Using ray intersection for dual isosurfacing

Isosurface extraction using " dual contouring " approaches have been developed to generate a surface that is " dual " in terms of the underlying extraction procedure used when compared to the standard Marching Cubes (MC) method. These approaches address some shortcomings of the MC methods including feature-detection within a cell and better triangles. One approach for preserving " sharp features " within a cell is to determine isosurface points inside each cell by minimizing a quadric error functions (QEF). However, this category of methods is constrained in certain respects such as finding just one isosurface point per cell or requiring Hermite data to calculate an isosurface. We present a simple method based on the MC method and the ray intersection technique to compute isosurface points in the cell interior. One of the advantages of our method is that it does not require Hermite data, i.e., the discrete scalar values at vertices suffice. We compute ray intersections to determine isosurface points in the interior of each cell, and then perform a complete analysis of all possible configurations to generate a look-up table for all configurations. Since complex features (e.g., tunnels) tend to be undersampled with " dual " points sufficient to represent sharp features and disjoint surfaces within the cell, we use the look-up table to optimize the ray intersection method to obtain minimum number of points necessarily sufficient for defining topologically correct isosurfaces in all possible configurations. Isosurface points are connected using a simple strategy.