Rubik's Cube Game Realization (a): The representation of any order Rubik's Cube

a simple representation of the first Rubik's Cube

For any n -order Rubik's Cube, there are six faces (surface) with n*n squares per polygon. In object-oriented programming, we can view the cube (cube), the surface of the cube (surface) and the blocks (block) as objects.

Definition of a Rubik's cube: Six faces stored in an array

" " <summary>" "represents a cube of a specified order" " </summary> Public ClassCubeclass" " <summary>    " "order of Rubik's Cube" " </summary>     PublicCuberank as Integer    " " <summary>    " "six surfaces of a Rubik's Cube" " </summary>     PublicSurfacearray (5) asCubesurfaceclassEnd Class

Cube's polygon definition: a two-dimensional array of blocks stored as N*n

" " <summary> " " a face that represents a Rubik's Cube " " </summary>  Public Class Cubesurfaceclass     " " <summary>    " " block data    for the cube surface " " </summary>     Public  as Cubeblockclass End Class

Block definition for Rubik's Cube: Each block has a separate color

" " <summary>" "represents a block on the magic side" " </summary> Public ClassCubeblockclass" " <summary>    " "the color of the current block" " </summary>     PublicBlockcolor asColor PublicX as Integer 'Number of columns     PublicY as Integer 'Number of rowsEnd Class

Above, we have completed a simple definition of the Rubik's Cube class, and established a subordinate relationship. One thing to note here is that a block (Blockclass) is a single color block of a Rubik's Cube.

So the N-order Rubik's Cube should have 6*n*n color blocks, taking the third-order Rubik's Cube as an example, it should have 54 color blocks (Blockclass).

the spatial relationship between the second section faces

　The six sides of the Rubik's Cube are not independent, but there is a certain spatial relationship. The previous definition of the Cubeclass in the Surfacearray () represents the six sides of the Rubik's Cube, now the index 0~5 respectively indicate the top of the Rubik's Cube, the bottom, left, right, front, rear six faces.

Surfacearray (0): Top floor

Surfacearray (1): Bottom

Surfacearray (2): Left

Surfacearray (3): Right

Surfacearray (4): Front

Surfacearray (5): Rear

Fig. 2.1 Space position of Rubik's Cube six plane

This determines the spatial orientation of each polygon and adds the following definition to Surfaceclass:

    " " <summary>    " " adjacent layers of the current surface (top, bottom, left, right, front, and    rear) " " </summary>     Public Neiboursurface (5 as Cubesurfaceclass

The index of Neiboursurface () is sequentially indicated from 0~5 when the front top, bottom, left, right, front, and rear. For example, in Figure 2.1, "right", its neiboursurface () should be

Neiboursurface (0): Top floor

Neiboursurface (1): Bottom

Neiboursurface (2): Front

Neiboursurface (3): Rear

Neiboursurface (4): On the right side, the "front" of each face is its own

Neiboursurface (5): Left

But above is the default "right" of "top" is the top layer. So we also need to make a strict definition of "top" of each face:

Fig. 2.2 Space position of Rubik's Cube six plane expansion

Fig. 2.3 The direction of the "top" of the Rubik's six face

From above, we can determine the spatial relationship between the faces:

        DimTemparray (,) as Integer= {{2,3,4,5,0,1},                                       {3,2,4,5,1,0},                                       {1,0,4,5,2,3},                                       {0,1,4,5,3,2},                                       {0,1,2,3,4,5},                                       {0,1,3,2,5,4}}'spatial adjacency Relationship matrix

The matrix row value refers to the index of a polygon in Surfacearray (), and the number of columns represents the index of the polygon adjacent to the polygon at Surfacearray (). The "front" of each polygon mentioned above is itself , and the fifth column of the matrix is from 0 to 5.

Add the following method to the Cubeclass class and call it in the constructor:

    " " <summary>    " "Initialize the spatial adjacency between each surface layer" " </summary>     Public Subinitsurface ()DimTemparray (,) as Integer= {{2,3,4,5,0,1},                                       {3,2,4,5,1,0},                                       {1,0,4,5,2,3},                                       {0,1,4,5,3,2},                                       {0,1,2,3,4,5},                                       {0,1,3,2,5,4}}'spatial adjacency Relationship matrix         fori =0  to 5             forj =0  to 5Surfacearray (i). Neiboursurface (j)=Surfacearray (Temparray (i, j))Next        Next    End Sub

The third section of the Rubik's Cube initialization

　　Rubik's Cube (Cubeclass) constructor: Six-side color standard: top-white, bottom-yellow, left-orange, right-red, front-green, rear-blue

    " " <summary>    " "Create a new cube of a specified order" " </summary>    " " <param name= "Nrank" >number of orders specified</param>     Public Sub New(ByValNrank as Integer)        DimColorarr () asColor ={color.white, Color.yellow, Color.orange, Color.Red, Color.green, Color.Blue} fori =0  to 5Surfacearray (i)=NewCubesurfaceclass (Nrank, I, Colorarr (i))NextCuberank=Nrank initsurface ()End Sub

The Magic aspect (Cubesurfaceclass) constructor:

    " " <summary>    " "the order of the current Rubik's Cube" " </summary>     PublicCuberank as Integer    " " <summary>    " "data on the cube surface" " </summary>     PublicBlockdata (,) asCubeblockclass" " <summary>    " "adjacent layers of the current surface (top, bottom, left, right, front, and rear)" " </summary>     PublicNeiboursurface (5) asCubesurfaceclass PublicIndex as Integer     Public Sub New(Nrank as Integer, NIndex as Integer, Ncolor asColor)ReDimBlockdata (Nrank-1, Nrank-1) Cuberank=Nrank Index=NIndexDim Rnd  as NewRandom fori =0  toNrank-1             forj =0  toNrank-1Blockdata (i, J)=NewCubeblockclass (i, J) Blockdata (I, J). Parentindex=Index Blockdata (i, J). Blockcolor=NcolorNext        Next    End Sub

The constructor of the cube block (cubeblockclass):

     PublicParentindex as Integer    " " <summary>    " "the color of the current block" " </summary>     PublicBlockcolor asColor PublicX as Integer 'Number of columns     PublicY as Integer 'Number of rows     Public Sub New(NX as Integer, NY as Integer) x=NX y=NYEnd Sub

At this point, an arbitrary order of the Rubik's Cube can be represented, and on this basis will be able to implement the magic cube twist logic.

resource sharing : Chinese Petroleum University (East China) Open class: Rubik's Cube and mathematical modelling (the course involves different methods than the above, and another way of thinking for your reference.) ）

Rubik's Cube Game Realization (a): The representation of any order Rubik's Cube