During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the meshing, is a bottle-neck. Several approaches have been developed to overcome this time-consuming step, e.g. Isogeometric Analysis (IGA), which applies the shape functions used for the geometry description (typically B-Splines and NURBS) directly to the numerical analysis. In contrast to IGA, which deals with boundary represented models (B-Rep), our approach focuses on parametric volumetric models such as Constructive Solid Geometries (CSG). These models have several advantages, as their geometry description is inherently watertight and they provide a description of the models interior. To be able to use the explicit mathematical description of these models, we employ the Finite Cell Method (FCM). Herein, the only necessary input is a reliable statement whether an (integration-) point lies inside or outside of the geometric model. This paper mainly discusses such point-in-membership tests on various geometric objects like sweeps and lofts, as well as several geometric operations such as filleting or chamfering. We demonstrate that, based on the information of the construction method of these objects, the point-in-membership-test can be carried out efficiently and robustly.
This paper proposes a computational methodology for the integration of Computer Aided Design (CAD) and the Finite Cell Method (FCM) for models with "dirty geometries". FCM, being a fictitious domain approach based on higher order finite elements, embeds the physical model into a fictitious domain, which can be discretized without having to take into account the boundary of the physical domain. The true geometry is captured by a precise numerical integration of elements cut by the boundary. Thus, an effective Point Membership Classification algorithm that determines the inside-outside state of an integration point with respect to the physical domain is a core operation in FCM. To treat also "dirty geometries", i.e. imprecise or flawed geometric models, a combination of a segment-triangle intersection algorithm and a flood fill algorithm being insensitive to most CAD model flaws is proposed to identify the affiliation of the integration points. The present method thus allows direct computations on geometrically and topologically flawed models. The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples.
Simulation-based testing is seen as a major requirement for the safety validation of highly automated driving. One crucial part of such test architectures are models of environment perception sensors such as camera, lidar and radar sensors. Currently, an objective evaluation and the comparison of different modeling approaches for automotive lidar sensors are still a challenge. In this work, a real lidar sensor system used for object recognition is first functionally decomposed. The resulting sequence of processing blocks and interfaces is then mapped onto simulation methods. Subsequently, metrics applied to the aforementioned interfaces are derived, enabling a quantitative comparison between simulated and real sensor data at different steps of the processing pipeline. Benchmarks for several existing sensor models at a concrete selected interface are performed using those metrics by comparing them to measurements gained from the real sensor. Finally, we outline how metrics on low-level interfaces can correlate with results on more abstract ones. A major achievement of this work lies within the commonly accepted interfaces and a common understanding of real and virtual lidar sensor systems and, even more important, an initial guideline for the quantitative comparison of sensor models with the ambition to support future validation of virtual sensor models.
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