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An algorithm is described that speeds up ray-tracing techniques by reducing the number of time-consuming object-ray intersection calculations that have to be made. The algorithm is based on subdividing space into an octree, associating a given voxel with only those objects whose surfaces pass through the volume of the voxel. It includes a technique for obtaining fast access to any node and a mechanism for finding the next node intersected by a ray when it has hit nothing in the current node. This new algorithm makes possible the ray tracing of complex scenes by medium-scale and small-scale computers.