Magic Cube

///////////////////////////////////////////////////////////////////////////////////////////////////

// Copyright 2019 Leszek Koltunski                                                               //

//                                                                                               //

// This file is part of Magic Cube.                                                              //

//                                                                                               //

// Magic Cube is free software: you can redistribute it and/or modify                            //

// it under the terms of the GNU General Public License as published by                          //

// the Free Software Foundation, either version 2 of the License, or                             //

// (at your option) any later version.                                                           //

//                                                                                               //

// Magic Cube is distributed in the hope that it will be useful,                                 //

// but WITHOUT ANY WARRANTY; without even the implied warranty of                                //

// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                                 //

// GNU General Public License for more details.                                                  //

//                                                                                               //

// You should have received a copy of the GNU General Public License                             //

// along with Magic Cube.  If not, see <http://www.gnu.org/licenses/>.                           //

///////////////////////////////////////////////////////////////////////////////////////////////////

package org.distorted.objects;

import android.content.res.Resources;

import android.graphics.Canvas;

import android.graphics.Paint;

import org.distorted.library.effect.VertexEffectDeform;

import org.distorted.library.effect.VertexEffectMove;

import org.distorted.library.effect.VertexEffectRotate;

import org.distorted.library.main.DistortedEffects;

import org.distorted.library.main.DistortedTexture;

import org.distorted.library.mesh.MeshBase;

import org.distorted.library.mesh.MeshJoined;

import org.distorted.library.mesh.MeshPolygon;

import org.distorted.library.mesh.MeshSquare;

import org.distorted.library.type.Static1D;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

import org.distorted.main.RubikSurfaceView;

import java.util.Random;

import static org.distorted.effects.scramble.ScrambleEffect.START_AXIS;

///////////////////////////////////////////////////////////////////////////////////////////////////

class RubikCube extends RubikObject

{

  static final float SQ2 = (float)Math.sqrt(2);

  // the three rotation axis of a RubikCube. Must be normalized.

  static final Static3D[] ROT_AXIS = new Static3D[]

         {

           new Static3D(1,0,0),

           new Static3D(0,1,0),

           new Static3D(0,0,1)

         };

  // the six axis that determine the faces

  static final Static3D[] FACE_AXIS = new Static3D[]

         {

           new Static3D(1,0,0), new Static3D(-1,0,0),

           new Static3D(0,1,0), new Static3D(0,-1,0),

           new Static3D(0,0,1), new Static3D(0,0,-1)

         };

  private static final int[] FACE_COLORS = new int[]

         {

           0xffffff00, 0xffffffff,   // FACE_AXIS[0] (right-YELLOW) FACE_AXIS[1] (left  -WHITE)

           0xff0000ff, 0xff00ff00,   // FACE_AXIS[2] (top  -BLUE  ) FACE_AXIS[3] (bottom-GREEN)

           0xffff0000, 0xffb5651d    // FACE_AXIS[4] (front-RED   ) FACE_AXIS[5] (back  -BROWN)

         };

  // All legal rotation quats of a RubikCube of any size.

  // Here's how to compute this:

  // 1) compute how many rotations there are (RubikCube of any size = 24)

  // 2) take the AXIS, angles of rotation (90 in RubikCube's case) compute the basic quaternions

  // (i.e. rotations of 1 basic angle along each of the axis) and from there start semi-randomly

  // multiplying them and eventually you'll find all (24) legal rotations.

