Clifford algebra, spin representation, and rational parameterization of curves and surfaces

Hyeong In Choi, Doo Seok Lee, Hwan Pyo Moon

Research output: Contribution to journalArticlepeer-review

129 Scopus citations

Abstract

The Pythagorean hodograph (PH) curves are characterized by certain Pythagorean n-tuple identities in the polynomial ring, involving the derivatives of the curve coordinate functions. Such curves have many advantageous properties in computer aided geometric design. Thus far, PH curves have been studied in 2- or 3-dimensional Euclidean and Minkowski spaces. The characterization of PH curves in each of these contexts gives rise to different combinations of polynomials that satisfy further complicated identities. We present a novel approach to the Pythagorean hodograph curves, based on Clifford algebra methods, that unifies all known incarnations of PH curves into a single coherent framework. Furthermore, we discuss certain differential or algebraic geometric perspectives that arise from this new approach.

Original languageEnglish
Pages (from-to)5-48
Number of pages44
JournalAdvances in Computational Mathematics
Volume17
Issue number1-2
DOIs
StatePublished - 2002

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