Fast Ray Tracing of Lunar Digital Elevation Models

Introduction: Ray-tracing (RT) of Lunar Digital Elevation Models (DEM)'s is performed to virtually derive the degree of radiation incident to terrain as a function of time, orbital and ephemeris constraints [1-4]. This process is an integral modeling process in lunar polar research and exploration due to the present paucity of terrain information at the poles and mission planning activities for the anticipated spring 2009 launch of the Lunar Reconnaissance Orbiter (LRO). As part of the Lunar Exploration Neutron Detector (LEND) and Lunar Crater Observation and Sensing Satellite (LCROSS) preparations RT methods are used to estimate the critical conditions presented by the combined effects of high latitude, terrain and the moons low obliquity [5-7]. These factors yield low incident solar illumination and subsequently extreme thermal, and radiation conditions. The presented research uses RT methods both for radiation transport modeling in space and regolith related research as well as to derive permanently shadowed regions (PSR)'s in high latitude topographic minima , e.g craters. These regions are of scientific and human exploration interest due to the near constant low temperatures in PSR's, inferred to be < 100° K. Hydrogen is thought to have accumulated in PSR's through the combined effects of periodic cometary bombardment and/or solar wind processes, and the extreme cold which minimizes hydrogen sublimation [8-9]. RT methods are also of use in surface position optimization for future illumination dependent on-surface resources e.g. power and communications equipment [10-11]. However, ray-tracing methods are computationally slow due to the inherent vector transport process and the subsequent search phase required to evaluate, identify , and interact with surfaces [12]. The issue is exacerbated if the DEM point surface is converted to a plate model due to the large number of floating point operations (48) required to evaluate each plate facet [13-14]. As a result, the computational complexity incurred in evaluating direct illumination without optimization constraints increases exponentially as a function of the product of the number of surfaces n in the model evaluated against all other surfaces during search s ~ |n|-1, floating point operations per surface evaluation f, number of vectors projected per pixel |v|, O(nsfv). In this case, the exponential time-complexity