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Abstruc t-Visibility sorting is one of the key techniques in volume rendering of unstructured grids. The efficiency of sorting algorithm greatly affects the efficiency of volume rendering. Hardware-Assisted Visibility Sorting (1) (HAVS) is one of the most important volume rendering algorithms. This paper proposes an optimization algorithm of HAVS by keeping a sorted list which could decrease the comparing time in the fragment-level sorting process of k-buffer. The range of k is also analyzed by experiments. The results of experiment show that the proposed optimization algorithm obviously improves the efficiency of HAVS. Volum e rendering is an important research field in science computing visualization and it can display the whole and details of 3D datasets. At present, volume rendering is considered to be the most important technique in 3D scalar sets visualization (2). According to the difference of sorting, the visibility sorting techniques of unstructured grid volume rendering are divided into visibility sorting algorithms based on image space(A-Buffer(3) and R-buffer(4)), visibility sorting algorithms based on object space(NNS(5) and GATOR(6)) and visibility sorting algorithms based on both object space and image space( ZSWEEP(7) and HAVS(1)). Visibility sorting of fragment-level is one of the key technique for implementing volume rendering based on GPU, and the efficiency of sorting algorithm will greatly affect the efficiency of volume rendering. Visibility sorting algorithms based on image space must store all the fragments. The storing cost is too much and the rendering efficiency is low. Visibility sorting algorithms based on object space sorts triangle faces before rasterization. The speed of GPU is limited by the complexion of sorting in object space and the classification of triangles. Visibility sorting algorithms based on both image space and object space takes advantage of the processing ability of GPU in fragments-level, which shifts much of work from CPU to GPU and improve the rendering efficiency. Although ZSWEEP and HAVS are both visibility sorting algorithm based on both image space and object space, the sorting efficiency of ZSWEEP in object space is not high, which leads to too much burden for GPU, making the efficiency of ZSWEEP lower than HAVS. At present, HAVS is one of the most important unstructured grid volume rendering algorithm frameworks based on GPU(7). However, fragments in k-buffer are out of order in the fragment process, and each time the algorithm needs 2k-1 comparisons to get 2 nearest fragments in depth, which lowers the rendering efficiency. This paper proposes a visibility sorting algorithm to optimize the HAVS algorithm by keeping the k-buffer sorted. Each time the proposed algorithm just needs k comparison times to get 2 nearest fragments in depth, which obviously decreases comparison times. In addition, k will affect the precision and efficiency of the rendering result (the bigger k is, the more precise of the result and the lower of the efficiency are). The existing HAVS algorithm restricks k to 6, which limits the performance of algorithm. This paper researches on the range of k and obtains a k value that makes the result more precise and the efficiency higher. The experimental results show that the proposed algorithm obviously improves the efficiency of HAVS algorithm and obtains better performance for large dataset.

Optimization and Implementation of Unstructured Grid Volume Rendering Algorithm