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.helpers.FactoryCubit;

import org.distorted.helpers.FactorySticker;

import org.distorted.library.main.DistortedEffects;

import org.distorted.library.main.DistortedTexture;

import org.distorted.library.mesh.MeshBase;

import org.distorted.library.mesh.MeshSquare;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

import org.distorted.main.R;

import java.util.Random;

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

class TwistyCube extends TwistyObject

{

  // 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)

         };

  private static final int[] BASIC_ANGLE = new int[] { 4,4,4 };

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

         {

           COLOR_YELLOW, COLOR_WHITE,

           COLOR_BLUE  , COLOR_GREEN,

           COLOR_RED   , COLOR_ORANGE

         };

  // 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 final double[][] VERTICES = new double[][]

          {

              { 0.5, 0.5, 0.5 },

              { 0.5, 0.5,-0.5 },

              { 0.5,-0.5, 0.5 },

              { 0.5,-0.5,-0.5 },

              {-0.5, 0.5, 0.5 },

              {-0.5, 0.5,-0.5 },

              {-0.5,-0.5, 0.5 },

              {-0.5,-0.5,-0.5 },

          };

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

          {

              {2,3,1,0},   // counterclockwise!

              {7,6,4,5},

              {4,0,1,5},

              {7,3,2,6},

              {6,2,0,4},

              {3,7,5,1}

          };

  private static final float[][] STICKERS = new float[][]

          {

              { -0.5f, -0.5f, 0.5f, -0.5f, 0.5f, 0.5f, -0.5f, 0.5f }

          };

  private static MeshBase[] mMeshes;

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

  TwistyCube(int size, Static4D quat, DistortedTexture texture,

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

    {

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

    }

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

  MeshBase createCubitMesh(int cubit, int numLayers)

    {

    if( mMeshes==null )

      {

      FactoryCubit factory = FactoryCubit.getInstance();

      factory.clear();

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

      }

    int ordinal= ObjectList.CUBE.ordinal();

    int index  = ObjectList.getSizeIndex(ordinal,getNumLayers());

    if( mMeshes[index]==null )

      {

      int extraI, extraV, num;

      float height;

      switch(numLayers)

        {

        case 2 : num = 6; extraI = 2; extraV = 2; height = 0.045f; break;

        case 3 : num = 5; extraI = 2; extraV = 2; height = 0.045f; break;

        case 4 : num = 5; extraI = 1; extraV = 1; height = 0.045f; break;

        default: num = 5; extraI = 0; extraV = 0; height = 0.045f; break;

        }

      float[][] bands     = new float[][] { {height,35,0.5f,0.7f,num,extraI,extraV} };

      int[] bandIndexes   = new int[] { 0,0,0,0,0,0};

      float[][] corners   = new float[][] { {0.036f,0.12f} };

      int[] cornerIndexes = new int[] { 0,0,0,0,0,0,0,0 };

      float[][] centers   = new float[][] { {0.0f, 0.0f, 0.0f} };

      int[] centerIndexes = new int[] { 0,0,0,0,0,0,0,0 };

      FactoryCubit factory = FactoryCubit.getInstance();

      factory.createNewFaceTransform(VERTICES,VERT_INDEXES);

      mMeshes[index] = factory.createRoundedSolid(VERTICES, VERT_INDEXES,

                                                  bands, bandIndexes,

                                                  corners, cornerIndexes,

                                                  centers, centerIndexes,

                                                  getNumCubitFaces() );

      }

    return mMeshes[index].copy(true);

    }

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

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

    {

    float R = 0.10f;

    float S = 0.08f;

    FactorySticker factory = FactorySticker.getInstance();

    factory.drawRoundedPolygon(canvas, paint, left, top, STICKERS[0], S, FACE_COLORS[face], R);

    }

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

  float[][] getCubitPositions(int numLayers)

    {

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

    float[][] tmp = new float[numCubits][];

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

    int currentPosition = 0;

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

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

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

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

            {

            tmp[currentPosition++] = new float[] {x-diff,y-diff,z-diff};

            }

    return tmp;

    }

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

  Static4D[] getQuats()

    {

    return QUATS;

    }

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

  boolean shouldResetTextureMaps()

    {

    return false;

    }

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

  int getNumFaces()

    {

    return FACE_COLORS.length;

