Object Extent Determination for Algebraic Solid Models

Abstract

This paper presents methods for determination of spatial extent of algebraic solid models. Algebraic solid models are a variation of implicit solid models defined by implicit polynomial functions with rational coefficients. Spatial extent information, which can be used to enhance the performance of visualization and property evaluation, includes silhouettes, outlines and profiles. Silhouettes are curves on the surface of the solid which separate portions of the surface which face towards or away from a given viewpoint. The projection of the silhouette onto the viewing plane gives the outline of the solid, and the bivariate implicit function which defines the area enclosed by the outline is called the profile . A method for outline determination is demonstrated using concepts from algebraic geometry including polar surfaces and variable elimination via the Gröbner basis method and/or resultants. Examples of outline generation are presented and a sample profile function is constructed.