Introduction to constructive shell representations for free-form surfaces and solids

Abstract

Free-form (`sculptured') surfaces are traditionally represented as unions of parametric patches of high implicit degree. Recently low degree algebraic patches have been introduced for representing free-form surfaces. This paper describes the use of algebraic patches in a new representation for free-form surfaces called Constructive Shell Representation (CSR). A CSR is a union of truncated tetrahedra, called trunctets, forming a `thick shell' that contains the free-form surface. One bounding face of each trunctet is an algebraic patch which is a subset of the free-form surface; the other faces are planar. CSRs for surfaces that are boundaries of free-form solids provide a new, complete hybrid Brep/CSG representation scheme for free-form solids. Properties and applications of this class of CSRs are the main focus of the paper. CSRs may solve some important problems in solid modeling, such as providing means to represent free-form solids in CSG, and hence extending the domain over which Brep→CSG conversion may be done. The paper outlines CSR-based solutions to these problems. Examples computed on an experimental system that exploits the RayCasting Engine (a highly parallel computer for CSG-based solid modeling) are provided.