The displacement method for implicit blending surfaces in solid models

Abstract

To date, methods that blend solids, that is, B-rep or CSG models, with implicit functions require successive composition of the blending functions to handle an arbitrary solid model. The shape of the resulting surfaces depends upon the algebraic distances defined by these functions. To achieve meaningful shapes, previous methods have relied on blending functions that have a pseudo-Euclidean distance measure. These methods are abstracted, resulting in some general observations. Unfortunately, the functions used can exhibit unwanted discontinuities. A new method, the displacement form of blending, embeds the zero surface of the blending functions in a form for which algebraic distance is C1 continuous in the entire domain of definition.Characteristics of the displacement form are demonstrated using the superelliptic blending functions. Intuitive and mathematical underpinnings are provided.