We propose an algorithm to produce a 3-D CAD model from a set of range data, based on non-uniform rational B-splines (NURBS) surface fitting technique. Our goal is to construct continuous geometric models, assuming that the topology of surface is unknown. In our approach, the triangulated surface is partitioned in quadrilateral patches, using Morse theory. The quadrilateral obtained mesh is reg...

An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed. The data structure, the directional refinement and coarsening, including the method for initializing the refined new cells, for the anisotropic adaptive method are described. It provides efficient high resolution of flow features, which are aligned with the original qu...

Define a graph GT (n) with one node for each triangulation of a convex n-gon. Place an edge between each pair of nodes that differ by a single flip: two triangles forming a quadrilateral are exchanged for the other pair of triangles forming the same quadrilateral. In this paper we introduce a tree of all triangulations of polygons with any number of vertices which gives a unified framework in w...

Hartsfield and Ringel proved that a complete graph Kn has an orientable quadrangular embedding if n ≡ 5 (mod 8), and has a nonorientable quadrangular embedding if n ≥ 9 and n ≡ 1 (mod 4). We complete the characterization of complete graphs admitting quadrangular embeddings by showing that Kn has an orientable quadrilateral embedding if n ≡ 0 (mod 8), and has a nonorientable quadrilateral embedd...

Geometric interpretation of the Hirota equation is presented as equation describing the Laplace sequence of two-dimensional quadrilateral lattices. Different forms of the equation are given together with their geometric interpretation: (i) the discrete coupled Volterra system for the coefficients of the Laplace equation, (ii) the gauge invariant form of the Hirota equation for projective invari...

We introduce the dual Koenigs lattices, which are the integrable discrete analogues of conjugate nets with equal tangential invariants, and we find the corresponding reduction of the fundamental transformation. We also introduce the notion of discrete normal congruences. Finally, considering quadrilateral lattices ”with equal tangential invariants” which allow for harmonic normal congruences we...

A complete quadrilateral in the Euclidean plane is studied. The geometry of such almost as rich a triangle, so there are lot associated points, lines and conics. Hereby, study was performed rectangular coordinates, symmetrically on all four sides with parameters a, b, c, d . In this paper we will properties some circles to quadrilateral. All these well known, but here they proved by same method...