Freeform surface modeling technology

Author: Zhu Xinxiong
Publisher:
Publish Date: 2000-01-01
Features: This book discusses the free-form surface modeling methods in CAD/CAM from an applied perspective. It includes topics such as differential geometry, Coon patches, Bézier methods, and NURBS methods, scattered point interpolation surfaces, intersection and smoothing, as well as new modeling techniques expected to be featured in CAD/CAM systems in the 21st century, such as free-form deformation, partial differential equations, energy optimization, and wavelet techniques. The book comprehensively reflects the author's 25 years of teaching and research achievements in the field of free-form curve and surface modeling. It consists of 18 chapters. Chapters 1 to 3 are the foundational part; Chapter 4 explains the principles of constructing free-form surfaces across boundaries using Coon patches; Chapter 5 covers the Bézier method; Chapters 6 to 10 discuss the principles and applications of B-spline methods, emphasizing the generation, properties of B-spline basis functions, and their impact on curve and surface shapes, with detailed coverage of the author's research achievements on NURBS surfaces; Chapters 11 to 15 sequentially discuss triangular domain surfaces, scattered point interpolation surfaces, free-form deformation, partial differential equation methods, and energy-based surface modeling, highlighting the principles, algorithmic steps, and applicability of these methods; Chapter 16 explores the application of wavelet techniques in multi-resolution representation, smoothing, and data compression for free-form curves and surfaces. Chapters 17 and 18 address the problems of curve and surface intersection and smoothing. This book is suitable as a textbook for specialized fields in higher education institutions, including aerospace, automotive, shipbuilding, computer science, mechanical engineering, mold design, geology, meteorology, medical engineering, and industrial design. Additionally, it serves as a valuable reference for researchers and engineering professionals engaged in the development and application of CAD/CAM/CAE systems or those interested in surface modeling.