We consider the computational problem of finding the point in 3D-space on a transformed surface corresponding to a coordinate pair given in a perspective mapping. The transformation is a rigid body transformation that is assumed to be small and vary. Initially, it is unknown but when it becomes known, the output must be accurate and quickly returned. Therefore, the computations are adapted for those conditions. Preprocessed shape information about the surface is computed in a perspective mapping where the surface is in an original position. We are discussing algorithms for solving the considered problem.