Invariant-geometry conditions for the rational bi-quadratic Bézier surfaces

Bez, Helmut

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Invariant-geometry conditions for the rational bi-quadratic Bézier surfaces

journal contribution

posted on 2014-05-28, 09:22 authored by Helmut Bez

A generalization of Patterson’s work (Patterson, 1985), on the invariants of the rational Bézier curves, to the case of surfaces is presented. An equation for the determination of the invariants for surfaces of degree (n, n) is derived and solved for the bi-quadratics – for which it is shown that seven independent, invariant functions exist. Explicit forms of the invariants are derived and a number of applications are presented.

History

School

Science

Department

Computer Science

Citation

BEZ, H.E., 2009. Invariant-geometry conditions for the rational bi-quadratic Bézier surfaces. Computer Aided Geometric Design, 26 (8), pp.877-887.

Publisher

Version

SMUR (Submitted Manuscript Under Review)

Publication date

2009

Notes

This is the author’s version of a work that was submitted for publication in Computer Aided Geometric Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://dx.doi.org/10.1016/j.cagd.2009.06.004