Linear angle based parameterization
Linear angle based parameterization
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DOI：
10.2312/sgp/sgp07/135-141
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发表时间：
2007-07
期刊：
影响因子：
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通讯作者：
Rhaleb Zayer;B. Lévy;H. Seidel
中科院分区：
文献类型：
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作者：
Rhaleb Zayer;B. Lévy;H. Seidel
在网格参数化领域中，由于角变形和边界变形对参数化质量的影响，需要一种鲁棒、高效的自由边界角保持方法。在这个方向上最突出的方法之一是基于角度的展平（ABF），它直接将问题公式化为角度方面的约束非线性优化。自ABF最初制定以来，一直致力于提高其效率。对于任何适定的数值问题，其解通常是基本数学方程的近似。解决方案的经济性和准确性在很大程度上受所使用的近似类型的影响。在这项工作中，我们重新制定的基础上估计误差的概念的问题。一个仔细的操作所得到的方程产生的角度为基础的参数化的线性版本的第一次。这种线性化引起的误差是二次的角度误差和近似的有效性进一步支持的数值结果。除了性能加速之外，当前设置的简单性使得重新实现和再现我们的结果变得简单。
In the field of mesh parameterization, the impact of angular and boundary distortion on parameterization quality have brought forward the need for robust and efficient free boundary angle preserving methods. One of the most prominent approaches in this direction is the Angle Based Flattening (ABF) which directly formulates the problem as a constrained nonlinear optimization in terms of angles. Since the original formulation of the ABF, a steady research effort has been dedicated to improving its efficiency. As for any well posed numerical problem, the solution is generally an approximation of the underlying mathematical equations. The economy and accuracy of the solution are to a great extent affected by the kind of approximation used. In this work we reformulate the problem based on the notion of error of estimation. A careful manipulation of the resulting equations yields for the first time a linear version of angle based parameterization. The error induced by this linearization is quadratic in terms of the error in angles and the validity of the approximation is further supported by numerical results. Besides performance speedup, the simplicity of the current setup makes re-implementation and reproduction of our results straightforward.