In many of the situations where ray casting is used, it is very common to cast hundreds of millions of rays. This usually takes a much longer time than it took to build the ray tracing data structures. A large percentage increase in the time it takes to build the data structures may provide a significant win even if the percentage decrease in the ray casting time of each ray is much smaller. Ideally you increase the complexity and sophistication of the hierarchy building stage in order to reduce the complexity and number of intersections computed during the ray traversal stage. This principle motivates Section 4.3.