Morse Decomposition of 3D Piecewise Linear Vector Fields

Morse decomposition has been shown a reliable way to compute and represent vector field topology. Its computation first converts the original vector field into a directed graph representation, so that flow recurrent dynamics (i.e., Morse sets) can be identified as some strongly connected components of the graph. In this paper, we present a framework that enables the user to efficiently compute Morse decompositions of 3D piecewise linear vector fields defined on regular grids. Specifically, we extend the 2D adaptive edge sampling technique to 3D for the outer approximation computation of the image of any 3D cell for the construction of the directed graph. To achieve finer decomposition, a hierarchical refinement framework is applied to procedurally increase the integration steps and subdivide the underlying grids that contain certain Morse sets. To improve the computational performance, we implement our Morse decomposition framework using CUDA. We have applied our framework to a number of analytic and real-world 3D steady vector fields to demonstrate its utility.