Random Polygon to Ellipse

dimension

2

3

number of points

10

20

30

iteration steps

1

	x
	y

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

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

[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.

Rongzhong Li