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Bock, K. and Stiller, J. (2014) Generation of High-Order Polynomial Patches from Scattered Data. In: Azaïez, M., El Fekih, H. and Hesthaven, J.S., Eds., Spectral and High Order Methods for Partial Differential Equations-ICOSAHOM 2012, Lecture Notes in Computational Science and Engineering, Vol. 95, Springer International Publishing, 157-167.

has been cited by the following article:

• TITLE: Energy-Minimizing Curve Fitting for High-Order Surface Mesh Generation

  AUTHORS: Karsten Bock, Jörg Stiller

  KEYWORDS: Curvilinear Mesh Generation, High-Order Methods, Bézier Curves, Curve Fitting, Energy Minimization

  JOURNAL NAME: Applied Mathematics, Vol.5 No.21, December 1, 2014

  ABSTRACT: We investigate different techniques for fitting Bézier curves to surfaces in context of high-order curvilinear mesh generation. Starting from distance-based least-squares fitting we develop an incremental algorithm, which incorporates approximations of stretch and bending energy. In the process, the algorithm reduces the energy weight in favor of accuracy, leading to an optimized set of sampling points. This energy-minimizing fitting strategy is applied to analytically defined as well as triangulated surfaces. The results confirm that the proposed method straightens and shortens the curves efficiently. Moreover the method preserves the accuracy and convergence behavior of distance-based fitting. Preliminary application to surface mesh generation shows a remarkable improvement of patch quality in high curvature regions.