A cube is the familiar three-dimensional solid with eight vertices, six faces and twelve edges. I have been working with cubes recently in posts about both the Menger sponge fractal and the 4-by-4 matrix from computer graphics.

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顶点

Cartesian coordinates,V, for the eight vertices of a cube can be generated from the binary representation of0：7.

j = (0:7)'

j = 0 1 2 3 4 5 6 7

k = dec2bin（j）

k = 8×3 char array '000' '001' '010' '011' '100' '101' '110' '111'

V = double(k-'0')

V = 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

边缘

立方体的十二个边缘由邻接矩阵描述Aof connections between its vertices.

A = adjacency(V) spy(A)

a = 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 10 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0

Wireframe

图的图A提供我们的立方体的线框视图。

g = graph（a）;p =图（g，...nodelabel =字符串（k），...NodeFontSize = 12,...XData = V(:,3),...YData = V(:,2),...zdata = v（：，1））;轴（[ -  1 4 -1 4 -1 4]/3）轴正方形离开vis3dview(3)

Let's replace the node labels with 1-based indices for rows ofV.

p.nodelabel =字符串（J+1）;

面孔

A cube has six square faces. This arrayFprovides the indices inVof the coordinates of the corners of each face. The ordering ensures that the normal to each face points out of the cube.

F = [ 1 5 7 3 3 7 8 4 1 3 4 2 2 4 8 6 1 2 6 5 5 6 8 7 ]

F = 1 5 7 3 3 7 8 4 1 3 4 2 2 4 8 6 1 2 6 5 5 6 8 7

If you Google "rgb gold", you will get links to Web sites offering red-green-blue values for dozens of shades of the color gold. My forthcoming post about the complement of the Menger sponge fractal uses just two shades.

gold = [212 175 55]/256 dark = gold/2

gold = 0.8281 0.6836 0.2148 dark = 0.4141 0.3418 0.1074

The singlepatchformed fromV和Fis just the skin enclosing our cube; its inside is hollow.

cla patch(Faces = F,...顶点= V,...FaceColor = gold,...edgecolor =黑暗，...线宽= 1.5）;轴（[ -  1 4 -1 4 -1 4]/3）轴正方形离开vis3dview(3)

获取MATLAB代码

Published with MATLAB® R2021a