The paper presents a new volume rendering algorithm that leverages a shear-warp factorization of the viewing transformation to achieve fast and high-quality rendering. The authors describe three main extensions of this factorization: a new object-order rendering algorithm that is significantly faster than existing methods with minimal loss in image quality, a shear-warp factorization for perspective viewing transformations, and a data structure for encoding spatial coherence in unclassified volumes. The algorithm uses spatial data structures based on run-length encoding to efficiently traverse both the volume and the intermediate image, allowing for synchronized access to data structures that encode coherence in both. The implementation on an SGI Indigo workstation can render a 256³ voxel medical dataset in one second, demonstrating near-interactive speeds. The paper also discusses the performance and image quality of the algorithm, showing that it outperforms previous methods while maintaining or improving image quality. The authors conclude by discussing future extensions to support mixed volumes and geometry, as well as parallelization for MIMD shared-memory multiprocessors.The paper presents a new volume rendering algorithm that leverages a shear-warp factorization of the viewing transformation to achieve fast and high-quality rendering. The authors describe three main extensions of this factorization: a new object-order rendering algorithm that is significantly faster than existing methods with minimal loss in image quality, a shear-warp factorization for perspective viewing transformations, and a data structure for encoding spatial coherence in unclassified volumes. The algorithm uses spatial data structures based on run-length encoding to efficiently traverse both the volume and the intermediate image, allowing for synchronized access to data structures that encode coherence in both. The implementation on an SGI Indigo workstation can render a 256³ voxel medical dataset in one second, demonstrating near-interactive speeds. The paper also discusses the performance and image quality of the algorithm, showing that it outperforms previous methods while maintaining or improving image quality. The authors conclude by discussing future extensions to support mixed volumes and geometry, as well as parallelization for MIMD shared-memory multiprocessors.