Cubicoids: modeling and visualization

The objective of this paper is to develop a new implicit representation of free-form surfaces which is well suited for modeling as well as for high-quality rendering purposes. The core of our approach is a scheme for constructing tangent plane continuous surfaces passing through an arbitrary set of points in R 3 according to some prescribed topology which is supposed to be given in terms of a piecewise triangular interpolant of the points. The constructed surface consists of algebraic patches of degree three and matches given normal directions at the data points. In contrast to an earlier scheme based on quadric patches it requires a significantly less complicated patch structure, is completely local, and involves a robust default choice for shape parameters which, in particular, supports selecting the “correct” zero sheets of the third-order patches.