[metapost] workaround for turningnumber bug

[Taco Hoekwater]

Werner LEMBERG wrote:
 >
> Thanks for the counterexample.  Is such a curve possible (this is,
> with a `reversed' order of the control points) in mpost if I don't
> specify the control points explictly?

I don't know (I am still doing empirical tests only, without theoretical
understanding), but it seems unlikely that MP would invent such control
points. However, if that is the case, then explicit control points are
the only way to create the desired curve, so the problem remains the
same :-)

> What are the constraints for a curve (P, P+, Q-, Q) so that there is a
> self-intersection?  

I've been playing, and I have a similar question. Is it true that, under
the assumption that P -- P+ and Q- -- Q intersect at X, there will be
self-intersection if, and only if, the area of triangle(P+,Q-,X) is
larger than the surface of triangle(P,Q,X)?

Greetings, Taco