Footnote:
Part of: Synthesis digital library of engineering and computer science. - Includes bibliographical references (pages 221-225) and index. - Compendex. INSPEC. Google scholar. Google book search. - Title from PDF title page (viewed on October 21, 2016)
Description:
Preface -- Notation -- 1. Introduction -- 2. Geometric continuity of curves: 2.1. Equations of geometric continuity; 2.2. Interpretation; 2.3. Geometric spline curves; 2.4. Tensor product geometric spline patches -- 3. Pairs of surface patches: 3.1. Geometric continuity at a common boundary; 3.2. Interpretation; 3.3. A little bit of algebra; 3.4. Polynomial solutions of equations of geometric continuity; 3.5. Constructing pairs of patches; 3.6. Approximating smooth junctions -- 4. Compatibility conditions: 4.1. Hahn's scheme of filling polygonal holes; 4.2. Compatibility conditions at a common corner; 4.3. Compatibility conditions around a point; 4.4. Beyond the curvature continuity and towards practice -- 5. Filling polygonal holes: 5.1. Theoretical background; 5.2. Constructing function spaces; 5.3. Minimisation of quadratic forms; 5.4. Constructions with shape optimisation; 5.5. Conclusion -- 6. Images of surface shape: 6.1. Characteristic lines and shape functions; 6.2. Planar sections; 6.3. Isophotes; 6.4. Reflection lines; 6.5. Highlight lines; 6.6. Surface curvatures -- A. Background -- A.1. Lagrange and Hermite interpolation -- A.2. BĐezier curves -- A.3. BĐezier patches -- A.4. B-spline curves -- A.5. Tensor product B-spline patches -- A.6. Meshes and generalised B-spline surfaces -- A.7. Rational curves and patches -- A.8. Spline curves of interpolation -- A.9. Coons patches -- A.10. Curvatures of curves and surfaces -- A.11. FÆaa di Bruno's formula -- Bibliography -- Author's biography -- Index
This book is written for students, CAD system users and software developers who are interested in geometric continuity--a notion needed in everyday practice of Computer-Aided Design and also a hot subject of research. It contains a description of the classical geometric spline curves and a solid theoretical basis for various constructions of smooth surfaces. Textbooks on computer graphics usually cover the most basic and necessary information about spline curves and surfaces in order to explain simple algorithms. In textbooks on geometric design, one can find more details, more algorithms and more theory. This book teaches how various parts of the theory can be gathered together and turned into constructions of smooth curves and smooth surfaces of arbitrary topology. The mathematical background needed to understand this book is similar to what is necessary to read other textbooks on geometric design; most of it is basic linear algebra and analysis. More advanced mathematical material is introduced using elementary explanations. Reading Geometric Continuity of Curves and Surfaces provides an excellent opportunity to recall and exercise necessary mathematical notions and it may be your next step towards better practice and higher understanding of design principles