Robust intersection of structured hexahedral meshes and degenerate triangle meshes with volume fraction applications
- 134 Downloads
Two methods for calculating the volume and surface area of the intersection between a triangle mesh and a rectangular hexahedron are presented. The main result is an exact method that calculates the polyhedron of intersection and thereafter the volume and surface area of the fraction of the hexahedral cell inside the mesh. The second method is approximate, and estimates the intersection by a least squares plane. While most previous publications focus on non-degenerate triangle meshes, we here extend the methods to handle geometric degeneracies. In particular, we focus on large-scale triangle overlaps, or double surfaces. It is a geometric degeneracy that can be hard to solve with existing mesh repair algorithms. There could also be situations in which it is desirable to keep the original triangle mesh unmodified. Alternative methods that solve the problem without altering the mesh are therefore presented. This is a step towards a method that calculates the solid area and volume fractions of a degenerate triangle mesh including overlapping triangles, overlapping meshes, hanging nodes, and gaps. Such triangle meshes are common in industrial applications. The methods are validated against three industrial test cases. The validation shows that the exact method handles all addressed geometric degeneracies, including double surfaces, small self-intersections, and split hexahedra.
KeywordsCut-cell Volume fraction Mesh repair Overlapping triangles Split hexahedra
This work was supported in part by the Swedish Governmental Agency for Innovation Systems, VINNOVA, through the FFI Sustainable Production Technology program, and in part by the Sustainable Production Initiative and the Production Area of Advance at Chalmers University of Technology. The support is gratefully acknowledged.
- 2.Aftosmis, M.J., Berger, M.J., Melton, J.E.: Adaptive Cartesian mesh generation. In: Weatherill, N. P., Soni, B. K., Thompson, J. (eds.) Handbook of Grid Generation, pp 22–1–22-21. CRC Press, Boca Raton (1998)Google Scholar
- 10.Botsch, M., Pauly, M., Kobbelt, L., Alliez, P., Levy, B.: Geometric modeling based on polygonal meshes http://lgg.epfl.ch/publications/2008/botsch_2008_GMPeg.pdf. Accessed 27 March 2016 (2007)
- 12.Ericson, C.: Real-Time Collision Detection. Morgan Kaufmann, Burlington (2004)Google Scholar
- 16.IBOFlow. http://www.iboflow.com. Accessed 27 March 2016
- 18.Liepa, P.: Filling holes in meshes. In: Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on geometry processing, pp 200–205 (2003)Google Scholar
- 19.Mark, A., Rundqvist, R., Edelvik, F.: Comparison between different immersed boundary conditions for simulation of complex fluid flows. Fluid Dyn. Mater. Process. 7(3), 241–258 (2011)Google Scholar
- 24.Schirra, S.: Robustness and precision issues in geometric computation. In: Sack, J.-R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp 597–632. Elsevier (1997)Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.