The Focal Surfaces of Offset Surface

Abstract

In surface modeling, constructing a new surface from a given regular surface is important. Focal surfaces are used to analyze the quality of a given surface. In this study, the relationships between the geometry of the focal surfaces of its offset of given a parametric surface with the geometry of the original surface are given. The geometric properties of this focal surfaces were calculated by using use of the basic forms and curvatures of the original surface, and some theorems are given. Thus, we find the geometric properties of the focal surfaces of its offset surface using only the geometric properties of a given parametric surface. In addition, the theorems given in the study are supported with examples.