Project Year: Oct 2019 - Mar 2025 Investigator(s): Kenji Kajiwara

We originate a novel geometry of discrete surfaces having the surfaces with good properties, such as developable surfaces, as the shape elements, incorporate the theory of aesthetic shapes and construct the technique of structural analysis/optimiz...

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

Nalini Joshi, Kenji Kajiwara, Tetsu Masuda and Nobutaka Nakazono

arXiv:1908.10060 Aug 2019

We derive the cross-ratio equations and similarity constraint that lead to discrete power functions and associated circle patterns on a hexagonal lattice from two starting points: the ABS equations and the Garnier systems. This provides a differen...

Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 2(CRC Press,2019) 356-381 Dec 2019 [Refereed]

A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage mechanisms whic...

After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We have decided to do the fairing pro...

Jun-ichi Inoguchi, Kenji Kajiwara, Kenjiro T. Miura, Hyeongki Park and Wolfgang K. Schief

arXiv:1808.03104 Aug 2018

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 Jul 2018 [Refereed]

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 ...

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

Computer Aided Geometric Design 61 1-5 Mar 2018 [Refereed]

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...

Journal of Integrable Systems 4(1) xyz003 Jul 2019 [Refereed]

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. ...

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...