Magic Cube

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

// Copyright 2020 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.effect.MatrixEffectQuaternion;

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 org.distorted.main.RubikSurfaceView;

import java.util.Random;

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

public class TwistyDiamond extends TwistyObject

{

  private static final int FACES_PER_CUBIT =8;

  // the four rotation axis of a Diamond. Must be normalized.

  static final Static3D[] ROT_AXIS = new Static3D[]

         {

           new Static3D(+SQ6/3,+SQ3/3,     0),

           new Static3D(-SQ6/3,+SQ3/3,     0),

           new Static3D(     0,-SQ3/3,-SQ6/3),

           new Static3D(     0,-SQ3/3,+SQ6/3)

         };

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

         {

           COLOR_ORANGE, COLOR_VIOLET,

           COLOR_WHITE , COLOR_BLUE  ,

           COLOR_YELLOW, COLOR_RED   ,

           COLOR_GREEN , COLOR_GREY

         };

  // All legal rotation quats of a Diamond: unit + three 180 deg turns + 8 generators

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

         {

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

           new Static4D(  0.0f,  1.0f,   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,  0.5f,   0.0f,  0.5f ),

           new Static4D(-SQ2/2,  0.5f,   0.0f,  0.5f ),

           new Static4D(  0.0f,  0.5f, +SQ2/2,  0.5f ),

           new Static4D(  0.0f,  0.5f, -SQ2/2,  0.5f ),

           new Static4D(+SQ2/2,  0.5f,   0.0f, -0.5f ),

           new Static4D(-SQ2/2,  0.5f,   0.0f, -0.5f ),

           new Static4D(  0.0f,  0.5f, +SQ2/2, -0.5f ),

           new Static4D(  0.0f,  0.5f, -SQ2/2, -0.5f )

         };

  private static final float DIST = 0.50f;

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

         {

             {6,10},

             {4, 8},

             {7,11},

             {5, 9},

             {7,11},

             {5, 9},

             {6,10},

             {4, 8}

         };

  private static final int[] mTetraToFaceMap = new int[] {1,2,3,0,5,6,7,4};

  private static final double[][] VERTICES_TETRA = new double[][]

          {

             {-0.5, SQ2/4, 0.0},

             { 0.5, SQ2/4, 0.0},

             { 0.0,-SQ2/4, 0.5},

             { 0.0,-SQ2/4,-0.5}

          };

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

          {

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

             {2,3,1},

             {3,2,0},

             {3,0,1}

          };

  private static final double[][] VERTICES_OCTA = new double[][]

          {

             { 0.5,   0.0, 0.5},

             { 0.5,   0.0,-0.5},

             {-0.5,   0.0,-0.5},

             {-0.5,   0.0, 0.5},

             { 0.0, SQ2/2, 0.0},

             { 0.0,-SQ2/2, 0.0}

          };

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

          {

             {3,0,4},   // counterclockwise!

             {0,1,4},

             {1,2,4},

             {2,3,4},

             {5,0,3},

             {5,1,0},

             {5,2,1},

             {5,3,2}

          };

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

          {

             { -0.4330127f, -0.25f, 0.4330127f, -0.25f, 0.0f, 0.5f }

          };

  private static MeshBase[] mMeshes;

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

  TwistyDiamond(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.DIAM, res, scrWidth);

    }

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

  double[][] getVertices(int cubitType)

    {

    if( cubitType==0 ) return VERTICES_OCTA;

    if( cubitType==1 ) return VERTICES_TETRA;

    return null;

    }

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

  int[][] getVertIndexes(int cubitType)

    {

    if( cubitType==0 ) return VERT_INDEXES_OCTA;

    if( cubitType==1 ) return VERT_INDEXES_TETRA;

    return null;

    }

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

  int getNumCubitTypes(int numLayers)

    {

    return 2;

    }

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

  float getScreenRatio()

    {

    return 0.65f;

    }

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

  Static4D[] getQuats()

    {

    return QUATS;

    }

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

  int getNumFaces()

    {

    return FACE_COLORS.length;

    }

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

  boolean shouldResetTextureMaps()

