  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 model's 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
