Planetary topography is the result of complex interactions between geological processes, of which faulting is a prominent component. Surface-rupturing earthquakes cut and move landforms which develop across active faults, producing characteristic surface displacements across the fault. Geometric models of faults and their associated surface displacements are commonly applied to reconstruct these offsets to enable interpretation of the observed topography. However, current 2D techniques are limited in their capability to convey both the three-dimensional kinematics of faulting and the incremental sequence of events required by a given reconstruction. Here we present a real-time system for interactive retro-deformation of faulted topography to enable reconstruction of fault displacement within a high-resolution (sub 1m/pixel) 3D terrain visualization. We employ geometry shaders on the GPU to intersect the surface mesh with fault-segments interactively specified by the user and transform the resulting surface blocks in realtime according to a kinematic model of fault motion. Our method facilitates a human-in-the-loop approach to reconstruction of fault displacements by providing instant visual feedback while exploring the parameter space. Thus, scientists can evaluate the validity of traditional point-to-point reconstructions by visually examining a smooth interpolation of the displacement in 3D. We show the efficacy of our approach by using it to reconstruct segments of the San Andreas fault, California as well as a graben structure in the Noctis Labyrinthus region on Mars.

Direct volume rendering and isosurfacing are ubiquitous rendering techniques in scientific visualization, commonly employed in imaging 3D data from simulation and scan sources. Conventionally, these methods have been treated as separate modalities, necessitating different sampling strategies and rendering algorithms. In reality, an isosurface is a special case of a transfer function, namely a Dirac impulse at a given isovalue. However, artifact-free rendering of discrete isosurfaces in a volume rendering framework is an elusive goal, requiring either infinite sampling or smoothing of the transfer function. While preintegration approaches solve the most obvious deficiencies in handling sharp transfer functions, artifacts can still result, limiting classification. In this paper, we introduce a method for rendering such features by explicitly solving for isovalues within the volume rendering integral. In addition, we present a sampling strategy inspired by ray differentials that automatically matches the frequency of the image plane, resulting in fewer artifacts near the eye and better overall performance. These techniques exhibit clear advantages over standard uniform ray casting with and without preintegration, and allow for high-quality interactive volume rendering with sharp C0 transfer functions.