Scale‐Invariant Minimum‐Cost Curves: Fair and Robust Design Implements

  title={Scale‐Invariant Minimum‐Cost Curves: Fair and Robust Design Implements},
  author={Henry P. Moreton and C. S{\'e}quin},
  journal={Computer Graphics Forum},
Four functionals for the computation of minimum cost curves are compared. Minimization of these functionals result in the widely studied Minimum Energy Curve (MEC), the recently introduced Minimum Variation Curve (MVC), and their scale‐invariant counterparts, (SI‐MEC, SI‐MVC). We compare the stability and fairness of these curves using a variety of simple interpolation problems. Previously, we have shown MVC to possess superior fairness. In this paper we show that while MVC have fairness and… Expand
33 Citations
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  • 11
Variational Design and Fairing of Spline Surfaces
  • G. Greiner
  • Mathematics, Computer Science
  • Comput. Graph. Forum
  • 1994
  • 151
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  • PDF
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  • 155
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  • R. F. Sarraga
  • Mathematics, Computer Science
  • Comput. Aided Geom. Des.
  • 1998
  • 27
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  • 35
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  • 38


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  • 424
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  • 2,266
  • PDF