A method is disclosed for reducing distortions introduced by deformation of a surface with an existing parameterization. In one embodiment, the distortions are reduced over a user-specified convex region in texture space ensuring optimization is locally contained in areas of interest. A distortion minimization algorithm is presented that is guided by a user-supplied rigidity map of the specified region. In one embodiment, non-linear optimization is used to calculate the axis-aligned deformation of a non-uniform grid specified over the region's parameter space, so that when the space is remapped from the original to the deformed grid, the distortion of the rigid features is minimized. Since grids require minimal storage and the remapping from one grid to another entails minimal cost, grids can be precalculated for animation sequences and used for real-time texture space remapping that minimizes distortions on specified rigid features.