  We present a simple, novel method of efficiently rendering ray cast soft
shadows on curved terrain by using dynamic programming and maximum mipmaps to
rapidly find a global minimum shadow cost in constant runtime complexity.
Additionally, we apply a new method of reducing view ray computation times that
pre-displaces the terrain mesh to bootstrap ray starting positions. Combining
these two methods, our ray casting engine runs in real-time with more than 200%
speed up over uniform ray stepping with comparable image quality and without
hardware ray tracing acceleration. To add support for accurate planetary
ephemerides and interactive features, we integrated the engine into
celestia.Sci, a general space simulation software. We demonstrate the ability
of our engine to accurately handle a large range of distance scales by using it
to generate videos of lunar landing trajectories. The numerical error when
compared with real lunar mission imagery is small, demonstrating the accuracy
and efficiency of our approach.
