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An approach to construct a three-dimensional isogeometric model from \(\mu\)-CT scan data with an application to the bridge of a violin. (English) Zbl 1472.65025

Summary: We present an algorithm to build a ready to use isogeometric model from scan data gained by a \(\mu\)-CT scan. Based on a three-dimensional multi-patch reference geometry, which includes the major topological features, we fit the outline, then the cross-section and finally the three-dimensional geometry. The key step is to fit the outline, where a non-linear least squares problem is solved with a Gauss-Newton approach presented by C. F. Borges and T. Pastva [Comput. Aided Geom. Des. 19, No. 4, 275–289 (2002; Zbl 0995.68137)]. We extend this approach by a regularisation and a precise interpolation of selected data points. The resulting NURBS geometry is ready for applying isogeometric analysis tools for efficient numerical simulations. As a particular example we examine the scan data of a violin bridge and present the complete workflow from the \(\mu\)-CT scan up to the numerical simulation based on isogeometric mortar methods. We illustrate the relevance of the constructed geometry with a vibro-acoustical application.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

Citations:

Zbl 0995.68137

Software:

NURBS; FITPACK
PDFBibTeX XMLCite
Full Text: DOI

References:

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