This document discusses, among other things, systems and methods for efficiently calculating a registration of multiple characteristic paths of a virtual three-dimensional object. Each path of discrete points is transformed into a piecewise linear parameterization as a function of path length. The paths are smoothed and normalized. The shorter path is partitioned into a number of discrete subintervals. The subintervals are mapped to the longer path using a minimization function that minimizes a cost function resulting in a locally optimal registration. The shorter path is incrementally positioned along the longer path and the minimization is attempted at each position. When the shorter path cannot be shifted any farther, the globally optimal registration is returned.