Subdivision surface modeling technology. (2017)

• Record Type: Book
• Further Information: Note: Wenhe Liao, Hao Liu, Tao Li.
• Authors: Liao, Wenhe; Liu, Hao; Li, Tao
• Contents: ""Foreword""; ""Table of Symbols""; ""Notation""; ""Roman""; ""Greek Letters""; ""Miscellaneous""; ""Functions""; ""Contents""; ""1 Introduction""; ""1.1 Surface Modeling""; ""1.2 Concept of Subdivision Surfaces""; ""1.3 Development of Subdivision Surfaces""; ""1.4 Idea of This Book""; ""2 Splines and Subdivision""; ""2.1 B-Splines""; ""2.2 B-Spline Curves and Surfaces""; ""2.2.1 B-Spline Curves and Their Properties""; ""2.2.2 B-Spline Surfaces and Their Properties""; ""2.3 Knot Insertion Algorithm and Refinement of B-Spline Curves and Surfaces""; ""2.3.1 Subdivision of B-Spline Curves"" ""2.3.2 Subdivision of B-Spline Surface""""2.4 Uniform Subdivision of B-Spline Curves and Surfaces""; ""2.4.1 Subdivision of Uniform B-Spline Curves""; ""2.4.2 Subdivision of Uniform B-Spline Surfaces""; ""2.5 Box Spline""; ""2.5.1 Vector Group and Support Mesh""; ""2.5.2 Inductive Definition of Box Splines""; ""2.5.3 Basic Properties of Box Splines""; ""2.6 Box Spline Surfaces""; ""2.6.1 Definition and Properties""; ""2.6.2 Subdivision of Box Spline Surfaces""; ""2.6.3 Generating Function of Box Spline""; ""2.7 Subdivision Mask of Box Spline Surface""; ""3 Meshes and Subdivision"" ""3.1 Topological Structure of Meshes for Subdivision""""3.2 Regular Mesh""; ""3.3 Subdivision Scheme""; ""3.4 Quadrilateral Subdivision""; ""3.4.1 Doo -- Sabin Subdivision""; ""3.4.2 Catmull -- Clark Subdivision""; ""3.4.3 Non-uniform Subdivision""; ""3.5 Triangular Subdivision""; ""3.5.1 Loop Subdivision""; ""3.5.2 Butterfly Subdivision""; ""3.5.3 sqrt3 Subdivision""; ""3.6 Hexagonal Subdivision""; ""3.6.1 Convexity-Preserving Subdivision Scheme""; ""3.6.2 Honeycomb Subdivision Scheme""; ""3.7 4 -- 8 Subdivision""; ""3.7.1 4 -- 8 Meshes""; ""3.7.2 Subdivision Rules"" ""3.8 Classification of Subdivision Schemes""""4 Analysis of Subdivision Surface""; ""4.1 Subdivision Matrix""; ""4.2 Discrete Fourier Transform""; ""4.2.1 Fundament of DFT""; ""4.2.2 Discrete Fourier Transform""; ""4.2.3 Eigenvalues and Eigenvectors from DFT""; ""4.3 Eigenvalues Analysis""; ""4.3.1 Calculation of Eigenvalues and Eigenvectors""; ""4.3.2 Property of the Limit Surface""; ""4.3.3 Another Example for Eigenvalues Analysis""; ""4.4 Characteristic Mapping""; ""4.4.1 Annular Surface and Its Gradualness""; ""4.4.2 Definition of Characteristic Mapping"" ""4.4.3 Characteristic Mapping and Continuity of Subdivision Surfaces""""4.5 Parameter Evaluation""; ""4.5.1 Notations and Assumpsits""; ""4.5.2 Mathematical Setting""; ""4.5.3 Eigenstructure of Subdivision Matrix""; ""4.5.4 Eigenbases and Evaluation for Non-regular Patches""; ""4.5.5 Subdivision Matrix and Their Eigenstructures""; ""4.5.6 Eigenbasis Functions""; ""4.5.7 Parameter Evaluation and Characteristic Mapping""; ""5 n-Sided Patches and Subdivision Surfaces""; ""5.1 Methods for Constructing n-Sided Patches""; ""5.2 C-C Subdivision Surfaces and G2 Continuity"" ""5.3 n-Sided Patches and Catmull -- Clark Subdivision""
• Publisher Details: Singapore Beijing, China : Springer Higher Education Press
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 516.3/6; Subdivision surfaces (Geometry); Computer graphics -- Mathematics; Computer-aided design -- Mathematics; MATHEMATICS -- Geometry -- General; COMPUTERS -- Mathematical & Statistical Software; Computer-aided design -- Mathematics; Computer graphics -- Mathematics; Subdivision surfaces (Geometry); Electronic books
• Languages: English
• ISBNs: 9789811035159; 9811035156
• Related ISBNs: 9789811035142; 9811035148
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed October 20, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.