# How to find the intersection of the area of multiple triangles

I have a couple of questions regarding finding the intersection of triangles. I have a system of 16 projectors that all have slightly different color gamuts. The color gamuts are represented by a triangle in the CIE chromaticity space. Here is a picture showing a few color gamuts in chromaticity space.

I need to restrict the lager gamut projectors so that all the projectors have the same gamut. I need to find the "greatest common gamut". Which I think boils down to finding the intersection of all 16 gamuts and drawing a triangle between the 3 vertices of the resulting polygon that are closest to the RGB "corners" of chromaticity space.

Is there a closed-form solution to finding the intersection of several triangles? Also I am assuming the intersection operator is associative right? ie ( A int B int C) = ( (A int B) int C ) = ( A int (B int C))? Sorry I don't know how to do the symbols :( Also does anyone know of functions or libraries in Matlab / Octave to find the intersection of polygons? Sorry if I used the wrong terminology anywhere I am not very knowledgeable when it comes to math.

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Any ideas at all? – vanattab Dec 29 '12 at 23:11