# Tag Info

### What is the "continuity" as a term in computable analysis?

Arno's answer provides some very useful background reading material, I would just like to address your specific question about $\mathbb{R}$. Let us first recall a result by Peter Hertling, see Theorem ...
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Accepted

### What is the "continuity" as a term in computable analysis?

Different people have different views on what the definition of continuity should be, but the way I see it, we should define continuity to be computability relative to some oracle. For example: ...
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### Convert NURBS curve into Cubic Bezier Curve

I assume that your cubic spline is non-rational, meaning $w$ = 1, then this is in general true that exact conversion is not possible. NURBS are rational, so you can model conics, say circle whereas ...
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### Meaning of topological distance between 2 pixels

Nonlinear Signal and Image Processing: Theory, Methods, and Applications defines topological distance as follows. First, you have to define when two pixels are neighbors. The book offers two ...
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### Topology vs sigma-algebra's as a framework for approximate information?

What sort of structure we get depends on what we are trying to model. Your starting assumptions may well lead to $\sigma$-algebras, but in computer science we have a certain understanding of "...
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### Minimum Number of Unique Identifiers for a Grid of Cells

This is one of the 800 possible optimal (2-colour) solutions (including reflections and rotations) to the 4x4 problem, found using an exhaustive search: The optimality is because 16 cells require 16 ...
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### What's an example of a planar graph with two embeddings whose geometric duals are nonisomorphic?

There is an answer in Graph Theory by Bondy and Murty: It is clear that both graphs are isomorphic. Their respective duals are not, because each face of the first dual has degree 3 (except the ...
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### Minimum Number of Unique Identifiers for a Grid of Cells

Each Even column of corners (blue arrows) encodes a single unique ‘X’ indicator: x0,x2,x4… (here colored using Red, Green, Blue) Each Odd column of corners (yellow arrows) encode a semi-incrementing ‘...
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### How to handle coplanarity in convex hull?

If You find a co-planar triangle candidate, it has to be one that does not contain any other points in that plane. I am not familiar with rust so here is a pseudo-code attempt to enhance your code: <...
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### How to topologically classify points in 3d space generating a surface?

You are looking for persistent homology, a branch of computational topology that studies precisely the question you asked. Roughly, the idea is as follows. Pick a "resolution radius $r$", ...
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1 vote
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1 vote

### How to do a reverse topological sort using depth first search?

In order to get the files in the desired order, simply follow the following rule: A node can be deleted iff all of its children have been deleted. This is the same as a postorder traversal of a tree. ...
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