Identify part of the model that is below certain point

Hello,

I am working on a project and I want to identify part of the object that is under a plane. So I have this big plane and I on that plane there is an object that can go through it, but only certain amount depending on many factors. What is the best way to track the part of the object that is below this plane in real time in an efficient way. One way is to get the vertices, but I am thinking if there is simpler way ?

Can you be some specific when you say “what part”? Like do you need to know how much volume is under that plane?

Hi the part that is under the plane I need to find out the center of that part not the entire object. For now I just want to know how to get that part. Finding the center should be easy from then on.

I still don’t know what you mean by “part”.

Hi I made an image hope this explains it bit better. The black line in the middle is the place and the box is the cube. I am trying to get the part of the cube that is below the plane and find its middle. Hope that makes sense now

If you are satisfied to define the “middle” as the average of the vertex positions under the plane, I would go as follow.
First given the normal n of the plane and point s on the plane surface, the shortest distance d from any point p to the plane is:
d = dot(p - s, n)
d is positive if p is above the plane, otherwise negative.

Then you select all the vertices having d negative and computer their average.

Hi Thanks for help!