Interactive direct rendering of trivariate B-spline scalar functions

This paper presents a direct rendering paradigm of trivariate B-spline functions that is able to incrementally update complex volumetric data sets in the order of millions of coefficients at interactive rates of several frames per second on modern workstations. This incremental rendering scheme can hence be employed in modeling sessions of volumetric trivariate functions, offering interactive volumetric sculpting capabilities. The rendering is conducted from a fixed viewpoint and in two phases. The first, preprocessing, stage accumulates the effect that the coefficients of the trivariate function have on the pixels in the image. This preprocessing stage is conducted offline and only once per trivariate and viewing direction. The second stage conducts the actual rendering of the trivariate functions. As an example, during a volumetric sculpting operation, the artist can sculpt the volume and get a displayed feedback, in interactive rates.