  // Example program in C, res/raw/compute_quats.c , is included.

  private static final Static4D[] QUATS = new Static4D[]

         {

         new Static4D(  0.0f,   0.0f,   0.0f,   1.0f),

         new Static4D(  1.0f,   0.0f,   0.0f,   0.0f),

         new Static4D(  0.0f,   1.0f,   0.0f,   0.0f),

         new Static4D(  0.0f,   0.0f,   1.0f,   0.0f),

         new Static4D( SQ2/2,  SQ2/2,  0.0f ,   0.0f),

         new Static4D( SQ2/2, -SQ2/2,  0.0f ,   0.0f),

         new Static4D( SQ2/2,   0.0f,  SQ2/2,   0.0f),

         new Static4D(-SQ2/2,   0.0f,  SQ2/2,   0.0f),

         new Static4D( SQ2/2,   0.0f,   0.0f,  SQ2/2),

         new Static4D( SQ2/2,   0.0f,   0.0f, -SQ2/2),

         new Static4D(  0.0f,  SQ2/2,  SQ2/2,   0.0f),

         new Static4D(  0.0f,  SQ2/2, -SQ2/2,   0.0f),

         new Static4D(  0.0f,  SQ2/2,   0.0f,  SQ2/2),

         new Static4D(  0.0f,  SQ2/2,   0.0f, -SQ2/2),

         new Static4D(  0.0f,   0.0f,  SQ2/2,  SQ2/2),

         new Static4D(  0.0f,   0.0f,  SQ2/2, -SQ2/2),

         new Static4D(  0.5f,   0.5f,   0.5f,   0.5f),

         new Static4D(  0.5f,   0.5f,  -0.5f,   0.5f),

         new Static4D(  0.5f,   0.5f,  -0.5f,  -0.5f),

         new Static4D(  0.5f,  -0.5f,   0.5f,  -0.5f),

         new Static4D( -0.5f,  -0.5f,  -0.5f,   0.5f),

         new Static4D( -0.5f,   0.5f,  -0.5f,  -0.5f),

         new Static4D( -0.5f,   0.5f,   0.5f,  -0.5f),

         new Static4D( -0.5f,   0.5f,   0.5f,   0.5f)

         };

  private static MeshBase[] mMeshes;

///////////////////////////////////////////////////////////////////////////////////////////////////

  RubikCube(int size, Static4D quat, DistortedTexture texture,

            MeshSquare mesh, DistortedEffects effects, int[][] moves, Resources res, int scrWidth)

    {

    super(size, 60, quat, texture, mesh, effects, moves, RubikObjectList.CUBE, res, scrWidth);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// paint the square with upper-right corner at (left,top) and side length 'side' with texture

// for face 'face'.

  void createFaceTexture(Canvas canvas, Paint paint, int face, int left, int top, int side)

    {

    final float R = side*0.10f;

    final float M = side*0.05f;

    paint.setColor(FACE_COLORS[face]);

    canvas.drawRoundRect( left+M, top+M, left+side-M, top+side-M, R, R, paint);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  Static3D[] getCubitPositions(int size)

    {

    int numCubits = size>1 ? 6*size*size - 12*size + 8 : 1;

    Static3D[] tmp = new Static3D[numCubits];

    float diff = 0.5f*(size-1);

    int currentPosition = 0;

    for(int x = 0; x<size; x++)

      for(int y = 0; y<size; y++)

        for(int z = 0; z<size; z++)

          if( x==0 || x==size-1 || y==0 || y==size-1 || z==0 || z==size-1 )

            {

            tmp[currentPosition++] = new Static3D(x-diff,y-diff,z-diff);

            }

    return tmp;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  Static4D[] getQuats()

    {

    return QUATS;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getNumFaces()

    {

    return FACE_COLORS.length;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getNumStickerTypes()

    {

    return 1;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getNumCubitFaces()

    {

    return FACE_COLORS.length;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  float getScreenRatio()

    {

    return 0.5f;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  int getFaceColor(int cubit, int cubitface, int size)

    {

    boolean belongs = isOnFace(cubit, cubitface/2, cubitface%2==0 ? size-1:0 );

    return belongs ? cubitface : NUM_FACES;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createCubitMesh(int cubit)

