[cairo] Playing with spline decomposition

[Bill Spitzak]

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 
independently.

-- 
Bill Spitzak, Senior Software Engineer
The Foundry, 618 Hampton Drive, Venice, CA, 90291, USA
Tel: +1 310 399-4555 * Fax: +1 310 450-4516 * Web: www.thefoundry.co.uk
The Foundry Visionmongers Ltd * Registered in England and Wales No: 4642027