This is in contrast to the more difficult case of rendering a curvilinear grid (or the most difficult case, an unstructured grid), in which the points are not all regularly spaced, but rather clustered closely together in some regions, and sparsely spaced in others. Computational fluid dynamics (CFD) is a typical application which uses a curvilinear grid [Gar]. In such a case, standard algorithms, requiring a regular grid, do not work well: they are either inefficient or inaccurate. Although curvilinear grids may be perceived as deformed rectilinear grids, this fact offers little assistance. Unless the transformation is known, transforming the curvilinear grid back to the original rectilinear one is difficult, if not impossible. Generally, this mapping is not part of the information provided with the curvilinear data.
To solve this problem, then, an algorithm in some way must process the irregular grid data. One approach is to resample the irregularly structured grid in a preprocessing phase, and then proceed with the rectilinear data. Another method is the direct volume rendering of the irregular data. (Some direct rendering algorithms are generic, working with either regularly or irregularly spaced grids.) Two of the more prominent ones are splatting and ray-casting.
This paper presents a new technique for the resampling of any curvilinear data set. Section II presents the problem background and its description. In Section III, current methods for volume rendering curvilinear data grids are highlighted. Section IV presents the new technique, including the original on which it is based. Results are discussed in Section V, while Section VI contains the conclusions. Section VII includes possible future work. The Appendix contains several images showing the visualization results for temperature and pressure of the two resampling techniques.