Algorithm for Smoothing Triangulated Surfaces

Abstract

Surfaces defined by linearly interpolating a two‐dimensional triangulation of a set of scattered data points are frequently used to describe geometry in computer applications. The linear nature of such surfaces simplifies many subsequent operations on the surface such as contouring and volume calculations. However, if the data points defining the surface are sparse, the resulting triangulated surface may be unacceptably rough or irregular. An algorithm is presented for smoothing a triangulated surface by adding extra data points at special locations in the interior of the triangulated region. The incremental addition of the supplemental data points forces the triangulated surface to approximate or converge to a previously specified smooth surface that interpolates the original data points. A unique feature of the algorithm is that any smooth interpolation scheme or surface can be used to smooth the triangulated surface. The algorithm has been implemented on a microcomputer and the results have been satisfactory.