Applying Rational Envelope curves for skinning purposes

TL;DR

This paper introduces a novel application of Rational Envelope (RE) curves for skinning in geometric design, enabling better interpolation of contact points on input circles to improve skinning quality.

Contribution

The paper proposes using RE curves for skinning, providing a new method to interpolate contact points on circles, enhancing geometric modeling techniques.

Findings

RE curves effectively interpolate contact points on circles.

The method improves skinning quality in geometric design.

Overcomes issues with inappropriate contact point placement.

Abstract

Special curves in the Minkowski space such as Minkowski Pythagorean hodographs play an important role in Computer Aided Geometric Design, and their usages have been thoroughly studied in the recent years. Also, several papers have been published which describe methods for interpolating Hermite data in R2,1 by MPH curves. Bizzarri et al.introduced the class of RE curves and presented an interpolation method for G1 Hermite data, where the resulting RE curve yields a rational boundary for the represented domain. We now propose a new application area for RE curves: skinning of a discrete set of input circles. We find the appropriate Hermite data to interpolate so that the obtained rational envelope curves touch each circle at previously defined points of contact. This way we overcome the problematic scenarios when the location of the touching points would not be appropriate for skinning purposes.