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In the application of engineering technology, a certain number of disturbed observation points with errors are often used to fit a plane circle. Considering the distribution characteristics of these points, two kinds of models are presented in this paper: an unconstrained non-linear least square model and a non-linear least square model constrained by the mosaic center coordinates for the plane circle fitting. The lsqnonlin function for nonlinear least square algorithm is applied to work out the unconstrained least square model. The searching method is adopted to figure out the constrained model by analyzing the symmetry of simulated data, determining the initial value for searching and simplifying the solving process. By contrasting the two fitting results, it is obvious that the constrained least square model can successfully simplify the computation with higher accuracy. Furthermore, this algorithm can also be used for the computation of spherical centers and radii in the three-dimensional space.