How to take some points uniformly on the surface of the 3D model

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三 2024-1-8

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评论：三 2024-3-17

I have an irregular three-dimensional surface, which includes points and surfaces. Now I want to evenly take some points on the surface of the model, and the interval between these points is 1 cm. I hope that the distance between them is the shortest distance along the surface of the model, rather than the space distance. The effect I want to achieve is shown in the image below, where yellow is the evenly distributed points.

What should I do specifically? Thank you!

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Matt J 2024-1-8

编辑：Matt J 2024-1-8

It needs more explanation. Suppose the surface was a sphere whose circuference at the equator is 4.5 cm. Obvously you would not be able to spread the points at 1 cm uniform intervals around the equator, or around any great circle of the sphere. What should happen?

三 2024-1-9

Thank you very much for reminding me, I would like to say that 1 cm is an arbitrary value, I mean how to distribute points evenly on the surface of such an irregular model, thank you!

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Answer 1

George Abrahams 2024-1-10

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编辑：George Abrahams 2024-1-10

Firstly, I'm assuming your model is in a triangular mesh format. If it's a point cloud, you can triangulate it with the alphaShape function. If it's a volume, you can use the isosurface function.

Then you have 2 options. Neither are trivial.

Lloyd's algorithm. This takes a set of points and iteratively moves them so that they're more evenly spaced. Gabriel Peyré made a MATLAB tutorial (code here) on applying this to a mesh by using their Fast Marching Toolbox. The algorithm was more clearly described in their paper. See the GIF below, from one of Gabriel's tweets.

Poisson disc sampling. This produces a tightly-packed set of random points with a minimum-distance between them. The naive approach is to repeatedly select random points on the surface and reject them if they're too close to any other points. Here are a few implementations applied to 3D meshes, although none in MATLAB: [1] [2] [3] [4] [5].