10809
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Random Polygon to Ellipse
Repeatedly averaging the neighboring vertices of a random polygon forms a sequence of polygons that converge to an ellipse.
Contributed by:
Rongzhong Li
THINGS TO TRY
Rotate and Zoom in 3D
Slider Zoom
Gamepad Controls
Automatic Animation
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
Rongzhong Li
"
Random Polygon to Ellipse
"
http://demonstrations.wolfram.com/RandomPolygonToEllipse/
Wolfram Demonstrations Project
Published: August 14, 2014
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Disks Centered on Vertices of Regular Polygons
Mark D. Normand
Approximating Pi with Inscribed Polygons
Rob Morris
One-Half the Apothem Times the Perimeter
Daniel Tokarz
Recursive Exercises XIII: Nested Pentagons
Jaime Rangel-Mondragon
Recursively Defined Partial Tilings of the Plane
Enrique Zeleny
Delannoy Path Exhaustion Diagonal
Michael Schreiber
Constrained Random Walk
Erik Mahieu
Self-Avoiding Random Walks
Rob Morris
Effect of Volatility and Drift on Random Walks
Felipe Dimer de Oliveira
Stability of Polygons Inscribed in an Ellipse
Tímea Deichler
Related Topics
Polygons
Recursion
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+