This paper presents an efficient algorithm for volume rendering of three-dimensional scalar or vector fields, which do not require fitting geometric primitives to the data. The algorithm, called front-to-back image-order volume rendering, uses a pyramid of binary volumes to encode spatial coherence and adaptive termination of ray tracing to reduce rendering time. The first optimization employs an octree hierarchical spatial enumeration, represented by a pyramid of binary volumes, to encode coherent regions of empty voxels. The second optimization adaptively terminates ray tracing when the opacity reaches a user-selected threshold, reducing the number of samples composited. The paper discusses the implementation and performance of the algorithm, showing significant speedups for datasets with useful size and complexity. Examples from medical imaging and molecular graphics are provided to illustrate the effectiveness of the algorithm.This paper presents an efficient algorithm for volume rendering of three-dimensional scalar or vector fields, which do not require fitting geometric primitives to the data. The algorithm, called front-to-back image-order volume rendering, uses a pyramid of binary volumes to encode spatial coherence and adaptive termination of ray tracing to reduce rendering time. The first optimization employs an octree hierarchical spatial enumeration, represented by a pyramid of binary volumes, to encode coherent regions of empty voxels. The second optimization adaptively terminates ray tracing when the opacity reaches a user-selected threshold, reducing the number of samples composited. The paper discusses the implementation and performance of the algorithm, showing significant speedups for datasets with useful size and complexity. Examples from medical imaging and molecular graphics are provided to illustrate the effectiveness of the algorithm.