Jun-ichi Inoguchi, Kenji Kajiwara, Kenjiro T. Miura, Hyeongki Park and Wolfgang K. Schief
arXiv:1808.03104 2018年8月
In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which is used in CAGD. We consider these curves in the context of similarity geometry and characterize them in terms of a ``stationary'' integr...
Hyeongki Park, Kenji Kajiwara, Takashi Kurose and Nozomu Matsuura
JSIAM Letters 10 25-28 2018年7月 [査読有り]
We show that plane curves in the centroaffine geometry admit a flow which is described by the defocusing modified KdV equation. We establish a correspondence between this flow and the KdV flow in the equicentroaffine geometry. We also present an e...
We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing mKdV equation. Two classes of exact solutions to the defocusing mKdV equation are also presented in terms of the τ functions. By using ...
In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Bur...
K.T. Miura, S. Suzuki, R.U. Gobithaasan, S. Usuki, J. Inoguchi, M. Sato, K. Kajiwara, Y. Shimizu
Computer-Aided Design and Applications 2017年10月 [査読有り]
A curve is considered fair if it consists of continuous and few monotonic curvature segments. Polynomial curves such as Bézier and B-spline curves have complex curvature function, hence the curvature
profile may oscillate easily with a little twea...
The local induction equation, or the binormal flow on space curves is a well-known model of
deformation of space curves as it describes the dynamics of vortex filaments, and the complex
curvature is governed by the nonlinear Schrödinger equation. ...
Kenji Kajiwara, Masatoshi Noumi and Yasuhiko Yamada
J. Phys. A: Math. Theoret. 50(7) 073001 2017年1月 [査読有り]
In this paper a comprehensive review is given on the current status of
achievements in the geometric aspects of the Painlevé equations, with a
particular emphasis on the discrete Painlevé equations. The theory is
controlled by the geometry of ...
Kenji Kajiwara, Toshinobu Kuroda and Nozomu Matsuura
Pacific Journal of Mathematics for Industry 8(1) 1-14 2016年3月 [査読有り]
We study deformations of plane curves in the similarity geometry. It is known that continuous deformations of smooth curves are described by the Burgers hierarchy. In this paper, we formulate the discrete deformation of discrete plane curves descr...
Modeling for CG based on discrete integrable systems
Kobe Studio Seminar:
研究期間: 2016年1月 代表者: 梶原健司
The purpose of this project is to develop modelling technique for computer graphics based on
discrete integrable systems. The theory of discrete integrable systems provides skeletons of
dynamics of geometric objects such as discrete curves and di...
imi.kyushu-u.ac.jp