    {

    return false;

    }

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

  int getNumStickerTypes(int numLayers)

    {

    return STICKERS.length;

    }

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

  float[] getCuts(int numLayers)

    {

    if( numLayers<2 )

      {

      return null;

      }

    else

      {

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

      float dist = SQ6*0.666f*DIST;

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

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

        {

        cuts[i] = cut;

        cut += dist;

        }

      return cuts;

      }

    }

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

  int getNumCubitFaces()

    {

    return FACES_PER_CUBIT;

    }

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

  private int getNumOctahedrons(int layers)

    {

    return layers==1 ? 1 : 4*(layers-1)*(layers-1) + 2;

    }

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

  private int getNumTetrahedrons(int layers)

    {

    return 4*layers*(layers-1);

    }

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

  private int createOctaPositions(float[][] centers, int index, int layers, float height)

    {

    float x = DIST*(layers-1);

    float z = DIST*(layers+1);

    for(int i=0; i<layers; i++, index++)

      {

      z -= 2*DIST;

      centers[index][0] = x;

      centers[index][1] = height;

      centers[index][2] = z;

      }

    for(int i=0; i<layers-1; i++, index++)

      {

      x -= 2*DIST;

      centers[index][0] = x;

      centers[index][1] = height;

      centers[index][2] = z;

      }

    for(int i=0; i<layers-1; i++, index++)

      {

      z += 2*DIST;

      centers[index][0] = x;

      centers[index][1] = height;

      centers[index][2] = z;

      }

    for(int i=0; i<layers-2; i++, index++)

      {

      x += 2*DIST;

      centers[index][0] = x;

      centers[index][1] = height;

      centers[index][2] = z;

      }

    return index;

    }

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

  private int createTetraPositions(float[][] centers, int index, int layers, float height)

    {

    float x = DIST*(layers-1);

    float z = DIST*layers;

    for(int i=0; i<layers-1; i++, index++)

      {

      z -= 2*DIST;

      centers[index][0] = x;

      centers[index][1] = height;

      centers[index][2] = z;

      }

    x += DIST;

    z -= DIST;

    for(int i=0; i<layers-1; i++, index++)

      {

      x -= 2*DIST;

      centers[index][0] = x;

      centers[index][1] = height;

      centers[index][2] = z;

      }

    x -= DIST;

    z -= DIST;

    for(int i=0; i<layers-1; i++, index++)

      {

      z += 2*DIST;

      centers[index][0] = x;

      centers[index][1] = height;

      centers[index][2] = z;

      }

    x -= DIST;

    z += DIST;

    for(int i=0; i<layers-1; i++, index++)

      {

      x += 2*DIST;

      centers[index][0] = x;

      centers[index][1] = height;

      centers[index][2] = z;

      }

    return index;

    }

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

  float[][] getCubitPositions(int layers)

    {

    int numO = getNumOctahedrons(layers);

    int numT = getNumTetrahedrons(layers);

    int index = 0;

    float height = 0.0f;

    float[][] CENTERS = new float[numO+numT][3];

    index = createOctaPositions(CENTERS,index,layers,height);

    for(int i=layers-1; i>0; i--)

      {

      height += SQ2*DIST;

      index = createOctaPositions(CENTERS,index,i,+height);

      index = createOctaPositions(CENTERS,index,i,-height);

      }

    height = DIST*SQ2/2;

    for(int i=layers; i>1; i--)

      {

      index = createTetraPositions(CENTERS,index,i,+height);

      index = createTetraPositions(CENTERS,index,i,-height);

      height += SQ2*DIST;

      }

    return CENTERS;

    }

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

  private int retFaceTetraBelongsTo(int tetra, int numLayers)

    {

    for(int i=numLayers-1; i>0; i--)

      {

      if( tetra < 8*i ) return mTetraToFaceMap[tetra/i];

      tetra -= 8*i;

      }

    return -1;

    }

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

  private Static4D getQuat(int cubit, int numLayers, int numO)

    {

    if( cubit<numO ) return QUATS[0];

    switch( retFaceTetraBelongsTo(cubit-numO, numLayers) )

