Re: [PyX-devel] Curves with infinite curvature

[Joerg L. <jo...@us...>]

Hi Michael!

On 09.09.05, Michael Schindler wrote:
> I have hit a problem concerning the geometry things of the normpaths.
> Consider a Bezier curve that contains a point with infinite curvature.
> This is very easy to produce by setting e.g. the last two points to
> the same coordinates
> 
>   n = normcurve_pt(0,0, 1,1, 1,0, 1,0)
> 
> The curveradius_pt returns "None" for parameter value 1. But the
> trafo/rotation does something quite unexpected. The tangent vector
> 
>   n.rotation([0.999999])[0].apply_pt(1, 0)
> 
> seems to converge against (-1, 0) while adding more "9"s to the
> parameter. However, the tangent at the parameter value 1 is (1, 0).
> 
> My question now is, how well do we want to really reproduce the true
> underlying geometry? We should return "None" for the rotation at such
> points also.

I think, we should return the correct rotation instead of None.
Geometrically, everything is well-defined, it's only that we commit some
numerical error because the length of (dx/dt, dy/dt) goes to zero. But
we should be able to treat this case better.

        Jörg