Abstracts Category : Other

[en] VOLUME RENDERING OF UNSTRUCTURED HEXAHEDRALMESHES

by MARKUS NUNES FABIO

[pt] Importantes aplicaes de engenharia usam malhasno estruturadas de hexaedros para simulaes numricas. Clulashexadricas, comparadas com tetraedros, tendem a ser maisnumericamente estveis e requerem um menor refinamento da malha.Entretando, visualizao volumtrica de malhas no estruturadas um desafio devido a variao trilinear do campo escalar dentro daclula. A soluo convencional consiste em subdividir cada hexaedroem cinco ou seis tetraedros, aproximando uma variao trilinear poruma inadequada srie de funes lineares. Isso resulta em imagensinadequadas e aumenta o consumo de memria. Nesta tese,apresentamos um algoritmo preciso de visualizao volumtricautilizando ray-casting para malhas no estruturadas de hexaedros.Para capturar a variao trilinear ao longo do raio, ns propomosusar uma integrao de quadratura. Ns tambm propomos umaalternativa rpida que melhor aproxima a variao trilinear,considerando os pontos de mnimo e mximo da funo escalar aolongo do raio. Uma srie de experimentos computacionais demonstramque nossa proposta produz resultados exatos, com um menor gasto dememria. Todo algoritmo implementado em placas grficas,garantindo uma performance competitiva. [en] Important engineering applications useunstructured hexahedral meshes for numerical simulations.Hexahedral cells, when compared to tetrahedral ones, tend to bemore numerically stable and to require less mesh refinement.However, volume visualization of unstructured hexahedral meshes ischallenging due to the trilinear variation of scalar fields insidethe cells. The conventional solution consists in subdividing eachhexahedral cell into five or six tetrahedra, approximating atrilinear variation by an inadequate piecewise linear function.This results in inaccurate images and increases the memoryconsumption. In this thesis, we present an accurate ray-castingvolume rendering algorithm for unstructured hexahedral meshes. Inorder to capture the trilinear variation along the ray, we proposethe use of quadrature integration. We also propose a fast approachthat better approximates the trilinear variation to a series oflinear ones, considering the points of minimum and maximum of thescalar function along the ray. A set of computational experimentsdemonstrates that our proposal produces accurate results, withreduced memory footprint. The entire algorithm is implemented ongraphics cards, ensuring competitive performance.Advisors/Committee Members: WALDEMAR CELES FILHO.