Extraction of Intersection curves from Iso-surfaces on co-located 3D grids

This paper presents new methods for efficient extraction of intersection curves between iso-surfaces of any pair of co-located 3D scalar fields. The first method is based on the Marching Cubes algorithm which has been enhanced to produce an additional data structure that makes it possible to reduce the complexity of the general surface intersection extraction from O(N) to O( √ N), where N denotes the number of triangles in the arbitrary surfaces. The second method directly extracts the intersection lines based on finding intersection points on the faces of the voxels for two iso-surfaces extracted from a regular grid. A simple classification scheme is used for early termination of testing of voxels that are not intersected by both surfaces. Also presented is an efficient method for fast curve generation through combination of line segments resulting from the explicit surface intersection method. An indexing structure is used to accelerate access and matching of intersection line segments to be combined into closed or open curves. The presented methods have been used to identify and visualize nodal lines in 3D quantum and wave chaos data. These data are represented by a volume of complex values and a nodal line is a connected curve where the complex iso-value ziso = 0 + i0. This type of chaos is believed to represent physical phenomena present in, for example, quantum mechanics, microwaves, fibre optics, and acoustics. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Boundary representations, Geometric algorithms; I.3.6 [Computer Graphics]: Methodology and Techniques—Graphics data structures