Systems and methods are provided for providing a fine-to-coarse look ahead in connection with parametrization in a graphics system. The use of a variety of parametrization metrics may be supplemented and improved by the fine-to-coarse look ahead techniques of the invention. First, the metric of a parametrization is minimized using a coarse-to-fine hierarchical solver, and then accelerated with a fine-to-coarse propagation. The resulting parametrizations have increased texture resolution in surface regions with greater signal detail at all levels of detail in the progressive mesh sequence.