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Newest 'topology' Questions - Mathematica Stack Exchange
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41 questions
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4
votes
3
answers
184
views
Canonical way to handle alternating tensors? Basis construction
Is there a canonical way to construct alternating tensors in mathematica? I have tried several different ways of constructing a basis for alternating tensors. However, all options seem rather clunky. ...
10
votes
2
answers
1k
views
Plotting the Warsaw circle
Out of pure curiosity, how can we plot the Warsaw Circle, defined as a subset of $\mathbb{R}^2$：
$$\left\{\left(x,\sin\frac{1}{x}\right): x\in\left(0,\frac{1}{2\pi}\right]\right\}\cup\left\{(0,y):-1\...
4
votes
3
answers
361
views
How to change the axis orientation of the cylinder in `ContourPlot3D`?
How to get the axis of the cylinder oriented along the red line shown in the figure below ?
Here is my code :
...
2
votes
1
answer
155
views
KnotTheory` Passing PD Encoding of a Knot Diagram to Kh
I have a bunch of knot diagrams I would like to use the Kh function in KnotTheory to compute the Khovanov homology for. Almost ...
1
vote
1
answer
268
views
Persistent homology and Mathematica
I have a cloud of roughly 200 points in the plane. I would like to use Mathematica to draw the barcode corresponding to the corresponding persistent homology.
There is a resource function ...
2
votes
0
answers
58
views
How to make an efficient SimplyConnectedQ (check for abscence of holes)?
I would like to find an efficient way to detect whether a region has a hole regardless of how many it has. This question (Separate boundaries of multiply connected region) shows some methods but it ...
3
votes
1
answer
351
views
Generating a non-convex polyhedron from polygons and normals
I am working on developing "directional offset" module, which requires pretty tricky mesh generation: offset values vary in different directions.
Suppose I have list of points and polygons, ...
7
votes
0
answers
585
views
Animating a Sphere Eversion (Turning a sphere inside out)
I'm interested in animating a sphere eversion like the one shown in the following gif.
The full video is here: https://www.youtube.com/watch?v=OI-To1eUtuU
Normally, I would offer my own code as a ...
8
votes
2
answers
295
views
MorphologicalEulerNumber misbehaving in 3D?
Context
I would like to compute the MorphologicalEulerNumber of 3D GaussianRandomField as a function of height above a given
threshold.
Attempt
I proceed as follows:...
7
votes
1
answer
200
views
Running Mathematica in 'SpouseMode'
In this previous question I looked into a deprecated capability of Mathematica from Version 2.
Mathematica command that allows it to read my intentions
Thanks to all for your answers. I note that ...
2
votes
1
answer
465
views
How can I reduce the error estimate of numerical integration in Mathematica?
Before introducing the integral I want to go through some definitions.
Define triangles $T_1$ and $T_2$ by the points $\{a,b,c\}$ and $\{d,e,f\}$ respectively.
Define $$D(u,v,x,y) = sign(\det (y-u,y-v,...
2
votes
1
answer
242
views
How can I create this graph in Mathematica?
I'm interested in illustrating a hyperbolic plane for a report I'm writing. Here's the metric that I'm using:
$$ds^2=dr^2+\sqrt{\lvert k\rvert}^{-1}\sinh\left(r\sqrt{\lvert k\rvert}\right)\left( d\...
0
votes
0
answers
83
views
How can Mathematica be used to compute distance from a metric?
I have a metric:
$$g_{\mu\nu}=\begin{bmatrix}-c & 0 & 0 & 0\\0 & a(t) & 0 & 0\\0 & 0 & a(t)\space r & 0\\0 & 0 & 0 & a(t)\space r\space \sinθ\end{...
- 1,630
3
votes
1
answer
142
views
Euler Characteristic of MengerMesh
When I ask Mathematica to give me the Euler characteristic of MengerMesh[1, 3], it returns 16. It seems to me the 1-step Menger sponge has genus 5 and should ...
1
vote
0
answers
118
views
Persistence diagram
Is there an easy way to get a persistence diagram of given planar points? For example the following points:
...
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Related Tags
plotting × 8
graphics × 5
geometry × 3
graphics3d × 3
animation × 3
visualization × 3
image-processing × 3
mesh × 2
packages × 2
programming × 2
knots × 2
xact × 1
tensors × 1
symbolic × 1
regions × 1
proof × 1
polyhedra × 1
neural-networks × 1
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