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IRTG Modern Inverse Problems (MIP)

Boundary Conforming Smooth Spline Spaces for Isogeometric Analysis

09. Oktober 2018 | von

Prof. Dr. Leif Kobbelt

The generation, adaptation, and modification of digital 3D models is an
essential prerequisite for many steps in a simulation task. Hence it is of fundamental importance to have efficient algorithms that automatically optimize geometry representations for a given set of requirements. The typical simulation workflow is based on a number of different geometry representations that are considered most suitable for the various stages i.e. NURBS B-rep representations for design or polygon meshes for numerical analysis. Consequently, data conversion steps are necessary which often make the overall process inefficient and error-prone.

In this project, we will investigate to what extend design representations can be used for analysis („isogeometric analysis“) or, vice versa, analysis
representations can be used for design („geometry processing“).
Towards this goal, we need to develop new techniques for the analysis of the geometric structure of a 3D object such that we can (automatically) derive a layout on which smooth spline spaces can be defined. This is a (very costly) step that is typically done manually by CAD designers today. Algorithmic solutions enable the automation of this step and its integration into numerics-driven (shape) optimization processes.
For this project it would be helpful to have some background in differential geometry and numerical optimization but also to have some experience in
C++ programming.

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