Basics of Computer Aided Geometric Design: An Algorithmic Approach

The aim of this book is to provide a good foundation of Computer Aided Geometric Design to students who are doing undergraduate courses in engineering, especially Mechanical Engineering, Computer Science, Geometric Modeling, and CAD/CAM. This Second Edition is organized in three parts: Part I deals with the basics of Differential Geometry of curves and surfaces, a good understanding of which is essential prerequisite to what follows in Part II. Part II is devoted entirely to the geometric designs of curves and surfaces, which are used in the development of Computer Graphics and profiles of hulls of ships, aircraft wings, satellites, (to name a few large-scale products) as also telephones, mobile phones, fancy flower vases (to name a few small-scale products). Part III deals with certain useful generalizations of the earlier concepts, like rational Bezier and B-Spline curves and surfaces and advanced techniques like blending and corner-cutting. Concepts introduced are illustrated with examples, which are completely worked out. A list of problems is also given at the end of each chapter. PART I: DIFFERENTIAL GEOMETRY Theory of Curves Theory of Surfaces PART II: COMPUTER AIDED GEOMETRIC DESIGN Bezier Curves Bezier Surfaces Spline Curves Spline Surfaces PART III: ADVANCED TOPICS IN COMPUTER AIDED GEOMETRIC DESIGN Rational B-Spline Curves and Surfaces Certain Assorted Methods Appendix Index