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Expanding pointlist into triangle mesh

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I'm currently working on a project which requires me to turn a list of points and radii into a full 3D model of the data it represents. Imagine a bunch of pipes which joins together into a web.

Expanding a single segment into a 3D cylinder is not really a problem, but problems arise when we start to join them together as they obviously doesn't fit together.

I'm writing here in hope there would be a clever guy out there who has a good idea on how to solve the joint genericly.


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