Exploring hypersurfaces with offset-like convolutions

Offsetting is one of the fundamental operations in Computer Aided Design. Due to their high applicability, studying offsets of hypersurfaces has become a popular research area and many interesting problems related to this topic have arisen. In addition, various generalizations of classical offsets have been introduced and then investigated. In this paper we study a generalization which is based on considering offsets to (not only parameterized) hypersurfaces as convolutions with hyperspheres. In other words, we study hypersurfaces sharing the same convolution properties with hyperspheres and thus yielding offset-like convolutions. We will present an algebraic analysis of these hypersurfaces and study their properties suitable for subsequent applications, e.g. in geometric modelling. Moreover, our approach allows to derive distinguished properties of the well-known PH/PN parameterizations as special subcases of the introduced QN parameterizations.

► Study of special class of rational hypersurfaces yielding convolutions with offset-like properties.
► A complete algebraic analysis of hypersurfaces with quadratic normal (QN) vector field.
► Generalization of classical offsets.
► Classification of QN hypersurfaces using associated coherent forms.
► Special results concerning convolutions of conics and quadrics.