This paper presents a novel scheme for accelerating ray traversal computation in ray tracing. By the scheme, a pre-computed stage is applied to constructing what is called a traversal field for each rigid object that records the destinations for all possible incoming rays. The field data, which could be efficiently compressed offline, is stored in a small number of big rectangles called ray-relays that enclose each approximate convex segment of an object. In the ray-tracing stage, the records on relays are retrieved in a constant time, so that a ray traversal is implemented as a simple texture lookup on GPU. Thus, the performance of our approach is only related to the number of relays rather than scene size, while the number of relays is quite small. In addition, because the traversal fields only depend on the internal construction of each convex segment, they can be used to ray trace objects undergoing rigid motions at a negligible extra cost. Experimental results show that interactive rates could be achieved for dynamic scenes with the effects of specular reflections and refractions on an ordinary desk PC with GPU.