Continuous quadric patch approximation of curved surfaces

Abstract

The use of quadric surface patches to form a continuous approximating surface to given curved surfaces is discussed. While the approach used in finite element methods yields an effective method for the construction of a continuous surface, the resulting patches will, in general, not be quadric. A method is proposed for the construction of continuous patches on a covering mesh of conic segments. Each patch consists of three quadric subpatches, and each conic boundary segment interpolates three points on the given surface.