Two types of fitting algorithms. In this and the next chapters we discuss practical solutions to the circle fitting problem. Recall that our main task is to minimize the nonlinear function F given by (3.1). Its minimum cannot be given in a closed form or computed by a finite algorithm. All the existing practical solutions can be divided into two large groups:

(A) iterative algorithms that are designed to converge to the minimum of

F = n

where di are geometric (orthogonal) distances from the data points to the circle. The minimization ofF is referred to as geometric fit;

(B) approximative algorithms that replace di with some other quantities, fi, and

then minimize

usually fi are defined by simple algebraic formulas (without radicals), and the resulting solution is called algebraic fit.