History: Alessio's Doutorado Thesis (in Portuguese)

Alguns  textos, programas e  imagensrelacionados com o tema da minha
tese de doutorado  "Traçado Não-Sobreposto de
Interseção de Superfícies Regulares com Passo de Contato de Ordem 3 ".
 

TEXTOS

• Tese: Traçado Não-Sobreposto de Interseção de Superfícies Regulares com Passo de Contato de Ordem 3 (compressed pdf).
Abstract:
The purpose at this work is to get a non-overlapping tracing of the intersection curve of two regular surfaces starting from a point on the curve. Solutions for two identified problems are proposed: 1) an adaptation of the marching direction at each point, either singular or regular; and 2) a robust determination of the end point of a tracing in order to guarantee only one turn in the tracing of a closed loop in the parametric domain. Differently from the previous works, which use directions of contact order up to 2, two news directions of contact order 3 were presented using tangent vector, curvature, and torsion. Moreover, a technique was considered in order
to estimate these quantities at points close to singular but not cuspidal points. It was also elaborated, on the basis of the Differential Topology, an efficient algorithm for estimating the rotation index of the closed loop based on parametrized loops and types of singular points determined along the curve tracing.  The use of Singularity Theory led to the development of criteria which are less sensitive to the numerical precisions of a digital, opening
perspectives for new paradigms.
• Complete and non-overlapping marching along a closed regular intersection curve (compressed PostScript or pdf)

Autores: Wu, Shin - Ting and Osmar Aléssio
Categoria: Este artigo foi selecionado no Sibgrapi 2001 para ser publicado em Computers & Graphics: An International Journal of Systems & Applications in Computer Graphics Vol. 26 No. 6
Abstract:
 In this paper we present an algorithm for estimating the rotation index of a closed regular intersection curve from its singular points. On the basis of this index we have also devised a procedure that guarantees that a closed intersection curve will be traced completely, without overlapping. Combining this procedure with marching steps derived from differential geometric properties has resulted in a robust intersection technique.
• On Estimating Local Geometric Properties of Intersection Curves ( compressed PostScript or pdf)

Autores: Wu, Shin - Ting, Osmar Aléssio, and Sueli I. R. Costa
Categoria: Sibgrapi 2000 conference proceedings
Abstract:
This paper presents a simple and robust algorithm for estimating the local geometric properties of intersection curves, namely the tangent, normal, binormal, curvature and torsion vectors at any point. In addition, two new marching directions that make use of these properties are given.