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Tight linear envelopes for splines

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Summary.

A sharp bound on the distance between a spline and its B-spline control polygon is derived. The bound yields a piecewise linear envelope enclosing spline and polygon. This envelope is particularly simple for uniform splines and splines in Bernstein-Bézier form and shrinks by a factor of 4 for each uniform subdivision step. The envelope can be easily and efficiently implemented due to its explicit and constructive nature.

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Authors and Affiliations

  1. Department of Computer Science, Purdue University, West Lafayette, IN 47907–1398, USA; e-mail: lutter@cs.purdue.edu , , , , , , US

    David Lutterkort

  2. Department of Computer and Information Science, University of Florida, Gainesville, FL 32611–6120, USA; e-mail: jorg@cise.ufl.edu , , , , , , US

    Jörg Peters

Authors
  1. David Lutterkort
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  2. Jörg Peters
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Received February 12, 1999 / Revised version received October 15, 1999 / Published online May 4, 2001

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Lutterkort, D., Peters, J. Tight linear envelopes for splines. Numer. Math. 89, 735–748 (2001). https://doi.org/10.1007/s002110100181

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  • DOI: https://doi.org/10.1007/s002110100181

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