Creates a horizontal 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 line element or an arc element. The length of the element will be all regression data (each point) that can project orthogonally onto the element.

Created element is automatically added to the regression complex, updating the slew values. Elements has standard geometry rules and manipulators, such as radius or extend controls.

Tool can work both on the plan view or on the curvature view. While it is possible to create a geometry in parts, using both plan view and curvature view, to switch from one view to other, tool should be restarted. When used in the curvature diagram, tool does not go through additional (2^nd and 3^rd) stages, and creates the element as soon as selection is done. Point selection in the regression diagram is done with a box selection, enabling skipping the outliers in the data.

This tool creates a single horizontal 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 plan view (regression line) or on the horizontal 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.

This tool creates a regression rule between the created geometry element and the regression line. This link allows dynamic regression analysis, that is changing the points used in the analysis of that element. Depending on where you used the regression tool (on plan or curvature diagram), you can modify the regression as follows.

If you used Curvature Diagram to create the element, use the manipulators on the regression box. You can also see the updated Maximum Slew and Standard error values in the properties of the created box or the geometry.

If you used Plan View to create the element, use the manipulators on the created geometry. You can see the updated Maximum Slew and Standard error values in the properties of the geometry.

Computation Methods

This tool 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.

Single Horizontal Dialog Option

• Geometry: Type of the geometry element to be created.
  • Automatic: Creates a linear or circular element based on the curvature
  • Linear: Creates a linear element based on the regression data.
  • Circle: Creates a circular element based on the regression data.
• Start Point: Start point of the regression analysis.
  • Start Distance: Distance to the start of the first element in the complex, excluding gaps.
• End Point: End point of the regression analysis.
  • End Point: First point to be used in the analysis
• Results: Results for the current state of regression analysis.
  • Maximum Slew: Displays the offset of the point that is farthest away from the created element. Values close to zero indicate a tight fit.
  • Standard Error: Displays the Standard Error (SE) of the regression analysis. The standard error of the regression provides the measure of the typical distance that the data points fall from the regression line representing how tightly the element fits the regression data. Values close to zero indicate a tight fit.