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.
31
votes
0answers
311 views
Reasons to prefer one large prime over another to approximate characteristic zero
Background:
In running algebraic geometry computations using software such as Macaulay2, it is often easier and faster to work over $\mathbb F_p = \mathbb Z / p\mathbb Z$ for a large prime $p$, rather ...
7
votes
0answers
130 views
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 ...
4
votes
0answers
102 views
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 ...
4
votes
0answers
368 views
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 ...
3
votes
0answers
49 views
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 ...
2
votes
0answers
61 views
Regularity of Delaunay triangulation of a hypercube
First using a three dimensional unit cube as an example for the term "regularity", we can have two possible triangulations:
(A)
(B)
We say the lower triangulation is more "regular" than upper ...
2
votes
0answers
181 views
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 ...
1
vote
0answers
56 views
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 ...
1
vote
0answers
55 views
optimization function: sum of root squares of sum of two quadratic
Full question (same question in jpg, pdf and doc\docx):
https://drive.google.com/folderview?id=0BxFEf1J4iYVeX2l2NlVjUldEUlE&usp=sharing
Hello
I am a graduate student in computer science, making ...
1
vote
0answers
137 views
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", ...
1
vote
0answers
103 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 ...
1
vote
0answers
178 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 ...
1
vote
0answers
167 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 ...
0
votes
0answers
29 views
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 ...
0
votes
0answers
153 views
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 ...
