Subdivision Kaleidoscope

When the parameters of subdivision are not in the ranges prescribed by smoothness and convergence conditions, and sometimes even within these ranges, The resulting surfaces may have rather surprising appearance. Searching the parameter space of subdivision, aside from producing interesting images, also demonstrates sensitivity of the surface to the perturbation of a parameter and provides us with extra controls over the appearance of the surface.

The following MPEG clips are from my animation "Subdivision Kaleidoscope". Each clip has two versions: a low resolution version that can be played at 30 frames per second and higher resolution versions with few frames. The latter are not meant to be played continuously: regard them as collection of frames.

Background: the initial mesh in all clips is an icosahedron. The modified Butterfly scheme which is an interpolating scheme, is used as a basis of all subdivision schemes used.

Behavior of the surface near a point is to large extent characterized by the subdivision matrix and its eigenvalues. In most cases, we modify the eigenvalues of the subdivision matrix corresponding only to the points of the original mesh, i.e. vertices of the icosahedron. The surface remains smooth almost everywhere, but the shape of the surface changes dramatically. In one case, we modify a global parameter of the scheme which affects the surfaces locally at any point.

parameter	loop in the range -1..1 starting with initial		increase to plus-infinity		increase to minus-infinity
	low-res. video	frames (*)	low-res. video	frames (*)	low-res. video	frames (*)
The largest eigenvalue with initial value 0.5 range -1..1	1.2 MB	412 KB	839 KB	228 KB	1.3 MB	357 KB
the second largest eigenvalue with initial value 0.25, range -1..1	1.2 MB	425 KB	808 KB	218 KB	1.4 MB	382 KB
A global parameter ("tension") is changed; the scheme may diverge everywhere	659 KB	370 KB	901 KB	259 KB	899 KB	254KB

* Note: The MPEG clips in the colums marked "frames" are not meant to be played continuously. These are collections of frames from the videos stored with low compression and at higher resolution. To look at them, step through the clip frame by frame or play it at a very low speed.