Voronoï Diagrams In Projective Geometry And Sweep Circle Algorithms For Constructing Circle-Based Voronoï Diagrams (Extended Abstract)

we want to construct an n-sites Vorono diagram, 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 non-connected. Therefore the wavefront, which is also part of a temporary subtractively weighted Vorono diagram, may also be non-connected at times. In order to have an optimal algorithm, it is necessary to manage wisely the wavefront when a non-connected edge is created or merged with another one. 2 Fig. 1-c Fig. 1-a Fig. 1-