Haptic rendering of data on unstructured tetrahedral grids

An algorithm is developed to interpolate data in unstructured tetrahedral meshes for improved real-time haptic rendering. Given a Cartesian location in the data set, the containing tetrahedral element in the unstructured mesh must be located. Then the data at the nodes of this tetrahedral element are interpolated to yield the proper data value(s) to render. Comparisons are made with a previously developed algorithm for structured hexahedral meshes in terms of storage requirements and off-line and on-line computational complexities, providing guidelines on when to decompose hexahedral meshes into tetrahedral meshes for haptic rendering.