This was based on looking up Simpson's integration on the web, from the wikipedia page and another page I found.
It cuts the samples into sets of 3, with an overlap of 1. Each set then weighs 1,4,1 in the average, to simulate the weight of the control points of a cubic curve. Since the overlapping samples of 1 add to 2 this results in 1,4,2,4,2,...4,1 as the weights. As there are two points per set and the total weight is 1+4+1=6, you divide the full sum by 6/2 = 3. It appears this implementation attempted to overlap them by 2, resulting in weights of 1,5,6,...6,5,1. However this is very close to a flat average of all the points. Also this is a total of 6 for every point so the divisor should be 6, but it was left at 3. Based on my reading the new version is correct. However I have not been able to see any visible difference in the filtering even if I reduce the number of samples to 3. On Thu, Dec 17, 2015 at 10:21 AM, Oded Gabbay <oded.gab...@gmail.com> wrote: > On Thu, Dec 17, 2015 at 8:20 PM, Oded Gabbay <oded.gab...@gmail.com> > wrote: > > On Sat, Dec 12, 2015 at 8:06 PM, <spit...@gmail.com> wrote: > >> 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 which produced > about 2x > >> the correct value, as it was still dividing by 3. The filter > normalization > >> removed this error. Also this is effectively a linear interpolation > except for > >> the ends. > >> --- > >> pixman/pixman-filter.c | 11 +++++++---- > >> 1 file changed, 7 insertions(+), 4 deletions(-) > >> > >> diff --git a/pixman/pixman-filter.c b/pixman/pixman-filter.c > >> index 15f9069..7c1da0d 100644 > >> --- a/pixman/pixman-filter.c > >> +++ b/pixman/pixman-filter.c > >> @@ -204,11 +204,14 @@ 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 > > > > You say: > > > > "The filter normalization removed this error. Also this is effectively > > a linear interpolation except for the ends." > > > > So if the error was removed, why is this change needed ? I can see it > > is more accurate (similar to the Simpson equation), but it also causes > > the code to run over the loop twice. > > > > Do you have some example we can see the difference ? > > > > > > Oded > > OK, now I see that in the next patch, you reduce the samples from 128 > to 16, so we are now running less iterations. > I still would be happy to see an example with my own eyes where this > makes a difference. > > Oded >
_______________________________________________ Pixman mailing list Pixman@lists.freedesktop.org http://lists.freedesktop.org/mailman/listinfo/pixman