Abstract-This paper presents a study of gradient estimation methods for rendering unstructured-mesh volume data. Gradient estimation is necessary for rendering shaded isosurfaces and specular highlights, which provide important cues for shape and depth. Gradient estimation has been widely studied and deployed for regular-grid volume data to achieve local illumination effects, but has been, otherwise, for unstructured-mesh data. As a result, most of the unstructured-mesh volume visualizations made so far were unlit. In this paper, we present a comprehensive study of gradient estimation methods for unstructured meshes with respect to their cost and performance. Through a number of benchmarks, we discuss the effects of mesh quality and scalar function complexity in the accuracy of the reconstruction, and their impact in lighting-enabled volume rendering. Based on our study, we also propose two heuristic improvements to the gradient reconstruction process. The first heuristic improves the rendering quality with a hybrid algorithm that combines the results of the multiple reconstruction methods, based on the properties of a given mesh. The second heuristic improves the efficiency of its GPU implementation, by restricting the computation of the gradient on a fixed-size local neighborhood.

In this paper, we present a high quality and interactive method for volume rendering curvilinear-grid data sets. This method is based on a two-stage parallel transformation of the sample position into intermediate computational space then into texture space through the use of multiple 1 and 2D deformation textures using hardware acceleration. In this manner, it is possible to render many curvilinear-grid volume data sets at high quality and with a low memory footprint, while taking advantage of modern graphic hardware's tri-linear filtering for the data itself. We also extend our method to handle volume shading. Additionally, we present a comprehensive study and comparisons with previous works, we show improvements both in quality and performance using our technique on multiple curvilinear data sets.