Distance from 3d point to an ellipse

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browser on 20 Jan 2015
Commented: browser on 21 Jan 2015
I want to calculate the distance from a 3d point (x,y,z) to an ellipse (described by xc,yc,zc,a,b,theta,phi,psi). (xc,yc,zc) is the center of the ellipse and the others are the standard variables from the equation of an ellipse.
The 3d point may not be on the same plane as the ellipse.
A lot of previous work on this problem has been in 2 dimensions.
Summary: Question: How do I find distance from 3d point to an ellipse given (x,y,z,xc,yc,zc,a,b,theta,phi,psi)?

Answers (1)

Alessandro Masullo
Alessandro Masullo on 20 Jan 2015
A simple and straightforward solution could be discretizing the points of the ellipse, evaluating the distance from all the points, and then looking for the minimum.
browser on 21 Jan 2015
Thanks - I had considered this but as has been mentioned the amount of computation becomes very large. I have this method implemented currently.

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