Ellipse from 5 Points

[Lipko]

Hi All!

Little background: I was searching for an implementation (or at least a full explanation) of constructing an ellipse from 5 points. 5 points exactly define an ellipse, so it's not a data fitting problem. To my surprise, I couldn't find any solutions that can be used as it is or any full explanations. All I could find was pointers into the proper direction (matrix math) but my math is so rusty that I could not implement anything from those information ("just calculate the determinant with some symbolic math library or do it on paper haha and goodness comes"). I was a bit upset because I wasn't doing homework, I actually needed that function.

 

Anyhow, after finding a small hint in one of the threads, I could go through the thing and implementet the algorithm. Maybe it will be useful for anyone who is looking for exactly that thing.

It's not that nice, not optimised, I guess many of the math could be optimized/simplified, but it's working at least.

Precision: I'm not sure. For my needs, it's precise enough, I'm not an expert in condition of the matrix or other calculations.

I think the names are self explaining, but If you have questions, don't hesitate to ask. The formulas and the thread I found most usable are included on the block diagram.
Input: array of coordinates (x,y in a cluster).
Output:

• ellipse parameters: center, two radii and angle of the first axis
• the coordinates of the axis endpoints
• the five t parameter values of the input points (t parameter for the parametric equation of the ellipse), so for example you can draw ellipse arc between two of the points
• If the ellipse cannot be constructed, it results in some NaNs here and there... No extra checks added

2 subvis are also implemented, but maybe they are already in the LV base package and just missed them:

• parametric equation for arbitrary ellipses (or polar equation, my math is that rusty I can't even express properly what I mean)
• CCW angle between two vectors (result in 0....2 PI range), it's used to calculate the t parameters for the points. This is where I feel there's some redundancy or redundant trigonometric calculations.

 

Thank's for any feedback!

EDIT: I added a small demo program. You can move the 5 points on a graph.

2D_ellipse_parametric_equation.vi 2D_ellipse_from_5pts.vi 2D_ccw_angle.vi

Ellipse_Demo.vi

Edited March 3, 2022 by Lipko