Publications

• A Complete and Non-Overlapping Tracing Algorithm for Closed Loops (compressed PostScript or pdf)
  Authors: Wu, Shin - Ting, Osmar Aléssio, and Sueli I. R. Costa
  Category: accepted for publication in the CAGD Journal
  Abstract:
  A procedure for tracing completely closed loops given implicitly by the intersection of two regular surfaces, without resorting to the parametric domain subdivisions or resulting in arc overlapping, is presented. Our primary hypothesis is that the rotation index, a global geometrical property, may be a useful complementary tool to the local differential geometrical properties for improving the efficiency of the well-known marching-based surface--surface intersection algorithms. To validate this hypothesis, we devised a novel approach for incrementally computing the rotation index of a closed plane curve given implicitly while the curve is traced. Moreover, we also proposed its integration in a marching procedure that employs adaptative circular steps.
• Complete and non-overlapping marching along a closed regular intersection curve (compressed PostScript or pdf)
  Authors: Wu, Shin - Ting and Osmar Aléssio
  Category: selected paper from Sibgrapi 2001 and published in 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)
  Authors: Wu, Shin - Ting, Osmar Aléssio, and Sueli I. R. Costa
  Category: 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.
• Marching along a regular surface/surface intersection with circular steps (submitted manuscript for publication in compressed PostScript or pdf)
  Authors: Wu, Shin - Ting and Lenimar Nunes de Andrade
  Category: published in CAGD Vol 16, p. 249 - 268, 1999
  Abstract:
  This paper presents a simple and elegant algorithm to estimate adaptively the stepping direction and size for tracing a branch of the intersection curve between two regular surfaces without any nonlinear equation system solver. The step is neither along the tangent vector at the current point nor along a parabola in a vicinity of the current point; it is along a circle at the current point. Although no curvature analysis or power series expansions about each point of the intersection curve were used in its construction, we demonstrate that our circle tends to the exact osculating circle, when the distance between two subsequent sampling points tends to zero. Through numerical examples, we also show that the performance of our algorithm by handling singular points, bifurcations, and points on the closely spaced branches, is equivalent to the ones based on embedding schemes.
• Caminhando sobre uma Interseção de Superfícies com Passos Circulares (in Portuguese) ( compressed PostScript)
  Authors: Wu, Shin - Ting and Lenimar N. Andrade
  Category: SIBGRAPI'96 conference proceedings
  Abstract:
  This paper presents an alternative way to calculate the next approximate point in marching techniques for the computation of the intersection of two parametric surfaces. Differing from the classical methods, the algorithm is based on the approximate osculating circle instead of tangent vector to estimate the next point. It provides closer estimation and a larger marching step in each iteration with relatively low computational cost.
• Classificação de Pertinência dos Pontos em Objetos da NM-Classe (in Portuguese) ( compressed PostScript)
  Authors: Wu, Shin - Ting and Luiz Gonzaga da Silveira Jr.
  Category: SIBGRAPI'96 conference proceedings
  Abstract:
  This paper presents a new set membership classification algorithm that can partition the points of two intersecting non-manifolds A and B in such a way that their Boolean combinations can be readily computed. A concept of minimal embbedding space is used to ensure the consistent point neighborhood classification.
• Operadores Booleanos para a Classe de NM-conjuntos (in Portuguese) ( compressed PostScript)
  Authors: Luiz Gonzaga da Silveira Jr. and Wu, Shin - Ting
  Category: SIBGRAPI'94 conference proceedings
  Abstract:
  In this paper we present an algorithm for boolean set operations to NM-sets that fulfil three requirements: closeness, interactivity and efficiency.
  We begin by showing that NM-sets are an extension of r-sets and are representable in TDM data structure. Then, a modified set of boolean operators under which the NM-sets are closed is presented. Finally, an implementation of these operators to an interactive process is discussed.

• Traçado Não-Sobreposto de Interseção de Superfícies Regulares com Passos de Contato de Ordem 3 ( pdf in Portuguese)
  Author: Osmar Aléssio
  Type: Doutorado
  
• Traço de Interseção de Superfícies Regulares com Passos Circulares ( pdf in Portuguese)
  Author: Lenimar Nunes de Andrade
  Type: Doutorado
  
• Operadores Booleanos para Objetos Modelados por Complexos Celulares ( pdf in Portuguese)
  Author: Luiz Gonzaga da Silveira Júnior
  Type: Mestrado