Split simple polygon into Monotone pieces

[christl]

Hi all!
I develop an application in computer science that shows the execution of an Algorithm that triangulates a simple polygon.

The first thing I have to do is to transform the given Polygon into monotone pieces, in order to do that I have to figure out the interior angles of the simple polygon.
I just know the coordinates of the vertices of my polygon.

Now my problem is how I should calculate the interior angle between two edges. And with interior I mean interior of the polygon. Two edges form a triangle which allows me to calculate angles easily but how do I know if I should calculate the exterior or the interior angle of that specific triangle. Is the interior angle of the triangle inside the polygon or the external angle?

Thanks in advance for any answers!

 

[HallsofIvy]

"Monotone" is an adjective that applies to polynomials, not polygons. What do you mean by "monotone pieces" of a polygon?

 

[christl]

No, I get a simple polygon defined like that: http://en.wikipedia.org/wiki/Simple_polygon
in Coordinates of its Vertices. It can be any simple polygon.

In order to triangulate this polygon I have to split the simple polygon in its monotone pieces. A monotone Polygon is defined like that:
http://en.wikipedia.org/wiki/Monotone_polygon

 

[HallsofIvy]

Thanks. I hadn't seen that use of "monotone" before. However, note that this does not say "monotone pieces" of a polygon or "monotone polygons". It talks about a polygon being "monotone" with respect to a given straight line.