TY - GEN

T1 - Voronoi diagram with respect to criteria on vision information

AU - Asano, Tetsuo

AU - Tamaki, Hisao

AU - Katoh, Naoki

AU - Tokuyama, Takeshi

PY - 2007/12/1

Y1 - 2007/12/1

N2 - Voronoi diagram for a set of geometric objects is a partition of the plane (or space in higher dimensions) into disjoint regions each dominated by some given object under a predetermined criterion. In this paper we are interested in various measures associated with criteria on goodness of an input line segment with respect to each point in the plane as the "point of view". These measures basically show how the segment or information displayed on the segment can be seen from the point. Mathematically, the measures are defined in terms of the shape of the triangle determined by the point and the line segment. Given any such measure, we can define a Voronoi diagram for a set of line segments. In this paper we are interested in investigating their common combinatorial and structural properties. We investigate conditions for those measures to de.ne regular Voronoi diagrams and also conditions that local optima on the measures lie only on Voronoi edges, not in the proper interior of Voronoi regions.

AB - Voronoi diagram for a set of geometric objects is a partition of the plane (or space in higher dimensions) into disjoint regions each dominated by some given object under a predetermined criterion. In this paper we are interested in various measures associated with criteria on goodness of an input line segment with respect to each point in the plane as the "point of view". These measures basically show how the segment or information displayed on the segment can be seen from the point. Mathematically, the measures are defined in terms of the shape of the triangle determined by the point and the line segment. Given any such measure, we can define a Voronoi diagram for a set of line segments. In this paper we are interested in investigating their common combinatorial and structural properties. We investigate conditions for those measures to de.ne regular Voronoi diagrams and also conditions that local optima on the measures lie only on Voronoi edges, not in the proper interior of Voronoi regions.

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U2 - 10.1109/ISVD.2007.44

DO - 10.1109/ISVD.2007.44

M3 - Conference contribution

AN - SCOPUS:47849117174

SN - 0769528694

SN - 9780769528694

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

SP - 25

EP - 32

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 -