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Texture mapping on 2D shapes, none polygons

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Hi all, I can only seem to find information on how to map a texture on a polygon or sphere. I've created a hexagon (among other shapes) using the trianglefan method and would like to map a png of a hexagon onto this shape. What is the method I need to go through in order to do this successfully? When i say it's a 2D shape i just mean all of the z coordinates are all set to 0. Thanks.

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