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Distance between points and ellipse

version 1.4 (4.32 KB) by Rody Oldenhuis
Compute the distances between an ellipse and an arbitrary number of points, in 3D


Updated 02 May 2020

GitHub view license on GitHub

The solution to the problem of calculating the distance between an ellipse and a point is less than straightforward. The problem can be solved analytically however, which boild down to solving a quartic equation in cos(f), with (f) the true anomaly on the ellipse.
This submission implements this and computes the distances between any 3-D ellipse and an arbitrary number of 3-D points.
This is part of:
Ik-Sung Kim: "An algorithm for finding the distance between two ellipses". Commun. Korean Math. Soc. 21 (2006), No.3, pp.559-567
See also my other submission, distanceEllipseEllipse.

Cite As

Rody Oldenhuis (2020). Distance between points and ellipse (, GitHub. Retrieved .

Comments and Ratings (2)


okay, so for the example in your .m file to work, u,v need to be normalized before calculating the coordinates of those two points.


a = [2.0 1.2];
b = [0.5 1.0];
c = {[0,0,0],[1,3,0]}; % location of centers

u = {[1,1,0], [1,0,0]}; % both oriented in XY-plane
v = {[-1,1,0], [0,1,0]}; % to visualize them more easily

does not seem to calculate a correct minimum distance?



See release notes for this release on GitHub:

Description update

[linked to Github]

Updated contact info

(1) Changed description (should've used the "preview" button..)
(2) Removed the ML 2009a/b tilde-syntax for better compatibility
(3) corrected small bug in the error handling (bracket bug)

MATLAB Release Compatibility
Created with R2009b
Compatible with any release
Platform Compatibility
Windows macOS Linux