Reliable Ray Tracing by Linear Interval Estimations

Recently Bühler has introduced a new type of bounding volume for parametric surfaces. These bounding volumes, which Bühler calls Linear Interval Estimations (LIEs), are parametrized with the same parametrization as the surfaces they bound. We report on the application of LIEs to the ray tracing of Bezier surfaces. The general nonlinear ray–surface intersection problem is replaced with a linear ray–LIE intersection method. A new ray–tracing algorithm is developed which is relatively simple and compares favorably to the method of Toth, being roughly comparable in speed and yet more reliable.