Maxim Shemanarev, the author of the open source anti-grain 2D rendering engine, seems to have tackled the curve stroking (dealing with cusps etc) pragmatically:

http://www.antigrain.com/research/adaptive_bezier/index.html#PAGE_ADAPTIVE_BEZIER

I also came across a kind of curve that I didn't know about yet, named "Pythagorean hodograph curves ". These are subsets of Bezier polynomials for which arclength is expressible as a polynomial, and for which offset curves (aka parallel curves) are rational polynomials again (for regular curves arclength and offsets must be approximated numerically). Offset curves could be used to avoid generating all those line segments to stroke a curve, even rendering them directly on the GPU, but I haven't found a fast way for doing this. There's even a full book about PH curves from his inventor: http://www.amazon.com/Pythagorean-Hodograph-Curves-Geometry-Inseparable-Computing/dp/3540733973

Personally I'm trying to do stroking by approximating cubic Bezier curves and their offset curves with simple quadratic polynomial curves, performing Delaunay triangulation, converting the quadratic curve segments to implicit form, and directly rendering the triangles that form the control points of the quadratics on the GPU. This is more for fun since it is most likely more computationally expensive than just doing very fine subdivision and rendering stroked line segments (although the implicits on the GPU is fully resolution independent of course)

On Wed, Mar 25, 2009 at 10:56 PM, Jules Bean <jules@jellybean.co.uk> wrote:

Tom Poliquin wrote:

Jules, thanks for uploading the code!

You're most welcome.

As a reactive newbie, examples are a gigantic help ..

It works great .. about 40FPS on my
ATI Technologies Inc RV515GL [FireGL V3350] using about 3% of my AMD Athlon(tm) 64 X2 Dual Core Processor 6000+
CPU.

Yes, capped to 40fps by the "25" (25 milliseconds = 1/40 seconds) in line 115 inside the idle callback.

If you change that to "0" then it will take up more or less 100% of your CPU and framerates will be much higher. On my machine (nvidia m 8xxx) it does 1000fps (!) for Pong, 400fps for the charts and 100fps for the flowers.

I had to make a small change to get it to work on my
system (perhaps I'm down rev somewhere) .. but I thought I'd share in case other newbies have the same
issue ..

crayon.hs:689:57:
Constructor `WeightedProperties' should have 4 arguments, but has been given 1
crayon.hs:699:8:
Constructor `WeightedProperties' should have 4 arguments, but has been given 1

I just changed the WeightedProperties args in each case to,
(WeightedProperties (_,p) _ _ _)
from
(WeightedProperties ((_, p) : _))

D'OH

That is the correct fix, yes.

I forgot that my HOpenGL bugfix actually changed the API.

Jules

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