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B-splines with homogenized knots

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Abstract

The use of homogenized knots for manipulating univariate polynomials by blossoming algorithms is extended to piecewise polynomials. A generalization of the B-spline to homogenized knots is studied. The new B-spline retains the triangular blossoming algorithms for evaluation, differentiation and knot insertion. Moreover, the B-spline is locally supported and a Marsden’s identity exists. Spaces of natural splines and certain polynomial spline spaces with more general continuity properties than ordinary splines have bases of B-splines over homogenized knots. Applications to nonpolynomial splines such as trigonometric and hyperbolic splines are made.

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Authors and Affiliations

  1. SINTEF, Blindern, P.O. Box 124, N-0314, Oslo, Norway

    Kyrre Strøm

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  1. Kyrre Strøm
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Communicated by R.N. Goldman

This project was supported by the Royal Norwegian Research Council for Science and the Humanities (NAVF), and the Department for Informatics, University of Oslo.

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Strøm, K. B-splines with homogenized knots. Adv Comput Math 3, 291–308 (1995). https://doi.org/10.1007/BF03028372

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  • DOI: https://doi.org/10.1007/BF03028372

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