We present an algorithm for robust Boolean operations of triangulated solids, which is suitable for real-word industrial applications involving meshes with large numbers of triangles. In order to avoid potential robustness problems, which may be caused by (almost) degenerate triangles or by intersections of nearly co-planar triangles, we use filtered exact arithmetic, based on the libraries CGAL and GNU Multi Precision Arithmetic Library. The method consists of two major steps: First we compute the exact intersection of the meshes using a sweep plane algorithm. Second we apply mesh cleaning methods which allow us to generate output which can safely be represented using floating point numbers. The performance of the method is demonstrated by several examples which are taken from applications at ECS Magna Powertrain.

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.

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