The Mate Face data structure and applications in mesh generation and movement

Author(s)

Ícaro Lins Leitão da Cunha

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2009-05-07

Examining board members

Antonio Castelo Filho; Hélio Côrtes Vieira Lopes; Marcelo Ferreira Siqueira

• Advisor: Antonio Castelo Filho

Abstract

Topological data Structures (DS) oer several advantages when performing a deformation on a mesh. These DSs allow movement throughout the mesh without modifying its topology, are relatively simple to implement, and there is always the possibility of merging it to simulation/deformation cycle on a completely automatic and ecient form. The main goal of this work is to design and implement a topological DS to represent elastic meshes. These meshes can be either of surface or volume kind, and even simple or mixed. For better performance, more reliability and lower memory consumption, it is necessary that the DSs allow the representation of incident and adjacent components of a given element to be implicit. The second objective to this work is to tackle the problem of mesh generation on arbitrary domains defined by implicit functions. The proposed method is an extension to the algorithm of Partition of Unity Implicits (PUI). For this the proposed method is based on an isosurface stung approach. It adaptively generates the tetrahedra in dierent levels of refinement accordingly to the level of detail presented by the regions of the domain. Dierently to previous work, this feature is done naturally without the aid of an auxiliary data structure. To this end, we use an algebraic structure, named Ja1 triangulation, which is capable of dealing with such refinements. In addition, the Ja1 triangulation permits traversing through the mesh by simply using algebraic rules which is another advantage to the proposed method (AU)

• FAPESP's process: 06/05120-0 - Topological data structure and elastic mesh with applications in aeroelasticity
• Grantee: Ícaro Lins Leitão da Cunha
• Support Opportunities: Scholarships in Brazil - Master