Convexification of Unstructured Grids

Unstructured tetrahedral grids are a common data representation of three-dimensional scalar fields. For convex unstructured meshes efficient rendering methods are known. For concave or cyclic meshes, however, a significant overhead is required to sort the grid cells in back to front order. In this paper we apply methods known from computational geometry to transform concave into convex grids. While this issue has been studied in theory it has not yet been applied to the specific area of unstructured volume rendering. This is mainly due to the complexity of the required geometrical operations. We demonstrate that the convexification of concave grids can be achieved by a combination of simple operations on triangle meshes. For convexified meshes the experimental results show that the performance penalty is only about 70% in comparison to approximately 300% for the fastest known concave sorting algorithm. In order to achieve high-quality visualizations we also adapt the preintegrated lighting technique to cell projection