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作者 Kiciak, Przemysław, author
書名 Geometric continuity of curves and surfaces / Przemysław Kiciak
出版項 [San Rafael, California] : Morgan & Claypool, 2017
國際標準書號 9781627054676 ebook
9781627059053 paperback
國際標準號碼 10.2200/S00729ED1V01Y201608VCP025
book jacket
說明 1 online resource(xv, 233 pages) : illustrations
text rdacontent
still image rdacontent
electronic isbdmedia
online resource rdacarrier
系列 Synthesis lectures on visual computing, 2469-4223 ; # 25
Synthesis digital library of engineering and computer science
Synthesis lectures on visual computing ; # 25. 2469-4223
附註 Part of: Synthesis digital library of engineering and computer science
Includes bibliographical references (pages 221-225) 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. 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. Fàa di Bruno's formula -- Bibliography -- Author's biography -- Index
Abstract freely available; full-text 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 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
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
B-spline 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
記錄 6 之 13
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