Efficient quadratic reconstruction and visualization of tetrahedral volume datasets

Most volume rendering algorithms for tetrahedral datasets employ linear reconstruction kernels, resulting in quality loss if the data contain fine features of high orders. In this paper, we present an efficient approach to reconstruct and visualize 3D tetrahedral datasets with a quadratic reconstruction scheme. To leverage a quadratic kernel in each tetrahedron, additional nodes with weighting functions are first constructed in the tetrahedron. The integration of quadratic kernels along a ray in a tetrahedron is efficiently accomplished by means of a pre-computation scheme, making the accumulation of optical contributions very fast. Our approach is compatible with both object-space (projected tetrahedra) and image-space (ray casting) volume rendering methods. Experimental results demonstrate that our approach can efficiently achieve volume visualization with more subtle details, and preserve higher accuracy where needed compared with conventional approaches with linear kernels. Graphical Abstract