Energy-Minimizing Curve Fitting for High-Order Surface Mesh Generation
Energy-Minimizing Curve Fitting for High-Order Surface Mesh Generation
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DOI：
10.4236/am.2014.521309
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发表时间：
2014-12
影响因子：
1
通讯作者：
Karsten Bock;J. Stiller
中科院分区：
文献类型：
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作者：
Karsten Bock;J. Stiller
我们研究了不同的技术拟合贝塞尔曲线曲面的背景下，高阶曲线网格生成。从基于距离的最小二乘拟合，我们开发了一个增量算法，它结合了拉伸和弯曲能量的近似。在此过程中，该算法降低了能量权重，有利于准确性，从而得到一组优化的采样点。这种能量最小化拟合策略适用于解析定义以及三角化曲面。实验结果表明，该方法能有效地缩短曲线长度。此外，该方法保留了基于距离的拟合的精度和收敛行为。在曲面网格剖分中的初步应用表明，该方法在高曲率区域的质量有了显著的提高。
We investigate different techniques for fitting Bezier 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.