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Variational formulation of the log-aesthetic curve

Authors:

Kenjiro T. Miura,

Shin Usuki,

R. U. GobithaasanAuthors Info & Claims

HCCE '12: Proceedings of the 2012 Joint International Conference on Human-Centered Computer Environments

Pages 215 - 219

https://doi.org/10.1145/2160749.2160793

Published: 08 March 2012 Publication History

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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.

References

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Cited By

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Suzuki SGobithaasan RSalvi PUsuki SMiura K(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
https://doi.org/10.1016/j.jcde.2017.08.003
Sato MShimizu Y(2016)Generalization of log-aesthetic curves by Hamiltonian formalismJSIAM Letters10.14495/jsiaml.8.498(49-52)Online publication date: 2016
https://doi.org/10.14495/jsiaml.8.49
Miura KGobithaasan R(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
https://doi.org/10.1007/978-981-10-1076-7_12
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Index Terms

Variational formulation of the log-aesthetic curve
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Abstract
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Graphical abstract
Highlights
- Log-aesthetic curves in the framework of similarity geometry are considered.
- ...

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Published In

HCCE '12: Proceedings of the 2012 Joint International Conference on Human-Centered Computer Environments

March 2012

277 pages

ISBN:9781450311915

DOI:10.1145/2160749

General Chairs:
Alexander Vazhenin
University of Aizu, Japan
,
Jens Herder
University of Applied Sciences, Duesseldorf, Germany
,
Kenjiro Miura
Shizuoka University, Japan

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]

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New York, NY, United States

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Published: 08 March 2012

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Shizuoka University in Hamamatsu
University of Aizu

HCCE '12: The Joint International Conference on Human-Centered Computer Environments

March 8 - 13, 2012

Aizu-Wakamatsu, Japan

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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

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Suzuki SGobithaasan RSalvi PUsuki SMiura K(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
https://doi.org/10.1016/j.jcde.2017.08.003
Sato MShimizu Y(2016)Generalization of log-aesthetic curves by Hamiltonian formalismJSIAM Letters10.14495/jsiaml.8.498(49-52)Online publication date: 2016
https://doi.org/10.14495/jsiaml.8.49
Miura KGobithaasan R(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
https://doi.org/10.1007/978-981-10-1076-7_12
Miura KGobithaasan R(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
https://doi.org/10.20965/ijat.2014.p0304

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Recommendations

Log-aesthetic space curve segments

Quintic polynomial approximation of log-aesthetic curves by curvature deviation

Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles▪

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