Parametric Offset Surface Approximation

Abstract

Offset surfaces are of interest in a variety of engineering applications. The formulation of a parametric offset surface involves division by the square root of a parametric equation, therefore, the offset surface is typically non-polynomial. Because of this complexity, offset surfaces cannot, in general, be written as members of the same class of functions or their generating or progenitor surface. Approximation of the offset surface is therefore desirable. Three contemporary methods of offset surface approximation are described which serve as models for the development of a new approximation algorithm. An adaptive offset surface approximation method based on a visually smooth triangular interpolant to position and tangent plane data defined in a triangular mesh is then developed. The criteria used to develop the approximation method are discussed, the components of the algorithm are described and the results of an implementation are illustrated. A conclusion about the success and possible refinement of the triangular offset surface approximation method is drawn and ideas for further research are outlined.