Figure 1: We render high-quality implicit surfaces on regular grids, e.g., distance fields or medical CT scans, in real-time without pre-computing additional per-voxel information. Gradients with C 1 continuity, second-order derivatives, and surface curvature are computed exactly for each output pixel using tri-cubic filtering. Applications include surface interrogation and visualizing levelset computations by color mapping curvature measures (center), and ridge and valley lines (left and right). AbstractThis paper presents a real-time rendering pipeline for implicit surfaces defined by a regular volumetric grid of samples. We use a ray-casting approach on current graphics hardware to perform a direct rendering of the isosurface. A two-level hierarchical representation of the regular grid is employed to allow object-order and image-order empty space skipping and circumvent memory limitations of graphics hardware. Adaptive sampling and iterative refinement lead to high-quality ray/surface intersections. All shading operations are deferred to image space, making their computational effort independent of the size of the input data. A continuous third-order reconstruction filter allows on-the-fly evaluation of smooth normals and extrinsic curvatures at any point on the surface without interpolating data computed at grid points. With these local shape descriptors, it is possible to perform advanced shading using high-quality lighting and non-photorealistic effects in real-time.

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