# Random Polygon to Ellipse

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Repeatedly averaging the neighboring vertices of a random polygon forms a sequence of polygons that converge to an ellipse.

Contributed by: Rongzhong Li (August 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The averaging operation is represented in the code by a matrix.

Snapshot 1: the initial state of 20 2D points

Snapshot 2: the final state of the 20 2D points

Snapshot 3: the middle state of 30 3D points

Reference

[1] A. Elmachtoub and C. Van Loan, "From Random Polygon to Ellipse: An Eigenanalysis," *SIAM Review*, 52(1), 2010 pp. 151–170. doi:10.1137/090746707.

## Permanent Citation

"Random Polygon to Ellipse"

http://demonstrations.wolfram.com/RandomPolygonToEllipse/

Wolfram Demonstrations Project

Published: August 14 2014