    {

    int size   = getSize();

    int ordinal= RubikObjectList.CUBE.ordinal();

    int index  = RubikObjectList.getSizeIndex(ordinal,size);

    float[] bands;

    float D = 0.027f;

    float E = 0.5f-D;

    float[] vertices = { -E,-E, +E,-E, +E,+E, -E,+E };

    int extraI, extraV;

    switch(size)

      {

      case 2 : bands = new float[] { 1.0f    ,-D,

                                     1.0f-D/2,-D*0.55f,

                                     1.0f-D  ,-D*0.25f,

                                     1.0f-2*D, 0.0f,

                                     0.50f, 0.040f,

                                     0.0f, 0.048f };

               extraI = 2;

               extraV = 2;

               break;

      case 3 : bands = new float[] { 1.0f    ,-D,

                                     1.0f-D*1.2f,-D*0.55f,

                                     1.0f-2*D, 0.0f,

                                     0.50f, 0.040f,

                                     0.0f, 0.048f };

               extraI = 2;

               extraV = 2;

               break;

      case 4 : bands = new float[] { 1.0f    ,-D,

                                     1.0f-D*1.2f,-D*0.55f,

                                     1.0f-2*D, 0.0f,

                                     0.50f, 0.040f,

                                     0.0f, 0.048f };

               extraI = 1;

               extraV = 2;

               break;

      default: bands = new float[] { 1.0f    ,-D,

                                     1.0f-2*D, 0.0f,

                                     0.50f, 0.025f,

                                     0.0f, 0.030f };

               extraI = 1;

               extraV = 1;

               break;

      }

    return createCubitMesh(index,vertices,bands,extraI,extraV);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createCubitMesh(int index, float[] vertices, float[] bands, int extraI, int extraV)

    {

    if( mMeshes==null )

      {

      mMeshes = new MeshBase[RubikObjectList.CUBE.getNumVariants()];

      }

    if( mMeshes[index]==null )

      {

      final int MESHES=6;

      int association = 1;

      MeshBase[] meshes = new MeshPolygon[MESHES];

      meshes[0] = new MeshPolygon(vertices,bands,extraI,extraV);

      meshes[0].setEffectAssociation(0,association,0);

      for(int i=1; i<MESHES; i++)

        {

        association <<=1;

        meshes[i] = meshes[0].copy(true);

        meshes[i].setEffectAssociation(0,association,0);

        }

      mMeshes[index] = new MeshJoined(meshes);

      Static3D axisY   = new Static3D(0,1,0);

      Static3D axisX   = new Static3D(1,0,0);

      Static3D center  = new Static3D(0,0,0);

      Static1D angle90 = new Static1D(90);

      Static1D angle180= new Static1D(180);

      Static1D angle270= new Static1D(270);

      float d1 = 1.0f;

      float d2 =-0.05f;

      float d3 = 0.12f;

      Static3D dCen0 = new Static3D( d1*(+0.5f), d1*(+0.5f), d1*(+0.5f) );

      Static3D dCen1 = new Static3D( d1*(+0.5f), d1*(+0.5f), d1*(-0.5f) );

      Static3D dCen2 = new Static3D( d1*(+0.5f), d1*(-0.5f), d1*(+0.5f) );

      Static3D dCen3 = new Static3D( d1*(+0.5f), d1*(-0.5f), d1*(-0.5f) );

      Static3D dCen4 = new Static3D( d1*(-0.5f), d1*(+0.5f), d1*(+0.5f) );

      Static3D dCen5 = new Static3D( d1*(-0.5f), d1*(+0.5f), d1*(-0.5f) );

      Static3D dCen6 = new Static3D( d1*(-0.5f), d1*(-0.5f), d1*(+0.5f) );

      Static3D dCen7 = new Static3D( d1*(-0.5f), d1*(-0.5f), d1*(-0.5f) );

      Static3D dVec0 = new Static3D( d2*(+0.5f), d2*(+0.5f), d2*(+0.5f) );

