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# 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} }

- Published 2006 in STOC
DOI:10.1145/1132516.1132565

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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