How can I tell if a closed path contains a given point?

Question

In Android, I have a Path object which I happen to know defines a closed path, and I need to figure out if a given point is contained within the path. What I was hoping for

Answer 1

For completeness, I want to make a couple notes here:

As of API 19, there is an intersection operation for Paths. You could create a very small square path around your test point, intersect it with the Path, and see if the result is empty or not.

You can convert Paths to Regions and do a contains() operation. However Regions work in integer coordinates, and I think they use transformed (pixel) coordinates, so you'll have to work with that. I also suspect that the conversion process is computationally intensive.

The edge-crossing algorithm that Hans posted is good and quick, but you have to be very careful for certain corner cases such as when the ray passes directly through a vertex, or intersects a horizontal edge, or when round-off error is a problem, which it always is.

The winding number method is pretty much fool proof, but involves a lot of trig and is computationally expensive.

This paper by Dan Sunday gives a hybrid algorithm that's as accurate as the winding number but as computationally simple as the ray-casting algorithm. It blew me away how elegant it was.

See https://stackoverflow.com/a/33974251/338479 for my code which will do point-in-path calculation for a path consisting of line segments, arcs, and circles.