      Static3D dVec1 = new Static3D( d2*(+0.5f), d2*(+0.5f), d2*(-0.5f) );

      Static3D dVec2 = new Static3D( d2*(+0.5f), d2*(-0.5f), d2*(+0.5f) );

      Static3D dVec3 = new Static3D( d2*(+0.5f), d2*(-0.5f), d2*(-0.5f) );

      Static3D dVec4 = new Static3D( d2*(-0.5f), d2*(+0.5f), d2*(+0.5f) );

      Static3D dVec5 = new Static3D( d2*(-0.5f), d2*(+0.5f), d2*(-0.5f) );

      Static3D dVec6 = new Static3D( d2*(-0.5f), d2*(-0.5f), d2*(+0.5f) );

      Static3D dVec7 = new Static3D( d2*(-0.5f), d2*(-0.5f), d2*(-0.5f) );

      Static4D dReg  = new Static4D(0,0,0,d3);

      Static1D dRad  = new Static1D(1);

      VertexEffectMove   effect0 = new VertexEffectMove(new Static3D(0,0,+0.5f));

      effect0.setMeshAssociation(63,-1);  // all 6 sides

      VertexEffectRotate effect1 = new VertexEffectRotate( angle180, axisX, center );

      effect1.setMeshAssociation(32,-1);  // back

      VertexEffectRotate effect2 = new VertexEffectRotate( angle90 , axisX, center );

      effect2.setMeshAssociation( 8,-1);  // bottom

      VertexEffectRotate effect3 = new VertexEffectRotate( angle270, axisX, center );

      effect3.setMeshAssociation( 4,-1);  // top

      VertexEffectRotate effect4 = new VertexEffectRotate( angle270, axisY, center );

      effect4.setMeshAssociation( 2,-1);  // left

      VertexEffectRotate effect5 = new VertexEffectRotate( angle90 , axisY, center );

      effect5.setMeshAssociation( 1,-1);  // right

      VertexEffectDeform effect6 = new VertexEffectDeform(dVec0, dRad, dCen0, dReg);

      VertexEffectDeform effect7 = new VertexEffectDeform(dVec1, dRad, dCen1, dReg);

      VertexEffectDeform effect8 = new VertexEffectDeform(dVec2, dRad, dCen2, dReg);

      VertexEffectDeform effect9 = new VertexEffectDeform(dVec3, dRad, dCen3, dReg);

      VertexEffectDeform effect10= new VertexEffectDeform(dVec4, dRad, dCen4, dReg);

      VertexEffectDeform effect11= new VertexEffectDeform(dVec5, dRad, dCen5, dReg);

      VertexEffectDeform effect12= new VertexEffectDeform(dVec6, dRad, dCen6, dReg);

      VertexEffectDeform effect13= new VertexEffectDeform(dVec7, dRad, dCen7, dReg);

      mMeshes[index].apply(effect0);

      mMeshes[index].apply(effect1);

      mMeshes[index].apply(effect2);

      mMeshes[index].apply(effect3);

      mMeshes[index].apply(effect4);

      mMeshes[index].apply(effect5);

      mMeshes[index].apply(effect6);

      mMeshes[index].apply(effect7);

      mMeshes[index].apply(effect8);

      mMeshes[index].apply(effect9);

      mMeshes[index].apply(effect10);

      mMeshes[index].apply(effect11);

      mMeshes[index].apply(effect12);

      mMeshes[index].apply(effect13);

      mMeshes[index].mergeEffComponents();

      }

    return mMeshes[index].copy(true);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  float returnMultiplier()

    {

    return getSize();

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  float[] getRowChances()

    {

    int size = getSize();

    float[] chances = new float[size];

    for(int i=0; i<size; i++)

      {

      chances[i] = (i+1.0f) / size;

      }

    return chances;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// PUBLIC API

  public Static3D[] getRotationAxis()

    {

    return ROT_AXIS;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public int getBasicAngle()

