Some of the complications here included making the outer box look transparent, but not distorting the inner box's shape, and still making it possible to visualize the outer shape. I used POV-Ray's glass texture, modified to turn off refraction, increase surface roughness, and decrease the amount of specular reflection. The QTVR version has better color resolution than the GIF, allows for a greater variety of viewpoints, and allows the user to understand the shape better by controlling the direction from which it is viewed. Views were chosen with 6 degrees of separation, decreased from QTVR's recommendation of 10 for greater smoothness of rotation. Because of the symmetry of the configuration, rendering only needed to be done through a 120 degree horizontal rotation, saving a factor of 3 in file size and rendering time.
More mathematical information is available on the associated web page .
Due to time and space limitations I only rendered one degree of freedom. Views were chosen with 6 degrees of separation, decreased from QTVR's recommendation of 10 for greater smoothness of rotation. From the Geometry Junkyard , computational and recreational geometry. David Eppstein , Theory Group , ICS , UC Irvine .