使用2D数组创建具有3D网格的多维数据集

Question

I need to create a cube using a mesh which is using these properties: "A two-dimensional array containing the mesh vertices. Each entry of the array specifies the vertices of one row of the mesh. The arrays for all rows must have the same length. There must be at least two rows, and each row must have at least two vertices"

If you think to a representation of a cube made of paper:

you can see it as 2 meshes, the 3 orizontal square and the 3 vertical. But in this case I would have to use two meshes, while I need one. I'd like to do not have overlap, and I was not able to find a solution. The best option I've found consists in filling the array with 9 rows.

Each rows contains two entry, and in this way it is creating the surface of the cube. I'm attaching few images to explain what it creates with the first rows, till when I reach the overlapping point:

I guess this problem has no solution, but in case any of you have any idea I will be open to any proposal.

(I'm sorry about the order that may not be accurate)

var row0 = [];  
x, y, l
x+t, y, l

var row1=[]        
x, y, l+400
x+t, y, l+400

var row2=[]        
x, y+t, l+400
x+t, y+t, l+400

var row3=[]       
x, y+t, l
x+t, y+t, l

var row4=[]         
x, y, l
x+t, y, l

var row5=[]      
x+t, y, l
x+t, y+t, l

var row6=[]         
x+t, y, l+400
x+t, y+t, l+400

var row7=[]       
x, y+t, l
x, y, l

var row8=[]
x, y+t, l+400
x, y, l+400

With "x,y" two random coordinates that are having a distance of 400."t" as a variable. While "l+40"0 indicates the distance in height from the "l".

Source here

Answer 1

You're totally overthinking the problem.

Let's step back for a moment: In 3D space each position is specified by 3 values; in a cartesian coordinate system those are usually called X, Y and Z.

We normally write those down as a row of scalar values:

x, y, z

A cube consists of 6 faces, each one made up of 4 points, where each point position is shared by 3 faces. Let's assume a cube with its center at the origin and a width of 2, then the two faces in the XY-plane would be

-1, -1, -1
 1, -1, -1
 1,  1, -1
-1,  1, -1
 1, -1,  1
-1, -1,  1
-1,  1,  1
 1,  1,  1
 …

there are 4 more faces (two in XZ and two in YZ) to make a full cube. What's really important (for your question) is, how these values are written down. Look up to the numbers I wrote. What do you see? A 2D array of numbers (3 numbers in a row), one row for every point the cube's mesh is made up from. That's all there is.

A mesh is simply such a list of vertices. Don't think of it as a "foldable mesh made from paper". Just a list of positions, where you can also duplicate positions. You may as well write down only the 8 positions once and use a second, 1D array that is a list of how to make a mesh from these positions.