    }

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

  float[][] getCuts(int numLayers)

    {

    float[][] cuts = new float[3][numLayers-1];

    for(int i=0; i<numLayers-1; i++)

      {

      float cut = (2-numLayers)*0.5f + i;

      cuts[0][i] = cut;

      cuts[1][i] = cut;

      cuts[2][i] = cut;

      }

    return cuts;

    }

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

  int getNumStickerTypes(int numLayers)

    {

    return STICKERS.length;

    }

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

  int getNumCubitFaces()

    {

    return FACE_COLORS.length;

    }

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

  float getScreenRatio()

    {

    return 0.5f;

    }

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

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

    {

    return CUBITS[cubit].mRotationRow[cubitface/2] == (cubitface%2==0 ? (1<<(size-1)):1) ? cubitface : NUM_FACES;

    }

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

  float returnMultiplier()

    {

    return getNumLayers();

    }

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

// PUBLIC API

  public Static3D[] getRotationAxis()

    {

    return ROT_AXIS;

    }

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

  public int[] getBasicAngle()

    {

    return BASIC_ANGLE;

    }

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

  public void randomizeNewScramble(int[][] scramble, Random rnd, int curr, int total)

    {

    if( curr==0 )

      {

      scramble[curr][0] = rnd.nextInt(NUM_AXIS);

      }

    else

      {

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

      scramble[curr][0] = (newVector>=scramble[curr-1][0] ? newVector+1 : newVector);

      // All three axis must be present among every four consecutive rotations.

      // Otherwise in case of odd-sized cubes we can get four consecutive rotations

      // that collapse to a NOP

      // (X,midLayer,180)->(Y,midLayer,180)->(X,midLayer,180)->(Y,midLayer,180) = NOP

      if( curr>=3 && scramble[curr-1][0]==scramble[curr-3][0] )

        {

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

          {

          if( scramble[curr-1][0]!=ax && scramble[curr-2][0]!=ax )

            {

            scramble[curr][0] = ax;

            break;

            }

          }

        }

      }

    float rowFloat = rnd.nextFloat();

    int numLayers = getNumLayers();

    for(int row=0; row<numLayers; row++)

      {

      if( rowFloat*numLayers <= row+1 )

        {

        scramble[curr][1] = row;

        break;

        }

      }

    switch( rnd.nextInt(4) )

      {

      case 0: scramble[curr][2] = -2; break;

      case 1: scramble[curr][2] = -1; break;

      case 2: scramble[curr][2] =  1; break;

      case 3: scramble[curr][2] =  2; break;

      }

    }

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

  public boolean isSolved()

    {

    int index = CUBITS[0].mQuatIndex;

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

      {

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

      }

    return true;

    }

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

// 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 layers = getNumLayers();

    int len = layers*layers;

    int cubitIndex, row, col, color,face;

    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/layers;

      col = i%layers;

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

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = RIGHT;

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

      {

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

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = FRONT;

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

      {

      row = i/layers;

      col = i%layers;

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

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

      else

        {

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

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

        }

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = DOWN;

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

      {

      row = i/layers;

      col = i%layers;

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

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = LEFT;

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

      {

      row = i/layers;

      col = i%layers;

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

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    face = BACK;

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

      {

      row = i/layers;

      col = i%layers;

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

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

      else

        {

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

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

        }

      color = getCubitFaceColorIndex(cubitIndex,face);

      objectString.append(FACE_NAMES[color]);

      }

    return objectString.toString();

    }

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

  public int getObjectName(int numLayers)

    {

    switch(numLayers)

      {

      case 2: return R.string.cube2;

      case 3: return R.string.cube3;

      case 4: return R.string.cube4;

      case 5: return R.string.cube5;

      }

    return R.string.cube3;

    }

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

  public int getInventor(int numLayers)

    {

    switch(numLayers)

      {

      case 2: return R.string.cube2_inventor;

      case 3: return R.string.cube3_inventor;

      case 4: return R.string.cube4_inventor;

      case 5: return R.string.cube5_inventor;

      }

    return R.string.cube3_inventor;

    }

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

  public int getComplexity(int numLayers)

    {

    switch(numLayers)

      {

      case 2: return 4;

      case 3: return 6;

      case 4: return 8;

      case 5: return 10;

      }

    return 6;

    }

}