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QI: Quadric Intersection

Online calculation server

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QI's GForge


(Model courtesy of SGDL Systems)

What is QI?

QI stands for "Quadrics Intersection". QI is the first exact, robust, efficient and usable implementation of an algorithm for parameterizing the intersection of two arbitrary quadrics, given in implicit form, with integer coefficients. This implementation is based on the parameterization method described in

QI has the following features:

Who uses QI?

We have had feedback from people using QI in the following contexts:

What is the status of QI?

QI is free for non-commercial use. Please read the accompanying license for details. Use of this software in published work should be acknowledged. Also, we would be pleased to hear whatever use you have of the code.

Additionally, the implementation used by QI of Uspensky's algorithm for isolating the real roots of a univariate polynomial (written by members of the Spaces and Vegas teams) is released under the terms of the GNU Lesser General Public License. You can get it here (with the accompanying template Makefile).

How do I get QI?

Go to the download page and read on.

Can I quickly give it a try?

Yes. We have set up an online intersection server where you can see for yourself what QI does without going through the compilation process. You can then decide whether you want to get the source and have a local installation.

What is the version history?

The first official version was released on June 2nd, 2004. The latest version is 0.9.0, released on January 9th, 2007.

Comments? Suggestions? Bugs?

For questions related to the algorithm itself, please mail to: For any question concerning the source code implementation and this website, please mail to: Sylvain Petitjean


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