c - Voronoi diagram bound by circular tour -

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I am facing the following problem:
I made a point cloud P and gave a subset of that point cloud In the BB, the node B (whole) point is the limit of cloud P (in fact, B is given in the form of closed, oriented circular tour). Now, I want to calculate the P Voronio diagram, which is intersected by B., and to extract the area of ​​every (transferred) Voroneini polygon. Here's an example of the situation: Basically I want to pierce the blue colored polygons with green segments. For my questions:

  • From the spot, is the C library that solves this exact problem?
  • If not, then there is a better way of solving this problem, computing Voronejo diagrams using some libraries, then explicitly penetrating (green) areas with polygons from library production ? Perhaps by exploiting a controversial Delaye triangle?

    PS: I know that this achievement may be possible through CGAL. However, CGAL is never used, CGAL is quite complex and optimizes the example code as if it is far from straight forward. Apart from this, I firmly like the solution in C.

    So I decided to go against alpha shapes because I already know the exact range and the interior I do not want to cure alpha to fix the hole to avoid the holes in. Instead, I had used the comment of ANT to apply in CGAL. If anyone is interested, then it can be found that my use of CGAL is actually clumsy and one can say that I am coming from the C-world, but it is a start test input (in.txt) and ( Bnd_ind.txt) can be found in the view of the output (the face is highlighted on the boundary):

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