A system and method for reconstructing a positional contour of a variably contoured surface includes a plurality of positional sensors and a plurality of orientation sensor disposed upon the surface, a processor and a memory. The system captures a positional description of the surface and produces a rotationally-invariant point cloud, and captures a first absolute orientation description of the surface and produces a first set of relative orientations. The first rotationally-invariant point cloud is resampled with respect to the orientation description to produce a first synchronized rotationally-invariant point cloud. The first set of relative orientations and the first synchronized rotationally-invariant point cloud are transformed to produce respective sets of dimensional representations and manifold transformer parameters, which are mapped to produce a trained mapping function definition. The system captures a second absolute orientation description of the surface and uses the trained mapping function definition to produce a reconstructed synchronized rotationally-invariant point cloud.