Accuracy-based sampling and reconstruction with 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 tetrahedra 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 and reconstruction technique, we call an adaptive grid, for hierarchical tetrahedrization of C¹ continuous volume data. We have developed a parallel algorithm of adaptive grid generation that recursively bisects tetrahedra 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 demonstrate the validity and effusiveness of the proposed approach.