published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 1988. / Also availalbe in microfilm.

No description available.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

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 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. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 87-91). Also available via the Internet.

Thesis (Ph. D.)--University of Hong Kong, 1992.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 139-150). Also available in electronic version. Access restricted to campus users.

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 computer-aided 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 high-quality 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 free-form surfaces, where the planarity of the faces is more concerned. Free-form meshes with planar hexagonal faces, to be called P-Hex 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 P-Hex meshes and present an algorithm for computing a free-form P-Hex mesh of a specified shape. Lastly, this thesis progresses to 3D volume case and proposes an automatic method for generating boundary-aligned all-hexahedron 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. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy