Definition 20 (simplex). A k-simplex σ is the convex hull of a set P of k + 1 affinely independent points. In particular, a 0-simplex is a vertex, a 1-simplex is an edge, a 2-simplex is a triangle, and a 3-simplex is a tetrahedron. A k-simplex is said to have dimension k. A face of σ is a simplex that is the convex hull of a nonempty subset of P. Faces of σ come in all dimensions from zero (σ’s...

The goal is to generate tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principle idea is that a vertex set in general positions guarantees existence of a unique triangulation which satisses the Delaunay empty-sphere property. (Algorithms for robust, parallel construction of such triangulations are available.) However, all of t...

In conventional nitride-based light emitting diodes, huge internal electric fields lead to a reduced overlap of electron and hole wave functions in the active GaInN quantumwells as a consequence of the piezoelectricity of these polar materials. In order to minimize these internal fields while still maintaining the well-established c-direction as main epitaxial growth direction for high-quality ...

The Grishukhin inequality is a facet of the cut polytope CUT7 of the complete graph K7, for which no natural generalization to a family of inequalities has previously been found. On the other hand, the Imm22 Bell inequalities of quantum information theory, found by Collins and Gisin, can be seen as valid inequalities of the cut polytope CUT¤(K1,m,m) of the complete tripartite graph K1,m,m. They...

Surface reconstruction of 3d reverse engineering data through the application of a triangulated mesh is a popular method. This is because triangles are the simplest polygons for computations. The purpose of a triangular mesh is to cover the point set with a surface mesh of triangular facets. During the last decade, reverse engineering and surface reconstruction have received much attention from...

We report the study of lasing modes in broad-area, equilateral-triangular laser cavities. An alternative approach is proposed to study optical modes in equilateral triangular cavities in an analytical form. The modes were obtained by examining the simplest optical paths inside the cavity, which yields the final solution with the boundary conditions. The cavities can be fabricated from semicondu...

We describe laboratory-grown snow crystals that exhibit a triangular, plate-like morphology, and we show that the occurrence of these crystals is much more frequent than one would expect from random growth perturbations of the more-typical hexagonal forms. We then describe an aerodynamic model that explains the formation of these crystals. A single growth perturbation on one facet of a hexagona...

Marching triangles is a method for producing a polygon mesh surface approximation composed of triangular facets which are approximately equilateral. This paper improves the Marching Triangles algorithm where the inputs are multiple range images of scenes. C discontinuities (fold edges) are detected and used to constrain the final triangulation, thus increasing the accuracy of the mesh at sharp ...

morphometric characteristics of anticlines can play an important role in the exploration of oil resources. the purpose of this research is to evaluate the effect of geomorphology on the exploration of oil resources in oil-rich bankol and oil-less danehkhoshk anticlines by means of geomorphological indices. to achieve the purpose of this study, topographic maps at a scale of 1:50000 and geologic...

Anisotropic wet etching of vicinal monocrystalline Si (111)4 o wafers was used to obtain blazed gratings that are highly efficient in the soft X-ray (SXR) and extreme ultraviolet (EUV) applications. An improved experimental technology for fabrication triangular-grooved gratings, both medium-frequency (250 500 mm -1 ) high-frequency (2500 ones, is presented. The stages forming a Cr-mask grooves ...