Combining CSG modeling with soft blending using Lipschitz-based implicit surfaces

Abstract

In this paper a general method is given for combining CSG modeling with soft blending using implicit surfaces. A class of various blending functions sharing some desirable properties like differentiability and intuitive blend control are given. The functions defining the CSG objects satisfy the Lipschitz condition which gives the possibility of fast root-finding, but can also prove useful in the field of collision detection and adaptive triangulation. Introduction Methods for defining smooth surfaces can be divided into two categories: ffl Parametric functions Parametric functions are functions of the form f(u; v) = (f x (u; v); f y (u; v); f z (u; v)). Typical examples are Bezier or B-spline patches (See [Bohm84] for an overview). The surface is defined by control points and the surface can be adjusted by moving the control points. The surface can be rendered by evaluating the function for different well-chosen values of u and v. ffl Implicit functions Implicit functions have th..