基于精确解的球面几何拟合快速算法
Fast Geometric Fit Algorithm for Sphere Using Exact Solution
摘要：
球面拟合是几乎所有科学和工程学科中的一个常见问题。现有的大多数方法在行为上是迭代的。这涉及在最小二乘意义上或在几何意义上拟合参数。在这里，我们扩展了Thomas Chan和Landau的方法，他们用圆拟合二维数据。这项工作与他们重新定义误差估计和精确解决球面拟合问题的工作非常相似。该算法可以精确求解球的中心和半径，并可以对方程进行硬编码以提高计算效率。我们还展示了与其他流行方法的一些比较以及该方法的行为。
英文摘要：
Sphere fitting is a common problem in almost all science and engineering disciplines. Most of methods available are iterative in behavior. This involves fitting of the parameters in a least square sense or in a geometric sense. Here we extend the methods of Thomas Chan and Landau who fitted the 2D data using circle. This work closely resemble their work in redefining the error estimate and solving the sphere fitting problem exactly. The solutions for center and radius of the sphere can be found exactly and the equations can be hard coded for high performance. We have also shown some comparison with other popular methods and how this method behaves.
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