Towards a mathematics of terrain

My big unsolved problem: Invent mathematics to easily represent legal terrain (elevation). Terrain properties: many maxima • few minima • often monotonically decreasing • occasional discontinuities. Applications: To put terrain operations like visibility, hydrography, compression on a proper formal foundation • To process large databases. Tools: very large memory • parallel HW (openMP, CUDA). Accomplishments to date: external memory algorithm to compute hydrography on 50000 × 50000 terrain and viewsheds on 100000 × 100000 terrain much faster than others • parallel algorithm to compute viewsheds on 8000 × 8000 terrain achieves 5× speedup with OpenMP, or 20× speedup with CUDA. International collaboration: M Andrade, UF Viçosa Brasil.