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Citation:

Helmut Pottmann, H.-Y. Chen, and In-Kwon Lee, "Approximation by Profile Surfaces", In The Mathematics of Surfaces VIII, (A. Ball et al. Eds), pp. 17-36, Information Geometers (presented in the Eighth IMA Conference on the Mathematics of Surfaces, Birmingham, U.K., Aug.31 - Sep.2, 1998), August 1998

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Abstract:

A new algorithm for approximation of a given surface or scattered points by a surface of revolution is presented. It forms the basis for a study of approximation with profile surfaces. Those are sweeping surfaces traced out by a planar curve when its plane is rolling on a developable surface. Important special cases include developable surfaces and pipe surfaces, where the moving curve is a straight line or circle, respectively. The methods are illustrated using applications in reverse engineering of geometric models.

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