A data model for scientific visualization with provisions for regular and irregular grids

This paper presents a mathematical data model for scientific visualization based on the mathematics of fiber bundles. The findings of previous works are extended to the case of piecewise field representations (associated with grid-based data representations), and a general mathematical model for piecewise representations of fields on irregular grids is presented. A discussion of the various types of regularity that can be found in computational grids and techniques for compact field representation based on each form of regularity are presented. These techniques can be combined to obtain efficient methods for representing fields on grids with various regular or partially regular structures.