Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Molecular shape analysis based upon the morse-smale complex and the connolly function
Proceedings of the nineteenth annual symposium on Computational geometry
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Applications of Forman's Discrete Morse Theory to Topology Visualization and Mesh Compression
IEEE Transactions on Visualization and Computer Graphics
A Topological Approach to Simplification of Three-Dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities
IEEE Transactions on Visualization and Computer Graphics
Topologically Clean Distance Fields
IEEE Transactions on Visualization and Computer Graphics
A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality
IEEE Transactions on Visualization and Computer Graphics
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Combinatorial Vector Field Topology
IEEE Transactions on Visualization and Computer Graphics
A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields
IEEE Transactions on Visualization and Computer Graphics
Two-Dimensional Time-Dependent Vortex Regions Based on the Acceleration Magnitude
IEEE Transactions on Visualization and Computer Graphics
Optimal Topological Simplification of Discrete Functions on Surfaces
Discrete & Computational Geometry
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
Parallel Computation of 2D Morse-Smale Complexes
IEEE Transactions on Visualization and Computer Graphics
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
A primal/dual representation for discrete morse complexes on tetrahedral meshes
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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The Morse-Smale complex is a topological structure that captures the behavior of the gradient of a scalar function on a manifold. This paper discusses scalable techniques to compute the Morse-Smale complex of scalar functions defined on large three-dimensional structured grids. Computing the Morse-Smale complex of three-dimensional domains is challenging as compared to two-dimensional domains because of the non-trivial structure introduced by the two types of saddle criticalities. We present a parallel shared-memory algorithm to compute the Morse-Smale complex based on Forman's discrete Morse theory. The algorithm achieves scalability via synergistic use of the CPU and the GPU. We first prove that the discrete gradient on the domain can be computed independently for each cell and hence can be implemented on the GPU. Second, we describe a two-step graph traversal algorithm to compute the 1-saddle-2-saddle connections efficiently and in parallel on the CPU. Simultaneously, the extremasaddle connections are computed using a tree traversal algorithm on the GPU. © 2012 Wiley Periodicals, Inc.