How to calculate the intersection of two polygons?

Computational Geometry: Is there a general equation for the area of the intersection of two polygons plotted on a radar chart?

• It should hold for an arbitrary number of axes. The goal is to attempt to quantify the similarity of two categorical distributions.

• Answer:

  I doubt this is a very informative number to compute, since it would change if you reordered the axes. However, let's answer the math problem anyway.  Here's a picture of two polygons on a radar chart: Compute the intersection This is easy.  Along each axis, we have a red vertex and a blue vertex.  Obviously whichever is innermost is contained in the intersection of the polygons.  Now, for each adjacent pair of axes, look at which color each innermost vertex is.  For instance, between "Sales" and "Marketing" on the graph above, both innermost vertices are blue, so we should take the edge of the blue polygon between these edges.  On the other hand, the innermost vertex for "Marketing" is blue, while the innermost vertex for "Development" is red.  Therefore, we need to calculate the intersection X of the red and blue edges between Marketing and Development.  The intersection of the polygons will take the blue edge between Marketing and X, and then the red edge between X and Development. Compute the area Now that we have a polygon representing the intersection, we just need to compute its area.  This is easy -- just cut it into triangles made from two adjacent points on the polygon and one point at the center of the radar chart and sum the areas.