Area and volume coherence for efficient visualization of 3D scalar functions

Authors:
Nelson Max;Pat Hanrahan;Roger Crawfis
Affiliations:
Lawrence Livermore National Laboratory, Livermore, CA and University of California, Davis, CA;Princeton University, Princeton, NJ;Lawrence Livermore National Laboratory, Livermore, CA
Venue:
VVS '90 Proceedings of the 1990 workshop on Volume visualization
Year:
1990

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Abstract

We present an algorithm for compositing a combination of density clouds and contour surfaces used to represent a scalar function on a 3-D volume subdivided into convex polyhedra. The scalar function is interpolated between values defined at the vertices, and the polyhedra are sorted in depth before compositing. For n tetrahedra comprising a Delaunay triangulation, this sorting can always be done in O(n) time. Since a Delaunay triangulation can be efficiently computed for scattered data points, this provides a method for visualizing such data sets. The integrals for opacity and visible intensity along a ray through a convex polyhedron are computed analytically, and this computation is coherent across the polyhedron's projected area.