Successful surface modeling requires, first of all, that an appropriate spatial framework be selected. The more diverse the surface modeling application, the more important this selection is. Of the four most obvious spatial frameworks—digital arrays, rectangular grids, parametric grids, and triangular meshes—triangular meshes seem to offer the most promise for many applications that involve both surface-fitting and the numerical solution of sets of equations. The use of triangular meshes is illustrated here in the context of a three-dimensional simulation of sediment build-up in a sedimentary basin. Triangle-based interpolation is first used to specify the initial conditions for the simulation, and then a triangle-based finite-difference technique gives the new sediment surface for successive steps in time.