In computer vision one often fits ellipses and other conics to observed points on a plane or ellipsoids/quadrics to spacial point clouds. The most accurate and robust fit is obtained by minimizing geometric (orthogonal) distances, but this problem has no closed form solution and most known algorithms are prohibitively slow. We revisit this issue based on recent advances by S. J. Ahn, D. Eberly,...

The isogeometric collocation method (IGA-C), which is a promising branch of analysis (IGA), can be considered fitting the load function with combination numerical solution and its derivatives. In this study, we develop an iterative method, least-squares progressive-iterative approximation (IG-LSPIA), to solve problem in method. IG-LSPIA starts initial blending function, where control coefficien...

Combining results presented in two papers in this Monthly yields the following elementary result. Any line of best fit for the zeros of a polynomial is a line of best fit for its critical points. This note gives a generalization of results on cubic polynomials presented in [1]. Our notation will follow that paper. A line of best fit for a set of points in the plane is defined, as in [1, p. 682]...