An efficient algorithm for hidden surface removal

Abstract

We give an efficient, randomized hidden surface removal algorithm, with the best time complexity so far. A distinguishing feature of this algorithm is that the expected time spent by this algorithm on junctions which are at the "obstruction level" l, with respect to the viewer, is inversely proportional to l. This provably holds for any input, regardless of the way in which faces are located in the scene, because the expectation is with respect to randomization in the algorithm, and does not depend on the input. In practice, this means that the time complexity is roughly proportional to the size of the actually visible output times logarithm of the average depth complexity of the scene (this logarithm is very small generally).