1. A method for encoding spatial data sets, comprising a hierarchically organized set of breakpoints that identify discontinuities that may exist on the arcs formed between points on a hierarchical grid, the steps of performing a breakpoint dependent transformation of the spatial data samples, the step of scalable encoding of the transformed spatial data samples, the step of partitioning the breakpoints into one subset known herein as vertex breakpoints and another subset of non-vertex breakpoints, the step of scalable encoding of the vertex breakpoints, such that their locations are successively refined by the appearance of progressively more bits from an embedded bit-stream, and the step of inferring the locations of the non-vertex breakpoints from vertex breakpoints in coarser levels of the hierarchy or the same level of the hierarchy.