Subdivision Surface Modeling Technology

This book offers a comprehensive introduction to Subdivision Surface Modeling Technology focusing not only on fundamental theories but also on practical applications. It furthers readers’ understanding of the contacts between spline surfaces and subdivision surfaces, enabling them to master the Subdivision Surface Modeling Technology for analyzing subdivision surfaces. Subdivision surface modeling is a popular technology in the field of computer aided design (CAD) and computer graphics (CG) thanks to its ability to model meshes of any topology. The book also discusses some typical Subdivision Surface Modeling Technologies, such as interpolation, fitting, fairing, intersection, as well as trimming and interactive editing. It is a valuable tool, enabling readers to grasp the main technologies of subdivision surface modeling and use them in software development, which in turn leads to a better understanding of CAD/CG software operations. "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 Front Matter ....Pages i-xvi Introduction (Wenhe Liao, Hao Liu, Tao Li)....Pages 1-13 Splines and Subdivision (Wenhe Liao, Hao Liu, Tao Li)....Pages 15-63 Meshes and Subdivision (Wenhe Liao, Hao Liu, Tao Li)....Pages 65-96 Analysis of Subdivision Surface (Wenhe Liao, Hao Liu, Tao Li)....Pages 97-134 n-Sided Patches and Subdivision Surfaces (Wenhe Liao, Hao Liu, Tao Li)....Pages 135-166 Energy Optimization Method and Subdivision Surfaces (Wenhe Liao, Hao Liu, Tao Li)....Pages 167-195 Interactive Shape Editing for Subdivision Surfaces (Wenhe Liao, Hao Liu, Tao Li)....Pages 197-216 Intersection and Trimming of Subdivision Surfaces (Wenhe Liao, Hao Liu, Tao Li)....Pages 217-231 Subdivision Surfaces and Curve Networks (Wenhe Liao, Hao Liu, Tao Li)....Pages 233-258 Fitting Unstructured Triangle Meshes Using Subdivision Surfaces (Wenhe Liao, Hao Liu, Tao Li)....Pages 259-275 Poisson Mesh Editing Guided by Subdivision Surface (Wenhe Liao, Hao Liu, Tao Li)....Pages 277-295 Back Matter ....Pages 297-307