Geometry and Interpolation of Curves and Surfaces

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Cambridge University Press, Jul 13, 1998 - Computers - 414 pages
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This text takes a practical, step-by-step approach to algebraic curves and surface interpolation motivated by the understanding of the many 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 coordinates 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 nonregular shapes. Professionals, students, and researchers in applied mathematics, solid modeling, graphics, robotics, and engineering design and analysis will find this a useful reference.
 

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Contents

Interpolation l
1
Conic Sections
48
Synthetic Geometry
114
Algebraic Projective Geometry
129
Algebraic Curves
185
Examples and Applications
257
Surfaces
323
Index
411
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