Question

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A simple algorithm for polygon intersection

I’m looking for an outline on how to quickly calculate the intersection of two arbitrarily oriented quadrilaterals (no preset corner angle or side length constraints). I am not looking to simply check whether they intersect, but wish to get the points making up the resulting intersecting region. I know that in general polygon intersection isn’t a trivial problem and there are libraries available that do a good job.

But since in this special case where I’m only concerned with four sided shapes, I was wondering if there was a quick method I could use without including an entire additional library in my application.

So far all I’ve thought of is:

1. Run ‘point in polygon’ on both shapes with respect to each other
2. Intersect each edge of each polygon with each other

Do the above two steps definitively get me all the points that make up the resulting intersection region? Is there a better method to use?

Also it would be nice if I could get the correct ordering of the points that make up the resulting region. It’s not mandatory — if you are aware of any clever/quick ways of doing this bit (convex hull?) I’d appreciate any suggestions.

Answer 1

You didn’t state wether the 2 quadriliterals are convex or not; if they are, you could use a regular convex polygon intersection algorithm such as http://www.iro.umontreal.ca/~plante/compGeom/algorithm.html

From what I can gather, it doesn’t require any exotic datastructures or operations, so it shouldn’t be difficult to implement.