      {

      case 0: return QUATS[0];                          // unit quat

      case 1: return new Static4D(0,-SQ2/2,0,SQ2/2);    //  90 along Y

      case 2: return QUATS[1];                          // 180 along Y

      case 3: return new Static4D(0,+SQ2/2,0,SQ2/2);    //  90 along

      case 4: return new Static4D(0,     0,1,    0);    // 180 along Z

      case 5: return new Static4D(SQ2/2, 0,SQ2/2,0);    //

      case 6: return new Static4D(     1,0,0,    0);    // 180 along X

      case 7: return new Static4D(-SQ2/2,0,SQ2/2,0);    //

      }

    return null;

    }

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

  MeshBase createCubitMesh(int cubit, int numLayers)

    {

    if( mMeshes==null )

      {

      FactoryCubit factory = FactoryCubit.getInstance();

      factory.clear();

      mMeshes = new MeshBase[2];

      }

    MeshBase mesh;

    int numO = getNumOctahedrons(numLayers);

    if( cubit<numO )

      {

      if( mMeshes[0]==null )

        {

        float[][] bands     = new float[][] { {0.05f,35,0.5f,0.8f,6,2,2} };

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

        float[][] corners   = new float[][] { {0.04f,0.20f} };

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

        FactoryCubit factory = FactoryCubit.getInstance();

        factory.createNewFaceTransform(VERTICES_OCTA,VERT_INDEXES_OCTA);

        mMeshes[0] = factory.createRoundedSolid(VERTICES_OCTA, VERT_INDEXES_OCTA,

                                                bands, bandIndexes,

                                                corners, cornerIndexes,

                                                getNumCubitFaces() );

        }

      mesh = mMeshes[0].copy(true);

      }

    else

      {

      if( mMeshes[1]==null )

        {

        float[][] bands     = new float[][] { {0.05f,35,0.5f,0.8f,6,2,2} };

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

        float[][] corners   = new float[][] { {0.08f,0.15f} };

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

        FactoryCubit factory = FactoryCubit.getInstance();

        factory.createNewFaceTransform(VERTICES_TETRA,VERT_INDEXES_TETRA);

        mMeshes[1] = factory.createRoundedSolid(VERTICES_TETRA, VERT_INDEXES_TETRA,

                                                bands, bandIndexes,

                                                corners, cornerIndexes,

                                                getNumCubitFaces() );

        }

      mesh = mMeshes[1].copy(true);

      }

    Static4D sQ = getQuat(cubit,numLayers,numO);

    MatrixEffectQuaternion quat = new MatrixEffectQuaternion( sQ, new Static3D(0,0,0) );

    mesh.apply(quat,0xffffffff,0);

    return mesh;

    }

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

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

    {

    int numO = getNumOctahedrons(size);

    if( cubit<numO )

      {

      int axis = 0;

      int layer= 1;

      switch(cubitface)

        {

        case 0: axis = 2; layer =             1; break;

        case 1: axis = 0; layer = (1<<(size-1)); break;

        case 2: axis = 3; layer =             1; break;

        case 3: axis = 1; layer = (1<<(size-1)); break;

        case 4: axis = 3; layer = (1<<(size-1)); break;

        case 5: axis = 1; layer =             1; break;

        case 6: axis = 2; layer = (1<<(size-1)); break;

        case 7: axis = 0; layer =             1; break;

        }

      return CUBITS[cubit].mRotationRow[axis] == layer ? cubitface : NUM_TEXTURES;

      }

    else

      {

      return cubitface>0 ? NUM_TEXTURES : retFaceTetraBelongsTo(cubit-numO, size);

      }

    }

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

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

    {

    float R = 0.06f;

    float S = 0.07f;

    FactorySticker factory = FactorySticker.getInstance();

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

    }

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

  float returnMultiplier()

    {

    return 1.5f;

    }

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

  float[] getRowChances(int numLayers)

    {

    float[] chances = new float[numLayers];

    for(int i=0; i<numLayers; i++) chances[i] = ((float)(i+1))/numLayers;

    return chances;

