Directional Search Algorithms for Visualizing and Mixing Star-Shaped Grids

Abstract

This paper describes different algorithmic approaches to solve some basic problems encountered in the building of various visualization tools intended for the grids generated by scientists. The visualization of the scalar and vector fields in such grids can lead to “traditional” geometric problems: point inclusion, point location, line intersection and line location. To be computational fast, any algorithm to solve these problems must appropriately exploit the geometric or even “topological” properties of the grids studied. We have noticed the frequency of a special type of grid that is called here “star-shaped”. We will show how the interesting nature of such a grid, concave but “not too concave”, can be used to build efficient algorithms for solving these problems. These algorithms are based on the adjacency properties of the grids used and on the simple remark that such problems can be reduced to 2D and ID problems by restricting the search to appropriate planes and lines. An extension to general grids is suggested, which takes full advantage of the special-purpose processors of modern graphics workstations. Some examples of applications are stressed, in particular for “slicing” grids with other grids and mixing grids together.