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**1 - 2**of**2**### Dynamic View-Dependent Partitioning of Grids with Complex Boundaries Track: Applied

, 1999

"... this paper, we will confine our attention to the most common deformation, the cavity. Since, by definition, those sections of the surface that belong to the convex hull are unable to "see" any other sections, we can safely ignore them for purposes of depth sorting. However, we may use the ..."

Abstract
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this paper, we will confine our attention to the most common deformation, the cavity. Since, by definition, those sections of the surface that belong to the convex hull are unable to "see" any other sections, we can safely ignore them for purposes of depth sorting. However, we may use the convex hull itself to assist in distinguishing the regions on the hull from the cavities. Consider the partial structured grid in Figure 3. Three boundaries are depicted, two of which are convex. The third is a BeziĆ©r curve such as one might expect as the result of a computer-aided design effort. Depending upon the application, a parallel solver may find it advantageous to use such a curve as a basis for data decomposition. Note that the curve is concave in some regions, preventing unambiguous depth sorting should another partition lie along that boundary Well-known algorithms exist to find 2D and 3D convex hulls for an arbitrary set of points (Cormen, Leiserson, and Rivest 1990) (Edelsbrunner and Shi 1991). In Figure 4, we see the convex hull of the sample grid from Figure 3. Note that the hull follows along the two convex edges on either side and stretches across the concave edge, forming a cavity. In 3D, the hull would be some sort of non-planar surface, composed of twisted quadrilaterals.