Least Squares Fit of Point Clouds

Abstract

We consider a least squares problem in coordinate metrology (see [2], [1]): m points of a workpiece, so-called nominal points are given by their exact coordinates from construction plans when the workpiece is in nominal position in a reference frame. We denote the coordinate vectors of the nominal points in this position by

$$\text{x}_{1},\dotso\text{x}_{m}, \text{x}_{i}\in R^{n}, 1\le n\le 3$$

.