Question

Which of the following statements is/are correct in the context of Voronoi polygon?

• A. A Voronoi polygon may contain more than one point, especially where the density of points is higher
• B. The center of a Voronoi polygon is a circumcenter of a Delaunay triangle
• C. Each intersection of Voronoi edges belongs to at least three Voronoi polygons
• D. Voronoi polygons and Delaunay triangles are geometric dual of each other

Hint:

Voronoi diagrams and Delaunay triangulations are closely related: Voronoi edges are perpendicular bisectors of Delaunay edges, and Voronoi vertices are circumcenters of Delaunay triangles.

Answer 1

The Correct Option is C, D

Option (A) is incorrect: By definition, a Voronoi polygon (or cell) contains exactly one generating point.
All locations inside a Voronoi cell are closer to that point than to any other.
So a Voronoi polygon cannot contain more than one point.

Option (B) is incorrect: The center of a Voronoi polygon is not necessarily the circumcenter of a Delaunay triangle.
Rather, the vertices (corners) of the Voronoi diagram correspond to the circumcenters of Delaunay triangles formed from neighboring generating points.

Option (C) is correct: In a Voronoi diagram, each point where three or more Voronoi edges meet (called a Voronoi vertex)
lies at the intersection of three or more cells, meaning it belongs to at least three Voronoi polygons.

Option (D) is correct: Voronoi diagrams and Delaunay triangulations are geometric duals.
Connecting the generating points of adjacent Voronoi cells forms the Delaunay triangulation.