# Questions tagged [discrete-geometry]

Discrete geometry includes the study of covering, illumination, packing, convex bodies, convex polytopes, and other metric geometry.

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### Algorithm for triangulation of 2D "point cloud" [closed]

EDIT: I need an algorithm which as an input takes 2D array of colors - white and black, and as an output array of 2D vectors which will be coordinates to the input array. Those vectors should form ...
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### Jacobi field on polygonal mesh

I want to compute Jacobi fields on polygonal meshes. The problem is that on each face, two geodesics starting parallel will remain parallel until they pass a vertex from different sides. Passing a ...
1 vote
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1 vote
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### Finding the 2-facets of a convex 4D polytope (algorithm)

I'm an undergraduate student and I'm currently working on my end-of-degree-project. The main goal of this project is studying the $A_4$ root lattice, the geometry of its Voronoï complex, and using the ...
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### Quantum''/ non-commutating extension of polytopes

Are there non-commutative (ie. quantum) extensions of polytopes? More specifically I was wondering if there are some deformation, say $\hbar$, to polytopes which when is taken to be zero, one gets ...
1 vote
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### Does there exist Eulerian quadrangulations that are not 1- or 2-degenerate?

I am looking for Eulerian planar quadrangulations that are not 1- or 2-degenerate, but I cannot seem to find such graphs. Note: a graph is Eulerian if and only if every vertex has an even degree. ... 1 vote
If I am looking at a Cartesian product of two graphs $G_1$ and $G_2$ (defined here https://en.wikipedia.org/wiki/Cartesian_product_of_graphs). I am trying to bound the diameter of the graph $G_1 \... 0 votes 0 answers 29 views ### Possibility of non-intersecting chord diagrams with given sets of endpoints Consider two finite subsets of a circle,$A,B \in S^1$, each with even number of elements. I want to construct two chord diagrams, one with endpoints set$A$, and one with endpoints set$B$in such a ... 1 vote 0 answers 59 views ### Every$\mathcal{V}$-polyhedron is an$\mathcal{H}$-polyhedron On page 32 of Ziegler's lectures, he wants to show that every$\mathcal{V}$-polyhedron is an$\mathcal{H}$-polyhedron. Ziegler defines the$\mathcal{V}$-polyhedron as the Minkowski sum of a convex ... • 469 1 vote 0 answers 24 views ### (2,3,7) tiling of Hurwitz surface I'm reading through the paper On the Geometry of Hurwitz Surfaces for an undergraduate project. Apologies for my basic questions; I've not met these ideas before. In the abstract, the source says: By ... • 51 0 votes 1 answer 35 views ### Simplify algebraic vector expressions with dot product and cross product I am trying to derive the bending force of a discrete curve, which requires the derivative of angles between two vectors represented tangent half angle. I follow this note for my derivation: https://... 1 vote 1 answer 40 views ### Group of isometries acting on a metric space is already discrete if a stabilizer is finite and an orbit is discrete My question is on page 163, the proof of Lemma 7 in the book Foundations of hyperbolic manifolds by John G. Ratcliffe. Let$\Gamma$be a group of isometries of a metric space$X$. If there is a point$...
I'm trying to print out nets of a cube on a sheet of paper, and I'm hoping to fit as many as I can on single sheets. The squares that make up the net are $\frac{1}{2}$ an inch wide, and I'm printing ...