Textbook in PDF format

Department of Mathematics Cranfield Institute of Technology.
This book deals with the mathematical techniques which have been developed in recent years for the representation, analysis and synthesis of "shape information" by computers. This area of mathematics is now assuming major importance in the manufacturing industries with the increasing use of computer-aided design and manufacture, which require a precise geometrical description of the product.
The authors gather together for the first time material from widely scattered sources in the technical and mathematical literature. There is extensive discussion given of splines and related means for defining composite curves and "patched" surfaces, and coverage of both parametric and non-parametric techniques. The book is primarily concerned with the mathematics of the various methods, and gives numerous references to descriptions of their practical application.
The foundations of the subject in classical and vector geometry are reviewed in the early chapters, while matrices and basic numerical analysis are dealt with in Appendices. The book should therefore be self-contained for readers familiar with elementary calculus.
Plane Co-ordinate Geometry
Three Dimensional Geometry and Vector Algebra
C0-ordinate Transformations
Three Dimensional Curve and Surface Geometry
Curve and Surface Design
Composite Curves and Splines
Composite Surfaces
Cross-sectional Designs
Computing Methods for Surface Design and Manufacture