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Variational formulation of the log-aesthetic curve

Published: 08 March 2012 Publication History

Abstract

The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. We reformulate the LA curve with variational principle in order to analyze its properties.

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Cited By

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  • (2017)Minimum variation log-aesthetic surfaces and their applications for smoothing free-form shapesJournal of Computational Design and Engineering10.1016/j.jcde.2017.08.0035:2(243-248)Online publication date: 18-Aug-2017
  • (2016)Generalization of log-aesthetic curves by Hamiltonian formalismJSIAM Letters10.14495/jsiaml.8.498(49-52)Online publication date: 2016
  • (2016)Aesthetic Design with Log-Aesthetic CurvesLog-aesthetic curve and SurfacesLog-aesthetic curve and surfaceMathematical Progress in Expressive Image Synthesis III10.1007/978-981-10-1076-7_12(107-119)Online publication date: 22-May-2016
  • Show More Cited By

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Published In

cover image ACM Other conferences
HCCE '12: Proceedings of the 2012 Joint International Conference on Human-Centered Computer Environments
March 2012
277 pages
ISBN:9781450311915
DOI:10.1145/2160749
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

  • Shizuoka University in Hamamatsu: Shizuoka University in Hamamatsu
  • University of Aizu: University of Aizu

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 March 2012

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Author Tags

  1. differential equation
  2. log-aesthetic curve
  3. radius of curvature
  4. variational principle

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  • Research-article

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HCCE '12
Sponsor:
  • Shizuoka University in Hamamatsu
  • University of Aizu

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HCCE '12 Paper Acceptance Rate 48 of 81 submissions, 59%;
Overall Acceptance Rate 48 of 81 submissions, 59%

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Cited By

View all
  • (2017)Minimum variation log-aesthetic surfaces and their applications for smoothing free-form shapesJournal of Computational Design and Engineering10.1016/j.jcde.2017.08.0035:2(243-248)Online publication date: 18-Aug-2017
  • (2016)Generalization of log-aesthetic curves by Hamiltonian formalismJSIAM Letters10.14495/jsiaml.8.498(49-52)Online publication date: 2016
  • (2016)Aesthetic Design with Log-Aesthetic CurvesLog-aesthetic curve and SurfacesLog-aesthetic curve and surfaceMathematical Progress in Expressive Image Synthesis III10.1007/978-981-10-1076-7_12(107-119)Online publication date: 22-May-2016
  • (2014)Aesthetic Curves and Surfaces in Computer Aided Geometric DesignInternational Journal of Automation Technology10.20965/ijat.2014.p03048:3(304-316)Online publication date: 5-May-2014

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