From 6ae281fbb7a02b94a3900b6677a51cdd28096ed7 Mon Sep 17 00:00:00 2001 From: Bill Spitzak Date: Tue, 30 Aug 2016 22:03:10 -0700 Subject: [PATCH] pixman-filter: Correct Simpsons integration MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit 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 1,2,0,6,0,6...,2,1. 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 v14: more whitespace changes Signed-off-by: Bill Spitzak Reviewed-by: Oded Gabbay Reviewed-by: Søren Sandmann --- pixman/pixman-filter.c | 21 +++++++++++++++------ 1 file changed, 15 insertions(+), 6 deletions(-) diff --git a/pixman/pixman-filter.c b/pixman/pixman-filter.c index c018a67..ecff852 100644 --- a/pixman/pixman-filter.c +++ b/pixman/pixman-filter.c @@ -189,13 +189,19 @@ integral (pixman_kernel_t kernel1, 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[kernel1].func ((a1)) * filters[kernel2].func ((a2) * scale)) 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 kernel1, double x1, { 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); - - if (i >= 2 && i < N_SEGMENTS - 1) - s += 4 * SAMPLE (a1, a2); } s += SAMPLE (x1 + width, x2 + width); -- 2.34.1