Complete \({\boldsymbol{SE(3)}}\) Invariants for a Comeagre Set of \({\boldsymbol{C^3}}\) Compact Orientable Surfaces in \(\mathbb{R}^{\boldsymbol{3}}\).

We introduce invariants for compact -orientable surfaces (with boundary) in up to rigid transformations. Our invariants are certain degree four polynomials in the moments of the delta function of the surface. We give an effective algorithm for retrieving successive approximations of surface from successive prefixes of the invariants, which works on a comeagre subset of -surfaces. The reconstruction algorithm is continuous in numerical geometric properties of the surface in question.