In the late 2000s, a novel formulation of Kirchhoff's celebrated rod theory was published by
Bergou et al.[4]. In this formulation, an elastic rod is discretized into a series of segments (or …

Discrete orthogonal geodesic nets (DOGs) are a quad mesh analogue of developable
surfaces. In this work we study continuous deformations on these discrete objects. Our main …

We consider integrable discretizations of some soliton equations associated with the
motions of plane curves: the Wadati–Konno–Ichikawa elastic beam equation, the complex …

The theory of Cosserat rods provides versatile models to simulate large spatial deformations
of slender flexible structures. As the strain measures of the mechanical theory are given in …

Efficient and productive manufacturing of freeform shapes requires a suitable three-
dimensional CAD model at the entrance to the CAM system. The paper deals with the impact …

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 …

We investigate the discrete-time motions of planar discrete curves, and derive discrete
integrable equations on a two-dimensional nonuniform lattice. In particular, we obtain the …

We construct explicit solutions to the discrete motion of discrete plane curves that has been
introduced by one of the authors recently. Explicit formulas in terms of the τ function are …

An elastic gridshell is a freeform structure, generally doubly curved, but formed out through
the reversible deformation of a regular and initially flat structural grid. Building curved …

A Darboux transformation for polarized space curves is introduced and its properties are
studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described …