Basics of Computer Aided Geometric Design: An Algorithmic Approach

Contents: I: Differential Geometry. 1. Theory of Curves. 2. Theory of Surface. II: Computer Aided Geometric Design. 3. Bezier Curves. 4. Bezier Surfaces. 5. Spline Curves. 6. Spline Surfaces. III: Advanced Topice in Computer Aided Gemetric Design. 7. Rational B-Spline Curves and Surfaces. 8. Certain Assorted Methods. Index.

The aim of the book is to provide a good foundation of Computer-Aided Geometric Design to students who are doing under-graduate courses in engineering, especially Mechanical Engineering, Computer Science, Geometric Modeling and CAD/CAM. This book is organized in two parts. Part-I deals with the basics of differential geometry of curves and surface, a good understanding of which is essential prerequisite to what follows in the 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 and 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.