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

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.