maxCircleInConvexPo​ly

Determines the origin position and radius of the largest possible circle within a convex 2D polygon with N vertices. Polygon vertices are specified as an Nx2 matrix, per Matlab's "boundary" function, and 'shrinkage' is the third input argument.

Algorithm: First, the polygon is rotated so that one side lies on the x-axis. Starting from its vertex, a "balloon" (circle) is created, which iteratively "expands" along the vector bisecting that vertex until the next side is reached. This process continues with new bisecting vectors each time the balloon hits a new side until the maximum distance is reached. See comments in code for details.

The maximum distance and circle origin position are rotated back to the original before being output.

Optional plotting commands are included to view the steps of the process. The two required subfunctions are included in the one .m file.