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Symmetries.pas
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Symmetries.pas
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unit Symmetries;
interface
uses CubeDefs;
//+++++++++corner and edge permutations/orientations of the 48 symmetries+++++++
var CornSym: array [SymIdx] of CornerCubie;
EdgeSym: array [SymIdx] of EdgeCubie;
CentSym: array [SymIdx] of CenterCubie;
//++++++++++++++++++S(Idx)*S(InvIdx[Idx])= ID+++++++++++++++++++++++++++++++++++
InvIdx: array [SymIdx] of SymIdx;
//++++++++++++++Group table for the symmetries++++++++++++++++++++++++++++++++++
SymMult: array[SymIdx,SymIdx] of SymIdx;
//+++++++++++conjugation S(SymIdx]*M*S(SymIdx)^-1+++++++++++++++++++++++++++++++
SymMove: array[SymIdx,Move] of Move;
procedure CreateSymmetryTables;
function MT(m:String;sym:Symmetry):String;
implementation
uses CubiCube,SysUtils,RubikMain;
//++++++++++++++++inititalize arrays CornSym and EdgeSym++++++++++++++++++++++++
procedure CreateSymmetries;
var cCube: CubieCube; i: Corner; e: Edge; cn: TurnAxis; index,urf3,f2,u4,lr2,j,k: Integer;
c:CornerCubie;
begin
cCube:= CubieCube.Create;
index:=0;
for urf3:= 0 to 2 do //generate all 48 symmetries
begin
for f2:= 0 to 1 do
begin
for u4:= 0 to 3 do
begin
for lr2:= 0 to 1 do
begin
for i:=URF to DRB do
begin
CornSym[index,i].c:=cCube.PCorn^[i].c;
CornSym[index,i].o:=cCube.PCorn^[i].o;
end;
for e:=UR to BR do
begin
EdgeSym[index,e].e:=cCube.PEdge^[e].e;
EdgeSym[index,e].o:=cCube.PEdge^[e].o;
end;
for cn:=U to B do
begin
CentSym[index,cn].c :=cCube.PCent^[cn].c;
CentSym[index,cn].o :=cCube.PCent^[cn].o;
end;
inc(index);
cCube.SymMult(S_LR2);
end;
cCube.SymMult(S_U4);
end;
cCube.SymMult(S_F2);
end;
cCube.SymMult(S_URF3);
end;
//now find the inverse symmetries
for j:=0 to 47 do
for k:= 0 to 47 do
begin
CornMult(CornSym[j],CornSym[k],c);
if (c[URF].c=URF) and (c[UFL].c=UFL) and (c[ULB].c=ULB) then
begin InvIdx[j]:=k; break; end;
end;
cCube.Free;
end;
//++++++++++++End inititalize arrays CornSym and EdgeSym++++++++++++++++++++++++
//++++++++++++++++++++++++++++Initialize array SymMult++++++++++++++++++++++++++
procedure CreateSymmetryGroupTable;
var i,j,k: SymIdx; corn:CornerCubie;
begin
for i:= 0 to 47 do
for j:= 0 to 47 do
begin
CornMult(CornSym[i],CornSym[j],corn);
for k:= 0 to 47 do
begin
if (CornSym[k,URF].c=corn[URF].c) and (CornSym[k,UFL].c=corn[UFL].c)
and (CornSym[k,ULB].c=corn[ULB].c) then
begin
SymMult[i,j]:=k;
break;
end;
end;
end;
end;
//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//+++++++++++++++Check if if corners are in their place+++++++++++++++++++++++++
function IsCornID(cc:CubieCube): Boolean;
var i: Corner;
begin
Result:=True;
for i:=URF to DRB do
if (cc.PCorn^[i].c<>i) or (cc.PCorn^[i].o<>0) then
begin
Result:=False;
break;
end;
end;
//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//+++++++++create images of the moves by conjugation with symmetries++++++++++++
procedure CreateSymMoveTable;
var c1,c2: CubieCube;prod: CornerCubie;j,m: TurnAxis;k,n: Integer;s: SymIdx;
begin
c1:= CubieCube.Create;
c2:= CubieCube.Create;
for j:= U to Fs do
begin
for k:= 0 to 3 do
begin
c1.Move(j);
if k<>3 then
begin
