About SDF of space position p

[lxl1115]

Thank you very much for your excellent work!
I'd like to ask if we use the regularization term of the Signed Distance Function (SDF) to constrain the optimization process of Gaussians, and I can store the SDF value of any point p in space in theory.
Can this SDF value be used as the true distance from point p to the surface in space and should we use a eikonal loss to optimize it?
Furthermore, can the SDF value of point p be used to determine if there is an object penetration? For example, if point p has two negative SDF values, it may indicate that point p exists inside two objects simultaneously, meaning that these two objects penetrate.
I am not sure if I have expressed my meaning clearly. If I could receive a response, it would be very helpful to me. Thanks again!