Selected Readings in Vision and Graphics

Volume 17

Andreas Hubeli

Multiresolution Techniques
for Non-Manifolds

First edition 2002, 252 pages, 64,00. ISBN 3-89649-789-9

This thesis introduces a novel geometric modeling environment to represent and interact with non-manifold models. This functionality is required in many application domains, where the complexity of models has been steadily increasing as a result of the improved acquisition systems. This project focuses on the domain of geoscience, a choice motivated by the cooperation between the Federal Institute of Technology (ETH) in Zurich, the Schlumberger Austin Technology Center (ATC) and the Schlumberger Cambridge Research (SCR) center.
The tools designed in this project are based on an extended boundary representation data structure, which accommodates semantics information in addition to geometric and topological data. In particular, the separation of the topological description of a simplicial complex from its embedding information and the definition of different types of embeddings results in a flexible description of models.
The core component of the system is a non-manifold fairing tool that attenuates the high frequencies present in models; the smoothing process is defined as an extension of the corresponding operators for manifold surfaces. The problem of the change in the volumes present in a non-manifold, which is caused by the application of this operator, has been addressed by constructing a novel local volume preservation technique.
The second component of the framework is a non-manifold subdivision tool, which iteratively refines and smooths an initially coarse model. This operation is constructed either by extending the classic Loop scheme or by defining a new subdivision operator based on the fairing tool.
The interaction with the system is enhanced by the simplification tool, which is responsible for the construction of a multiresolution representation of both height field data and non-manifolds. The principal applications of these structures comprise the generalization of other tools to a multiresolution setting and the construction of approximations for rendering and further data processing.
The fairing and simplification components are combined to define a multiresolution editing tool for non-manifold models. In contrast to other techniques this component operates directly on the model and it does not rely on the extraction and subsequent processing of manifold surfaces.
The construction of a feature detection tool for triangulated two-manifold surfaces automates the extraction of the salient characteristics of a surface, which are defined as coherent regions of high curvature. This data is applied both to the analysis and interpretation of models and to guide the fairing, subdivision and simplification tools.
A novel approach to mesh morphing is introduced, which computes the paths of each mesh vertex in the deformation process as the result of a Laplace equation. This elegant formulation offers a variety of advantages, such as the capability of specifying constraints that are smoothly integrated into the problem formulation.
These operators have been integrated into a modeling framework and they have been combined to implement data processing pipelines to construct and interact with models. Their strengths and limitations will be analyzed on a variety of geological and graphics models.

Andreas Hubeli is a senior engineer at the Schlumberger Austin Technology Center in Austin, Texas. He received a degree and a Ph.D. in Computer Science from the Federal Institute of Technology (ETH) in Zürich. He is currently researching novel representations for geological non-manifold models. His technical interests include geometric modeling, multiresolution methods and interactive entertainment technologies.

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