Conclusions

We have presented a sampling scheme for volume data which saves 29.3% samples as compared to Cartesian grids. We assume that the functions we are dealing with are isotropic and band-limited, i.e., their frequency spectra are spheres. Therefore, a sampling pattern can be used in a way such that the replicas in frequency domain (introduced by the sampling process) are packed closely. There is no unique sampling pattern which achieves this. However, a body centered cubic grid results in a close packing in frequency domain and is easy to use. With this sampling pattern we reduce data size and improve rendering rates without loss of quality.

To demonstrate the applicability in volume rendering, we have adopted the splatting algorithm to bcc grids. This requires just a few changes of an existing code and is straightforward to implement. In order to perform classification and shading of the data we developed two gradient reconstruction schemes. Empirical experiments with analytical 3D functions show that these are comparable with central differences commonly used on Cartesian grids. We believe that significant gains can be achieved by using bcc grids in volume visualization and volume graphics in general.