    {

    return 4;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public int computeRowFromOffset(float offset)

    {

    return (int)(getSize()*offset);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public float returnRotationFactor(float offset)

    {

    return 1.0f;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public int randomizeNewRotAxis(Random rnd, int oldRotAxis)

    {

    int numAxis = ROTATION_AXIS.length;

    if( oldRotAxis == START_AXIS )

      {

      return rnd.nextInt(numAxis);

      }

    else

      {

      int newVector = rnd.nextInt(numAxis-1);

      return (newVector>=oldRotAxis ? newVector+1 : newVector);

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public int randomizeNewRow(Random rnd, int oldRotAxis, int oldRow, int newRotAxis)

    {

    float rowFloat = rnd.nextFloat();

    for(int row=0; row<mRowChances.length; row++)

      {

      if( rowFloat<=mRowChances[row] ) return row;

      }

    return 0;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public boolean isSolved()

    {

    int index = CUBITS[0].mQuatIndex;

    for(int i=1; i<NUM_CUBITS; i++)

      {

      if( !thereIsNoVisibleDifference(CUBITS[i], index) ) return false;

      }

    return true;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// return if the Cubit, when rotated with its own mQuatScramble, would have looked any different

// then if it were rotated by quaternion 'quat'.

// No it is not so simple as the quats need to be the same - imagine a 4x4x4 cube where the two

// middle squares get interchanged. No visible difference!

//

// So: this is true iff the cubit

// a) is a corner or edge and the quaternions are the same

// b) is inside one of the faces and after rotations by both quats it ends up on the same face.

  private boolean thereIsNoVisibleDifference(Cubit cubit, int quatIndex)

    {

    if ( cubit.mQuatIndex == quatIndex ) return true;

    int belongsToHowManyFaces = 0;

    int size = getSize()-1;

    float row;

    final float MAX_ERROR = 0.01f;

    for(int i=0; i<NUM_AXIS; i++)

      {

      row = cubit.mRotationRow[i];

      if( (row     <MAX_ERROR && row     >-MAX_ERROR) ||

          (row-size<MAX_ERROR && row-size>-MAX_ERROR)  ) belongsToHowManyFaces++;

      }

    switch(belongsToHowManyFaces)

      {

      case 0 : return true ;  // 'inside' cubit that does not lie on any face

      case 1 :                // cubit that lies inside one of the faces

               Static3D orig = cubit.getOrigPosition();

               Static4D quat1 = QUATS[quatIndex];

               Static4D quat2 = QUATS[cubit.mQuatIndex];

               Static4D cubitCenter = new Static4D( orig.get0(), orig.get1(), orig.get2(), 0);

               Static4D rotated1 = RubikSurfaceView.rotateVectorByQuat( cubitCenter, quat1 );

               Static4D rotated2 = RubikSurfaceView.rotateVectorByQuat( cubitCenter, quat2 );

               float row1, row2, row3, row4;

               float ax,ay,az;

               Static3D axis;

               float x1 = rotated1.get0();

               float y1 = rotated1.get1();

               float z1 = rotated1.get2();

               float x2 = rotated2.get0();

               float y2 = rotated2.get1();

               float z2 = rotated2.get2();

               for(int i=0; i<NUM_AXIS; i++)

                 {

                 axis = ROTATION_AXIS[i];

                 ax = axis.get0();

                 ay = axis.get1();

                 az = axis.get2();

                 row1 = ((x1*ax + y1*ay + z1*az) - mStart) / mStep;

                 row2 = ((x2*ax + y2*ay + z2*az) - mStart) / mStep;

                 row3 = row1 - size;

                 row4 = row2 - size;

                 if( (row1<MAX_ERROR && row1>-MAX_ERROR && row2<MAX_ERROR && row2>-MAX_ERROR) ||

                     (row3<MAX_ERROR && row3>-MAX_ERROR && row4<MAX_ERROR && row4>-MAX_ERROR)  )

