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Look Inside Geometry and Interpolation of Curves and Surfaces

Geometry and Interpolation of Curves and Surfaces


  • Date Published: July 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521159395

£ 42.99

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About the Authors
  • 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.

    • Applications include curve design in the aircraft industry, finite element analysis, computer graphics and curve plotting
    • Many figures included
    • Many useful constructions
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    Reviews & endorsements

    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

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    Product details

    • Date Published: July 2011
    • format: Paperback
    • isbn: 9780521159395
    • length: 430 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.63kg
    • availability: Available
  • Table of Contents

    1. Interpolation
    2. Conic sections
    3. Synthetic geometry
    4. Algebraic projective geometry
    5. Algebraic curves
    6. Examples and applications
    7. Surfaces.

  • Authors

    Robin J. Y. McLeod, Saltire Software Inc., Oregon

    M. Louisa Baart, Potchefstroom University for Christian Higher Education, South Africa

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