Distance Trisector of a Segment and a Point

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  • CHUN Jinhee
    Graduate School of Information Sciences, Tohoku University
  • OKADA Yuji
    Graduate School of Information Sciences, Tohoku University
  • TOKUYAMA Takeshi
    Graduate School of Information Sciences, Tohoku University

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Motivated by the work of Asano et al. [1], we consider the distance trisector problem and zone diagram considering segments in the plane as the input geometric objects. As the most basic case, we first consider the pair of curves (distance trisector curves) trisecting the distance between a point and a line, as shown in Figure 1. This is a natural extension of the bisector curve (that is a parabola) of a point and a line. In this paper, we show that these trisector curves C1 and C2 exist and are unique.

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