Multifario Demo - interactive covering of a plane


Left mouse button on a point determines the next center, drag the mouse, and mouse up determines the radius. If you're not sure, hit the "Pick a point for me" button.
Red - boundary of the union of the circular disks
Yellow - Circular disks that lie on the boundary of the union. At least one vertex of the polygon is outside the circle.
Blue - Circular disks that are interior to the union. The polygon is entirely inside the disk.
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.

Michael E. Henderson, "Multiple parameter continuation: Computing implicitly defined surfaces", Int. J. Bifurcation and Chaos, 12, pp. 451-476, 2002.


Multifario

Michael E. Henderson michael.e.henderson.10590 at gmail.com