Contents

The Movie

Here is a link to“ Qube，电影”, a video made withQube，我的数字魔方立方体模拟器。从数学上讲，所有动作均由显示的3 x-3矩阵驱动。

Scaling

Qubeuses a3x3x3array of identicalcubelets. The coordinates[x,y,z]of the centers of the cubelets are all of the possible combinations of-2,0和+2. The vertices of an individual cubelet form a 8-by-3 matrix. The width of a cubelet is controlled by multiplying its vertices by a 3-by-3 diagonal scaling matrix.

我们的视频始于接近零的宽度，因此中心似乎是要点。宽度增加到一个值几乎相互接触的值。保持小间隙的视觉效果。

Rubik's Rotations

The primary operations with a Rubik's cube are the simultaneous rotation of all the cubelets contained in one of the six faces. For example,this videoshows a slow-motion rotation of the "Left" face about thex-axis.

It is also possible to rotate the three interior "slices", as well as the entire cube about one of the coordinate axes.

Types

Thetypeof a cubelet is the number of nonzeros in the coordinates of its center.

type = nnz（[x，y，z]）

The cubelet in the center of the puzzle hastype = 0和the six cubelets withtype = 1are located at the center of each face. We use0:1to denote the set of these seven cubelets. In a real, physical Rubick's Cube,0:1is a single solid central core that holds the entire puzzle together.

There are twelvetype = 2cubelets located on the edges of each face and eighttype = 3拼图的角落。所以，0:3denotes the entire cube and2:3is the corners and edges without the central core.Qube，电影以此顺序显示类型：

0：3、0：2、0：1、0、1、2、3、2：3

Careful readers of this blog should recognize2:3as level one of theMenger sponge fractal.

获取MATLAB代码

Published with MATLAB® R2022a