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On the bisectors of weakly separable sets. (English) Zbl 0952.68144

The editors of the journal point out the following: “This article plagiarizes the original article of L. R. Nackman and V. Srinivasan [Discrete Comput. Geom. 6, No.3, 263–275 (1991; Zbl 0716.68087)]. The editors regret the publication of the copied article.”
Summary: A bisector of two sets is the set of points equidistant to them. Bisectors arise naturally in several areas of computational geometry. We show that bisectors of weakly linearly separable sets in \(\mathbb{E}^d\) share many properties with separating lines. Among these, the bisector of a restricted class of linearly separated sets is a homeomorphic image of the linear separator. We also give necessary and sufficient conditions for the existence of a particular continuous map from a portion of any linear separator to the bisector.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
51M05 Euclidean geometries (general) and generalizations

Citations:

Zbl 0716.68087
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