The Geometric Modeling of Bitangency

University Of Alabama At Birmingham, Birmingham AL

Investigators

Abstract

ABSTRACT 0203586 Johnstone, John U of Alabama @ Birmingham The work of this proposal can be divided into three categories: (1) the study of dual representations of the tangent space of a curve and surface, (2) the application of these dual representations to the computation of bitangency, and (3) the application of bitangency to several problems in geometric modeling, computer graphics and robotics such as visibility, lighting and motion. The problem that binds together these areas of study is bitangency. There are basically three bitangent structures: the bitangent line (a line that is tangent to two curves), the bitangent plane (a plane that is tangent totwo surfaces), and the bitangent developable (the envelope of a familyof bitangent planes). While the tangent is important in the analysis of individual curves and surfaces in isolation, the bitangent is important in the analysis of collections of curves and surfaces, since it relates two curves or two surfaces. As the analysis of large scenes becomes increasingly important, the bitangent becomes an important tool.