Construction of rational curves with rational rotation-minimizing frames via Möbius transformations

Michael Bartoň; Bert Jüttler; Wenping Wang

doi:10.1007/978-3-642-11620-9_2

Construction of rational curves with rational rotation-minimizing frames via Möbius transformations

Michael Bartoň^*, Bert Jüttler, Wenping Wang

^*Corresponding author for this work

Visual Computing Center (VCC)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

15 Scopus citations

Abstract

We show that Möbius transformations preserve the rotation-minimizing frames which are associated with space curves. In addition, these transformations are known to preserve the class of rational Pythagorean- hodograph curves and rational frames. Based on these observations we derive an algorithm for G ¹ Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minimizing frames.

Original language	English (US)
Title of host publication	Mathematical Methods for Curves and Surfaces - 7th International Conference, MMCS 2008, Revised Selected Papers
Pages	15-25
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-642-11620-9_2
State	Published - 2010
Event	7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008 - Tonsberg, Norway Duration: Jun 26 2008 → Jul 1 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5862 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008
Country/Territory	Norway
City	Tonsberg
Period	06/26/08 → 07/1/08

Keywords

Möbius transformations
Pythagorean-hodograph curve
Rational rotation-minimizing frame

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-11620-9_2

Cite this

Bartoň, M., Jüttler, B., & Wang, W. (2010). Construction of rational curves with rational rotation-minimizing frames via Möbius transformations. In Mathematical Methods for Curves and Surfaces - 7th International Conference, MMCS 2008, Revised Selected Papers (pp. 15-25). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5862 LNCS). https://doi.org/10.1007/978-3-642-11620-9_2

Bartoň, Michael ; Jüttler, Bert ; Wang, Wenping. / Construction of rational curves with rational rotation-minimizing frames via Möbius transformations. Mathematical Methods for Curves and Surfaces - 7th International Conference, MMCS 2008, Revised Selected Papers. 2010. pp. 15-25 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We show that M{\"o}bius transformations preserve the rotation-minimizing frames which are associated with space curves. In addition, these transformations are known to preserve the class of rational Pythagorean- hodograph curves and rational frames. Based on these observations we derive an algorithm for G 1 Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minimizing frames.",

keywords = "M{\"o}bius transformations, Pythagorean-hodograph curve, Rational rotation-minimizing frame",

author = "Michael Barto{\v n} and Bert J{\"u}ttler and Wenping Wang",

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doi = "10.1007/978-3-642-11620-9_2",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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booktitle = "Mathematical Methods for Curves and Surfaces - 7th International Conference, MMCS 2008, Revised Selected Papers",

note = "7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008 ; Conference date: 26-06-2008 Through 01-07-2008",

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Bartoň, M, Jüttler, B & Wang, W 2010, Construction of rational curves with rational rotation-minimizing frames via Möbius transformations. in Mathematical Methods for Curves and Surfaces - 7th International Conference, MMCS 2008, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5862 LNCS, pp. 15-25, 7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008, Tonsberg, Norway, 06/26/08. https://doi.org/10.1007/978-3-642-11620-9_2

Construction of rational curves with rational rotation-minimizing frames via Möbius transformations. / Bartoň, Michael; Jüttler, Bert; Wang, Wenping.
Mathematical Methods for Curves and Surfaces - 7th International Conference, MMCS 2008, Revised Selected Papers. 2010. p. 15-25 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5862 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Construction of rational curves with rational rotation-minimizing frames via Möbius transformations

AU - Bartoň, Michael

AU - Jüttler, Bert

AU - Wang, Wenping

PY - 2010

Y1 - 2010

N2 - We show that Möbius transformations preserve the rotation-minimizing frames which are associated with space curves. In addition, these transformations are known to preserve the class of rational Pythagorean- hodograph curves and rational frames. Based on these observations we derive an algorithm for G 1 Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minimizing frames.

AB - We show that Möbius transformations preserve the rotation-minimizing frames which are associated with space curves. In addition, these transformations are known to preserve the class of rational Pythagorean- hodograph curves and rational frames. Based on these observations we derive an algorithm for G 1 Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minimizing frames.

KW - Möbius transformations

KW - Pythagorean-hodograph curve

KW - Rational rotation-minimizing frame

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DO - 10.1007/978-3-642-11620-9_2

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SN - 3642116191

SN - 9783642116193

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 15

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BT - Mathematical Methods for Curves and Surfaces - 7th International Conference, MMCS 2008, Revised Selected Papers

T2 - 7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008

Y2 - 26 June 2008 through 1 July 2008

ER -

Bartoň M, Jüttler B, Wang W. Construction of rational curves with rational rotation-minimizing frames via Möbius transformations. In Mathematical Methods for Curves and Surfaces - 7th International Conference, MMCS 2008, Revised Selected Papers. 2010. p. 15-25. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-11620-9_2

Construction of rational curves with rational rotation-minimizing frames via Möbius transformations

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