Re: Symmetry in joseki and fuseki

[Mousheng Xu <xu@xxxxxxxxxx>]

Compgo123@xxxxxxxxxxxxxxxxx wrote:

> There are 8 different symmetry positions in joseki and fuseki. The size of the
>

    8? I thought it was 16.
    2 color * 4 rotation * 2 reflection = 16?
    Thanks.

-- Mousheng Xu

> data file is reduced if symmety is considered. It's not a complicated problem.
> To save a new starter couple hours of time, I'll list all symmetry operators
> in the following.
>
> To use symmetry, two things have to be determined first. One is the coordinate
> system, because the form of the symmetry operator depends on the coordinate
> system. The second thing is that all your data has to follow certain rules.
> These rules in large part is arbitrary, but one has to follow them to take the
> full advantage of the symmetry.
>
> For Windows, the origin of the coordinate is at the upper-left. Thus it's
> natural and convenient to set the origin of the coordinate in a Go board at
> the upper-left corner. The positions on a Go board can be assigned in two
> ways. One is to use 0,1,...,18. The other way is to use -9,-8,...,8,9. The
> former is more convenient in programming. However, the later is needed to use
> the symmetry operators.
>
> I use follwoing rules to build a data file. They pretty much follow those in
> most Go books.
> 1. The first move is always at the upper-right quadrant of the Go board.
> 2. The first move is always at the lower-right half of the Go board, if it's
> not at a symmetry position (on the diagonal line).
> 3. If the all moves so far are at symmetry positions (on the diagonal line),
> the first move that breaks the symmetry determines the symmetry of the joseki
> or fuseki according to rule 4.
> 4. If the first symmetry breaking move is black, it's always at the lower-
> right half of the Go board. If it's white, it's always at the upper-left half
> of the Go board.
>
> There are 8 symmetry positions. They are the four corners and in each corner,
> there is the basic position and the mirror image of the basic position.
> Following is a list of the 8 symmetry matrix. To transform any position (x,y)
> into the data file position (X,Y), use follwing formula
>
>                        X=symop[0][i]*x+symop[2][i]*y
>                        Y=symop[3][i]*x+symop[4][i]*y
> where i is the number of the symmetry. All the coordinates are designated by
> -9,-8,...,8,9. The matrix for reverse transform are also listed and the
> formula is
>
>                        x=symopb[0][i]*X+symopb[1][i]*Y
>                        y=symopb[3][i]*Y+symopb[4][i]*Y
>
> I assigned the value i in following way.
>
> 0 - upper-right corner, no mirror reflection
> 1 - upper-right corner, with mirror reflection
> 2 - lower-right corner, no mirror reflection
> 3 - lower-right corner, with mirror reflection
> 4 - lower-left corner, no mirror reflection
> ....... and so on.
>
> The symmetry operators are
> symop[0,0] =1
> [1,0]=0
> [2,0]=0
> [3,0]=1
> [0,1]=0
> [1,1]=-1
> [2,1]=-1
> [3,1]=0
> [0,2]=0
> [1,2]=1
> [2,2]=-1
> [3,2]=0
> [0,3]=1
> [1,3]=0
> [2,3]=0
> [3,3]=-1
> [0,4]=-1
> [1,4]=0
> [2,4]=0
> [3,4]=-1
> [0,5]=0
> [1,5]=1
> [2,5]=1
> [3,5]=0
> [0,6]=0
> [1,6]=-1
> [2,6]=1
> [3,6]=0
> [0,7]=-1
> [1,7]=0
> [2,7]=0
> [3,7]=1
>
> The symmetry operators for reverse transform are
> symopb[0,0]=1
> [1,0]=0
> [2,0]=0
> [3,0]=1
> [0,1]=0
> [1,1]=-1
> [2,1]=-1
> [3,1]=0
> [0,2]=0
> [1,2]=-1
> [2,2]=1
> [3,2]=0
> [0,3]=1
> [1,3]=0
> [2,3]=0
> [3,3]=-1
> [0,4]=-1
> [1,4]=0
> [2,4]=0
> [3,4]=-1
> [0,5]=0
> [1,5]=-1
> [2,5]=-1
> [3,5]=0
> [0,6]=0
> [1,6]=1
> [2,6]=-1
> [3,6]=0
> [0,7]=-1
> [1,7]=0
> [2,7]=0
> [3,7]=1
>
> Dan Liu