Time-Varying Interval Volumes

Abstract

In this paper, we study the interval segmentation and direct rendering of time-varying volumetric data to provide a more effective and interactive volume rendering of time-varying structured and unstructured grids. Our segmentation is based upon intervals within the scalar field between time steps, producing a set of geometrically defined time-varying interval volumes. To construct the time-varying interval volumes, we cast the problem one dimension higher, using a five-dimensional iso-contour construction for interactive computation or segmentation. The key point of this paper is how to render the time-varying interval volumes directly. We directly render the 4D interval volumes by projecting the 4D simplices onto 3D, decomposing the projected 4-simplices to 3-simplices and then rendering them using a modified hardware-implemented projected tetrahedron method. In this way, we can see how interval volumes change with the time in one view. The algorithm is independent of the topology of the polyhedral cells comprising the grid, and thus offers an excellent enhancement to the volume rendering of time-varying unstructured grids. Another advantage of this algorithm is that various volumetric and surface boundaries can be embedded into the time-varying interval volumes.