A Fast Radiosity Method for Thermal Modeling on Rough Planetary Surfaces

Abstract:

The presence of ice on the Moon, and other airless bodies, depends critically on temperature. Thermal and illumination modeling on large and complex planetary surfaces is dominated by costly scattering computations, whose cost is proportional to the square of the number of elements (e.g., triangles) discretizing the surface. Since occlusion and scattering by rough features significantly affects the accuracy of such models, it is important to incorporate the details provided by high-resolution shape models collected by recent missions, such as MRO, LRO, and MESSENGER. We present the latest version of a library implementing a fast algorithm for radiosity which is particularly suitable for rough planetary surfaces, and which can be used to compute all orders of scattering between surface elements, under the common assumption of Lambertian reflectance. Our algorithm is based on hierarchical matrix methods, in which shape elements are ordered using a spatial data structure, and where off-diagonal interaction matrices are compressed using a low-rank matrix approximation. This allows us to trade time and space requirements for accuracy. We use this algorithm to accelerate a thermal model of the Haworth crater near the lunar south pole. We use nonuniform meshes generated using distmesh, with elevations derived from LRO LOLA digital elevation maps (DEMs). Thermal modeling is carried out with meshes with as many as two million elements. We also demonstrate using a second mesh for direct illumination occlusion. For each of these methods, we conduct long running thermal simulations, with 1D subsurface heat models for each element. We report timings and compare our current results with previous approaches used for similar problems.