Wu Yiu-Bun. / Thesis submitted in: September 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 122-123). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Previous Works --- p.2 / Chapter 2.1. --- Surface Patch Approach / Chapter 2.2. --- Triangular Facet Approach / Chapter Chapter 3. --- The Decomposition Algorithm --- p.7 / Chapter 3.1. --- Input to the Algorithm / Chapter 3.2. --- Overview of the Algorithm / Chapter 3.2.1. --- Voronoi Diagram Development / Chapter 3.2.2. --- Feature Point Determination / Chapter 3.2.3. --- Correspondence Establishment / Chapter 3.2.4. --- Surface Approximation / Chapter 3.3. --- Output of the Algorithm / Chapter Chapter 4. --- Voronoi Diagram Development --- p.16 / Chapter 4.1. --- Triangulation of the Parametric Space / Chapter 4.1.1. --- Degree of Triangulation / Chapter 4.2. --- Locating Bisectors / Chapter 4.2.1. --- Bisector Centroids / Chapter 4.2.2. --- Sub-triangulation / Chapter 4.3. --- Finalizing Bisectors / Chapter Chapter 5. --- Feature Point Determination --- p.31 / Chapter 5.1. --- Definition of Feature Points / Chapter 5.1.1. --- Continuous Sharp Turns / Chapter 5.1.2. --- Discrete Sharp Turns / Chapter 5.2. --- Parametric Coordinates of Feature Points / Chapter Chapter 6. --- Vertices Correspondence Attachment --- p.42 / Chapter 6.1. --- Validity of Correspondences / Chapter 6.2. --- Shape Normalization / Chapter 6.2.1. --- Normalization with Relative Position / Chapter 6.3. --- Ranking Process / Chapter 6.3.1. --- Forward and Backward Attachment / Chapter 6.3.2. --- Singly Linked Bisector Vertices / Chapter Chapter 7. --- Surface Fitting --- p.58 / Chapter 7.1. --- Parametric Patches / Chapter 7.1.1. --- Definition of Parametric Patch Region / Chapter 7.1.2. --- Local Parametric Coordinate System / Chapter 7.2. --- Parametric Grids / Chapter 7.2.1. --- Sample Points on the Patch Boundary / Chapter 7.2.2. --- Grid Generation / Chapter 7.3. --- Surface Patches Construction / Chapter 7.3.1. --- Knot Vectors / Chapter 7.3.2. --- Control Vertices / Chapter Chapter 8. --- Worked Example --- p.71 / Chapter 8.1. --- Example 1: Deformed Plane 1 / Chapter 8.2. --- Example 2: Deformed Plane 2 / Chapter 8.3. --- Example 3: Sphere / Chapter 8.4. --- Example 4: Hemisphere 1 / Chapter 8.5. --- Example 5: Hemisphere 2 / Chapter 8.6. --- Example 6: Shoe / Chapter 8.7. --- Example 7: Shark Main Body / Chapter 8.8. --- Example 8: Mask 1 / Chapter 8.9. --- Example 9: Mask 2 / Chapter 8.10. --- Example 10: Toy Car / Chapter Chapter 9. --- Result and Analysis --- p.101 / Chapter 9.1. --- Continuity between Patches / Chapter 9.2. --- Special Cases --- p.102 / Chapter 9.2.1. --- Degenerated Patch / Chapter 9.2.2. --- S-Shaped Feature / Chapter 9.3. --- Comparison --- p.105 / Chapter 9.3.1. --- Example 1: Deformed Plane 1 / Chapter 9.3.2. --- Example 2: Deformed Plane 2 / Chapter 9.3.3. --- Example 3: Sphere / Chapter 9.3.4. --- Example 4: Hemisphere 1 / Chapter 9.3.5. --- Example 5: Hemisphere 2 / Chapter 9.3.6. --- Example 6: Shoe / Chapter 9.3.7. --- Example 7: Shark Main Body / Chapter 9.3.8. --- Example 8: Mask 1 / Chapter 9.3.9. --- Example 9: Mask 2 / Chapter 9.3.10. --- Example 10: Toy Car / Chapter Chapter 10. --- Conclusion --- p.119 / References --- p.122

published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Electrical and Electronic Engineering / Master / Master of Philosophy

Orientador: Edson Agustini / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação / Made available in DSpace on 2018-08-11T14:52:52Z (GMT). No. of bitstreams: 1 Coimbra_JosedeRibamarViana_M.pdf: 2680384 bytes, checksum: d91c9e63f3b142a2ff60c4d2fb586e86 (MD5) Previous issue date: 2008 / Resumo:A presente dissertação é um texto de Geometria Diferencial baseado nos principais textos editados em língua portuguesa sobre o assunto. A principal intenção ao redigir a dissertação foi compilar um material que possa ser utilizado em cursos introdutórios de Geometria Diferencial tanto em nível de licenciatura quanto de bacharelado. Para tornar o texto mais acessível, notas históricas sobre o desenvolvimento da Geometria Diferencial e seus principais personagens foram introduzidas logo no primeiro capítulo. Para facilitar o entendimento e o estudo do assunto, procurou-se inserir muitos exemplos e ilustrar fartamente o texto com figuras ¿Observação: O resumo, na íntegra poderá ser visualizado no texto completo da tese digital / Abstract: This dissertation is a text of Differential Geometry based on the most important texts edited in Portuguese about this subject. Our aim in this work were to compile a material that can be used as introduction to Differential Geometry in undergraduate courses. In order to turn the text more accessible, historical notes about the beautiful development of Differential Geometry and its great persons were introduced in the first chapter. Besides, in order to help the reader with the study of this subject, we put many examples and figures to illustrate the theory...Note: The complete abstract is available with the full electronic digital thesis or dissertations / Mestrado / Mestre em Matemática