L discretizes the integrated discrete Laplacian in the sense that:
x' * L * x discretizes Dirichlet energy: ∫ ‖∇x‖² dx. Via Green's idenity this energy is related to the Laplacian as:
∫ ‖∇x‖² dx = -∫ x∆x dx + boundary terms
So, there are at least 3 reasons you won't get all twos:
1) If n,t is a curved surface (as in, all vertices are not on the same plane) then L also encodes the non-Euclidean metric,
2) if n,t has a boundary, then for vertices along the boundary you'll get the integrate Laplacian + boundary terms
3) L computes integrated values, to convert to intergral average, pointwise values you can "unintegrate" (i.e., divide by local area) by multiplying with the inverse of the mass matrix: M \ L * x
