Multifario - interactive covering of a plane

Left mouse button on a point determines the next center, drag the mouse, and mouse up determines the radius.
Red - boundary of the union of the circular disks
Yellow - Partial circular disks that lie on the boundary of the union. At least one vertex of the polygon is outside the circle.
Blue - Partial circular disks that are interior to the union. There is no red circle inside the polygon.
Black - Polygons associated with the circular disks - restricting the disks to their polygons gives a collection of disjoint sets which cover the union. A restricted Laguerre-Voronoi diagram. If two circles overlap there is (usually) an edge in the diagram through the points at which the circles intersect.
Green - The dual of the polygons - a restricted Delaunay triangulation. If two circles overlap there is a green edge between their centers.

Points in the polygon that are on the circle bounding it's disk are on the boundary of the union.