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postgraduate thesis: From geometry processing to surface modeling
Title  From geometry processing to surface modeling 

Authors  
Issue Date  2015 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Pan, H. [潘浩]. (2015). From geometry processing to surface modeling. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5435651 
Abstract  Geometry processing has witnessed tremendous development in the last few decades. Starting from acquiring 3D data of real life objects, people have developed practical methods for polishing the raw data usually in the format of point clouds, reconstructing surfaces from the point clouds, cleaning up the surfaces by denoising or fairing, texturing the object surfaces by parametrization to 2D domain, deforming the objects realistically and in real time, and many other advanced tasks. Along with the notable methods is the sophistication of knowledge for working with discrete geometric data, in particular points, triangles, quadrangles and polygons for object representation, with a large body summarized and principled in the field known as discrete differential geometry.
Meanwhile, geometric modeling has come to a new era: unlike the previous industrial practice of splinebased modeling where people tune control points to search for aesthetic shapes, now people want novel ways of interaction. For example, find unknown shapes that are usually characterized to have variational and physical properties of interest. Also userfriendly modeling methods like sketching have gained remarkable attention and advances. We note that many of these surface modeling problems could be regarded as asking for surfaces with special differential geometric properties. To be specific, people find surfaces of minimal area for modeling soap films that are balanced under surface tension; surfaces that if fabricated could stand firmly and are therefore important in real life architectural structures, are described by having homogeneous relative mean curvatures; even for surfaces filling up sketched 3D curves, the significant property of a good filling surface is that the curves follow principal curvature directions of the surface.
This thesis presents our results in developing effective algorithms for modeling the above mentioned surfaces, by adapting knowledge and techniques in geometry processing, especially from computational and discrete differential geometry. In particular, we extend surface remeshing techniques to model high quality Constant Mean Curvature (CMC) surfaces that are models of soap films and bubbles, use power diagrams and the dual regular triangulations to parametrize and process selfsupporting surfaces, and apply direction field modeling and discrete curvature adaptation to surfacing sketch curve networks. 
Degree  Doctor of Philosophy 
Subject  Geometrical models Geometry  Data processing 
Dept/Program  Computer Science 
Persistent Identifier  http://hdl.handle.net/10722/209486 
DC Field  Value  Language 

dc.contributor.author  Pan, Hao   
dc.contributor.author  潘浩   
dc.date.accessioned  20150423T23:10:51Z   
dc.date.available  20150423T23:10:51Z   
dc.date.issued  2015   
dc.identifier.citation  Pan, H. [潘浩]. (2015). From geometry processing to surface modeling. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5435651   
dc.identifier.uri  http://hdl.handle.net/10722/209486   
dc.description.abstract  Geometry processing has witnessed tremendous development in the last few decades. Starting from acquiring 3D data of real life objects, people have developed practical methods for polishing the raw data usually in the format of point clouds, reconstructing surfaces from the point clouds, cleaning up the surfaces by denoising or fairing, texturing the object surfaces by parametrization to 2D domain, deforming the objects realistically and in real time, and many other advanced tasks. Along with the notable methods is the sophistication of knowledge for working with discrete geometric data, in particular points, triangles, quadrangles and polygons for object representation, with a large body summarized and principled in the field known as discrete differential geometry. Meanwhile, geometric modeling has come to a new era: unlike the previous industrial practice of splinebased modeling where people tune control points to search for aesthetic shapes, now people want novel ways of interaction. For example, find unknown shapes that are usually characterized to have variational and physical properties of interest. Also userfriendly modeling methods like sketching have gained remarkable attention and advances. We note that many of these surface modeling problems could be regarded as asking for surfaces with special differential geometric properties. To be specific, people find surfaces of minimal area for modeling soap films that are balanced under surface tension; surfaces that if fabricated could stand firmly and are therefore important in real life architectural structures, are described by having homogeneous relative mean curvatures; even for surfaces filling up sketched 3D curves, the significant property of a good filling surface is that the curves follow principal curvature directions of the surface. This thesis presents our results in developing effective algorithms for modeling the above mentioned surfaces, by adapting knowledge and techniques in geometry processing, especially from computational and discrete differential geometry. In particular, we extend surface remeshing techniques to model high quality Constant Mean Curvature (CMC) surfaces that are models of soap films and bubbles, use power diagrams and the dual regular triangulations to parametrize and process selfsupporting surfaces, and apply direction field modeling and discrete curvature adaptation to surfacing sketch curve networks.   
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.subject.lcsh  Geometrical models   
dc.subject.lcsh  Geometry  Data processing   
dc.title  From geometry processing to surface modeling   
dc.type  PG_Thesis   
dc.identifier.hkul  b5435651   
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_b5435651   