The distance trisector curve

@inproceedings{Asano2006TheDT,
  title={The distance trisector curve},
  author={Tetsuo Asano and Jir{\'i} Matousek and Takeshi Tokuyama},
  booktitle={STOC},
  year={2006}
}
Given points P and Q in the plane, we are interested in separating them by two curves C<sub>1</sub> and C<sub>2</sub> such that every point of C<sub>1</sub> has equal distance to P and to C<sub>2</sub>, and every point of C<sub>2</sub> has equal distance to C<sub>1</sub> and to Q. We show by elementary geometric means that such C<sub>1</sub> and C<sub>2</sub> exist and are unique. Moreover, for P = (0,1) and Q = (0,-1), C<sub>1</sub> is the graph of a function ƒ: R → R, C<sub>2</sub> is the… CONTINUE READING
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