How can I determine whether a 2D Point is within a Polygon?

Question

I\'m trying to create a fast 2D point inside polygon algorithm, for use in hit-testing (e.g. Polygon.contains(p:Point)). Suggestions for effective tech

Answer 1

I did some work on this back when I was a researcher under Michael Stonebraker - you know, the professor who came up with Ingres, PostgreSQL, etc.

We realized that the fastest way was to first do a bounding box because it's SUPER fast. If it's outside the bounding box, it's outside. Otherwise, you do the harder work...

If you want a great algorithm, look to the open source project PostgreSQL source code for the geo work...

I want to point out, we never got any insight into right vs left handedness (also expressible as an "inside" vs "outside" problem...

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UPDATE

BKB's link provided a good number of reasonable algorithms. I was working on Earth Science problems and therefore needed a solution that works in latitude/longitude, and it has the peculiar problem of handedness - is the area inside the smaller area or the bigger area? The answer is that the "direction" of the verticies matters - it's either left-handed or right handed and in this way you can indicate either area as "inside" any given polygon. As such, my work used solution three enumerated on that page.

In addition, my work used separate functions for "on the line" tests.

...Since someone asked: we figured out that bounding box tests were best when the number of verticies went beyond some number - do a very quick test before doing the longer test if necessary... A bounding box is created by simply taking the largest x, smallest x, largest y and smallest y and putting them together to make four points of a box...

Another tip for those that follow: we did all our more sophisticated and "light-dimming" computing in a grid space all in positive points on a plane and then re-projected back into "real" longitude/latitude, thus avoiding possible errors of wrapping around when one crossed line 180 of longitude and when handling polar regions. Worked great!