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Voronoï Diagrams In Projective Geometry And Sweep Circle Algorithms For Constructing CircleBased Voronoï Diagrams (Extended Abstract)
"... agram, we will in fact have, at any time during the algorithm, an (n+1)sites Vorono diagram, which will be fully constructed in the whole plane. Finally, if the location of the sweep centre is well chosen (inside one and only one site) the sweep circle and the wavefront will disappear altogether at ..."
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agram, we will in fact have, at any time during the algorithm, an (n+1)sites Vorono diagram, which will be fully constructed in the whole plane. Finally, if the location of the sweep centre is well chosen (inside one and only one site) the sweep circle and the wavefront will disappear altogether at the end of the sweep because the site which contains the centre of the sweep will dominate the sweep circle when its radius is small enough. The second one is that a subtractively weighted Vorono diagram can be nonconnected. Therefore the wavefront, which is also part of a temporary subtractively weighted Vorono diagram, may also be nonconnected at times. In order to have an optimal algorithm, it is necessary to manage wisely the wavefront when a nonconnected edge is created or merged with another one. 2. Shrinking circle sweep. This algorithm is a generalization of the Fortune algorithm [Fortune 1987]; the quick desc