TY - GEN

T1 - Distance trisector of segments and zone diagram of segments in a plane

AU - Jiyon, Jinhi

AU - Okada, Yuji

AU - Tokuyama, Takeshi

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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. 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 C 1 and C2 exist and are unique. We then give a practical algorithm for computing the Zone diagram of a set of segments in a digital plane.

AB - 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. 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 C 1 and C2 exist and are unique. We then give a practical algorithm for computing the Zone diagram of a set of segments in a digital plane.

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U2 - 10.1109/ISVD.2007.19

DO - 10.1109/ISVD.2007.19

M3 - Conference contribution

AN - SCOPUS:47849086142

SN - 0769528694

SN - 9780769528694

T3 - Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007

SP - 66

EP - 73

BT - Proceedings - ISVD 2007 The 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007

T2 - 4th International Symposium on Voronoi Diagrams in Science and Engineering 2007, ISVD 2007

Y2 - 9 July 2007 through 11 July 2007

ER -