How to find the one to one mapping of vertices from an arbitrary 3d model to a predefined sphere?

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How to find the one to one mapping of vertices from an arbitrary 3d model to a predefined sphere?

xiaojin
In my program, I want to map an arbitrary 3d model to a predefined sphere.

I have known that I can map an 3d model to a sphere using  spherical
parameterization
<https://www.numerical-tours.com/matlab/meshdeform_2_parameterization_sphere/>
. But it's not what I really want, because the result sphere of spherical
parameterization has two problems:

1.The number of vertices of the resulting sphere depends on the original
model, which means that different models(which have different number of
vertices) result in different spheres.
2.The distribution of vertices of the resulting sphere is not uniform.
So, in order to solve this two problems, I found that I can predefine a
uniform sphere(with n vertices), and then map an arbitrary 3d model(with m
vertices, m < n) to it.

In other words, I want to do the following things:

1.Predefine an uniform sphere with n vertices(like  this
<https://i.stack.imgur.com/kOHM7.png>  )
2.Given an arbitrary 3d model with m vertices(n > m)
3.Find the one to one mapping of vertices from the 3d model to the
sphere(There may be some vertices in the sphere without mapping from the 3d
model since n > m, but it's ok for my program)

And There is  a sample
<https://luozhongjin.gitee.io/dataset/data/meshes_smp/Cat/18.ply>   of 3d
models.

So, does anyone has some strategies to do the one to one mapping of vertices
from the 3d model to the predefined sphere?



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