Transfinite surface interpolation over irregular n-sided domains

Abstract

Parametric representations of surfaces in Computer-Aided Geometric Design (CAGD) are often based on connected patches with rectangular parameter domains. Given a loop of four space curves and normal-derivative curves, we want to find a parametric surface that interpolates the boundary data in a C^1-continuous way. The Coons patch developed by Steven A. Coons in the 1960s, is a well known technique for constructing such surfaces. However, the need to construct patches with non-rectangular domains can often occur within a rectangular patch framework. In a recent paper by Várady, Rockwood & Salvi (2011), three different methods which generalizes the original Coons patch to match n boundary curves using irregular n-sided domains, were presented. Another transfinite interpolation method called cubic mean value interpolation based on mean value coordinates was introduced by Floater & Schulz (2008). The purpose of this thesis is to review and compare these methods. All the methods were successfully implemented in MATLAB®. We discuss the pros and cons of the different constructions, and provide several numerical examples to compare the shape qualities and computational efficiency.