منابع مشابه
Transformations of quadrilateral lattices
Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogues: the multidimensional quadrilateral lattices, i.e. lattices x : Z −→ R , N ≤ M , whose elementary quadrilaterals are planar. Our investigation is based on the discrete analogue of the theory of the rectilinear congruences, which we also ...
متن کاملDiscrete Levy Transformations and Casorati Determinant Solutions of Quadrilateral Lattices
Sequences of discrete Levy and adjoint Levy transformations for the multidimensional quadrilateral lattices are studied. After a suitable number of iterations we show how all the relevant geometrical features of the transformed quadrilateral lattice can be expressed in terms of multi-Casorati determinants. As an example we dress the Cartesian lattice. On leave of absence from Beijing Graduate S...
متن کاملQuadratic reductions of quadrilateral lattices
It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour-type reduction of the fundamental transformation of quadrilateral lattices is found as well, and superposition of the Ribaucour transformations is presented in the vectorial framework. Finally, the quadratic reduction a...
متن کاملAdvancing Front Quadrilateral Meshing Using Triangle Transformations
Quad-morphing is a new technique used for generating quadrilaterals from an existing triangle mesh. Beginning with an initial triangulation, triangles are systematically transformed and combined. An advancing front method is used to determine the order of transformations. An all-quadrilateral mesh containing elements aligned with the area boundaries with few irregular internal nodes can be gene...
متن کاملIntegrable Discrete Geometry: the Quadrilateral Lattice, its Transformations and Reductions
We review recent results on Integrable Discrete Geometry. It turns out that most of the known (continuous and/or discrete) integrable systems are particular symmetries of the quadrilateral lattice, a multidimensional lattice characterized by the planarity of its elementary quadrilaterals. Therefore the linear property of planarity seems to be a basic geometric property underlying integrability....
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2000
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.533175