Abstract: This paper describes shear-image order ray casting, a new method for volume rendering. This method renders sampled data in three dimensions with image quality equivalent to the best of ray-per-pixel volume rendering algorithms (full image order), while at the same time retaining computational complexity and spatial coherence near to that of the fastest known algorithm (shear-warp). In shear-image order, as in shear-warp, the volume data set is resampled along slices parallel to a face of the volume. Unlike shear-warp, but like the texture-based methods, rays are cast through the centers of pixels of the image plane and sample points are at the intersections of rays with each slice. As a result, no post-warp step is required. Unlike texture methods, which realize shear and warp by transformations in a commodity graphics system, the shear-image ray casting methods use a new factorization that preserves memory and interpolation efficiency. In addition, a method is provided for accurately and efficiently embedding conventional polygon graphics and other objects into volumes. Both opaque and translucent polygons are supported.We also describe a method, included in shear-image order but applicable to other algorithms, for rendering anisotropic and sheared volume data sets directly with correct lighting.The shear-image order method has been implemented in the VolumePro™ 1000, a single chip real-time volume rendering engine capable of processing volume data at a pipeline rate of 109 samples per second. Figure 1 on the color page shows a shear-image order gallery of volumes rendered with different translucency, lighting, and some embedded geometry.