Abstract
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.
Highlights
The need for computing intersections between polyhedral objects is common in many applications, such as computer graphics, simulations, and robotics [12]
The algorithms have been implemented in the multiphase flow framework IBOFlow and will be used to improve the accuracy in the calculation of fluxes between fluids and solids
The solid area and volume fractions indicate how much of each fluid cell that is intersected by the solid
Summary
The need for computing intersections between polyhedral objects is common in many applications, such as computer graphics, simulations, and robotics [12]. Degeneracies such as hanging nodes (T-vertices), gaps, cracks, overlapping meshes, or overlapping triangles are common in triangle meshes used for engineering applications This aspect is important to consider when designing or using an algorithm that extracts the geometry of a cut cell. Our method handles more general self-intersecting meshes This is an improvement since large-scale triangle overlaps appear frequently in engineering applications and are hard to repair without undesirable side effects (see Section 2). The approximate method is intended for highly resolved hexahedral grids, for which it is reasonable to approximate the cell-triangle mesh intersection with a plane It has some limitations and is a complement to the exact method. This has been taken into account in the development of the methods
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