Geometry and Interpolation of Curves and Surfaces - Hardcover

McLeod, Robin J. Y.; Baart, M. Louisa

Hardcover

ISBN 10: 0521321530 ISBN 13: 9780521321532

Publisher: Cambridge University Press, 1998

Synopsis

This text takes a practical, step-by-step approach to algebraic curves and surface interpolation motivated by the understanding of the many practical applications in engineering analysis, approximation, and curve plotting problems. Because of its usefulness for computing, the algebraic approach is the main theme, but a brief discussion of the synthetic approach is also presented as a way of gaining additional insight before proceeding with the algebraic manipulation. The authors start with simple interpolation, including splines, and extend this in an intuitive fashion to the production of conic sections. They then introduce projective co-ordinates as tools for dealing with higher order curves and singular points. They present many applications and concrete examples, including parabolic interpolation, geometric approximation, and the numerical solution of trajectory problems. In the final chapter they apply the basic theory to the construction of finite element basis functions and surface interpolants over non-regular shapes.

About this title

Review

Review of the hardback: 'The authors have displayed considerable erudition and ability in dealing with a difficult topic. Their practical, step-by-step approach to algebraic curves and surface interpolation is very commendable in view of the complexity of the subject.' J. A. Prescott, Robotica

Review of the hardback: 'This looks like a delightful way to introduce students to the subject.' The Mathematical Association of America

Review of the hardback: '... an elegant and serious introduction to the basic concepts and results of (elementary) algebraic geometry.' European Maths Society Journal

Book Description

This text takes a practical, step-by-step approach to algebraic curves and surface interpolation, motivated by the many practical applications in engineering analysis, approximation, and curve plotting problems. The authors start with simple interpolation and extend this in an intuitive fashion to the production of more complicated curves and surfaces.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1998
• ISBN 10: 0521321530
• ISBN 13: 9780521321532
• Binding: Hardcover
• Language: English
• Number of pages: 430