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

Hee Cheol Cho; Hyeong In Choi; Song Hwa Kwon; Doo Seok Lee; Nam Sook Wee

doi:10.1016/j.cagd.2003.11.001

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

Hee Cheol Cho, Hyeong In Choi, Song Hwa Kwon, Doo Seok Lee, Nam Sook Wee

School of Undergraduate Studies

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

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 ℝ^3,1. Drawing upon this formalism and utilizing the underlying Lorentzian geometry, the problem is reduced to simple algebraic manipulations. We also illustrate how our work relates to the previous work of Pottmann and Peternell. Finally, we give an outline of an approach toward the rotation-minimizing parametrization of canal surfaces.

Original language	English
Pages (from-to)	327-339
Number of pages	13
Journal	Computer Aided Geometric Design
Volume	21
Issue number	4
DOIs	https://doi.org/10.1016/j.cagd.2003.11.001
State	Published - Apr 2004

Bibliographical note

Funding Information:
This research was also financially supported by Hansung University in the year 2004. * Corresponding author. E-mail address: [email protected] (H.I. Choi).

Funding Information:
✩ Supported in part by KOSEF R01-2001-000-00396-0, KOSEF—SRCCS at SNU, and Overhead Research Fund of SNU.

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10.1016/j.cagd.2003.11.001

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title = "Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces",

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 relates to the previous work of Pottmann and Peternell. Finally, we give an outline of an approach toward the rotation-minimizing parametrization of canal surfaces.",

author = "Cho, {Hee Cheol} and Choi, {Hyeong In} and Kwon, {Song Hwa} and Lee, {Doo Seok} and Wee, {Nam Sook}",

note = "Funding Information: This research was also financially supported by Hansung University in the year 2004. * Corresponding author. E-mail address: [email protected] (H.I. Choi). Funding Information: ✩ Supported in part by KOSEF R01-2001-000-00396-0, KOSEF—SRCCS at SNU, and Overhead Research Fund of SNU.",

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doi = "10.1016/j.cagd.2003.11.001",

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AU - Cho, Hee Cheol

AU - Choi, Hyeong In

AU - Kwon, Song Hwa

AU - Lee, Doo Seok

AU - Wee, Nam Sook

N1 - Funding Information: This research was also financially supported by Hansung University in the year 2004. * Corresponding author. E-mail address: [email protected] (H.I. Choi). Funding Information: ✩ Supported in part by KOSEF R01-2001-000-00396-0, KOSEF—SRCCS at SNU, and Overhead Research Fund of SNU.

PY - 2004/4

Y1 - 2004/4

N2 - 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 relates to the previous work of Pottmann and Peternell. Finally, we give an outline of an approach toward the rotation-minimizing parametrization of canal surfaces.

AB - 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 relates to the previous work of Pottmann and Peternell. Finally, we give an outline of an approach toward the rotation-minimizing parametrization of canal surfaces.

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DO - 10.1016/j.cagd.2003.11.001

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SN - 0167-8396

VL - 21

SP - 327

EP - 339

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 4

ER -

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

Abstract

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