Although subdivision surfaces were first explored in the CAD/CAM context nearly quarter of a century ago, there has been a resurgence of interest in the last five years, now that commodity computers have large enough memories to hold dense mesh surfaces. They provide a technology for defining "in one" smooth surfaces of general topology in terms of the positions of the vertices of a polyhedron.
The tutorial will start by identifying just what this technology offers to the solid modelling community. It will continue by introducing key ideas by examples, listing some half a dozen schemes of theoretical significance.
It will then continue by showing how such schemes (and others) fit into a single classification.
Given that there are many different possible schemes, the question is then "which one is best ?", but this cannot be answered yet. What we can do is try to make a list of "what aspects matter ?", and a tentative list of issues will be presented, together with the mathematical techniques for finding how a given scheme performs with respect to them.
A final part of the tutorial will be dedicated to the question of "Street Wisdom", the knowledge of how to use a surface definition scheme effectively to achieve the shape that you want, which has not received the attention it needs for previous generations of surface models.
Malcolm runs his own company, Numerical Geometry Ltd., offering consulting on shape representations to vendor companies in the CAD/CAM/CAE sector. His experience in surface definitions started in the late 1960's when he built one of the first parametric surface software systems for the British Aircraft Corporation. He has also been involved with writing software for NC part programming, for NC control systems and for FE meshing. He has BA and MA degrees from Cambridge University, and a PhD earned part-time in his 50s from Leeds University. His current research interests are in subdivision surfaces, cellular solid modelling and programmable feature recognition.
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