Equally distributed points of known distance on a 3D solid body/3d surface

Hi,

I am trying to plot a pattern of points on a solid 3d body (a cone of known dimension), which can also be a 3d conic surface. I need the points on the surface/body to be in an equal triangular pattern or tesselation such that the distance between points in always an equal known, changeable value (such as 10mm for example). I require the x,y,z coordinates of these points on the cone. I also need to be able to change the distance between the points (i.e. the side length). Something like the image below, but the sides need to be equilateral and I need to be able to specify the triangle dimension. I thought using a mesh might be the easiest way.

I have found several meshing tools, however none of them let me change/specify the distance constraint. I have also tried for a 3d surface but have the same issue. Is there a way to do this in Matlab? Otherwise is there perhaps a better method of getting the same result? I have the stl file of the body, as well as the 3d surface.

Any assistance would be appreciated.

Thanks and kind regards,

Sabrina

[John D'Errico]

I would point out that the triangulation you show is not truly equidistant, but merely a good one, perhaps reasonably close. However, I don't think there is a tool in MATLAB that will produce such a triangulation for a fully general surface. It would be nice, as others have asked for something similar, surprisingly often.

[Sabrina Myburgh]

Hi John,

Thanks for the reply. It does not have to be exact, rather reasonably close. As long as I can specify the distance between points it is fine. Any suggestions?

Thanks,

Sabrina

Answer 1

[Sarthak]

Hi Sabrina,

I understand that you need the points on the surface/body to be in an equal triangular pattern.

You can use the “surf” function to plot the surface of the body, and then use the “trimesh” function to create a triangular mesh of the surface. You can then use the “trisurf” function to plot the triangular mesh.

There is no current way to set the spacing between adjacent triangles in a triangular mesh in MATLAB. You can still create a triangular mesh of a surface, but you will not be able to control the spacing between the triangles.

For more information about the above functions, you can refer to the documentation of trimesh and trisurf.