Optimal adaptive algorithms for finding the nearest and farthest point on a parametric black-box curve

@article{Baran2004OptimalAA,
  title={Optimal adaptive algorithms for finding the nearest and farthest point on a parametric black-box curve},
  author={Ilya Baran and Erik D. Demaine},
  journal={Int. J. Comput. Geom. Appl.},
  year={2004},
  volume={15},
  pages={327-350}
}
We consider a general model for representing and manipulating parametric curves, in which a curve is specified by a black box mapping a parameter value between 0 and 1 to a point in Euclidean <i>d</i>-space. In this model, we consider the nearest-point-on-curve and farthest-point-on-curve problems: given a curve <i>C</i> and a point <i>p</i>, find a point on <i>C</i> nearest to <i>p</i> or farthest from <i>p</i>. In the general black-box model, no algorithm can solve these problems. Assuming a… 

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