Lunar craters visualization based on orthogonal spline basis

Impact crater is the major geomorphic feature on the lunar surface. More than 8.2 million valid data samples were obtained by the Chang'E-1 Laster Altimeter(LAM) and the craters are hidden among them. In order to visualize the topographical structure of these craters with high accuracy and computational stability, a novel scattered data fitting method was proposed in this paper. Based on the characteristics analyses of the data, an new class of orthogonal spline functions named as GF-system was used in our method. To verify the effectiveness of the proposed fitting algorithm, a typical surface models was chosen to be approximated by a series of random sampling data sets. Finally, we provide numerical results for two typical lunar crater data sets, demonstrating that our algorithm works efficiently and accurate for large data sets with highly non-uniform sampling densities.