[Pixman] [PATCH 05/15] pixman-filter: Correct Simpsons integration

[Bill Spitzak]

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.gabbay at gmail.com> wrote:

> On Thu, Dec 17, 2015 at 8:20 PM, Oded Gabbay <oded.gabbay at gmail.com>
> wrote:
> > On Sat, Dec 12, 2015 at 8:06 PM,  <spitzak at gmail.com> wrote:
> >> From: Bill Spitzak <spitzak at 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 at 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
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.freedesktop.org/archives/pixman/attachments/20151217/ca412b4d/attachment.html>