Efficient Lipschitz function evaluation for CSG implicit surfaces

The rendering of an implicit surface requires many function evaluations of the underlying implicit function. The time efficiency of the rendering is dominated by the number of function evaluations times the efficiency of these evaluations. If the implicit surface is created by means of a constructive solid geometry (CSG) model, the function evaluations can be made more efficient if the underlying function is a Lipschitz function. In this paper, implicit surfaces defined as a blended CSG model with Lipschitz functions are considered. It is shown how bounding volumes can be integrated in this framework and how they can be exploited to improve the evaluation efficiency.