Computational Geometry

Curve and Surface Modeling

Su Bu-qing, Liu Ding-yuan

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483272283
• Topic: Mathematics
• Subtopic: Geometry
• Index: Mathematics

Computational Geometry: Curve and Surface Modeling provides information pertinent to the fundamental aspects of computational geometry. This book discusses the geometric properties of parametric polynomial curves by using the theory of affine invariants for algebraic curves. Organized into eight chapters, this book begins with an overview of the objects studies in computational geometry, namely surfaces and curves. This text then explores the developments in the theory and application of spline functions, which began with cubic spline functions. Other chapters consider the mechanical background of the cubic spline functions, which is the wooden spline with small deflection. This book discusses as well that in mathematical lofting the information of a geometric shape is given by a set of data points, while in geometric design other ways of representations are available. The final chapter deals with the concepts in the theory of algebraic curves. This book is a valuable resource for mathematicians.

Table of contents

• Front Cover
• Computational Geometry: Curve and Surface Modeling
• Copyright Page
• Table of Contents
• Preface to the English Edition
• CHAPTER I. Introduction
• CHAPTER II. Spline Functions
• CHAPTER III. Parametric Cubic Spline Curves
• CHAPTER IV. Bézier Curves and B-Spline Curves
• CHAPTER V. Spline Surfaces
• CHAPTER VI. Nonlinear Splines
• CHAPTER VII. Curves and Net Fairing
• CHAPTER VIII. The Intrinsic Affine Invariants of Parametric Curves in Affine Hyperspace
• References
• Additional References
• Index