We define texture mapping as an optimization problem for which the goal of preserving the maximum amount of information in the mapped texture. We derive a solution that is optimal in the least-squares sense and that corresponds to the pseudo-inverse of a reverse transformation mapping. In practice, a first order approximation of the least-squares solution is used as an initial estimate for the mapped texture. This initial solution is refined by successive approximation to yield the least-squares optimal result. In essence, the proposed multi-pass method acts like an adaptive anti-aliasing filter.