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Tetrahedral Adaptive Grid for Parallel Hierarchical Tetrahedrization

Recent advances in volume scanning techniques have made the task of acquiring volume data of 3-D objects easier and more accurate. Since the quantity of such acquired data is generally very large, a volume model capable of compressing data while maintaining a specified accuracy is required. The objective of this work is to construct a multi-resolution tetrahedral representation of input volume data. This representation adapts to local field properties while preserving their discontinuities. In this paper, we present an accuracy-based adaptive sampling technique to construct a multi-resolution model, we call a tetrahedral adaptive grid, for hierarchical tetrahedrization of C1 continuous volume data. We have developed a parallel algorithm of tetrahedral adaptive grid generation that recursively bisects tetrahedral gird elements by increasing the number of grid nodes, according to local field properties and such as orientation and curvature of isosurfaces, until the entire volume has been approximated within a specified level of view-invariant accuracy. We have also developed a parallel algorithm that detects and preserves both C0 and C1 discontinuities of field values, without the formation of cracks which normally occur during independent subdivision. Experimental results obtained using a PC cluster system demonstrate the validity and effectiveness of the proposed approach.