說明 
1 online resource(xv, 233 pages) : illustrations 

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系列 
Synthesis lectures on visual computing, 24694223 ; # 25


Synthesis digital library of engineering and computer science


Synthesis lectures on visual computing ; # 25. 24694223

附註 
Part of: Synthesis digital library of engineering and computer science 

Includes bibliographical references (pages 221225) and index 

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. Bézier curves  A.3. Bézier patches  A.4. Bspline curves  A.5. Tensor product Bspline patches  A.6. Meshes and generalised Bspline 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. Fàa di Bruno's formula  Bibliography  Author's biography  Index 

Abstract freely available; fulltext restricted to subscribers or individual document purchasers 

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Mode of access: World Wide Web 

System requirements: Adobe Acrobat Reader 

This book is written for students, CAD system users and software developers who are interested in geometric continuitya notion needed in everyday practice of ComputerAided 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 

Also available in print 

Title from PDF title page (viewed on October 21, 2016) 
鏈接 
Print version: 9781627059053

主題 
Continuity


Curves


Surfaces


Spline theory


parametric curves and surfaces


Bézier curves and patches


Bspline curves and patches


Coons patches


cubic splines of interpolation


trigonometric spline functions


geometric splines


geometric continuity


modules


mesh refinement


compatibility conditions


filling polygonal holes


shape badness measures


shape optimisation


shape functions


shape visualisation


Fàa di Bruno's formula

