Computational Differential Geometry Tools for Surface Interrogation, Fairing, and Design
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2006
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Abstract
This thesis presents a set of new mesh processing methods which are based on computational
differential geometry techniques. The underlying idea of the methods consists of using proper
discrete approximations of differential surface properties. The methods developed in the thesis
contribute to the areas of curvature feature detection, mesh parameterization, fair mesh generation,
mesh denoising, and free-form and variational mesh deformations. Comparisons of the
developed methods with several state-of-the-art techniques and algorithms are done. The results
of numerous numerical experiments demonstrate significant advantages of the proposed methods
over conventional techniques. Applications of the methods are discussed and demonstrated.
The main contributions of the thesis are as follows:
Similarity-based Mesh Denoising. A new, powerful, and high quality feature preserving
mesh/soup denoising technique and a new scheme for comparing different mesh/soup
smoothing methods are proposed. The technique is based on a similarity-weighted averaging
procedure and a new and robust similarity measuring scheme.
Fair Mesh Generation via Elastica. A new numerical scheme for generating fair meshes is
developed. Applications to shape restoration are considered. The scheme is build upon
a discrete approximation of Willmore flow. A tangent speed component is introduced to
the discrete Willmore flow in order to improve the quality of the evolving mesh and to
increase computational stability.
Fast and Robust Detection of Feature Lines on Meshes. A new, fast, and robust crest line detection
method is developed. Applications to feature-adaptive mesh simplification and
segmentation are considered. A novel thresholding scheme and a simple new formula for
computing directional curvature derivatives are also introduced.
Fast Low-Stretch Mesh Parameterization. A new, fast, simple, and valid low-stretch mesh
parameterization scheme and its application for effcient remeshing are proposed by using
a moving mesh approach. The scheme is based on a weighted quasi-conformal parameterization
which equalizes the local stretch distribution. Particularly, the scheme does not
generate regions of undesirable high anisotropic stretch.
Free-Form Skeleton-driven Mesh Deformations. A new and powerful approach for generating
natural-looking large-scale mesh deformations is proposed. An interesting feature of
the approach consists of preserving original shape thickness. New self-intersection fairing
schemes are also developed. Multiresolutional and variational extensions of the approach
are considered.
Description
@inproceedings{10.2312:diss.200614681,
booktitle = {EG Graphics Dissertation Online},
editor = {},
title = {{Computational Differential Geometry Tools for Surface Interrogation, Fairing, and Design}},
author = {Yoshizawa, Shin},
year = {2006},
publisher = {},
ISBN = {},
DOI = {10.2312/diss.200614681}
}