# Single Vertical Regression

You can access this dialog from the following:

This tool creates a single vertical geometry element that is a "best fit" to a set of regression points. "Best fit" means that the orthogonal projection from the element to the regression points is minimized. This tool generates either a linear element or a circular element. The length of the element will be all regression data (each point) that can project orthogonally onto the element.

This tool can work both on the profile view (regression line) or on the vertical curvature view (curvature line). While it is possible to create a geometry in parts, using both regression line and curvature line, to switch from one view to other, tool should be restarted.

Computation Methods

This performs linearization based on nonlinear least squares techniques and Newton-like methods, all of which are iterative processes. There are two least squares solvers in this tool. One is based on the Gauss-Jordan Method and the other is based on Singular Value Decomposition. For an introduction to these topics, see Matrix Computations, by Gene Golub and Charles Van Loan. For a discussion of initialization and linearization issues, see Least Squares Fitting of Circles and Ellipses, by Walter Gander, Gene Golub, and Rolf Strebel.