Robust Intersection of Structured Hexahedral Meshes and Degenerate Triangle Meshes with Volume Fraction Applications
Journal article, 2018

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.

Split hexahedra

Mesh repair

Overlapping triangles


Volume fraction


Frida Svelander

Chalmers, Mathematical Sciences

Fraunhofer-Chalmers Centre

University of Gothenburg

Gustav Kettil

University of Gothenburg

Chalmers, Mathematical Sciences

Fraunhofer-Chalmers Centre

Tomas Johnson

Fraunhofer-Chalmers Centre

Andreas Mark

Fraunhofer-Chalmers Centre

Anders Logg

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Fraunhofer-Chalmers Centre

Fredrik Edelvik

Fraunhofer-Chalmers Centre

Numerical Algorithms

1017-1398 (ISSN) 15729265 (eISSN)

Vol. 77 4 1029-1068

Areas of Advance

Building Futures (2010-2018)


Subject Categories

Computational Mathematics


Basic sciences



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