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postgraduate thesis: A study on surface and volume tiling for geometric modeling
Title  A study on surface and volume tiling for geometric modeling 

Authors  
Advisors  Advisor(s):Wang, WP 
Issue Date  2012 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Abstract  Surface tiling, as well as its counterpart in 3D, i.e. volume tiling, is a fundamental research problem in the subject of computer graphics and geometric modeling, which has found applications in numerous areas, such as computeraided design (CAD), physical simulation, realtime rendering and architectural modeling. The objective of surface tiling is to compute discrete mesh representations for given surfaces which are often required to possess some desirable geometric properties. Likewise, volume tiling focuses on the study of discretizing a given 3D volume with complex boundary into a set of highquality volumetric elements.
This thesis starts with the study of computing optimal sampling for parametric surfaces, that is, decompose the surface into quad patches such that 1) each quad patch should have their sides with equal length; and 2) the shapes and sizes of all the quad patches should be the same as much as possible. Then, the similar idea is applied to the discrete case, i.e. optimizing the face elements of a quad mesh surface with the goal of making it possess, as much as possible, face elements of desired shapes and sizes.
This thesis further studies the computation of hexagonal tiling on freeform surfaces, where the planarity of the faces is more concerned. Freeform meshes with planar hexagonal faces, to be called PHex meshes, provide a useful surface representation in discrete differential geometry and are demanded in architectural design for representing surfaces built with planar glass/metal panels. We study the geometry of PHex meshes and present an algorithm for computing a freeform PHex mesh of a specified shape.
Lastly, this thesis progresses to 3D volume case and proposes an automatic method for generating boundaryaligned allhexahedron meshes with high quality, which possess nice numerical properties, such as a reduced number of elements and high approximation accuracy in physical simulation and mechanical engineering. 
Degree  Doctor of Philosophy 
Subject  Geometrical models  Data processing. Computer graphics. 
Dept/Program  Computer Science 
DC Field  Value  Language 

dc.contributor.advisor  Wang, WP   
dc.contributor.author  Li, Yufei   
dc.contributor.author  李宇飛   
dc.date.issued  2012   
dc.description.abstract  Surface tiling, as well as its counterpart in 3D, i.e. volume tiling, is a fundamental research problem in the subject of computer graphics and geometric modeling, which has found applications in numerous areas, such as computeraided design (CAD), physical simulation, realtime rendering and architectural modeling. The objective of surface tiling is to compute discrete mesh representations for given surfaces which are often required to possess some desirable geometric properties. Likewise, volume tiling focuses on the study of discretizing a given 3D volume with complex boundary into a set of highquality volumetric elements. This thesis starts with the study of computing optimal sampling for parametric surfaces, that is, decompose the surface into quad patches such that 1) each quad patch should have their sides with equal length; and 2) the shapes and sizes of all the quad patches should be the same as much as possible. Then, the similar idea is applied to the discrete case, i.e. optimizing the face elements of a quad mesh surface with the goal of making it possess, as much as possible, face elements of desired shapes and sizes. This thesis further studies the computation of hexagonal tiling on freeform surfaces, where the planarity of the faces is more concerned. Freeform meshes with planar hexagonal faces, to be called PHex meshes, provide a useful surface representation in discrete differential geometry and are demanded in architectural design for representing surfaces built with planar glass/metal panels. We study the geometry of PHex meshes and present an algorithm for computing a freeform PHex mesh of a specified shape. Lastly, this thesis progresses to 3D volume case and proposes an automatic method for generating boundaryaligned allhexahedron meshes with high quality, which possess nice numerical properties, such as a reduced number of elements and high approximation accuracy in physical simulation and mechanical engineering.   
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  Creative Commons: Attribution 3.0 Hong Kong License   
dc.source.uri  http://hub.hku.hk/bib/B48329733   
dc.subject.lcsh  Geometrical models  Data processing.   
dc.subject.lcsh  Computer graphics.   
dc.title  A study on surface and volume tiling for geometric modeling   
dc.type  PG_Thesis   
dc.identifier.hkul  b4832973   
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_b4832973   
dc.date.hkucongregation  2012   