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

The Eric Haines article cited by bobobobo is really excellent. Particularly interesting are the tables comparing performance of the algorithms; the angle summation method is really bad compared to the others. Also interesting is that optimisations like using a lookup grid to further subdivide the polygon into "in" and "out" sectors can make the test incredibly fast even on polygons with > 1000 sides.

Anyway, it's early days but my vote goes to the "crossings" method, which is pretty much what Mecki describes I think. However I found it most succintly described and codified by David Bourke. I love that there is no real trigonometry required, and it works for convex and concave, and it performs reasonably well as the number of sides increases.

By the way, here's one of the performance tables from the Eric Haines' article for interest, testing on random polygons.

                       number of edges per polygon
                         3       4      10      100    1000
MacMartin               2.9     3.2     5.9     50.6    485
Crossings               3.1     3.4     6.8     60.0    624
Triangle Fan+edge sort  1.1     1.8     6.5     77.6    787
Triangle Fan            1.2     2.1     7.3     85.4    865
Barycentric             2.1     3.8    13.8    160.7   1665
Angle Summation        56.2    70.4   153.6   1403.8  14693

Grid (100x100)          1.5     1.5     1.6      2.1      9.8
Grid (20x20)            1.7     1.7     1.9      5.7     42.2
Bins (100)              1.8     1.9     2.7     15.1    117
Bins (20)               2.1     2.2     3.7     26.3    278