Topic

# Polygonal chain

About: Polygonal chain is a(n) research topic. Over the lifetime, 729 publication(s) have been published within this topic receiving 15168 citation(s). The topic is also known as: polygonal curve & polygonal path.

##### Papers published on a yearly basis

##### Papers

More filters

••

TL;DR: An approximation algorithm is presented which uses an iterative method to produce polygons with a small—but not minimum—number of vertices that lie on the given curve that justifies the abandonment of the minimum-vertices criterion.

Abstract: The approximation of arbitrary two-dimensional curves by polygons is an importanttechnique in image processing. For many applications, the apparent ideal procedure is to represent lines and boundaries by means of polygons with minimum number of vertices and satisfying a given fit criterion. In this paper, an approximation algorithm is presented which uses an iterative method to produce polygons with a small—but not minimum—number of vertices that lie on the given curve. The maximum distance of the curve from the approximating polygon is chosen as the fit criterion. The results obtained justify the abandonment of the minimum-vertices criterion which is computationally much more expensive.

1,201 citations

01 May 1997

TL;DR: Methods for simplifying and approximating polygonal surfaces from computer graphics, computer vision, cartography, computational geometry, and other fields are classified, summarized, and compared both practically and theoretically.

Abstract: : This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewise-linear surface in 3-D defined by a set of polygons; typically a set of triangles. Methods from computer graphics, computer vision, cartography, computational geometry, and other fields are classified, summarized, and compared both practically and theoretically. The surface types range from height fields (bivariate functions), to manifolds, to non-manifold self-intersecting surfaces. Piecewise-linear curve simplification is also briefly surveyed.

589 citations

••

TL;DR: A simple and robust Matlab code for polygonal mesh generation that relies on an implicit description of the domain geometry and the centroidal Voronoi diagrams used for its discretization that offers great flexibility to construct a large class of domains via algebraic expressions.

Abstract: We present a simple and robust Matlab code for polygonal mesh generation that relies on an implicit description of the domain geometry. The mesh generator can provide, among other things, the input needed for finite element and optimization codes that use linear convex polygons. In topology optimization, polygonal discretizations have been shown not to be susceptible to numerical instabilities such as checkerboard patterns in contrast to lower order triangular and quadrilaterial meshes. Also, the use of polygonal elements makes possible meshing of complicated geometries with a self-contained Matlab code. The main ingredients of the present mesh generator are the implicit description of the domain and the centroidal Voronoi diagrams used for its discretization. The signed distance function provides all the essential information about the domain geometry and offers great flexibility to construct a large class of domains via algebraic expressions. Examples are provided to illustrate the capabilities of the code, which is compact and has fewer than 135 lines.

376 citations

••

TL;DR: It is shown that the embedding of data into 3-D polygonal models is a practicable technique through several data embedding algorithms based on fundamental methods.

Abstract: This paper discusses techniques for embedding data into three-dimensional (3-D) polygonal models of geometry. Given objects consisting of points, lines, (connected) polygons, or curved surfaces, the algorithms described in produce polygonal models with data embedded into either their vertex coordinates, their vertex topology (connectivity), or both. Such data embedding can be used, for example, for copyright notification, copyright protection, theft deterrence, and inventory of 3-D polygonal models. A description of the background and requirements is followed by a discussion of where, and by what fundamental methods, data can be embedded into 3-D polygonal models. The paper then presents several data embedding algorithms, with examples, based on these fundamental methods. By means of these algorithms and examples, we show that the embedding of data into 3-D polygonal models is a practicable technique.

320 citations

••

TL;DR: This survey focuses specifically on polygonal shape functions that satisfy the properties of barycentric coordinates: form a partition of unity, and are non-negative; interpolate nodal data (Kronecker-delta property), and are smooth within the domain.

Abstract: This paper is an overview of recent developments in the construction of finite element interpolants, which areC
0-conforming on polygonal domains. In 1975, Wachspress proposed a general method for constructing finite element shape functions on convex polygons. Only recently has renewed interest in such interpolants surfaced in various disciplines including: geometric modeling, computer graphics, and finite element computations. This survey focuses specifically on polygonal shape functions that satisfy the properties of barycentric coordinates: (a) form a partition of unity, and are non-negative; (b) interpolate nodal data (Kronecker-delta property), (c) are linearly complete or satisfy linear precision, and (d) are smooth within the domain. We compare and contrast the construction and properties of various polygonal interpolants—Wachspress basis functions, mean value coordinates, metric coordinate method, natural neighbor-based coordinates, and maximum entropy shape functions. Numerical integration of the Galerkin weak form on polygonal domains is discussed, and the performance of these polygonal interpolants on the patch test is studied.

270 citations