[cairo] Playing with spline decomposition
spitzak at thefoundry.co.uk
Fri Oct 17 14:05:13 PDT 2008
Carl Worth wrote:
> On Tue, 2008-10-14 at 21:56 +0100, Chris Wilson wrote:
>> As the spline is immediately feed into the tessellator for
>> trapezoidation, even a small reduction can have a dramatic impact on
>> performance. (For example, my first foray is just a bisection search for
>> the best step length, and achieves a 20% reduction in tessellation -
>> about an 8% speed up for the whole benchmark).
> Interesting stuff!
>> The second aspect sounds
>> even more promising as it suggests that we can entirely avoid using the
>> pen whilst stroking curve segments, and generate more accurate results
>> with even fewer points.
> What are the expected savings from this part? The whole of "using the
> pen" is a linear-time walk of the flattened path with additions to
> compute points. Oh, and some slope comparisons as the path turns---is
> that what you're hoping so save here?
I did not understand the math at all, but it looks like it produces a
different set of straight line segments for each side of the path. This
makes it have a lot fewer segments. Fig 10 shows this clearly.
I think it approximates the Bezier as straight lines and circular arcs.
It is relatively easy to find the edges of the pens path of a circular
arc, as that is also a circular arc (except when the circle is too
small). All these arcs are then decomposed into straight lines
Bill Spitzak, Senior Software Engineer
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