Convex decomposition of polyhedra and robustness
SIAM Journal on Computing
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Strategies for polyhedral surface decomposition: an experimental study
Computational Geometry: Theory and Applications
Level set diagrams of polyhedral objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
Computing contour trees in all dimensions
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Loops in reeb graphs of 2-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Quality meshing for polyhedra with small angles
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Augmented Reeb Graphs for Content-Based Retrieval of 3D Mesh Models
SMI '04 Proceedings of the Shape Modeling International 2004
Partitioning of 3D Meshes using Reeb Gra
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
Mesh Generation: Application to Finite Elements
Mesh Generation: Application to Finite Elements
Sliver-free perturbation for the Delaunay tetrahedrization
Computer-Aided Design
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Approximate convex decomposition of polyhedra and its applications
Computer Aided Geometric Design
Efficient Output-Sensitive Construction of Reeb Graphs
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Efficient algorithms for computing Reeb graphs
Computational Geometry: Theory and Applications
A Minimal Contouring Approach to the Computation of the Reeb Graph
IEEE Transactions on Visualization and Computer Graphics
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees
IEEE Transactions on Visualization and Computer Graphics
Simple and optimal output-sensitive construction of contour trees using monotone paths
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Characterization of polyhedron monotonicity
Computer-Aided Design
Sweeping of unstructured meshes over generalized extruded volumes
Finite Elements in Analysis and Design
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In dip-coating processes a three-dimensional object, e.g. an entire car body, is dipped into a liquid bath. In order to simulate such processes, the space surrounding the object is decomposed into the so-called flow volumes, for which each intersection with a horizontal plane is connected. At any time the liquid's surface then has a unique level within such a flow volume, which greatly simplifies the simulation of the liquid. The decomposition into flow volumes corresponds to the Reeb graph of the object's exterior (considered as 3-manifold with boundary) with respect to the height function. This article presents an algorithm which computes this decomposition for an object represented as oriented triangular boundary mesh. First critical vertices of the surface are identified, which include the upper and lower ends of flow volumes. Using local information about horizontal intersection planes near the critical points, a sweep plane algorithm then constructs the volume decomposition in a second step. It is shown that the method can deal with realistic data.