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postgraduate thesis: Shape-preserving meshes and generalized Morse-Smale complexes
Title | Shape-preserving meshes and generalized Morse-Smale complexes |
---|---|
Authors | |
Advisors | Advisor(s):Wang, WP |
Issue Date | 2011 |
Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
Citation | Sun, F. [孙峰]. (2011). Shape-preserving meshes and generalized Morse-Smale complexes. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4786963 |
Abstract | Discrete representation of a surface, especially the triangle mesh, is ubiquitous in numerical
simulation and computer graphics. Compared with isotropic triangle meshes,
anisotropic triangle meshes provide more accurate results in numerical simulation by
capturing anisotropic features more faithfully. Furthermore, emerging applications in
computer graphics and geometric modeling require reliable differential geometry information
estimated on these anisotropic meshes. The first part of this thesis proposes
a special type of anisotropic meshes, called shape-preserving meshes, provides guaranteed
convergence of discrete differential operators on these meshes and devises an
algorithm for generating shape-preserving meshes on free-form surfaces based on the
mesh optimization framework with centroidal Voronoi tessellation (CVT). To improve
the numerical stability in simulation, we discuss how to reduce the number of obtuse
triangles in the mesh. The second part of the thesis discusses the non-uniqueness
of anisotropic meshes to represent the same anisotropy defined on a domain, shows
that of all anisotropic meshes, there exists one instance minimizing the number of
obtuse triangles, and proposes a variational approach to suppressing obtuse triangles
in anisotropic meshes by introducing a Minkowski metric in the CVT framework.
On a complex shape, its topological information is also highly useful to guide the
mesh generation. To extract topology properties, the Morse-Smale complex (MSC) is
a classical tool and widely used in computer graphics. However, on a manifold with
boundary, its MSC is not well defined. The final part of this thesis generalizes the MSC
to manifolds with boundaries. Based on this generalized MSC (GMSC), an operator to
merge n GMSCs of manifolds partitioning a large manifold is proposed. The merging
operator is used in a divide-and-conquer approach on a massive data set, providing
the potential to employ the computational power in a parallel manner. |
Degree | Doctor of Philosophy |
Subject | Computer graphics - Mathematical models. |
Dept/Program | Computer Science |
Persistent Identifier | http://hdl.handle.net/10722/161523 |
HKU Library Item ID | b4786963 |
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Wang, WP | - |
dc.contributor.author | Sun, Feng | - |
dc.contributor.author | 孙峰 | - |
dc.date.issued | 2011 | - |
dc.identifier.citation | Sun, F. [孙峰]. (2011). Shape-preserving meshes and generalized Morse-Smale complexes. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4786963 | - |
dc.identifier.uri | http://hdl.handle.net/10722/161523 | - |
dc.description.abstract | Discrete representation of a surface, especially the triangle mesh, is ubiquitous in numerical simulation and computer graphics. Compared with isotropic triangle meshes, anisotropic triangle meshes provide more accurate results in numerical simulation by capturing anisotropic features more faithfully. Furthermore, emerging applications in computer graphics and geometric modeling require reliable differential geometry information estimated on these anisotropic meshes. The first part of this thesis proposes a special type of anisotropic meshes, called shape-preserving meshes, provides guaranteed convergence of discrete differential operators on these meshes and devises an algorithm for generating shape-preserving meshes on free-form surfaces based on the mesh optimization framework with centroidal Voronoi tessellation (CVT). To improve the numerical stability in simulation, we discuss how to reduce the number of obtuse triangles in the mesh. The second part of the thesis discusses the non-uniqueness of anisotropic meshes to represent the same anisotropy defined on a domain, shows that of all anisotropic meshes, there exists one instance minimizing the number of obtuse triangles, and proposes a variational approach to suppressing obtuse triangles in anisotropic meshes by introducing a Minkowski metric in the CVT framework. On a complex shape, its topological information is also highly useful to guide the mesh generation. To extract topology properties, the Morse-Smale complex (MSC) is a classical tool and widely used in computer graphics. However, on a manifold with boundary, its MSC is not well defined. The final part of this thesis generalizes the MSC to manifolds with boundaries. Based on this generalized MSC (GMSC), an operator to merge n GMSCs of manifolds partitioning a large manifold is proposed. The merging operator is used in a divide-and-conquer approach on a massive data set, providing the potential to employ the computational power in a parallel manner. | - |
dc.language | eng | - |
dc.publisher | The University of Hong Kong (Pokfulam, Hong Kong) | - |
dc.relation.ispartof | HKU Theses Online (HKUTO) | - |
dc.rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works. | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.source.uri | http://hub.hku.hk/bib/B4786963X | - |
dc.subject.lcsh | Computer graphics - Mathematical models. | - |
dc.title | Shape-preserving meshes and generalized Morse-Smale complexes | - |
dc.type | PG_Thesis | - |
dc.identifier.hkul | b4786963 | - |
dc.description.thesisname | Doctor of Philosophy | - |
dc.description.thesislevel | Doctoral | - |
dc.description.thesisdiscipline | Computer Science | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.5353/th_b4786963 | - |
dc.date.hkucongregation | 2012 | - |
dc.identifier.mmsid | 991033516099703414 | - |