I have two polygons. One small one big.

Is there a formula that gives the polygon of the where the two polygons overlap? I want to paint this area so I need to calculate it.

I'm using Objective-C so have two arrays contains the points of the polygon.

Many Thanks, -C


closed as off-topic by Sahiba Arora, Claude Leibovici, Gautam Shenoy, Joel Reyes Noche, user223391 Jan 26 '18 at 19:47

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  • $\begingroup$ Please give examples. $\endgroup$ – David G. Stork Jan 23 '18 at 18:08
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    $\begingroup$ Are both polygons convex? This is an important detail. By the way, you're looking for an intersection algorithm. This might be useful, it just showed up when I looked for objective c polygon intersection: github.com/SunGard-Labs/MKPolygon-GPC $\endgroup$ – Larry B. Jan 23 '18 at 18:09
  • $\begingroup$ This is generally known as polygon intersection or polygon clipping. If you know that one of your polygons is convex then it becomes a little easier, but in general this can be very hard - two non-convex polygons with $n$ vertices can have up to $O(n^2)$ different polygons in the intersection. Have a look at Wikipedia's page on Weiler-Atherton clipping ; that should point you to more resources. $\endgroup$ – Steven Stadnicki Jan 23 '18 at 18:11
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    $\begingroup$ I'm voting to close this question as off-topic because it appears to be requesting an algorithm. It would be better served in cs.stackexchange $\endgroup$ – Gautam Shenoy Jan 24 '18 at 12:54
  • $\begingroup$ This is a well-studied problem. Perhaps start with this question and its answers: How do I combine complex polygons?. $\endgroup$ – Joseph O'Rourke Jan 24 '18 at 16:59

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