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postgraduate thesis: From geometry processing to surface modeling

TitleFrom geometry processing to surface modeling
Authors
Issue Date2015
PublisherThe 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
AbstractGeometry 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 spline-based 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 user-friendly 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 self-supporting surfaces, and apply direction field modeling and discrete curvature adaptation to surfacing sketch curve networks.
DegreeDoctor of Philosophy
SubjectGeometrical models
Geometry - Data processing
Dept/ProgramComputer Science
Persistent Identifierhttp://hdl.handle.net/10722/209486

 

DC FieldValueLanguage
dc.contributor.authorPan, Hao-
dc.contributor.author潘浩-
dc.date.accessioned2015-04-23T23:10:51Z-
dc.date.available2015-04-23T23:10:51Z-
dc.date.issued2015-
dc.identifier.citationPan, 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.urihttp://hdl.handle.net/10722/209486-
dc.description.abstractGeometry 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 spline-based 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 user-friendly 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 self-supporting surfaces, and apply direction field modeling and discrete curvature adaptation to surfacing sketch curve networks.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subject.lcshGeometrical models-
dc.subject.lcshGeometry - Data processing-
dc.titleFrom geometry processing to surface modeling-
dc.typePG_Thesis-
dc.identifier.hkulb5435651-
dc.description.thesisnameDoctor of Philosophy-
dc.description.thesislevelDoctoral-
dc.description.thesisdisciplineComputer Science-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.5353/th_b5435651-

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