I'm working on a design project in nTopology which is an implicit representation design software. So geometry objects are represented as implicit fields defined by continuous functions.
Bodies are represented by scalar distance fields. Boundaries of objects are zero, interiors of objects are negative, and fields are positive outside of bodies. What I'm trying to is take a "slice" of a 3D field on a plane defined by a normal vector and an origin point.
Let say the field is a function of unknown form: $$ f(x, y, z) $$
And I have a plane defined by normal vector $n$ and origin $o$.
Is there a clean mathematical representation for the evaluation of this function on the arbitrary plane? nTopology has a robust mathematics back end, and I may be able to rig together an expression that will evaluate.