This paper presents a forward mapping rendering algo-rithm to display regular volumetric grids that may not have the same spacings in the three grid directions. It takes advantage of the fact that convolution can be thought of as distributing energy from input samples into space. The renderer calculates an image plane footprint for each data sample and uses the footprint to spread the sample's energy onto the image plane. A result of the technique is that the forward mapping algorithm can support perspective without excessive cost, and support adaptive resampling of the three-dimensional data set during image generation.

Volumetric data sets require enormous storage capacity even at moderate resolution levels. The excessive storage demands not only stress the capacity of the underlying storage and communications systems, but also seriously limit the speed of volume rendering due to data movement and manipulation. A novel volumetric data visualization scheme is proposed and implemented in this work that renders 2D images directly from compressed 3D data sets. The novelty of this algorithm is that rendering is performed on the compressed representation of the volumetric data without pre-decompression. As a result, the overheads associated with both data movement and rendering processing are significantly reduced. The proposed algorithm generalizes previously proposed whole-volume frequency-domain rendering schemes by first dividing the 3D data set into subcubes, transforming each subcube to a frequency-domain representation, and applying the Fourier Projection Theorem to produce the projected 2D images a...