Volume rendering is a popular visualization technique for scientific computing and medical imaging. By assigning proper transparency, it allows us to see more information inside the volume. However, because volume rendering projects complex 3D structures into the 2D domain, the resultant visualization often suffers from ambiguity and its spatial relationship could be difficult to recognize correctly, especially when the scene or setting is highly transparent. Stereoscopic displays are not the rescue to the problem even though they add an additional dimension which seems helpful for resolving the ambiguity. This paper proposes a thaumatrope method to enhance 3D understanding with stereoscopic transparency for volume rendering. Our method first generates an additional cue with less spatial ambiguity by using a high opacity setting. To avoid cluttering the actual content, we only select its prominent feature for displaying. By alternating the actual content and the selected feature quickly, the viewer only perceives a whole volume while its spatial understanding has been enhanced. A user study was performed to compare the proposed method with the original stereoscopic volume rendering and the static combination of the actual content and the selected feature using a 3D display. Results show that the proposed thaumatrope approach provides better spatial understanding than compared approaches.

A new multiple resolution volume rendering method for finite element analysis (FEA) data is presented. Our method is composed of three stages: in the first stage, the Gauss points of the FEA cells are calculated. The function values, gradients, diffusions, and influence scopes of the Gauss points are computed. By representing the Gauss points as graph vertices and connecting adjacent Gauss points with edges, an adjacency graph is created. The adjacency graph is used to represent the FEA data in the subsequent computation. In the second stage, a hierarchical structure is established upon the adjacency graph. Any two neighboring vertices with similar function values are merged into a new vertex. The similarity is measured by using a user-defined threshold. Consequently, a new adjacency graph is constructed. Then the threshold is increased, and the graph reduction is triggered again to generate another adjacency graph. By repeating the processing, multiple adjacency graphs are computed, and a level of detail (LoD) representation of the FEA data is established. In the third stage, the LoD structure is rendered by using a splatting method. At first, a level of adjacency graph is selected by users. The graph vertices arc sorted based on their visibility orders and projected onto the image plane in back-to-front order. Billboards are used to render the vertices in the projection. The function values, gradients, and influence scopes of the vertices are utilized to decide the colors, opacities, orientations, and shapes of the billboards. The billboards are then modulated with texture maps to generate the footprints of the vertices. Finally, these footprints are composited to produce the volume rendering image.