Jun-ichi Inoguchi, Kenji Kajiwara, Kenjiro T. Miura, Masayuki Sato, Wolfgang K. Schief, Yasuhiro Shimizu

preprint, arXiv:1711.09549, to appear in Computer Aided Geometric Design(2018) Nov 2017

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 Oct 2017 [Refereed]

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 Jan 2017 [Refereed]

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 Mar 2016 [Refereed]

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...

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 Schödinger equation (N...

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant defor...

Discrete Model of Isoperimetric Deformations of Planar Discrete Curve and DIscrete Integrabls Systems

Kenji Kajiwara

MI Lecture Note "Mathematical Approaches to Research Topics in Science and Technology-Foundation and Development of Mathematical Modeling" 46 57-62 Mar 2013 [Invited]

Introduction to Integrable Systems

Kenji Kajiwara

MI Lecture Note "Tutorial on Discrete Integrable Systems and Discrete Differential Geometry 2012" 40 1-24 Mar 2012 [Invited]

We consider an integrability test for ultradiscrete equations based on the
singularity confinement analysis for discrete equations. We show how
singularity pattern of the test is transformed into that of ultradiscrete
equation. The ultradiscrete s...

Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma, Basil Grammaticos, Alfred Ramani

Oct 1993

We present a class of solutions to the discrete Painlevé-II equation for
particular values of its parameters. It is shown that these solutions can be
expressed in terms of Casorati determinants whose entries are discrete Airy
functions. The anal...

Development and Extension of Integrable Discrete Differential Geometry

JSPS: KAKENHI (Scientific Research (B))

Project Year: Apr 2016 - Mar 2020 Investigator(s): Kenji Kajiwara

Construction of Discrete-time Geometric Models Based on Discrete Differential Geometry

JSPS: KAKENHI (Challenging Exploratory Research)

Project Year: Apr 2016 - Mar 2018 Investigator(s): Kenji Kajiwara

Modeling for CG based on discrete integrable systems

Kobe Studio Seminar:

Project Year: Jan 2016 Investigator(s): Kenji Kajiwara

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...