Analysis-aware higher order smooth three-dimensional representations: creation, simulation and visualization

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Publication Type dissertation
School or College School of Computing
Department Computer Science
Author Martin, Tobias
Title Analysis-aware higher order smooth three-dimensional representations: creation, simulation and visualization
Date 2012-05
Description Volumetric parameterization is an emerging field in computer graphics, where volumetric representations that have a semi-regular tensor-product structure are desired in applications such as three-dimensional (3D) texture mapping and physically-based simulation. At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions. One of the main advantages of the IA framework is that the user gets feedback directly as attributes of the NURBS model representation, which can represent geometry exactly, avoiding both the need to generate a finite element mesh and the need to reverse engineer the simulation results from the finite element mesh back into the model. Research in this area has largely been concerned with issues of the quality of the analysis and simulation results assuming the existence of a high quality volumetric NURBS model that is appropriate for simulation. However, there are currently no generally applicable approaches to generating such a model or visualizing the higher order smooth isosurfaces of the simulation attributes, either as a part of current Computer Aided Design or Reverse Engineering systems and methodologies. Furthermore, even though the mesh generation pipeline is circumvented in the concept of IA, the quality of the model still significantly influences the analysis result. This work presents a pipeline to create, analyze and visualize NURBS geometries. Based on the concept of analysis-aware modeling, this work focusses in particular on methodologies to decompose a volumetric domain into simpler pieces based on appropriate midstructures by respecting other relevant interior material attributes. The domain is decomposed such that a tensor-product style parameterization can be established on the subvolumes, where the parameterization matches along subvolume boundaries. The volumetric parameterization is optimized using gradient-based nonlinear optimization algorithms and datafitting methods are introduced to fit trivariate B-splines to the parameterized subvolumes with guaranteed order of accuracy. Then, a visualization method is proposed allowing to directly inspect isosurfaces of attributes, such as the results of analysis, embedded in the NURBS geometry. Finally, the various methodologies proposed in this work are demonstrated on complex representations arising in practice and research.
Type Text
Publisher University of Utah
Subject Analysis-aware; Finite elements; Geometric modeling; Isogeometric analysis; Visualization; Volumetric parameterization
Dissertation Institution University of Utah
Dissertation Name Doctor of Philosophy
Language eng
Rights Management Copyright © Tobias Martin 2012
Format Medium application/pdf
Format Extent 56,284,061 bytes
Identifier us-etd3,87343
Source Original in Marriott Library Special Collections, QA3.5 2012 .M37
ARK ark:/87278/s6rx9sw7
Setname ir_etd
Date Created 2012-11-16
Date Modified 2017-11-02
ID 195645
Reference URL https://collections.lib.utah.edu/ark:/87278/s6rx9sw7
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