We propose to apply to planetary terrain mapping an alternative, multiresolution method, subdivision surfaces (subdivs), in place of conventional digital elevation maps (DEMs) and fixed-resolution meshes. The proposed research is innovative in that it presents a new setting for subdivs that demands novel extensions to subdivision algorithms, techniques and theory. The primary objectives of this work are to: (1) demonstrate suitability of subdivs as a representation for terrain data with highly varied spatial resolution and 3-D features; (2) demonstrate their ability to encode, and later re-register, local detail non-destructively through hierarchical edits; and (3) prototype a software user interface introducing new capabilities enabled by the subdiv representation. The expected benefits are: (a) higher-fidelity terrain visualization with reduced infrastructure requirements; (b) ability to visualize 3-D features, such as overhangs, missed in DEM's; (c) compact encoding with natural level-of-detail control for interactive viewing even on mobile devices; (d) greater algorithmic efficiency for non-visualization scientific computation; and (e) enablement of new software-tool capabilities for dynamic mapping of alternative local-terrain datasets, non-destructive experimentation, collaboration, and data traceability. The innovation also promises capability and reliability benefits to a surface robot by unifying terrain representations and enabling minimal upload of only incremental terrain details from the ground.