All Questions
Tagged with computational-geometry triangulations
13
questions
1
vote
1
answer
72
views
Partitioning polygons into obtuse isosceles triangles
Ref:
Partitioning polygons into acute isosceles triangles
Partition of polygons into 'strongly acute' and 'strongly obtuse' triangles
https://math.stackexchange.com/questions/1052063/...
1
vote
0
answers
53
views
What are some other methods for partitioning an n-dimensional space based on a set of points in that space?
So this is a very general question, but I'm curious if there are any other methods for partitioning an n-dimensional space based on the location of a set of points, either randomly chosen or specified,...
1
vote
0
answers
214
views
How to do an elevated 2D Delaunay triangulation?
This is what I call an elevated Delaunay triangulation:
This is also called a 2.5D Delaunay triangulation.
To do it, I simply perform an ordinary 2D Delaunay triangulation with the (x,y)-coordinates, ...
1
vote
1
answer
50
views
On triangulations and "coverage" of circumcircles
Let $P$ be a convex quadrilateral defined by four vertices $a$, $b$, $c$, and $d$. Suppose that the circumcircle of $\triangle abd$ contains $c$.* Let $D(\triangle abc)$ to denote the area enclosed by ...
15
votes
1
answer
612
views
Acute triangles in "obtuse" polygons?
Let $P$ be a convex polygon. Suppose every interior angle of $P$ is obtuse. Is it always the case that there exist three vertices $p, q, r$ of $P$ such that $\triangle pqr$ is acute?
I conjecture ...
2
votes
0
answers
23
views
What is known about $\operatorname{card}_E(\mathrm{MST}\cap\mathrm{MWT})$?
It is a wellknown fact of computational geometry that the edges of Minimum-weight Spanning Tree are also found in the Delaunay Triangulation of a planar pointset $\mathcal{P}$, i.e. $\operatorname{...
0
votes
0
answers
35
views
Restrictions on crossing edges in Delaunay triangulations
what can be said about crossing edges in Delaunay triangulations, i.e. about pairs of edges that constitute to the heaviest perfect matching int the $K_4$ induced by the quadruplet of adjacent ...
4
votes
2
answers
385
views
Complexity of Random Delaunay Triangulation in 3D
My question:
Is the number of cells in a three-dimensional Poisson-Delaunay triangulation with $n$ vertices $\mathcal O(n)$ with probability one?
which is equivalent to the question
Is the ...
5
votes
1
answer
260
views
Do random triangulation edge-flips maintain randomness?
Let $S$ be a fixed set of $n$ points in the plane in general position.
Let $T$ be a triangulation
of $S$, (somehow) selected
uniformly at random from all triangulations of $S$.
(There are an ...
2
votes
1
answer
114
views
mean length of the non-crossing graphs on n points
My original question is rather vague so I'll start with a precise example and then indicate possible generalisations.
Given a n-tuple $x=(x_1,\dots,x_n)$ in, say, a square with side-length $1$ in the ...
9
votes
1
answer
424
views
Hamiltonian circuit
Let us consider a disk with one labelled point on the boundary and $n$ labelled points in the interior.
Let T be a triangulation of the whole disk with vertices on the labelled points such that T ...
4
votes
1
answer
319
views
What properties does generalized Delaunay triangulation have?
Suppose that instead of the usual circle, we pick some other convex set D and make the Delaunay triangulation of a finite planar point set with respect to this set, i.e. connect two points if there is ...
3
votes
1
answer
2k
views
practical algorithm for constrained triangulation in two dimensions?
I'm looking for an algorithm that is easy to implement in practice (resulting in small amount of code), preferably incremental. As far as I know, the biggest problem with incremental constrained ...