Discrete differential geometry aims to develop discrete equivalents of the geometric notions
and methods of classical differential geometry. This survey contains a discussion of the …

We study the Desargues maps, which generate lattices whose points are collinear with all
their nearest (in positive directions) neighbours. The multi-dimensional compatibility of the …

This article demonstrates the design potentials of a recently developed approach for
generating smooth poly-hypar surfaces, freeform surfaces made of combinations of …

A new field of discrete differential geometry is presently emerging on the border between
differential and discrete geometry. Whereas classical differential geometry investigates …

Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces
parametrized along asymptotic lines. The defining property of A-nets is planarity of vertex …

We discuss discretization of Koenigs nets (conjugate nets with equal Laplace invariants)
and of isothermic surfaces. Our discretization is based on the notion of dual quadrilaterals …

We give an elaborated treatment of discrete isothermic surfaces and their analogues in
different geometries (projective, Möbius, Laguerre and Lie). We find the core of the theory to …

Encyclopedia of integrable systems Page 1 Encyclopedia of integrable systems version 0043
31.12.2010 The Encyclopedia contains basics of the theory of nonlinear integrable systems; …

In the spirit of Klein's Erlangen Program, we investigate the geometric and algebraic
structure of fundamental line complexes and the underlying privileged discrete integrable …

We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral
lattice (discrete conjugate net) and provides natural integrable discrete analog of the …