Computational Geometry Column 42

A compendium of thirty previously published open problems in computational geometry is presented.Comment: 7 pages; 72 reference

Linear-Time Triangulation of a Simple Polygon Made Easier Via Randomization

We describe a randomized algorithm for computing the trapezoidal decomposition of a simple polygon. Its expected running time is linear in the size of the polygon. By a well-known and simple linear time reduction, this implies a linear time algorithm for triangulating a simple polygon. Our algorithm is considerably simpler than Chazelle's (1991) celebrated optimal deterministic algorithm and, hence, positively answers his question of whether a simpler randomized algorithm for the problem exists. The new algorithm can be viewed as a combination of Chazelle's algorithm and of non-optimal randomized algorithms due to Clarkson et al. (1991) and to Seidel (1991), with the essential innovation that sampling is performed on subchains of the initial polygonal chain, rather than on its edges. It is also essential, as in Chazelle's algorithm, to include a bottom-up preprocessing phase previous to the top-down construction phase. 1 Introduction Polygon triangulation is a classic problem in comp..

Simulação interativa de tecidos e roupas: técnicas para o desenvolvimento de um simulador

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Ciências da Computação, Florianópolis, 2014.Há o interesse na simulação de roupas em qualquer aplicação onde há a presença de humanos virtuais. Contudo, simular o comportamento de tecidos no corpo de uma pessoa é uma tarefa complexa. Além disso, existe a constante necessidade de se obter resultados mais rápidos que viabilizem a simulação de indumentárias cada vez mais detalhadas. Este trabalho aborda técnicas relativas a diferentes etapas e aspectos do processo de simulação. Propõe-se uma otimização para um método para gerar efeitos de rasgo e corte. Ainda, introduz-se um algoritmo para a geração de linhas de costura em malhas de triângulos. As técnicas aqui descritas são utilizadas na implementação de um simulador cujo propósito é agilizar o desenvolvimento de sistemas para projeto e confecção de roupas.Abstract : There is interest in the simulation of clothes in any application where there is the presence of virtual humans. However, simulate the behavior of fabric on the body of a person is a complex task. In addition, there is a constant need to get faster results that allow the simulation of increasingly detailed garment. This work discusses techniques for different stages and aspects of the simulation process. We propose an optimization for a method used to generate effects of tearing and cutting. Also, we introduce an algorithm to generate seam lines for triangle meshes. The techniques described herein are used in the implementation of a simulator whose purpose is to facilitate the development of systems for designing and making clothes