<title>High-speed integrated rendering algorithm for interpreting multiple-variable 3-D data</title>

Abstract

Many data visualization problems require both volumetric data representing sampled scalar or vector functions of 3D spatial dimensions and geometric data representing 3D geometric objects to be displayed together in a single image. In 3D data visualization with multiple variables, it is necessary to use various representations in order to extract the relations between several variables. This paper proposes an integrated rendering algorithm for visualizing 3D volumetric and geometric data such as surfaces, lines, and points, simultaneously with depth information, and another algorithm for speeding up the first. The approach proposed is to extend a volume rendering algorithm based on ray-tracing so that it can handle both 3D volumetric and geometric data. The algorithm processes these data in accordance with their original representation formats to eliminate conversion artifacts such as spurious or missing surfaces, and also gives special treatment to volume segments so as to avoid errors in visibility at the intersections between the volume segments and the geometric data. It uses several techniques to improve the performance of the rendering process. Adaptive termination of ray-tracing, elimination of rays that do not intersect the volume, and adaptive undersampling over a pixel plane improve the performance by three to seven times over the brute-force approach. The cost and versatility of the algorithm are evaluated by using data from the results of 3D computational fluid dynamics.