# Questions tagged [topology]

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### Minimum Number of Unique Identifiers for a Grid of Cells

I have a grid of cells, X cells wide by Y cells high. Each cell has four corners, NW, NE, SW and SE. Each corner is shared with adjacent neighbors; i.e., a cell's SW corner is the NW corner of the ...
137 views

### Does this esoteric representation of integers have decidable equality?

Consider the following datatypes in Haskell: data Foo = Halt | Iter Foo newtype BigInt = BigInt {nthBit :: Foo -> Bool} Foo ...
1 vote
186 views

### How to turn a 3D polytope into a mesh?

Let us say you have a polyotpe define as the intersection of halfplanes. That is you are given N half-spaces. The polytope is the volume defined by all points which lie on the positive side of all N ...
22 views

### Convert NURBS surface into Cubic Bezier Surface

The following post discussed how to convert(approximate) NURBS curve into cubic Bézier curve: Convert NURBS curve into Cubic Bezier Curve I am trying to come up with an algorithm that converts(...
41 views

### Can a computer demonstrate that a topological space is compact?

Since all admissible spaces are second-countable and $T_0$, along with Urysohn's metrization theorem, this gives the hierarchy of topological properties of admissible spaces as Hausdorff ⇐ metrizable ⇐...
84 views

### How to handle coplanarity in convex hull?

I implemented the $O(n^2)$ convex hull algorithm. That is: Find a triangle known to be in the hull (by finding the lowest point, a point connected to it in the 2D convex hull, and the point that ...
75 views

### Recovering graph given degrees and connectivity information

I have a graph and don't know how nodes in it are connected to each other. I know the number of nodes in the graph. I know the degree of each node in the graph. I know that given any node $A$ that ...
1 vote
72 views

### If a computer can demonstrate singleton sets are closed, is the space Hausdorff?

In Haskell, I made a class of admissible (that is, second-countable and $T_0$) spaces: ...
38 views

### How to get the minimal enclosed polyhedra in a Line framework (points connectivity lists)?

Greetings all and thank you. I'm a Ph.D. candidate working on a force structure's 3D tessellation project and get stuck. I've simplified the system into a set of lines linked together which formed a ...
1 vote
32 views

### How to compute all inequivalent (under Aut(P)) nonnegative integer weight assignments (with fixed sum) to the vertices of a finite poset P?

Let $P$ be a poset on $n$ points, $\text{Aut}(P)$ its automorphism group, and $a_1,a_2,\dots,a_k$ the lengths of the orbits under $\text{Aut}(P)$. Goal: An algorithm to generate a member from each ...
1 vote
397 views

### What's an example of a planar graph with two embeddings whose geometric duals are nonisomorphic?

How to prove that the dual of the dual of a connected planar graph $G$ is isomorphic to $G$? In the post linked above, the user "plop" gives a great response where they claim, in particular, ...
95 views

### Is it valid to make an admission of a topological space by a "partial quotient map"?

It is well-known that the Sierpiński space, $\{F,T\}$ endowed with topology $\{\emptyset, \{F\},\{F,T\}\}$, is admissible. I tried to implement it in Haskell. First I implement $\mathbb{N}$ (including ...
23 views

### Classification of the Summit supercomputer

Can we classify a supercomputer in more than one group? For example, Flynn's classification, classification according to topology, classification according to memory access. For the Summit ...
56 views

### What does point-free mean mathematically?

Point-free style is generally taken to mean a style of programming without explicit variables. I have some intuitions on point-free style but I want to know what the formal mathematical definition is. ...
100 views

### Closest point in embedded simplicial complex

Suppose I have a simplicial $k$-complex $\mathcal S$ whose vertices are embedded in Euclidean space $\mathbb R^n$, for roughly $k< n\leq 6$. Examples include triangle mesh surfaces ($k=2$) embedded ...
23 views

1 vote
180 views

### Determining on whether topology is a tree or a hypercube

Assume that the nodes know that the topology G is either a hypercube or a tree. Assuming a unique initiator, design an algorithm to discover the topology. In other words, you would like a node to ...
2k views

### Divide self-intersecting polygon into simple polygons

My question is similar to question here Divide self-intersecting polygon I have points of self-intersecting polygon, its edges and also I am able to find points where it intersects. I have to divide ...
I have a tetrahedron $t$ and a polyhedron $p$. $t$ is constrained such that it always shares all its vertices with $p$. I want to determine whether $t$ lies inside $p$. I would like to add one detail ...