From: Bill Spitzak <spit...@gmail.com>
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. Likely even 16 samples is too many.
---
pixman/pixman-filter.c | 17 +++++++++++------
1 file changed, 11 insertions(+), 6 deletions(-)
diff --git a/pixman/pixman-filter.c b/pixman/pixman-filter.c
index 15f9069..5677431 100644
--- a/pixman/pixman-filter.c
+++ b/pixman/pixman-filter.c
@@ -189,8 +189,10 @@ 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
+ */
+#define N_SEGMENTS 16
#define SAMPLE(a1, a2) \
(filters[reconstruct].func ((a1)) * filters[sample].func ((a2) / scale))
@@ -204,11 +206,14 @@ 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);
--
1.9.1
_______________________________________________
Pixman mailing list
Pixman@lists.freedesktop.org
http://lists.freedesktop.org/mailman/listinfo/pixman
