# Tag Info

### How to estimate geodesics on discrete surfaces?

Geodesics in Heat Algorithm At the suggestion of @user21 I am splitting up my answers to help make the code(s) for calculating geodesics distances easier to find for other people interested in these ...
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### How to speed up estimation of Mean and Gaussian curvatures on triangular meshes?

Note added 1/29/2020: the routines here have a bug where the mean curvature is sometimes computed with the opposite sign. I still need to work on how to fix this. I guess I should not have been ...
Accepted

### How to estimate geodesics on discrete surfaces?

Nothing really new from my side. But since I really like the heat method and because the authors of the Geodesics-in-Heat paper are good friends of mine (Max Wardetzky is even my doctor father), here ...

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

It took me a while, but the suggestion of @Michael E2 was quite helpful, and especially the post (Optimize inner loops). For those of you (like me) who are new to this style of programming in ...
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### The time-like geodesics (orbits) in the Schwarzschild spacetime

Studying basic solutions at the theoretical physics it is advantageous when one can get an exact solution. At the first sight one can see that the solution can be given in terms of elliptic functions ...
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### How to estimate geodesics on discrete surfaces?

Here is an exact algorithm but heavier to implement and to optimise. I chose to implement the "Line of Sight Algorithm" from Balasubramanian, Polimeni and Schwartz (REF). Exact Line of Sight ...
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### Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

Okay, this'll be a short answer just to show what you can do. What you are trying for here is essentially an inverse to FrenetSerretSystem, which will give the ...
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### Can Mathematica solve nonlinear, coupled differential equations?

There were syntactic and conceptual problems with your formulation. Conceptually, NDSolve is a numerical solver, so you need to specify boundary conditions as ...
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### How does a Pringle lose its curvature?

You need to delay the evaluation of the right-hand side of ScalarCurvature: ...
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### How to calculate scalar curvature, Ricci tensor and Christoffel symbols in Mathematica?

Since Version 9, functions to do this have been built into Mathematica but not documented. They live in the SymbolicTensors package which underlies ...
• 14.1k
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### RegionNearest and neighborhoods

If you don't mind using undocumented stuff, you can access lots of useful properties by converting the BoundaryMeshRegion to a ...
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### Estimating Principal Curvature Directions on Discrete Surfaces

For this answer, I shall be doing something slightly more ambitious. In particular, I will be computing the so-called curvature tensor, which encodes information on the normal vector $\mathbf n$, the ...

### How to estimate geodesics on discrete surfaces?

IGraph/M's IGMeshGraph function makes it easy to implement the graph-based solution. This function constructs a graph in which vertices correspond to mesh vertices ...
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### Expand wedge product

One idea is to use TensorReduce. I will assume that r is real, and that Dt[r] and ...
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### Curve shortening flow

This is roughly the algorithm in the link. Like it says there, it's potentially numerically unstable. The funny curlicue example in the OP was not provided, so I can't check that. In fact, most of the ...
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### Compute covariant derivative in Mathematica

There is undocumented functionality in the SymbolicTensors package, which underlies CoordinateChartData, CoordinateTransformData,...
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### How can I draw a sphere in the Minkowski space?

A sphere means all point that have the same distance from the some origin, for simplicity we consider the unit sphere at the origin. The only thing that is different from the usual R^3 is the metric ...
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### Coordinate-free derivative

Maybe you could use the following approach: ...
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### Estimating Principal Curvature Directions on Discrete Surfaces

OK, at least here is an attempt to solve my problem. Hopefully these thoughts and code may be useful to others. It seems like there is no single ideal algorithm to solve this problem. Some work ...
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### Trying to plot a wormhole; getting bad results

Providing your math is correct, I see two problems: You need to do the revolution with a single slice through your surface ...
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