Branching blend of natural quadrics based on surfaces with rational offsets

Authors:
Rimvydas Krasauskas
Affiliations:
Vilnius University, Faculty of Mathematics and Informatics, Naugarduko 24, LT-03225 Vilnius, Lithuania
Venue:
Computer Aided Geometric Design
Year:
2008

Citing 10
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Abstract

A new branching blend between two natural quadrics (circular cylinders/cones or spheres) in many positions is proposed. The blend is a ring shaped patch of a PN surface (surface with rational offset) parametrized by rational bivariant functions of degree (6,3). The general theory of PN surfaces is developed using Laguerre geometry and a universal rational parametrization of the Blaschke cylinder. The construction is extended via inversion to a PN branching blend of degree (8,4) between Dupin cyclide and a natural quadric.