://graphics.cs.cmu.edu/nsp/course/15-462/Fall07/462/papers/jaggy.pdf
+ */
static double
-nice_kernel (double x)
+nice_kernel (double x, double r)
{
- return lanczos3_kernel (x * 0.75);
+ return lanczos3_kernel (x, r * (4.0/3));
}
+/* Cubic functions described in the Mitchell-Netravali paper.
+ * http://mentallandscape.com/Papers_siggraph88.pdf. This describes
+ * all possible cubic functions that can be used for sampling.
+ */
static double
-general_cubic (double x, double B, double C)
+general_cubic (double x, double r, double B, double C)
{
- double ax = fabs(x);
+ double ax;
+ if (r < 1.0)
+ return
+ general_cubic(x * 2 - .5, r * 2, B, C) +
+ general_cubic(x * 2 + .5, r * 2, B, C);
+
+ ax = fabs (x / r);
if (ax < 1)
{
- return ((12 - 9 * B - 6 * C) * ax * ax * ax +
- (-18 + 12 * B + 6 * C) * ax * ax + (6 - 2 * B)) / 6;
+ return (((12 - 9 * B - 6 * C) * ax +
+ (-18 + 12 * B + 6 * C)) * ax * ax +
+ (6 - 2 * B)) / 6;
}
- else if (ax >= 1 && ax < 2)
+ else if (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;
+ return ((((-B - 6 * C) * ax +
+ (6 * B + 30 * C)) * ax +
+ (-12 * B - 48 * C)) * ax +
+ (8 * B + 24 * C)) / 6;
}
else
{
- return 0;
+ return 0.0;
}
}
+/* PIXMAN_KERNEL_CUBIC: Cubic recommended by the Mitchell-Netravali
+ * paper. This has negative values and because the values at +/-1 are
+ * not zero it does not interpolate the pixels, meaning it will change
+ * an image even if there is no translation.
+ *
+ * Warning: this is not what a lot of other software calls "cubic".
+ * That often refers to the Catmull-Rom spline, or another interpolating
+ * function. (0.0, 0.5) would give us the Catmull-Rom spline, but
+ * that one seems indistinguishable from Lanczos2.
+ */
static double
-cubic_kernel (double x)
+cubic_kernel (double x, double r)
{
- /* 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);
+ return general_cubic (x, r, 1/3.0, 1/3.0);
}
static const filter_info_t filters[] =
@@ -140,163 +212,62 @@ 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_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 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)
+/* Fills in one dimension of the filter array */
+static void get_filter(pixman_kernel_t filter, double r,
+ int width, int subsample,
+ pixman_fixed_t* out)
{
- pixman_fixed_t *params, *p;
- double step;
- double size;
int i;
+ pixman_fixed_t *p = out;
+ int n_phases = 1 << subsample;
+ double step = 1.0 / n_phases;
+ kernel_func_t func = filters[filter].func;
- 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;
+ /* special-case the impulse filter: */
+ if (width <= 1)
+ {
+ for (i = 0; i < n_phases; ++i)
+ *p++ = pixman_fixed_1;
+ return;
+ }
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);
- }
+ double frac = (i + .5) * step;
+ /* Center of left-most pixel: */
+ double x1 = ceil (frac - width / 2.0 - 0.5) - frac + 0.5;
+ double total = 0;
+ pixman_fixed_t new_total = 0;
+ int j;
+
+ for (j = 0; j < width; ++j)
+ {
+ double v = func(x1 + j, r);
+ total += v;
+ p[j] = pixman_double_to_fixed (v);
+ }
/* Normalize */
- p -= *width;
total = 1 / total;
- new_total = 0;
- for (x = x1; x < x2; ++x)
- {
- pixman_fixed_t t = (*p) * total + 0.5;
+ for (j = 0; j < width; ++j)
+ new_total += (p[j] *= total);
- new_total += t;
- *p++ = t;
- }
+ /* Put any error on center pixel */
+ p[width / 2] += (pixman_fixed_1 - new_total);
- if (new_total != pixman_fixed_1)
- *(p - *width / 2) += (pixman_fixed_1 - new_total);
+ p += width;
}
-
- return params;
}
+
/* Create the parameter list for a SEPARABLE_CONVOLUTION filter
* with the given kernels and scale parameters
*/
@@ -313,38 +284,63 @@ pixman_filter_create_separable_convolution (int *n_values,
{
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;
+ int width_x, width_y, size_x, size_y;
+ pixman_fixed_t *params;
- subsample_x = (1 << subsample_bits_x);
- subsample_y = (1 << subsample_bits_y);
+ /* Simulate older version of this function:
+ *
+ * Old version attempted to convolve two filters, the "reconstruct"
+ * filter at a scale of 1 and the main filter at the given scale.
+ *
+ * These filter generators simulate a BOX or IMPULSE
+ * reconstruction filter depending on the scale and other
+ * factors. If another filter is specified as the reconstruction
+ * filter, then it is used at scale = 1 if the scale <= 1 to
+ * simulate the previous results. Since these filters are
+ * supposed to be low pass filters, the convolution is achieved by
+ * just choosing the larger one.
+ */
+ if (reconstruct_x > PIXMAN_KERNEL_BOX && sx < 1.0)
+ {
+ sample_x = reconstruct_x;
+ sx = 1.0;
+ }
+ if (reconstruct_y > PIXMAN_KERNEL_BOX && sy < 1.0)
+ {
+ sample_y = reconstruct_y;
+ sy = 1.0;
+ }
+
+ width_x = filters[sample_x] . width;
+ if (width_x < 1.0)
+ { width_x = 1.0; subsample_bits_x = 0; }
+ else if (width_x < 2.0)
+ width_x = sx < 1.0 ? 2 : ceil (sx + width_x);
+ else
+ width_x = MAX (2, ceil (sx * width_x));
+
+ width_y = filters[sample_y] . width;
+ if (width_y < 1.0)
+ { width_y = 1.0; subsample_bits_y = 0; }
+ else if (width_y < 2.0)
+ width_y = sy < 1.0 ? 2 : ceil (sy + width_y);
+ else
+ width_y = MAX (2, ceil (sy * width_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);
+ size_x = (1 << subsample_bits_x) * width_x;
+ size_y = (1 << subsample_bits_y) * width_y;
+ *n_values = 4 + size_x + size_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;
+ if (!params) return 0;
- params[0] = pixman_int_to_fixed (width);
- params[1] = pixman_int_to_fixed (height);
+ params[0] = pixman_int_to_fixed (width_x);
+ params[1] = pixman_int_to_fixed (width_y);
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);
+ get_filter(sample_x, sx, width_x, subsample_bits_x, params + 4);
+ get_filter(sample_y, sy, width_y, subsample_bits_y, params + 4 + size_x);
return params;
}
--
1.7.9.5
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