Best Fit Circle

This command draws a least-squares best-fit circle based on points on the perimeter. The program handles four or more perimeter points. A design point for the circle center can optionally be specified as a reference to compare with the best-fit center in the report. The report shows the residuals for each point, the residuals standard deviation, the difference between the design point and the circle center, and the circle parameters. The residuals are calculated as the perpendicular distance from the point to the circle. The best-fit circle can be calculated in 2D or 3D. In 2D mode, the elevation of the points is not used. In 3D mode, a best-fit plane is calculated for the points. Then the points are projected onto the plane and the best-fit circle is calculated on this plane. Then the resulting circle is projected back into world coordinates and drawn as a 3D polyline with short chords to represent the 3D circle since CAD doesn't support a 3D circle entity. Applications for 3D circles are tunnel sections and architectural arches.

After specifying the points, the program calculates the best-fit circle and shows the results in the dialog show here. You can toggle each point for whether to include in the calculations. You can also modify the radius.

Prompts

Create 2D or 3D circle [<2D>/3D]? press Enter
Select points from screen or by point number [<Screen>/Number]? N
Point numbers: 2-6
Point numbers (Enter to continue): press Enter
Enter design center point# (Enter for None):Sample Report:

Source Coordinates

Point#        Northing  Easting   Residual

2       5253.198  5070.233  0.126

3  5246.623  5084.077  0.045

4  5232.963  5078.608  -0.131

5         5235.610  5065.105  0.217

6  5247.392  5064.165  -0.264

Residuals Standard Deviation: 0.174

Circle Center: 5242.678,5073.785 Radius: 10.977

Design Center Point#: 1

Design Center: 5242.718,5073.688

Center Distance Difference: 0.105

Best Fit Circle

Pulldown Menu Location: COGO
Keyboard Command: bfitcir
Prerequisite: Four or more points