# Tagged Questions

Using computers to solve geometric problems. Questions with this tag should typically have at least one other tag indicating what sort of geometry is involved, such as ag.algebraic-geometry or mg.metric-geometry.

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### Where to submit this work with several unusual features?

I appreciate that questions about where to submit are generally considered off-topic, but I hope that the unusual features of the present case may make it acceptable. I have put a monograph on github ...
1answer
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### Graph spectra and topology

This is a somewhat vague question, but I'm wondering if there has been any research into connections between the spectrum of a graph and some notion of the "topology" of that graph. To give an ...
1answer
188 views

### Ascertain properties of a new kind of rectilinear-convex set

PREABMLE TO MY QUESTION I am reading about convex sets and hulls in orthogonal/rectilinear spaces. As can be seen in this publication, for a given set of points in $\mathbb{R}^{2}$, there are many ...
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### Covering the annulus of symmetric convex body

Consider a symmetric convex body $A$ in $\mathbb{R}^d$. Now, we draw another object, $A'$, concentric and translated with respect to $A$ and having radius slightly greater than twice to the radius of ...
1answer
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### Efficiently Generating the Convex Hulls of Two Polytopes and Counting Faces

Suppose you have two polytopes $P_1, P_2 \in \Bbb{R}^n$ given by $$P_1 = \lbrace x: A_1 x \le b_1\rbrace$$ $$P_2 = \lbrace x: A_2 x \le b_2\rbrace$$ I wish to find their convex hull, that is a ...
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### Term for meshes bounding a non-degenerate tetrahedral mesh in 3D?

Is there a term in the literature referring to triangle meshes that are the closed boundary of some non-self-intersecting, non-degenerate tetrahedral mesh embedded in $R^3$? This class of triangle ...
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108 views

### cohomology ring of compact submanifolds of Euclidean spaces

Suppose we have a compact $m$-dimensional submanifold $M$ of $\mathbb{R}^N$ and we want to know the cohomology ring $H^*(M;\mathbb{Z})$. Let $\epsilon>0$ and a $m$-dimensional finite simplicial ...
4answers
135 views

### Show that the Minkowski sum of two triangles in 3D is the union of Minkowski sums of each triangle along the other's edges?

I'd like to show (or disprove) the claim that the Minkowski sum of two triangles with vertices in $\mathbb{R}^3$, $A+B$, is equal to the union of the unions of the Minkowski sums of $A$ along all ...
2answers
407 views

### “Average” Voronoi diagrams without probability?

A plane Poisson process with uniform intensity scatters "sites" about the plane. If I'm not mistaken, in a sense the "average" Voronoi diagram of that set of sites is a honeycomb. I know it's been ...
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156 views

### Determining N d-points yielding equal sums of Euclidean distances from M s-points

Given M source points (s-points), determine N, the number of destination points (d-points), and their locations (coordinates), such that the sum of the N Euclidean distances from each source point to ...
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70 views

### conformal deformation with fixed boundaries

For a flat plane with certain boundary, e.g., a rectangular patch, is it possible to conformally displace or deform such patch to a curved bump with exact same boundary? In this thesis, Dr. Keenan ...
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55 views

### VC dimension of infinite cones [closed]

What is the VC dimension of infinite $d$-dimensional cones? ( single cones not double). I would say $2d + 1$ or $O(d^2)$ Does anybody have any reference or ideas?
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### Efficient sampling from a polytope with large number of contraints [duplicate]

As far as I know, the most popular way to sample from a polytope (in H-representation) $$\mathcal{P} := \{z \in \mathbb{R}^n | (Az)_j \le b_j\; \forall j=1,2,\ldots,m\}$$ ...
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### Find minimum-area ellipse which encloses two ellipses

I need an efficient algorithm to find the ellipse with the smallest possible area which encloses two given ellipses. The given ellipses are constrained to have coincident centers at the origin but can ...
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257 views

### Find minimum-area ellipse enclosing a set of ellipses, all centered at the origin

Given a set of N > 2 (two-dimensional and coplanar) ellipses, all centered at the origin, how do I find the ellipse with the minimum area which encloses all of them? Background: Thanks to Will Jagy ...
2answers
339 views

### What are the applications of Voronoi diagrams in pure mathematics? [closed]

Voronoi diagrams have interesting mathematical properties and applications in algorithms and modeling. But what are its applications in pure mathematics? For example, what theorems can be proved using ...
1answer
191 views