Improved visually C1 condition for scattered 3-dimensional data interpolation using triangular bezier polynomial patch

Abstract

Described in this thesis is a visually C``(VC``) condition between two adjacent triangular patches. The main motivation was to improve the Farin``s 3-dimensional scattered point data fitting(3-D SPF) procedure. Two results were obtained in this thesis. One is the improved VC`` condition which can be used in composite triangular surface construction. This condition requires no restriction on boundary curve determination. So, we can select more natural boundary curves, and hence the overall smoothness of fitting surface can be improved. A modified 3-D SPF procedure using this condition was proposed. The other is a generalised solution for corner filleting problem and surface fairing problem. In corner filleting problem, a method to connect a triangular patch VC continuously to existing non-C" rectangular patches was proposed. And a new VC`` condition which enables the local modification of composite triangular surface while satisfying VC`` continuity was also derived.