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16
votes
3answers
531 views

How to speed up estimation of Mean and Gaussian curvatures on triangular meshes?

I am trying to estimate curvatures on a triangulated surface/manifold using the algorithm of : Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003). Discrete differential-geometry operators ...
0
votes
0answers
4 views

Isothermal coordinates [migrated]

Is there an application or interest in studying the isothermal surfaces where the metric is $ds^2=E∗(du^2+dv^2)$ and where $E>0$ is an harmonic function? I know that this metric is a special kind ...
10
votes
1answer
1k views

How does a Pringle lose its curvature?

Nom! As part of a bigger project, I've was writing some code to calculate the scalar curvature of surfaces of the form $z = f(x,y)$. This uses a general calculation of the scalar curvature to produce ...
1
vote
1answer
71 views

Extract coefficient list of a differential form

I know may be this could be a duplicate of Extract coefficients of differential form in package RGTC, but the question was not solved and in a sense different from mine. I am going to explain better: ...
6
votes
1answer
106 views
12
votes
1answer
162 views

RegionNearest and neighborhoods

In this previous question we see that RegionNearest isn't quite as 'capable' as Nearest for some things. Similarly, I need to ...
4
votes
1answer
318 views

Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

I wish to solve for the curvature and torsion functions $k_1 = \dfrac{1}{1+s^2}, k_2 = \dfrac{s}{1+s^2}$ using the Frenet Serret system and obtain the parametric equations for the curve. I need the ...
4
votes
1answer
359 views

Visualization of Gaussian Curvature

I need to visualize Gaussian Curvature of a parametric surface. There is a solution in this math.SE post. However, I'm not sure its working because when I draw a sphere it's all white, but it should ...
26
votes
3answers
8k views

Differential geometry add-ons for Mathematica

I need a differential geometry tool for Mathematica. Is there any add-on? Unfortunately, Mathematica does not include such functionality or I can not find it.