Direct visualization of algebraically defined densities

An important data structure for visualization is the 3D scalar field and its graphical representation as a 3D transparent gaslike object. Besides discrete arbitrary scalar data e.g. from computer tomograms in medicine, there is a need to visualize continuous scalar data defined in algebraic functions e.g. electric potentials. Traditional volume visualization techniques work on latter fields in a very complicated way and with great overhead in computation and storage. Improvements are achieved by direct computation of transparency values with the mathematical theory of curve integrals.