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Curves & Surfaces

Author(s): Lyche, T.

Editor: SIAM

ISBN: 0-89871-306-4

Language: English

Edition: Philadelphia PA,Society for industrial and applied Mathematics, 1993

1967 pages, 26 cm thick.

 

Main topics covered by this book are:

	blossoming
	algorithms for progressive curves: extending B-Spline and blossoming techniques to the monomial, power, and newton dual bases
	factored knot insertion
	knot insertion algorithms
	conversion between B-Spline bases using the generalized oslo algorithm
	how much can the size of the B-Spline coefficients be reduced by inserting one knot?
	an envelope approach to a sketching editor for hierarchical free-form curve design and modification

For those not so familiar with the nurbs machinery that is, may be, useful to give some hints about  how fundamental are  knot insertion and deletion. Here are some points directly related to that topic.

	point evaluation
	calculation of derivatives, curvature and the like
	degree elevation
	interactive modification of a curve or surface
	piecewise linear approximation of curve and surface
	how control points are related to the B-spline itself.
	also related to fairing, fitting and interpolation.

Knot insertion and deletion algorithms are the basis of any B-spline library and the right way for a deep and "intuitive" understanding of B-splines.

 

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