Abstract
Lofting—also denoted as surface skinning—is one of the fundamental operations for creating free-form surfaces in Computer Aided Design. This process generates a surface from a given sequence of section curves. It is particularly useful for airfoils and turbine blades, since these shapes are often defined by cross sections with a family of auxiliary surfaces. The use of tensor-product B-splines, which is currently the standard technology, leads to large data volumes if section curves with incompatible knot vectors are used. We adopt the framework of Patchwork B-splines, which supports very flexible refinement strategies, and apply it to the construction of lofting surfaces. This approach not only reduces the resulting data volume but also limits the propagation of derivative discontinuities.
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Notes
- 1.
Note that the PB-spline construction defined in [3] allows arbitrary domains and admits more general open subsets of the \(\mathbb R^d\) as patches. However, for the lofting problem this simpler setting is sufficient.
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Acknowledgements
Supported by the Austrian Science Fund (FWF) though NFN S117 “Geometry + Simulation”. The authors thank MTU Aero Engines AG for kindly providing the airfoil data sets.
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Engleitner, N., Jüttler, B. (2019). Lofting with Patchwork B-Splines. In: Giannelli, C., Speleers, H. (eds) Advanced Methods for Geometric Modeling and Numerical Simulation. Springer INdAM Series, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-030-27331-6_5
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