Re: Interior of a polygon

*To*: mathgroup at smc.vnet.net*Subject*: [mg28577] Re: Interior of a polygon*From*: dennisw555 at aol.com (DennisW555)*Date*: Sat, 28 Apr 2001 21:36:02 -0400 (EDT)*References*: <9cb9nr$cjb@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

To find if a point is inside a polygon simply start at one vertex and accumulate the angles from the point to each sucessive vertex, all the way around to that starting vertex. Keep track of the sense, as some will be negative angles and some positive. If the magnitude of the sum of angles is 2 Pi the point is inside. If the sum is zero the point is outside. I set the decision threshold at Pi for simplicity. With this method the polygon does not need to be convex. I pretend the polygon points are in the xy plane and take cross products between successive vectors from the point to the vertex. Then the magnitude of the sum of the z components of the cross products is the quantity to test. To do this a vertex at coordinates {x,y} becomes {x,y,0}, likewise for the point. I hope this helps, Dennis Wangsness