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For example, could the iPad or iPhone accurately detect the difference between conductive pieces of plastic in the following shapes using Objective C…
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If the above can’t work is it possible to detect the number of points touching the screen?
As Mr. Weinberg notes, you can’t do it with FLAT touches. But, if you put small nubs on the pieces you could use them to stand in for a multi-touch (ie one small nub at each vertex). You could then figure out the shape of the convex hull these points would create.