Related papers: Dehn's Algorithm for Simple Diagrams
This paper considers a simple geometric construction, called the Pentagram map. The pentagram map, performed on N-gons, gives rise to a birational mapping on the space of all N-gons. This paper finds what conjecturally are all the…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
This article presents an algorithm to compute digital images of Voronoi, Johnson-Mehl or Laguerre diagrams of a set of punctual sites, in a domain of a Euclidean space of any dimension. The principle of the algorithm is, in a first step, to…
An algorithm is given for explicitly computing Penrose diagrams for spacetimes of the form $ds^2 = -f(r)\, dt^2 + f(r)^{-1} \, dr^2 + r^2 \, d\Omega^2$. The resulting diagram coordinates are shown to extend the metric continuously and…
We give a new, simple distributed algorithm for graph colouring in paths and cycles. Our algorithm is fast and self-contained, it does not need any globally consistent orientation, and it reduces the number of colours from $10^{100}$ to $3$…
Given two closed curves in a surface, we propose an algorithm to detect whether they are of the same type or not.
We present algorithms used in the computational part of the article "Special homogeneous linear systems on Hirzebruch surfaces".
We investigate the problem of determining if a given graph corresponds to the dual of a triangulation of a simple polygon. This is a graph recognition problem, where in our particular case we wish to recognize a graph which corresponds to…
This paper presents a model structure for natural transformations of diagrams of simplicial presheaves of a fixed shape, in which the weak equivalences are defined by analogy with pro-equivalences between pro-objects.
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We give a new proof of McShane's classification of simple cuspidal geodesics, using simple equivariant methods in the hyperbolic plane.
We present an algorithm that computes a shortest non-contractible and a shortest non-separating cycle on an orientable combinatorial surface of bounded genus in O(n \log n) time, where n denotes the complexity of the surface. This solves a…
We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient,…
Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of…
An $h$-queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ queues, such that no two independent edges of the same queue nest. The minimum $h$ such that $G$ admits an $h$-queue layout…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…
A simple formula is given for generating Chern characters by repeated exterior differentiation for n-dimensional differentiable manifolds having a general linear connection.
The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to…