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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Practical Algorithm for Comparing the Discrepancy of Point Sets (on Unit Hyper Spheres)

I have devised a simple geometric algorithm for generating a sequence of points on unit hyper spheres; that algorithm depends on a single real parameter, which I would like to optimize in order to get ...
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Nearest Point to a real algebraic set

Suppose I have a compact bounded real algebraic (eventually: or analytic or semialgebraic or semianalytic set) $V$ in $\mathbb R^3$ and a point $x\in\mathbb R^3$ not in $V$. How much do we know about ...
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Fractional Helly for more than one piercing

Fractional Helly Theorem says the following: For every $0<\alpha\leq 1$ there exists $\beta = \beta(d, \alpha)$ with the following property. Let $C_1 , C_2 , ..., C_n$ be convex sets in $R^d$, $n ...
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Constructing a polyhedron of maximal possible volume from given bounds on areas of its faces

Consider $n$ variables $a_1,...,a_n$ ranging over $\mathbb{R}^+$. Suppose we are given $n$ pairs of positive rational numbers $(p_1,q_1),...,(p_n,q_n)$ where each pair imposes bounds on the ...
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Upper bounds on art gallery problems using independent witnesses

Given a polygon $P$, the art gallery problem looks to find a smallest set of points that sees all of $P$. One way of bounding the number of guards necessary (from below) is to find a largest set of ...
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Generating random polygons from a given triangulation of points

Given a triangulation $T$ of a planar set point $S$, we would like to randomly generate a polygon (hamiltonian cycle) $P$. However, it has been proved that Hamiltonian Circuit Problem on maximal ...
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Find shift direction for min overlap area of 2 polygons

I have 2 arbitrary polygons (concave or convex) with certain overlap. Now there is some relative shift between these 2 polygons (vector s with a constant length). I want to find the direction of s ...
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Intuition behind minimizing the Dirichlet energy of a mapping

What does minimizing the Dirichlet energy of a mapping $\Phi$ achieve intuitively? Roughly it is the integral (or sum, if discrete) of $|\nabla \Phi(\;)|^2 dV$, with $V$ the volume. So is it, in some ...
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Computing with Graphs in Surfaces

I asked this question yesterday on math.stackexchange, but the only response so far hasn't really addressed the question, so I thought I'd cross-post it. I am currently working on a research project ...
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Dissection of a polygon into convex polygons

Problem: for a fixed integer $m\geqslant 3$ find all $n$ such that no $n$-gon can be dissected into convex $m$-gons. I would be very grateful for any information on this problem. Remark 1. There ...
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Determining feasibility of specific intersection structures between closed paths in the plane

I have two arrays, each containing a different ordering of the same set of integers. Each integer is a label for a point in which two closed paths intersect in the plane. The two arrays are ...
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Representing a Pullback as an Infinite Matrix

Let $M$ and $N$ be manifolds and let $T: M \to N$ be a bijective map. Let $ \mathcal{F}(M,\mathbb{R})$ (resp.$ \mathcal{F}(N,\mathbb{R})$) be the space of all functions from $M$ (resp. $N$) to ...
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Non-Convex Polygons with “Antipodal Visibility”

by "antipodal visibility" of planar, simple polygons I mean the following property: if two points $p$ and $q$ on the polygon's boundary divide the polygon's boundary into two polylines of equal ...
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Covering a set of points by bounded geometric object/objects

1) Let $S$ be a set of $n$ points in $R^d$. Now, given a bounded geometric object $G$, the problem is to check whether $S$ can be contained in $G$. 2) Also, in general setting, the problem is to ...
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Boundary surfaces in a 3d Voronoi tessellation with obstacles

Let $x_1,\dots,x_n$ be a set of points in $\mathbb{R}^3$ and let $\mathcal{O}_1 ,\dots, \mathcal{O}_m$ denote a set of polyhedral obstacles. What is the name for the surfaces that describe the ...
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minimizing the sum of euclidean norms

minimizing the sum of euclidean norms with box constraints I am a graduate student in computer science, making a thesis on uncertainty geometry. During my thesis I came across the following ...
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Solving 3D equation system (inverse-projecting a triangle)

Please, how is the equation system below named exactly (to search further literature)? Does it have an analytical solution? If it doesn't, then what could be the fastest numerical method for it ...
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Compute generalized pentagram map

Hi, (This is my first question on MathOverflow! :-) Imagine you have a set of points $S = \{p_1, \ldots, p_n\}$ in $\mathbb{R}^d$, of which $t$ are "bad". I want to compute a "safe convex hull", ...
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146 views

Techniques for refining or constraining a Voronoi diagram?

I have a dataset coming from weather stations where each vertex used to generate the Voronoi diagram is the lat/long of the station. As such, each cell represents the area whose weather is being ...
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189 views

Which rational subfields are corresponding to the two dimensional subspaces of holomorphic differentials

I implemented the algorithm that Felipe Voloch's suggested in his reply to the question: Subfields of a function field the algorithm is here: Subfields of a function field I considered the ...
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174 views

Finding equations for projective bundles associated to vector bundles over explicitly given varieties

Suppose I have a projective variety V over a field k. It is given explicitly in terms of homogeneous equations. Moreover, say I have an explicitly given vector bundle E (in terms of a module ...
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Trilateration issues, when circles don't intersect

I'm working on Indoor localization where I've deployed multiple iBeacons in my environment. I'm taking distances from all the beacons through their RSSI values. They are not 100% accurate though. Now ...
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Any software that can symmetrize input sets?

Is there any software that contains symmetrization techniques ex. polarization, Steiner Symmetrization etc. I suppose not. Which software would you suggest for rigid transformations? Thank you
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plotting parametrized algebraic curves near singularities

I have a parametrized algebraic curve: x(t)=A(t)/D(t); y(t)=B(t)/D(t); with A(t) and B(t) being polynomials in t. The curve is solution of a linear system in two unknowns x and y with Cramer's ...
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Covering the annulus of symmetric convex body

Consider a symmetric convex body $A$ in $R^d$. Now, we draw another object, $A'$, concentric and translated with respect to A and having radius slightly greater than twice to the radius of $A$. Now ...
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Determining the simplices in freudenthal triangulation

HI, I have a doubt on Freudenthal Triangulation. I want to partition a simplex into finer simplices. The FT gives me the vertices of the simplices which partition my original simplex into ...
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Orientation predicate CG

Shewchuk 97 gives me the orientation of 4 points, by finding the sign of a determinant, where the matrix is composed of the coordinates of the points. So, the signed volume of a tetrahedron, or which ...