Ellipse from set of 3d points

[Chipping]

I have a set of 3d points surveyed from a mitre joint on 385mm OD Tube.

Therefore the shape when viewed in the best fit plane is an ellipse with a minor axis of 385mm

I can produce a best fit plane through these points.

I can then project those points onto the new plane in inventor, place a interprolated spline curve through the points in inventor.

My objective is to create a best fit ellipse and find the centre. I heard Autocad Civil has create best fit ellipse from a set of points.

QUESTION - Does anyone one know the best software to create best fit ellipse from a set of 2d points or a set of 3d points?

Inventor is good for projecting the 3d points onto an alreay establised best fit plane but when it comes to a best fit ellipse I get the feeling I should be doing that outside of inventor.

[WHolzwarth]

I think, this can be done in Inventor as well. For fully constraining a circle, a plane through 3 points and these points are needed (Sketch5)

For fully constraining an ellipse, a plane with 5 points is needed (Sketch4). Less points are not enough, more points are too much.

Walter

[Chipping]

Thanks for that I have attached the 3d surveyed data. This data should produce an elipse not a circle and the 4 points around the data are points from a plane that was made as a best fit through all of the data point

I can get more survey data to fill the missing quadrant but I do not believe that the data should be nessesaryto produce the result??

The minor axis of the surveyed elipse is 385mm By the way survey data obtained from photomodeler and should be accurate to 2 or 3 mm.

Inventor can create a plane from 3 of the 4 points on the best fit plane.

Anyway I need to find a way to best fit this data to a perfect ellipse

[WHolzwarth]

I took a look at your points and saw, that most of them still had a distance relative to the best-fit plane.

I've tried 5 of your points, projected them to the best-fit plane and created an ellipse with them. I've tried 5 other point projections, and created a similar ellipse, but not the same. I think, I could get 3,4,5 differing results with other points.

But IMO, that's mainly a problem of your point inputs. The error level is not low enough.

Walter

[Chipping]

Surely the error from the center of the ellipses in mm no matter what 5 points you use must be within 2 - 3mm??

If all points were projected onto the plane and then I could get the x,y co ords and apply a math function, program to create an ellipse from the 2d points - I have read that is possible. Uses least square method or something....

I am still curious as to if or not anyones knows of cad software that will enable selection of the points and then can simply create a best fit ellipse.

Given that it is mathmatically possible I would have thought then that the functuanility would have been available in many cad packages.

Alternativley at this stage I can just use your method. 

[Chipping]

Description

This function uses the Least-Squares criterion for estimation of the best fit to an ellipse from a given set of points (x,y). The LS estimation is done for the conic representation of an ellipse (with a possible tilt). Conic Ellipse representation = a*x^2+b*x*y+c*y^2+d*x+e*y+f=0    (Tilt/orientation for the ellipse occurs when the term x*y exists (i.e. b ~= 0))      Later, after the estimation, the tilt is removed from the ellipse (using a rotation matrix) and then, the rest of the parameters which describes an ellipse are extracted from the conic representation. For debug purposes, the estimation can be drawn on top of a given axis handle. Note:  1) This function does not work on a three-dimensional axis system. (only 2D)  2) At least 5 points are needed in order to estimate the 5 parameters of the ellipse.  3) If the data is a hyperbola or parabula, the function return empty fields and a status indication

MATLAB release

MATLAB 6.1 (R12.1) So I could project all the 3d points on to the plane then get the point data and run the MATLAB Function