# Determine the distance between two ellipses (in 3D) 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : BSD - BSD License

Created : Apr 19, 2010

Downloads : 5

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## The function distanceEllipseEllipse() is based on a ...

The function distanceEllipseEllipse() is based on a practical algorithm which stops itself to minima in the distance function.

It is based on repeatedly finding the distance between a point and an ellipse, which can be done analytically.

The algorithm by itself is not very robust (it frequently finds a local minimum, which is *not* the true distance).

This function executes the algorithm 4 times, for 4 different initial values, which greatly improves its reliability.

Some numerical experimentation (comparing with a brute-force search) has shown that the true minimum distance is returned in more than 95% of the cases.

The algorithm is implemented such that MATLAB's JIT-accelerator can accelerate it to the fullest extent, which makes it pretty fast and well-suited to handle large datasets requiring this calculation.

It is based on repeatedly finding the distance between a point and an ellipse, which can be done analytically.

The algorithm by itself is not very robust (it frequently finds a local minimum, which is *not* the true distance).

This function executes the algorithm 4 times, for 4 different initial values, which greatly improves its reliability.

Some numerical experimentation (comparing with a brute-force search) has shown that the true minimum distance is returned in more than 95% of the cases.

The algorithm is implemented such that MATLAB's JIT-accelerator can accelerate it to the fullest extent, which makes it pretty fast and well-suited to handle large datasets requiring this calculation.

**• MATLAB 7. 9 or higher**

**Demands:****Determine the distance between two ellipses (in 3D) 1.0 scripting tags:**algorithm, calculate distance, ellipse distance, true.

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