8. A Survey of Parametric Scattered Data Fitting Using Triangular Interpolants

Abstract

This paper has been published as a chapter in \Curve and Surface Design", H. Ha-gen, (ed), SIAM, 1992 Some of the gures from that paper are missing from this version, as are all of the black-and-white photographs. There are currently a number of methods for solving variants of the following problem: Given a triangulated polyhedron P in three space with or without boundary, construct a smooth surface that interpolates the vertices of P. In general, while the methods satisfy the continuity and interpolation requirements of the problem, they often fail to produce pleasing shapes. The purpose of this paper is to present a unifying survey of the published methods, to identify causes of shape defects, and to ooer suggestions for improving the aesthetic quality of the interpolants. The problem of passing a surface through a set of data points arises in numerous areas of application such as medical imaging, geological modeling, scientiic visualization, and geometric modeling. Variants of this problem have been approached from many directions. Tensor-product B-splines work well for modeling surfaces based on rectilinear control nets but are not suu-cient for more general topologies. Triangulated data, however, can represent 1