How to form a Concave shape out of Convex shapes?

Question

i\'m trying to get around the rule of only being able to form convex shapes in the SFML c++ library.

To do this I\'m planning on testing given vertices,

Answer 1

You can test for a shape being a convex hull by going round all the edges and checking the next edge is always moving in the same direction (left/right handed). This is a quick and cheap algorithm. There is an implementation of this here: en.wikipedia.org/wiki/Graham_scan

If you don't have a convex hull, perform a package wrapping algorithm to get a convex hull that encompasses all your points (again quite fast). en.wikipedia.org/wiki/Gift_wrapping_algorithm

Now, look for points that are on your shape, but aren't on the convex hull. For each run of these points, create a new shape from these points (plus the 2 either side on the convex hull).

Recursion is now your friend: do the exact same process on each of the sub-shapes you have just made.

I have used this techniques to test for a point being contained inside an arbitrary shape: i.e. the point must be inside the convex hull (easy to test), but not any of the sub-shapes, or their sub-shapes, or their sub-shapes....