自由曲线和曲面的形状一致性验证通常通过最小化测量点和标称曲线/曲面之间的平方偏差之和来实现，从而解决最佳参数估计（OPE）问题。寻找测量点和标称表面之间的最佳刚体变换（ORB）是OPE问题中的一个重要步骤，传统上涉及迭代求解六变量非线性优化问题。本文证明了六元优化问题可以归结为四元二次隐式方程组的求解，这可以看作是一个特征值问题。 这将大大节省计算量。文中对节省的计算量进行了深入分析，并给出了几个例子。

Verification of shape conformance for freeform curves and surfaces is commonly achieved by minimizing the sum of square deviations between measured points and a nominal curve/surface, thereby solving an optimal parameter estimation (OPE) problem. Finding the optimal rigid body transformation (ORB) between the measured points and nominal surface, an important step in the OPE problem, traditionally has involved iteratively solving a nonlinear optimization problem in six variables. In this paper we demonstrate that the optimization problem in six variables may be reduced to solving four, degree two implicit equations in four variables, which can be regarded as an eigen value problem. This results in considerable savings in the number of computations. A thorough analysis of the savings in computations and several examples are presented.