Linear Envelopes for Uniform B-spline Curves

Abstract

We derive an efficiently computable, tight bound on the distance between a uniform spline and its B-Spline control polygon in terms of the second differences of the control points. The bound yields a piecewise linear envelope enclosing the spline and its control polygon. For quadratic and cubic splines the envelope has minimal possible width at the break points, and for all degrees the maximal width shrinks by a factor of 4 under uniform refinement. We extend the construction to tight envelopes for parametric curves.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP012034

Entities

People

  • David Lutterkort
  • Jörg Peters

Organizations

  • Purdue University

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Computations
  • Efficiency
  • Intervals
  • Polynomials
  • Precision
  • Sequences
  • Technical Information Centers
  • Two Dimensional

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.
  • Robotics and Automation.