    }

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

// PUBLIC API

  public Static3D[] getRotationAxis()

    {

    return ROT_AXIS;

    }

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

  public int getBasicAngle()

    {

    return 3;

    }

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

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

    {

    if( num==0 )

      {

      scramble[num][0] = rnd.nextInt(ROTATION_AXIS.length);

      }

    else

      {

      int newVector = rnd.nextInt(ROTATION_AXIS.length-1);

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

      }

    float rowFloat = rnd.nextFloat();

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

      {

      if( rowFloat<=mRowChances[row] )

        {

        scramble[num][1] = row;

        break;

        }

      }

    switch( rnd.nextInt(2) )

      {

      case 0: scramble[num][2] = -1; break;

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

      }

    }

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

  int mulQuat(int q1, int q2)

    {

    Static4D result = RubikSurfaceView.quatMultiply(QUATS[q1],QUATS[q2]);

    float rX = result.get0();

    float rY = result.get1();

    float rZ = result.get2();

    float rW = result.get3();

    final float MAX_ERROR = 0.1f;

    float dX,dY,dZ,dW;

    for(int i=0; i<QUATS.length; i++)

      {

      dX = QUATS[i].get0() - rX;

      dY = QUATS[i].get1() - rY;

      dZ = QUATS[i].get2() - rZ;

      dW = QUATS[i].get3() - rW;

      if( dX<MAX_ERROR && dX>-MAX_ERROR &&

          dY<MAX_ERROR && dY>-MAX_ERROR &&

          dZ<MAX_ERROR && dZ>-MAX_ERROR &&

          dW<MAX_ERROR && dW>-MAX_ERROR  ) return i;

      dX = QUATS[i].get0() + rX;

      dY = QUATS[i].get1() + rY;

      dZ = QUATS[i].get2() + rZ;

      dW = QUATS[i].get3() + rW;

      if( dX<MAX_ERROR && dX>-MAX_ERROR &&

          dY<MAX_ERROR && dY>-MAX_ERROR &&

          dZ<MAX_ERROR && dZ>-MAX_ERROR &&

          dW<MAX_ERROR && dW>-MAX_ERROR  ) return i;

      }

    return -1;

    }

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

// The Diamond is solved if and only if:

//

// 1) all octahedrons are rotated with the same quat

// 2) all tetrahedrons might be also optionally rotated by a 'face neutral' pair of quats

//    (indexes of those are kept in the 'mFaceNeutralQuattIndex' table)

//

// Note: this works for any size, because even if layers>3 - and then there are 'face-internal'

// octahedrons which, it would seem, can be rotated by those 'face neutral' pairs of quats - but

// in reality no, because if they were, the octahedrons would then not fit in the lattice...

  public boolean isSolved()

    {

    int q = CUBITS[0].mQuatIndex;

    int layers = getNumLayers();

    int numO = getNumOctahedrons(layers);

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

      {

      if( CUBITS[i].mQuatIndex != q ) return false;

      }

    int qI, q1Index, q2Index, face;

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

      {

      face    = retFaceTetraBelongsTo(i-numO,layers);

      q1Index = mFaceNeutralQuatIndex[face][0];

      q2Index = mFaceNeutralQuatIndex[face][1];

      qI      = CUBITS[i].mQuatIndex;

      if(  qI != q && qI != mulQuat(q,q1Index) && qI != mulQuat(q,q2Index) ) return false;

      }

    return true;

    }

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

// only needed for solvers - there are no Diamond solvers ATM

  public String retObjectString()

    {

    return "";

    }

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

  public int getObjectName(int numLayers)

    {

    switch(numLayers)

      {

      case 2: return R.string.diam2;

      case 3: return R.string.diam3;

      }

    return 0;

    }

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

  public int getInventor(int numLayers)

    {

    switch(numLayers)

      {

      case 2: return R.string.diam2_inventor;

      case 3: return R.string.diam3_inventor;

      }

    return 0;

    }

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

  public int getComplexity(int numLayers)

    {

    switch(numLayers)

      {

      case 2: return 5;

      case 3: return 7;

      }

    return 0;

    }

}