for s:= 0 to 47 do
begin
CornMult(CornSym[s],c1.PCorn^,prod);//conjugate
CornMult(prod,CornSym[InvIdx[s]],c2.PCorn^);
for m:= U to Fs do//find the move
begin
for n:= 0 to 3 do
begin
c2.Move(m);
if n<>3 then if IsCornID(c2) then
begin
SymMove[s,Move(3*Ord(j)+k)]:=Move(3*Ord(m)+(2-n));
end;
end;
end;
end;
end;
end;
end;
c1.Free;
c2.Free;
end;
//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
procedure CreateSymmetryTables;
begin
CreateSymmetries;
CreateSymmetryGroupTable;
CreateSymMoveTable;
end;
//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//+++++++++Transform maneuver strings according to symmetry conjugation+++++++++
function MT(m:String;sym:Symmetry):String;
var t: array[' '..'z'] of Char;s,r:String;
mv:set of 'B'..'z';i,n:Integer;
foundMove: Boolean;
//Kleinbuchstaben e,m,a symbolisieren inverse Richtungen von E,M,S, a statt s wg. z.B. (17s)
//Großbuchstaben X,Y,Z symbolisieren inverse Richtungen von x,y,z
begin
s:=m;
mv:=['U','R','F','D','L','B','E','M','S','e','m','a','x','y','z','X','Y','Z'];
case sym of
S_URF3:
begin
t['U']:='R';t['R']:='F';t['F']:='U';t['D']:='L';t['L']:='B';t['B']:='D';
t['E']:='M';t['M']:='a';t['S']:='e'; t['x']:='z';t['z']:='y';t['y']:='x';
end;
S_F2:
begin
t['U']:='D';t['D']:='U';t['R']:='L';t['L']:='R';t['F']:='F';t['B']:='B';
t['E']:='e';t['M']:='m';t['S']:='S'; t['x']:='X';t['y']:='Y';t['z']:='z';
end;
S_U4:
begin
t['U']:='U';t['D']:='D';t['R']:='F';t['F']:='L';t['L']:='B';t['B']:='R';
t['E']:='E';t['M']:='a';t['S']:='M';t['x']:='z';t['y']:='y';t['z']:='X';
end;
S_R4:
begin
t['U']:='B';t['B']:='D';t['D']:='F';t['F']:='U';t['R']:='R';t['L']:='L';
t['E']:='S';t['M']:='M';t['S']:='e'; t['x']:='x';t['y']:='Z';t['z']:='y';
end;
S_F4:
begin
t['U']:='R';t['R']:='D';t['D']:='L';t['L']:='U';t['F']:='F';t['B']:='B';
t['E']:='M';t['M']:='e';t['S']:='S';t['x']:='Y';t['y']:='x';t['z']:='z';
end;
S_LR2: //Ergebnis wird noch invertiert!
begin
t['U']:='U';t['D']:='D';t['R']:='L';t['L']:='R';t['F']:='F';t['B']:='B';
t['E']:='E';t['M']:='m';t['S']:='S'; t['x']:='X';t['y']:='y';t['z']:='z';
end;
end;
for i:=1 to Length(m) do //alle Achsen transformieren
if (m[i] in mv) and (m[i]<>manSep) then s[i]:=t[m[i]] else s[i]:=m[i];
s:=s+' ';r:='';
if sym=S_LR2 then //change the move directions
begin
n:=Length(s);
foundMove:=false;
i:=1;
while (i<=n) do
begin
case s[i] of
'U','R','F','D','L','B','E','M','S','x','y','z','e','m','a','X','Y','Z':
foundMove:=true;
end;
r:=r+s[i];
if (foundMove) then
begin
case s[i+1] of
'3','''': begin r:=r+'';Inc(i) end;
'2': begin r:= r+'2'; Inc(i) end;
else
r:=r+'''';
end;
foundMove:=false;
end;
Inc(i);
end;
s:=r;
end;
r:=''; //jetzt wieder E,M,X,x,y,z substituieren
n:=Length(s);
foundMove:=false;
i:=1;
while (i<=n) do
begin
case s[i] of
'e','m': begin r:=r+UpperCase(s[i]);foundMove:=true; end;
'a': begin r:=r+'S';foundMove:=true; end;
'X','Y','Z': begin r:=r+LowerCase(s[i]);foundMove:=true; end;
else
r:=r+s[i];
end;
if (foundMove) then
begin
case s[i+1] of
'3','''': begin r:=r+'';Inc(i) end;
'2': begin r:= r+'2'; Inc(i) end;
else
r:=r+'''';
end;
foundMove:=false;
end;
Inc(i);
end;
Result:= trim(r);
end;
//+++++End Transform maneuver strings according to symmetry conjugation+++++++++
end.