Boolean operation of geometric models is an essential element in computational geometry. An efficient approach is developed in this research to perform Boolean operation for triangulated meshes represented by B-rep. This approach is much fast and robust than many existing methods. The Octree technique is adapted to facilitate the division of the common space of two meshes in order to reduce the time of Octree's construction and intersection detection. Floating point arithmetic errors and singularity of intersections are then analyzed to guarantee the unique intersection between a segment and a face, and the continuity of intersections. A novel technique based on intersecting triangles is finally proposed to create required sub-meshes based on the type of Boolean operations. Some experimental results and comparisons with other methods are presented to prove that the proposed method is fast and robust.
Increasing diversity of types and decreasing batch sizes along with a growing complexity of products manufactured by forming technology result in new challenges for developers and designers. The construction of a full parametric model of a deep drawing tool in a 3D CAD system is usually considered time-consuming and associated with high cost, and thus discourages many designers. In order to render this type of modeling easier and faultless, a new method for the model-driven design of deep drawing tools is developed. For this purpose the analysis of fully parametric 3D CAD models of deep drawing tools is necessary. This analyzing contributes to the newly developed graphical domain-specific language, which makes the modeling of deep drawing tools more flexible and time-efficient.
In this paper we consider the problem of obtaining an implicit form for the canal surface whose spine is the arc and the radius changes linearly in respect to the angle. We present a number of different solutions to the problem including exact and approximated ones and discuss the scenarios where each of the solutions is appropriate to use in solid modeling with real functions.
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