We present 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.

Isosurfaces of distance fields (left: 512x256x256; right: 512x512x256) with color mappings of maximum principal curvature magnitude using 1D color look-up tables.

Accessibility shading based on maximum curvature. Left: Standard lighting. Right: Lighting modulated with accessibility values.

Isosurfaces of a 512x512x333 CT scan with ridge and valley lines computed from implicit surface curvature, and contours.

Left: Ridge and valley lines (black and white) specified with a two-dimensional curvature transfer function, and contour s (gray). Right: Dense flow advected in the direction of maximum principal curvature.

Michelangelo's David extracted and shaded with tri-cubic filtering as isosurface of a 576x352x1536 16-bit distance field at 10 fps. The distance field is subdivided into two levels: a fine level for empty space skipping during raycasting (blue) and a coarse level for texture caching (green).