[geometry-ml:03472] 九州可積分系セミナー(D. Brander) 10/19

[Kenji Kajiwara]

幾何学MLの皆様：

10月19日（金）に以下のようなセミナーを行います．「可積分系セミナー」ですが，
幾何学MLの方々で興味を持たれる方もいらっしゃると思いますので，こちらにも
ご案内させていただきます．

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九州可積分系セミナー

日時 : 2018 年10月19 日 （金） 15:00 - 17:00
場所 : 九州大学伊都キャンパス ウエスト1号館5F C502 大講義室
(C502, 5th floor, West No.1 Building, Ito Campus, Kyushu University)

(1)  
Speaker: David Brander (Technical University of Denmark)
Title:  Designing with elastic curves

Abstract:  Euler's elastica are natural curves that appeared in design before the 
introduction of computers, because these curves are the natural shape for the wooden
splines that were used in drafting. Although they have natural aesthetic properties,
they were abandoned when computers were introduced because polynomial splines are
much easier to deal with mathematically. Motivated by new fabrication processes, we 
have studied the practical problem of designing with elastic curves and 
splines on a computer. We show in [1] that the problems of non-uniqueness and instability, 
inherent in the nonlinear mathematics of elastic splines, can be solved by introducing
a suitable proxy curve to represent the elastica. In this talk, I will describe this
work, as well as some remaining issues.

[1] Bézier curves that are close to elastica.
D. Brander, J.A. Bærentzen, A. Fisker and J. Gravesen,
Computer-Aided Design, 104, (2018), 36--44. 

[2] Approximation by planar elastic curves.
D. Brander,  J. Gravesen and T. Nørbjerg.
Adv. Comput. Math. DOI: 10.1007/s10444-016-9474-z 

(2) 
Speaker: Sebastián Graiff-Zurita (Graduate School of Mathematics, Kyushu University）
Title:  Discrete Euler’s elastica – characterization and application.

Abstract: After characterizing the discrete Euler’s elastica proposed
by Sogo (“Variational discretization of Euler’s Elastica problem”,
2006), we consider the problem of approximating a given discrete plane
curve by an appropriate discrete Euler’s elastica, according to a
suitable criteria. We have decided to do the approximation process via
a L2-distance minimization, because other approaches presented
numerical instabilities. The optimization problem was solved via a
gradient-driven optimization method (IPOPT). This optimization problem
is non-convex and the result strongly depends on the initial
guess. So, we have decided to discretize the algorithm provided by
Brander et al. (“Approximation by planar elastic curves”, 2016),
which gives an initial guess to the IPOPT method.

問い合わせ先：
九州大学マス・フォア・インダストリ研究所
梶原健司 kaji ＠ imi.kyushu-u.ac.jp
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