Instead of computing intersections along a ray, an algorithm is proposed that determines a point of intersection in object space. The method is based on the classical refinement of a hierarchy of axisaligned bounding boxes that is computed on the fly. Typical rendering artifacts are avoided by taking into consideration the precision of floating point arithmetic. In addition the method lends itself to a simple solution of the self-intersection problem. Considering the obtained precision the algorithm is efficient, simple to use, and to implement.