Sanghun Park
School of Computer &
Information Communications Engineering
Catholic University of Daegu
Gyungsan, 712-702, Korea
email: mshpark@cu.ac.kr
Adaptive mesh refinement (AMR) is a computational technique for improving the efficiency of numerical simulations of systems of partial differential equations. The basic idea of AMR is to refine, both in space and in time, regions of the computational domain where high resolution is needed to resolve developing features, while leaving the less interesting parts of the domain at lower resolutions. AMR techniques have been shown to be very successful in reducing the computational and storage requirements and used in various engineering applications where there are regions of greater interest such as global atmospheric modeling and numerical cosmology.
Although AMR data has a hierarchical multi-resolution structure, traditional direct volume rendering algorithms such as ray-casting and splatting cannot handle the form without converting it to a sophisticated data structure. Furthermore, interactive rendering of time-varying volume datasets is one of the major challenges in computer graphics.
In this paper, we present hierarchical data structures for interactive multi-resolution display of time- varying AMR data. Our scheme is based on binary space partitioning (BSP) tree and octree structure. In preprocessing step, partitioning AMR data into bricks recursively, our algorithm constructs hierarchical tree structures. Since each brick corresponding to leaf nodes has a set of function values in the same level of detail, it can be easily rendered by modified visualization techniques. The proposed data structures are suitable for implementing real-time AMR data visualization system on a general purpose PC. Actually, experimental results obtained on a PC equipped with NVIDIA ELSA GLORIA4 graphics card demonstrate interactive rendering speed (over 20 frames per second). Such a system allows users to analyze the change of AMR data in process of time with properly selected level of detail.