Voronoi Diagram Drawing Variations and Charateristics I am learning about Voronoi diagrams and I have seen that the Voronoi diagram of a set of points is drawn with straight line segments and rays.

Similarly how can we draw the Voronoi diagram for the following: 
(a) A set of lines and points?
(b) A set of disjoint line segments?
(c) A set of line segments forming a convex polygon?
(d) A set of circles (non intersecting and no circle contains another)?

For each of these sets of objects, how can we describe the shape of the boundary pieces that form the Voronoi diagram. 

I believe that the distance between a point and another object is the smallest distance between the point and any point of the object.
The Voronoi diagram of disjoint segments (b) has been thoroughly studied.

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Image from GIS.


See:


  CGAL Manual, Chapter 43:
  2D Segment Voronoi Diagrams. CGAL link.




For the Voronoi diagram of circles (d), see:


  Jin, Li, Donguk Kim, Lisen Mu, Deok-Soo Kim, and Shi-Min Hu. "A sweepline algorithm for Euclidean Voronoi diagram of circles." Computer-Aided Design 38, no. 3 (2006): 260-272. Journal link.
  
  Huber, Stefan. Computation of Voronoi diagrams of circular arcs and straight lines. Magisterarbeit, 2008.


To quote the latter: "Lemma 1.4. The bisector between two circles (...) consists of ellipses and hyperbolas." 
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