Morse Decomposition of 3D Piecewise Linear Vector Fields

Morse decomposition has been shown a reliable way to com-pute and represent vector field topology. Its computation first con-verts the original vector field into a directed graph representation, so that flow recurrent dynamics (i.e., Morse sets) can be iden-tified as some strongly connected components of the graph. In this paper, we present a framework that enables the user to ef-ficiently 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 approx-imation computation of the image of any 3D cell for the construc-tion of the directed graph. To achieve finer decomposition, a hier-archical refinement framework is applied to procedurally increase the integration steps and subdivide the underlying grids that con-tain certain Morse sets. To improve the computational perfor-mance, 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. 1