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interesecting bezier surfaces (patches)

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I am trying to find the common shared point between three intersecting bezier patches. I have done this manually in maya by finding the intersecting curve between two bezier surfaces and than 'cutting' that curve with a third surface. In effect determining the point shared by all three bezier surfaces. I am now writing for OpenGl and trying to intersect a fairly large number of these.... Any thoughts out there? Thanks Bruce

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