Euclidean Voronoi Diagrams for Circles in a Circle
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Euclidean voronoi diagram for circles in a circle
Presented in this paper is an algorithm to compute a Euclidean Voronoi diagram for circles contained in a large circle. The radii of circles are not necessarily equal and no circle inside the large circle wholly contains another circle. The proposed algorithm uses the ordinary point Voronoi diagram for the centers of inner circles as a seed. Then, we apply a series of edge-flip operations to th...
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We extend the concept of Voronoi diagram in the ordinary Euclidean geometry for n points to the one in the Laguerre geometry for n circles in the plane, where the distance between a circle and a point is defined by the length of the tangent line, and show that there is an O(n log n) algorithm for this extended case. The Voronoi diagram in the Laguerre geometry may be applied to solving effectiv...
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The sweep circle algorithm is based on the concept of wavefront developed by Dehne and Klein [Dehne, 1997]. In this case, because the sweep line is a site of the same nature as the sites being considered, we get an economy of scale for the objects to be treated. It uses the definition of a Voronoï diagram in projective geometry to simplify the treatment of the non-connected wavefront and vertex...
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Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others. The proposed algorithm constructs the correct Voronoi diagram as a sweepline moves on the plane from top to bot...
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Voronoi diagrams are among the most important data structures in geometric modeling. Among many efficient algorithms for computing 2D Voronoi diagrams, Fortune’s sweepline algorithm (Fortune, 1986 [5]) is popular due to its elegance and simplicity. Dehne and Klein (1987) [8] extended sweepline to sweepcircle and suggested computing a type of transformed Voronoi diagram, which is parallel in nat...
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تاریخ انتشار 2008