Voronoï diagrams in projective geometry and sweep circle algorithms for constructing circle-based voronoï diagrams

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 events. The paper gives an application of this kind of algorithm to the computation of a subtractively weighted Voronoï diagram. However the properties of the sweep circle algorithm in projective geometry can be used to construct other circle-based Voronoï diagrams and another application of these concepts is being developed for the construction of a Voronoï diagram of circles in Euclidean geometry.