Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces

Authors:
Hee Cheol Cho;Hyeong In Choi;Song-Hwa Kwon;Doo Seok Lee;Nam-Sook Wee
Affiliations:
Department of Mathematics, Seoul National University, Seoul, South Korea;Department of Mathematics, Seoul National University, Seoul, South Korea;Department of Mathematics, Seoul National University, Seoul, South Korea;Research Lab., Amisys Corp., Seoul, South Korea;Department of Industrial Engineering, Hansung University, Seoul, South Korea
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

We present a new approach toward the rational parametrization of canal surfaces. According to our previous work, every canal surface with rational (respectively polynomial) spine curve and rational (respectively polynomial) radius function is a rational (respectively polynomial) Pythagorean hodograph curve in R3,1. Drawing upon this formalism and utilizing the underlying Lorentzian geometry, the problem is reduced to simple algebraic manipulations.We also illustrate how our work related to the previous work of pottmann and Peternell. Finally, we give an outline of an approach toward the rotation minimizing parametrization of canal surfaces.