# Questions tagged [delaunay-triangulation]

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### Strongly edge-guarding a 3d triangulation

Let $T$ be a planar triangulation. It is known that one can guard the faces of $T$ using at most $\lfloor n/3 \rfloor$ edge-guards (Worst-case-optimal algorithms for guarding planar graphs and ...
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### Triangulation with maximum greatest area

Given a point set $P$ and a triangulation $T$ of $P$ with $d$ triangles, let's define $$\alpha(T) = (\alpha_1, \alpha_2, \ldots, \alpha_{3d})$$ which denotes the series of interior angles of $T$, ...
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### Voronoi diagrams applications where the input order has some known properties?

Are there applications of Voronoi diagrams or Delaunay triangulations where the order in which the points are generated (and given to the algorithm) have some known properties (e.g. concatenation of ...
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### Maximum number of triangles in a constrained delaunay triangulation

I'm looking for an upper bound for the number of triangles in a constrained planar delaunay triangulation. I know for d=2 delaunay triangulation, there are at most n+1 triangles where n is the number ...
108 views

### Worst-case optimal Delaunay algorithm based on spatial sort and walking?

Buchin [2] showed that under "reasonable" assumptions, (polynomial point spread) incremental construction of Delaunay triangulations using the biased randomized ordering of Amenta et al. [1] with a ...
29 views

### Extending Delaunay graphs in d-space

I am new to computational geometry so pardon me for the lack of formalism. I am currently experimenting with an algorithm of mine in which I need to extend recursively a Delaunay graph in $d$-space. ...
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### Partition planar graph of vertices with at most degree 3 into connected subgraphs

I'm currently working on my thesis which deals with pathfinding over a Delaunay triangulated graph. I want to be able to partition my Delaunay triangulation into disjoint (regarding vertices) ...
53 views

### Finding if an edge lies within a set of disjoint rectangles

I'm using a triangulation library to compute the Constrained Delaunay Triangulation of a set of rectangles within some large boundary. The algorithm returns all the edges, but also adds edges inside ...
We denote by a triangulation a (simple) maximal planar graph. How many triangulations on $n$ vertices are there? How many triangulations are there if we cannot distinguish the vertices, i.e. ...