W. Barth, R. Lieger, M. Schindler, "Ray Tracing General Parametric Surfaces Using Interval Arithmetic", The Visual Computer, International Journal of Computer Graphics, 1994, Vol. 10, No. 7, pp. 363-371.

This paper describes an algorithm for ray tracing general parametric surfaces. After dividing the surface adaptively into small parts a binary tree of these parts is built. For each part a bounding volume is calculated with interval arithmetic. From linear approximations and intervals for the partial derivatives it is possible to construct parallelepipeds that adapt the orientation and shape of the surface parts very well and form very tight enclosures. Therefore an algorithm for rendering can be developed which is similar to that used with Bezier- and B-Spline-surfaces, where the bounding volumes are derived from the convex hull property. The tree of enclosures (generated once in a preprocessing step) guarantees that each ray that may hit the surface leads to an iteration on a very small surface part; this iteration can be robustly (and very fast) performed in real arithmetic.

W. Barth