CGAL users discussion list

[Ben Supnik <>]

Hi Efi,


 wrote:

> > In other words, if the new curve must be the same point as the old two 
> > curves, your direction can't change as long as the new curve must be 
> > monotone.  But this somewhat reduces the utility of the merge_edge for 
> > certain weird cases.

> The improved (complete) condition is:
>
> The 2 input (x-monotone) curves share a common end-point, and the new 
> (x-monotone) curve is the union of the 2 input (x-monotone) curves (or 
> at least the new curve and the union curve are topologically equivalent.)

Wait - not to beat this to death, but...

It seems that there should be cases where the replacement curve is not 
the union, is topologically equivalent, but the direction must still be 
recalculated.

With a curve type of segment_2, Consider a single strictly simple 
polygon that partitions an arrangement into one bounded face and one 
unbounded face.

I want to replace a pair of curves (one directed right, and one directed 
left) with a new curve that directly connects the non-shared end-ponts. 
 (Cutting off the triangle, so to speak.)  Because of the shape of the 
polygon, I can do this without any intersections occuring, and the 
resulting polygon is still strictly simple - there is no topological change.

But depending on the relative position of the non-shared endpoints, the 
new edge could be directed right or left, so a recalculation may be 
necessary.

I think you have to require the new curve to be the union of the old 
curves with a shared endpoint to avoid a geometric operation.

cheers
ben