All the Point on the Surface of a Sphere, Visual Representation.
All the Point on the Surface of a Sphere
Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space. ...
These are also referred to as the radius and center of the sphere, respectively.
There are two qualitatively different ways in which we could try to achieve equidistribution of points on a surface.
One is to randomly place them in such a way that the probability of ending up in some particular region is proportional to the area of that region (two-dimensional Poisson statistics). This gives equidistribution on average.
The second is to regularly place points such that their distance in two orthogonal directions is locally always the same. This gives typically a better result (no fluctuations and no accidental overlap), but the emerging partial crystallinity could sometimes be undesirable.
For the case of a sphere an example for both strategies is presented.
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