Finding a triangular mesh with a constant number of different edge lengths
نویسندگان
چکیده
We consider the problem of triangulating an x-monotone polygon with a small number of different edge lengths using Steiner points. Given a parameter α, where 0 < α < 1, we shall present an algorithm for finding an almost uniform triangular mesh with 3π/8α2 + o(1/α2) different edge lengths such that every edge length is between l and (2 + √ 2α)l. Experiments demonstrate the effectiveness of this algorithm. key words: computational geometry, Delaunay triangulation, Voronoi diagram
منابع مشابه
An Inequality on the Edge Lengths of Triangular Meshes
We give a short proof of the following geometric inequality: for any two triangular meshes A and B of the same polygon C, if the number of vertices in A is at most the number of vertices in B, then the maximum length of an edge in A is at least the minimum distance between two vertices in B. Here the vertices in each triangular mesh include the vertices of the polygon and possibly additional St...
متن کاملVibration Analysis of Orthotropic Triangular Nanoplates Using Nonlocal Elasticity Theory and Galerkin Method
In this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s approach in conjunction with the area coordinates is used as a basis for the solution. Nonlocal theories are employed to bring out the...
متن کاملBearing Capacity of Triangular Shell Foundations Adjacent to the Reinforced Sandy Slopes
This paper investigates response of triangular shell strip footings situated on the sandy slope. A series of reduced-scale plate load tests were conducted to cover different parameters including three shell footing types with different apex angles in addition to a flat footing, four different distances for strip footings from the crest of the slope namely “edge distance” and reinforcement statu...
متن کاملMHD Natural Convection and Entropy Generation of Variable Properties Nanofluid in a Triangular Enclosure
Natural convection heat transfer has many applications in different fields of industry; such as cooling industries, electronic transformer devices and ventilation equipment; due to simple process, economic advantage, low noise and renewed retrieval. Recently, heat transfer of nanofluids have been considered because of higher thermal conductivity coefficient compared with those of ordinary fluid...
متن کاملInteractive Modeling and Subdivision of Flexible Equilateral Triangular Mechanisms
Based on the requests from architects, we developed a system which allows to interactively design and subdivide flexible triangular surfaces. Due to economical reasons the number of different types of building elements should be small. For that reason we only use equilateral base triangles of unique size with the possibility of subdivision. To allow to interactively move vertices and to ensure ...
متن کامل