Best software for triangulating a polygon with given boundary edges

I want to triangulate a polygon given points on the boundary and points in the interior. (This step has to be performed at the end of every iteration of an algorithm that I am implementing; the mesh should change from one iteration to the next since the points in the interior of the polygon are changing position at the end of the iteration. See picture)

Consider the following picture

I would like to triangulate these points while ensuring that the black edges are forced to be edges of triangles in the computed triangulation. All the remaining edges of triangles should be within the polygon connecting orange points to orange points or orange points to the black points. The triangles should also be as well-shaped as possible.

Is there any easily installable and simple to use software to do this?

I use Windows 7 and I have Cygwin and Visual Studio 2012 installed on my system. Solutions which work on either of these systems or in any of the languages C++, Python, MATLAB are acceptable.

NOTE: CGAL initially seemed like the right software package for this problem but it has been a nightmare to install on my Windows 7 system.