Geometric Fitting of Line, Plane, Circle, Sphere and Ellipse

The least squares fitting minimizes the squares sum of error-of-fit in predefined measures. By the geometric fitting, the error distances are defined with orthogonal, or shortest, distances from the given points to the geometric feature to be fitted. The geometric fitting problems for line and plane are reviewed and solved using the modern matrix computation and method of moment. For the geometric fitting of circle, sphere and ellipse, robust algorithms are proposed. These are based on the coordinate description of the corresponding point on the circle/sphere/ellipse for the given point, where the connecting line of the two points is the shortest path from the given point to the circle/sphere/ellipse.