Newton-Okounkov bodies and Segre classes

Given a homogeneous ideal in polynomial ring over $\Bbb{C}$, we adapt the construction of Newton-Okounkov bodies to obtain convex subset Euclidean space such that suitable integral this set computes {\it Segre zeta function\/} ideal. That is, extract numerical information class subscheme projective from an associated (unbounded) set. The result generalizes arbitrary subschemes form previously known for monomial schemes.