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Questions tagged [topology]

39 questions
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Testing whether a tetrahedron lies inside a Polyhedron

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 to the problem in case it may contribute to the…
Pranav
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Analogue of the topology-computability correspondence for computational complexity

There is an interesting correspondence between notions of topology and notions of computability theory originating from the ingenious idea of Dana Scott to identify computable functions with continuous functions (in fact it can perhaps be traced…
helianthus
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Data Structures for Non-Orientable Manifolds

I am looking for a data structure to represent non-orientable manifolds (i.e. meshes like Moebius Strip, but without self-intersection). I will then implement other algorithms using this DS such as, but not limited to, Catmull-Clark Subdivision,…
user63364
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1 answer

Is there a continuous hash?

Questions: Can there be a (cryptographically secure) hash that preserves the information topology of $\{0,1\}^{*}$? Can we add an efficiently computable closeness predicate which given $h_k(x)$ and $h_k(y)$ (or $y$ itself) tells us if $y$ is very…
Kaveh
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Minimum Number of Edges Added to a DAG to get Unique Topological Order

The question is simple: Given an unweighted directed acyclic graph, $G = (V, E)$, what is the minimum number of directed edges we need to add to $E$ such that the resulting graph $G = (V, E')$ has a unique topological ordering? I initially…
ryan
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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 in $\mathbb R^3$ ($n=3$) and one-dimensional chains…
Justin Solomon
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Elementary proof of compact space = exhaustible space?

The work of Martín Escardó has demonstrated close parallels between classical topology o one hand and computability on the other hand. (See for example "Infinite sets that admit fast exhaustive search" 22nd Annual IEEE Symposium on Logic in…
Mark Dominus
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Topology vs sigma-algebra's as a framework for approximate information?

In the book "topology via logic" by Steven Vickers, topology is introduced for computer scientists, with the idea that topology captures the idea of approximate information. I am somewhat confused by the explanation. In particular, I'm confused by…
user56834
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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 cell just below it. In any grid of (X,Y) cells,…
Mike Metcalf
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Find internal surfaces in an oriented mesh

I have a solid with internal holes. My solid is mostly a union between walls/floors/ceilings. Each of them is a mesh with polygons oriented counter-clockwise. Then with those polygons I do a union that serves to delete the intersection between the…
Marouane
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Meaning of topological distance between 2 pixels

I came across the notion of topology and topological distance in the context of image processing several times (especially when it came to mathematical morphology). I looked for a not too abstract explanation of "topological distance" but haven't…
S.E.K.
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Scott/Lawson topology for function space domain

Given two domains, $D_1$, $D_2$, already equipped with Scott (or Lawson) topology, the product domain $D=D_1\times D_2$ has the Tychonoff product topology, e.g., Mathematical Theory of Domains, page 124. I can't seem to find a similar discussion…
John Forkosh
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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 it into simple polygons and tessellate them later.…
user3406792
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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 is Peano numbers compactified by one limit point, namely fix Iter. BigInt represents arbitrary-length integers in two's…
Dannyu NDos
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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 Line-Framework (points connectivity list). Now I…
Simon Shi
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