Dedicated to André Galligo on the occasion of his 60th birthday. Abstract This paper studies shapes (curves and surfaces) which can be described by (piece-wise) polynomial support functions. The class of these shapes is closed under con-volutions, offsetting, rotations and translations. We give a geometric discussion of these shapes and present methods for… (More)
The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve… (More)
We analyze the class of surfaces which are equipped with rational support functions. Any rational support function can be decomposed into a symmetric (even) and an antisymmetric (odd) part. We analyze certain geometric properties of surfaces with odd and even rational support functions. In particular it is shown that odd rational support functions… (More)
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may… (More)
For a surface with non vanishing Gaussian curvature the Gauss map is regular and can be inverted. This makes it possible to use the normal as the parameter, and then it is trivial to calculate the normal and the Gauss map. This in turns makes it easy to calculate offsets, the principal curvatures, the principal directions, etc. Such a parametrization is not… (More)
Given a smooth surface patch we construct an approximating piecewise linear structure. More precisely, we produce a mesh for which virtually all vertices have valency three. We present two methods for the construction of meshes whose facets are tangent to the original surface. These two methods can deal with elliptic and hyperbolic surfaces , respectively.… (More)
The support function (SF) representation of surfaces is useful for analyzing curvatures and for representing offset surfaces. After reviewing basic properties of the SF representation, we discuss several techniques for approximating the SF of a given surface.
The convolution of two simple closed oriented curves or surfaces, which is closely related to the Minkowski sum of the domains bounded by them, can be computed with the help of support functions. Based on the approximation of the support functions of the given objects we formulate two strategies for computing convolutions and Minkowski sums. These… (More)