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Projected Tetrahedra Revisited: A Barycentric Formulation Applied to Digital Radiograph Reconstruction Using Higher-Order Attenuation Functions
July/August 2006 (vol. 12 no. 4)
pp. 461-473

Abstract—This paper presents a novel method for volume rendering of unstructured grids. Previously [CHECK END OF SENTENCE], we introduced an algorithm for perspective-correct interpolation of barycentric coordinates and computing polynomial attenuation integrals for a projected tetrahedron using graphics hardware. Here, we enhance the algorithm by providing a simple and efficient method to compute the projected shape (silhouette) and tessellation of a tetrahedron, in perspective and orthographic projection models. Our tessellation algorithm is published here for the first time. Compared with works of other groups on rendering unstructured grids, the main contributions of this work are: 1) A new algorithm for finding the silhouette of a projected tetrahedron. 2) A method for interpolating barycentric coordinates and thickness on the faces of the tetrahedron. 3) Visualizing higher-order attenuation functions using GPU without preintegration. 4) Capability of applying shape deformations to a rendered tetrahedral mesh without significant performance loss. Our visualization model is independent of depth-sorting of the cells. We present imaging and timing results of our implementation, and an application in time-critical "2D-3D” deformable registration of anatomical models. We discuss the impact of using higher-order functions on quality and performance.

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Index Terms:
Volume rendering, unstructured grids, projected tetrahedra, DRR, higher-order volumetric functions.
Citation:
Ofri Sadowsky, Jonathan D. Cohen, Russell H. Taylor, "Projected Tetrahedra Revisited: A Barycentric Formulation Applied to Digital Radiograph Reconstruction Using Higher-Order Attenuation Functions," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 4, pp. 461-473, July-Aug. 2006, doi:10.1109/TVCG.2006.77
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