"Meshing statistics" in SPH

In conventional CFD using FVM and thereby meshes a lot of parameters like skewness, mesh density etc. are used to describe the status of the mesh, whether it is unacceptable, suitable or top notch. What parameters exists in the SPH methodology to do this?

Just on the top of my head, I would define it as that no point in the space of the simulation should be allowed to be described by less than half of the poins in the initial smoothing space, ie. for an example see the rough example:

So that if a point loses half of the initial particles used to describe it, the result would be "un-trustworthy".

Has anyone had some similar thoughts or seen some other ways to approach this problem?

Kind regards
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