[reactive] crayon - a 2D opengl curve renderer, with Reactive animations

[Jules Bean]

Peter Verswyvelen wrote:
> Excellent work! I have been looking into curve rendering myself lately, 
> and found some links that you might find interesting (besides the 
> Loop/Blinn article Bob already forwarded to you)

Hey! I showed that article to Bob, not the other way around. Mind you, 
he was already aware of the technique, of course.

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

That looks very interesting.

> 
> I also came across a kind of curve that I didn't know about yet, 
> named "Pythagorean hodograph curves 
> <http://www.research.ibm.com/journal/rd/345/ibmrd3405J.pdf> ". 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)

I'm concerned about the cost of repeated triangulation; I'm trying to 
find an algorithm fast enough for realtime animation (where the control 
points may move every frame). Mind you some kind of repeated calculation 
can't be avoided - it's interesting to consider algorithms which can 
reduce the work for 'small perturbation' (e.g. where the topology hasn't 
changed) but it's not obvious how to make that efficient.

Loop-Blinn is obvious a good way to go for a fixed vector input (e.g. a 
font) which can be preprocessed.

Jules