Computation with splines and B-splines
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Computation with splines and B-splines by Donald E. Amos

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Published by Dept. of Energy, [Office of the Assistant Secretary for Defense Programs], Sandia Laboratories, for sale by the National Technical Information Service] in Albuquerque, N.M, [Springfield, Va .
Written in English


  • Splines.

Book details:

Edition Notes

StatementDonald E. Amos, Numerical Mathematics Division 5642 ; prepared by Sandia Laboratories for the United States Department of Energy under contract AT(29-1)-789.
SeriesSAND ; 78-1968, SAND (Series) (Albuquerque, N.M.) -- 78-1968.
ContributionsUnited States. Dept. of Energy., Sandia Laboratories. Numerical Mathematics Division 5642., Sandia Laboratories.
The Physical Object
Pagination47 p. :
Number of Pages47
ID Numbers
Open LibraryOL17649910M

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Dierkx demonstrates in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data by: In addition, we derive recursions for the computation of integrals of products of B-splines (of possibly different orders and on possibly different knot sequences). As an application, we consider the numerical computation of the Gram matrix which arises in least squares fitting using by: B-spline functions are defined recursively, so the direct computation is very difficult. In this article new direct proof of the formula used for simpler direct computation is shown.   This approach is particularly useful when working with B-splines and natural splines. B-splines have d+K, while a natural cubic spline basis function with K knots has K+1 degrees of freedom, respectively. By default, the function bs in R creates B-splines of degree 3 with no interior knots and boundary knots defined at the range of the X Cited by: 3.

In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are equidistant from each other. This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory that are especially useful in calculations and stresses the representation of splines as weighted sums of B-splines. This revised edition has . There are some fifty FORTRAN (sub) programs throughout the book together with an abundance of worked-out examples and many helpful comments (also in the case of pitfalls in computation) which reflect the author's ample experience in calculating with splines." "This book is Cited by: B-spline Basis Functions: Computation Examples. Two examples, one with all simple knots while the other with multiple knots, will be discussed in some detail on this page. Simple Knots Suppose the knot vector is U = { 0, , , , 1 }. Hence, m = 4 and u 0 = 0, u 1 = , u 2 = , u 3 = and u 4 = 1. The basis functions of degree.

A Unified Architecture for the computation of B-Spline Curves Article (PDF Available) in IEEE Transactions on Parallel and Distributed Systems 8(12) - January with 75 Reads.   The B-Splines’ computation in computational devices is also illustrated. An industry application based on image processing where B-Spline curve reconstructs the 3D surfaces for CT image datasets of inner organs further highlights the strength of these curves. The computation of B-spline functions requires a preallocated workspace. gsl_bspline_workspace * gsl_bspline_alloc (const size_t k, const size_t nbreak) This function allocates a workspace for computing B-splines of order k. The number of breakpoints is given by nbreak. This leads to basis functions. Cubic B-splines are specified by. A PRIMER ON REGRESSION SPLINES 5 an equal number of sample observations lie in each interval while the intervals will have di erent lengths (as opposed to di erent numbers of points lying in equal length intervals). B ezier curves possess two endpoint knots, t 0 and t 1, and no interior knots hence are a limiting case, i.e. a B-spline for which File Size: KB.