diff options
| author | Bill Spitzak <spitzak@gmail.com> | 2016-02-08 00:06:55 -0800 |
|---|---|---|
| committer | Oded Gabbay <oded.gabbay@gmail.com> | 2016-02-08 10:22:08 +0200 |
| commit | 59dc82b47277abba37073db1473f7bb31835324b (patch) | |
| tree | 0971bc23bfb68259126933da4290c63d643a066c | |
| parent | 3849c5366cd21a9bb131aee1ce504fd86f7bf88e (diff) | |
pixman-filter: Correct Simpsons integration
Simpsons uses cubic curve fitting, with 3 samples defining each cubic. This
makes the weights of the samples be in a pattern of 1,4,2,4,2...4,1, and then
dividing the result by 3.
The previous code was using weights of 1,2,6,6...6,2,1. Since it divided by
3 this produced about 2x the desired value (the normalization fixed this).
Also this is effectively a linear interpolation, not Simpsons integration.
With this fix the integration is accurate enough that the number of samples
could be reduced a lot. Multiples of 12 seem to work best.
v7: Merged with patch to reduce from 128 samples to 16
v9: Changed samples from 16 to 12
v10: Fixed rebase error that made it not compile
v11: minor whitespace change
Signed-off-by: Bill Spitzak <spitzak@gmail.com>
Reviewed-by: Oded Gabbay <oded.gabbay@gmail.com>
| -rw-r--r-- | pixman/pixman-filter.c | 23 |
1 files changed, 16 insertions, 7 deletions
diff --git a/pixman/pixman-filter.c b/pixman/pixman-filter.c index 69ac3ab..8b8fb82 100644 --- a/pixman/pixman-filter.c +++ b/pixman/pixman-filter.c @@ -189,13 +189,19 @@ integral (pixman_kernel_t reconstruct, double x1, } else { - /* Integration via Simpson's rule */ -#define N_SEGMENTS 128 + /* 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[reconstruct].func ((a1)) * filters[sample].func ((a2) / size)) double s = 0.0; - double h = width / (double)N_SEGMENTS; + double h = width / N_SEGMENTS; int i; s = SAMPLE (x1, x2); @@ -204,11 +210,14 @@ integral (pixman_kernel_t reconstruct, double x1, { double a1 = x1 + h * i; double a2 = x2 + h * i; + s += 4 * SAMPLE(a1, a2); + } - s += 2 * SAMPLE (a1, a2); - - if (i >= 2 && i < N_SEGMENTS - 1) - 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); |