FREE-FORM CLOSED SURFACE MODELING

Abstract

The description of geometry for three-dimensional objects is a fundamental problem in computer aided geometric design and computer graphics. Two often used approaches for representing three dimensional surfaces in these areas of research are implicit and parametric surface modeling. This thesis focuses on these two geometric modeling methods that address free-form closed surface modeling. Firstly, a series of asymmetric primitive field functions are defined to enhance the power of soft object modeling. Secondly, a more flexible method of modeling freeform closed smooth piecewise surfaces is developed using rational bicubic splines defined on a simple quadrilateral mesh. The formulation is based on a previous work. It enhances the power of this free-form surface design scheme by providing ease of local shape control. This is achievable as the set of control parameters associated with each control vertex, previously global is made localized with a large range of usability. Many more B-spline bases are derived. Together with those extended form previous work, a complete set of B-Spline bases is now available for various topologies of simple quadrilateral mesh. Finally, a surface modeling system that combines implicit and parametric surface modelings is developed.