CGAL users discussion list

Quoting Remi 
<>:

> I have an instance of Polygon_with_holes_2. First I call
> connect_holes(..) to get rid of the holes and then I call
> optimal_convex_partition_2(..) with the list of vertices
> connect_holes(..) gave me.
> But the precondition check in optimal_convex_partition_2(..) fails. It
> says that the list of input vertices doesn't represent a simple
> polygon! (is_simple_2(..) returns false). Isn't connect_holes(..)
> supposed to produce a simple polygon?

No! It is definitely not simple.

> Is optimal_convex_partition_2(..) the best way to triangulate
> polygons, especially polygons with holes?

Define "best".

One easy way to do it is to use what is called "vertical  
decomposition", which decomposes an arrangement into pseudo  
trapezoids. You insert your object of type Polygon_with_holes_2 into  
an object of type Polygon_set_2 and obtain the underlying arrangement.  
Then, you use the decompose () free function to obtain the pairs of  
features that lie above and below every vertex of the arrangement. You  
discard all features but the ones that induce vertical segments that  
are contained in the original input polygon with holes. You still need  
to split real trapezoids into triangles. This process constructs many  
new points --- it may not suits you.

> I'm a beginner so any input is appreciated.
>
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