                   {

                   return true;

                   }

                 }

               return false;

      default: return false;  // edge or corner

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// order: Up --> Right --> Front --> Down --> Left --> Back

// (because the first implemented Solver - the two-phase Cube3 one - expects such order)

//

// Solved 3x3x3 Cube maps to "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB"

//

// s : size of the cube; let index = a*s + b    (i.e. a,b = row,column)

//

// Up    :   index --> b<s-1 ? (s-1)*(s+4b)+a : 6*s*s -13*s +8 +a

// Right :   index --> 6*s*s - 12*s + 7 - index

// Front :   index --> if b==0  : s*s - 1 - index

//                     if b==s-1: 6*s*s -11*s +6 - index

//                     else

//                         a==0: s*s + s-1 + 4*(b-1)*(s-1) + 2*(s-2) + s

//                         else: s*s + s-1 + 4*(b-1)*(s-1) + 2*(s-1-a)

// Down  :   index --> b==0 ? (s-1-a) : s*s + s-1 + 4*(b-1)*(s-1) - a

// Left  :   index --> (s-1-a)*s + b

// Back  :   index --> if b==s-1: s*(s-1-a)

//                     if b==0  : 5*s*s -12*s + 8 + (s-1-a)*s

//                     else

//                        if a==s-1: s*s + 4*(s-2-b)*(s-1)

//                        else     : s*s + 4*(s-2-b)*(s-1) + s + (s-2-a)*2

  public String retObjectString()

    {

    StringBuilder objectString = new StringBuilder();

    int size = getSize();

    int len = size*size;

    int cubitIndex=-1, row=-1, col=-1;

    int color=-1, face=-1;

    final int RIGHT= 0;

    final int LEFT = 1;

    final int UP   = 2;

    final int DOWN = 3;

    final int FRONT= 4;

    final int BACK = 5;

    // 'I' - interior, theoretically can happen

    final char[] FACE_NAMES = { 'R', 'L', 'U', 'D', 'F', 'B', 'I'};

    face = UP;

    for(int i=0; i<len; i++)

      {

      row = i/size;

      col = i%size;

      cubitIndex = col<size-1 ? (size-1)*(size+4*col) + row : 6*size*size - 13*size + 8 + row;

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = RIGHT;

    for(int i=0; i<len; i++)

      {

      cubitIndex = 6*size*size - 12*size +7 - i;

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

     face = FRONT;

    for(int i=0; i<len; i++)

      {

      row = i/size;

      col = i%size;

      if( col==size-1 ) cubitIndex = 6*size*size - 11*size + 6 -i;

      else if( col==0 ) cubitIndex = size*size - 1 - i;

      else

        {

        if( row==0 ) cubitIndex = size*size + size-1 + 4*(col-1)*(size-1) + 2*(size-2) + size;

        else         cubitIndex = size*size + size-1 + 4*(col-1)*(size-1) + 2*(size-1-row);

        }

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = DOWN;

    for(int i=0; i<len; i++)

      {

      row = i/size;

      col = i%size;

      cubitIndex = col==0 ? size-1-row : size*size + size-1 + 4*(col-1)*(size-1) - row;

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = LEFT;

    for(int i=0; i<len; i++)

      {

      row = i/size;

      col = i%size;

      cubitIndex = (size-1-row)*size + col;

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = BACK;

    for(int i=0; i<len; i++)

      {

      row = i/size;

      col = i%size;

      if( col==size-1 ) cubitIndex = size*(size-1-row);

      else if( col==0 ) cubitIndex = 5*size*size - 12*size + 8 + (size-1-row)*size;

      else

        {

        if( row==size-1 ) cubitIndex = size*size + 4*(size-2-col)*(size-1);

        else              cubitIndex = size*size + 4*(size-2-col)*(size-1) + size + 2*(size-2-row);

        }

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    return objectString.toString();

    }

}