# How to find the percentage of overlapping n-gons of the circle?

Good afternoon.

It is necessary to solve the following problem: there are one or more arbitrary n-gon(may not be convex), which intersect with the circle. You need to find the percentage of overlapping n-gons circle. Coordinates of all points of the n-gon and center coordinates of a circle and its radius are known. For clarity, the screenshot is attached.
Me the necessary mathematical apparatus for this task. It is possible in English. In principle, the implementation of YAP.
How to solve the problem of intersection of n-triangles to each other I know. But with no circumference.

Screen:
July 8th 19 at 15:31
July 8th 19 at 15:33
July 8th 19 at 15:35
To triangulate the polygon, to solve the problem for each triangle. With the triangle still. Looking for points of intersection, we consider the square of the segment + triangle / quadrangle is cut by a chord.

For triangle ABC to fold the square triangle (1) and the chord (2). For triangle BCD chord + the quadrangle.
Thank you. What if the polygon is concave? - Frieda.Heaney20 commented on July 8th 19 at 15:38
It's not terrible. There are different libraries that can do that. For example https://www.cs.cmu.edu/~quake/triangle.html python wrapper for it: dzhelil.info/triangle/delaunay.html, CGAL, if you are using C++. - chaz_Wiso commented on July 8th 19 at 15:41

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