Computing geodesic distances from structural data

In summary, the individual is seeking assistance with computing geodesic distances on manifolds with sparse structural data. They have some knowledge of differential geometry but are struggling with applying it in a real-world scenario where the type of manifold is unknown. They are looking for guidance on how to solve this problem.
  • #1
Munich
1
0
Greetings,

I am attempting to compute geodesic distances on manifolds where structural data have been sparsely sampled.

First, off I am not well versed in the mathematics of differential geometry but I do have some knowledge (from an introductory differential geometry class in my undergrad). So forgive me if this question may seem simple.

The structural data that I have includes point locations of the manifold/surface in R^3 along with normals which describe the orientation of the manifold/surface.

In all examples in my DF class notes the type of manifold/surface was always known prior ( e.g. sphere, torus) to solving the geodesic equation and computing the geodesic distance. For these cases, it was easy to compute the metric since these surfaces are easy to parameterize. Now that I am trying to apply what I learned from the class (which was 10 years ago) in a real world scenario I am having a lot of trouble trying to determine how I solve it.

Surely there is a way to compute geodesic distances in this real world scenario. Can someone please help me with this problem?

Any help is greatly appreciated
 
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  • #2
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 

1. What is the purpose of computing geodesic distances from structural data?

Computing geodesic distances from structural data is important in understanding the spatial relationships and distances between different components or elements in a structure. This information can be used in various fields such as engineering, architecture, and geography to optimize designs, plan routes, and study the physical properties of structures.

2. How are geodesic distances calculated from structural data?

Geodesic distances are calculated using mathematical algorithms that take into account the coordinates and connectivity of the structural elements. These algorithms use geometric principles such as the Pythagorean theorem and trigonometry to determine the shortest distance between two points on a curved surface.

3. What types of structural data can be used to compute geodesic distances?

Geodesic distances can be computed from any type of structural data that has spatial information, such as maps, blueprints, 3D models, or geographic coordinates. The data must also be in a digital format that can be processed by the algorithm.

4. Are there any limitations to computing geodesic distances from structural data?

While geodesic distances provide valuable insights, they are not always accurate due to the simplifications and assumptions made by the algorithm. Factors such as terrain, obstacles, and the curvature of the Earth can also affect the accuracy of the calculations. Additionally, the quality and resolution of the structural data can impact the precision of the results.

5. How can geodesic distances be visualized from structural data?

Geodesic distances can be visualized in various ways, such as 2D or 3D maps, graphs, or diagrams. Some software programs also offer interactive tools to visualize and manipulate the data. This allows for a better understanding of the spatial relationships and can aid in decision making for design or planning purposes.

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