Geometry and Interpolation of Curves and Surfaces
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Product details:
- Publisher Cambridge University Press
- Date of Publication 13 July 1998
- ISBN 9780521321532
- Binding Hardback
- No. of pages430 pages
- Size 238x160x28 mm
- Weight 750 g
- Language English 0
Categories
Short description:
This text gives a step-by-step approach to the production of conics, cubics, more general curves, and rational surfaces.
MoreLong description:
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.
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
Table of Contents:
1. Interpolation; 2. Conic sections; 3. Synthetic geometry; 4. Algebraic projective geometry; 5. Algebraic curves; 6. Examples and applications; 7. Surfaces.
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