The floating column algorithm for shaded, parallel display of function surfaces without patches

The floating column algorithm is a new method for the shaded rendering of function surfaces. Derived from the monochromatic floating horizon algorithm, it uses the partial derivatives of the function to compute surface normals, thus enabling intensity or normal-interpolation shading. Current rendering methods require tiling the surface with patches, so higher-resolution patching is required for zoom-in views, interactive modification or time-varying surfaces. The new algorithm requires no patching and uses only constant space, so it can be implemented on graphics cards and hand-held devices. Each pixel column is displayed independently of the others, and this "independent column mode" makes the algorithm inherently parallel in the image space, so it is suitable for multiprocessor workstations and clusters and it is scalable in the resolution size. Furthermore, the sampling frequency of the surface can be controlled locally, matching local surface features, distance or artifact elimination requirements. Space-efficient super-sampling for anti-aliasing is also possible. The new algorithm, which allows orthogonal and perspective projections, produces pixel-wide strips which can be displayed in software or hardware. Various extensions are described, including shadows and texture mapping. These properties, together with the algorithm\´s parallelism, make it potentially useful for the real-time display of functionally-defined textured terrains and the animated display of time-varying surfaces