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Geometric Separators | |
==================== | |
[Imgur](http://i.imgur.com/e5PkQ4a.png) | |
This program is based off the paper [Geometric Separators and the Parabolic Lift](http://donsheehy.net/research/sheehy13geometric.pdf) by Don Sheehy. It implements a new algorithm to calculate a geometric separator for a set of 2D input points. | |
About: | |
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This Processing program will allow you to input a number of 2D points and will calculate the geometric separator for the input set. It will graphically show the centerpoint and the spherical separator projected down to the 2D plane. | |
Usage: | |
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There are three buttons on the application window: **Calculate**, **Reset**, and **Randomize**. | |
You can click anywhere on the canvas to add input points. Then, use the **Calculate** button, which will show the centerpoint (if it can) and the separator projected down to the 2D plane. If you don't have specific points, you can use the **Randomize** button to add 25 random points to the canvas. To remove added points, just click **Reset**. | |
Note: The centerpoint is estimated using Radon Points - according to Radon's Theorem, we can only find a partition for sets of 5 points, so we must only have powers of 5 for our input set. | |
References: | |
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http://donsheehy.net/research/sheehy13geometric.pdf | |
http://dl.acm.org/citation.cfm?id=161004 | |
http://steve.hollasch.net/cgindex/geometry/ptintet.html | |
http://geomalgorithms.com/a06-_intersect-2.html |