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.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 static org.distorted.objects.FactoryCubit.COS18;

import static org.distorted.objects.FactoryCubit.COS54;

import static org.distorted.objects.FactoryCubit.SIN18;

import static org.distorted.objects.FactoryCubit.SIN54;

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

public class TwistyMegaminx extends TwistyMinx

{

  static final float MEGA_D = 0.04f;

  private static final int NUM_CORNERS = 20;

  private static final int NUM_CENTERS = 12;

  private static final int NUM_EDGES   = 30;

  // the five vertices that form a given face. Order: the same as colors

  // of the faces in TwistyMinx.

  private static final int[][] mCenterMap =

         {

           { 0, 12,  4, 14,  2},

           { 0,  2, 18,  6, 16},

           { 6, 18, 11, 19,  7},

           { 3, 15,  9, 11, 19},

           { 4,  5, 15,  9, 14},

           { 1, 13,  5, 15,  3},

           { 1,  3, 19,  7, 17},

           {10, 16,  6,  7, 17},

           { 0, 12,  8, 10, 16},

           { 8, 13,  5,  4, 12},

           { 1, 13,  8, 10, 17},

           { 2, 14,  9, 11, 18},

         };

  // the quadruple ( vertex1, vertex2, face1, face2 ) defining an edge.

  // In fact the 2 vertices already define it, the faces only provide easy

  // way to get to know the colors. Order: arbitrary. Face1 arbitrarily on

  // the 'left' or right of vector vertex1 --> vertex2, according to Quat.

  private static final int[][] mEdgeMap =

         {

           {  0, 12,  0,  8},

           { 12,  4,  0,  9},

           {  4, 14,  0,  4},

           { 14,  2,  0, 11},

           {  2,  0,  0,  1},

           { 14,  9,  4, 11},

           {  9, 11,  3, 11},

           { 11, 18,  2, 11},

           { 18,  2,  1, 11},

           { 18,  6,  1,  2},

           {  6, 16,  1,  7},

           { 16,  0,  8,  1},

           { 16, 10,  7,  8},

           { 10,  8, 10,  8},

           {  8, 12,  9,  8},

           {  8, 13,  9, 10},

           { 13,  5,  9,  5},

           {  5,  4,  9,  4},

           {  5, 15,  5,  4},

           { 15,  9,  3,  4},

           { 11, 19,  2,  3},

           { 19,  7,  2,  6},

           {  7,  6,  2,  7},

           {  7, 17,  7,  6},

           { 17, 10,  7, 10},

           { 17,  1, 10,  6},

           {  1,  3,  5,  6},

           {  3, 19,  3,  6},

           {  1, 13, 10,  5},

           {  3, 15,  3,  5},

         };

  private static final int[] QUAT_EDGE_INDICES =

      {

        56, 40, 43, 59,  0, 55, 10, 17, 25, 49,

        48, 57, 18,  7, 53, 32, 20, 11, 31, 38,

        37, 30,  8, 28, 36, 44,  1, 46, 12, 14

      };

  private static final int[] QUAT_CENTER_INDICES =

      {

        16, 18, 22,  1, 20, 13, 14, 15,  0, 12,  2,  3

      };

  private static final float[][] mCenterCoords = new float[NUM_CENTERS][3];

  static

    {

    for(int center=0; center<NUM_CENTERS; center++)

      {

      int[] map = mCenterMap[center];

      float x = CORNERS[map[0]].get0() +

                CORNERS[map[1]].get0() +

                CORNERS[map[2]].get0() +

                CORNERS[map[3]].get0() +

                CORNERS[map[4]].get0() ;

      float y = CORNERS[map[0]].get1() +

                CORNERS[map[1]].get1() +

                CORNERS[map[2]].get1() +

                CORNERS[map[3]].get1() +

                CORNERS[map[4]].get1() ;

      float z = CORNERS[map[0]].get2() +

                CORNERS[map[1]].get2() +

                CORNERS[map[2]].get2() +

                CORNERS[map[3]].get2() +

                CORNERS[map[4]].get2() ;

      mCenterCoords[center][0] = x/5;

      mCenterCoords[center][1] = y/5;

      mCenterCoords[center][2] = z/5;

      }

    }

  private static MeshBase[] mCenterMeshes, mCornerMeshes;

  private static MeshBase[][] mEdgeMeshes;

  private static final Static4D[] mBasicCornerV, mCurrCornerV;

  static

    {

    mBasicCornerV = new Static4D[3];

    mCurrCornerV  = new Static4D[3];

    mBasicCornerV[0] = new Static4D( (SQ5+1)*0.125f, (SQ5-1)*0.125f, -0.250f, 0.0f );

    mBasicCornerV[1] = new Static4D(-(SQ5+1)*0.125f, (SQ5-1)*0.125f, -0.250f, 0.0f );

    mBasicCornerV[2] = new Static4D(              0,        -0.500f,    0.0f, 0.0f );

    };

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

  TwistyMegaminx(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.MEGA, res, scrWidth);

    }

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

  private int numCubitsPerCorner(int numLayers)

    {

    return 3*((numLayers-1)/2)*((numLayers-3)/2) + 1;

    }

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

  private int numCubitsPerEdge(int numLayers)

    {

    return numLayers-2;

    }

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

  int getNumStickerTypes(int numLayers)

    {

    return (numLayers+3)/2;

    }

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

  float[] getCuts(int numLayers)

    {

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

    float D = numLayers*MovementMinx.DIST3D;

    float E = 2*C1;           // 2*cos(36 deg)

    float X = 2*D*E/(1+2*E);  // height of the 'upper' part of a dodecahedron, i.e. put it on a table,

                              // its height is then D*2*DIST3D, it has one 'lower' part of height X, one

                              // 'middle' part of height Y and one upper part of height X again.

                              // It's edge length = numLayers/3.0f.

    int num = (numLayers-1)/2;

    float G = X*(0.5f-MEGA_D)/num; // height of one Layer

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

      {

      cuts[        i] = -D + (i+0.5f)*G;

      cuts[2*num-1-i] = -cuts[i];

      }

    return cuts;

    }

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

  private void computeCenter(Static3D pos, int center, int numLayers)

    {

    float[] coords = mCenterCoords[center];

    float A = numLayers/3.0f;

    pos.set( A*coords[0], A*coords[1], A*coords[2] );

    }

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

// Fill out mCurrCorner{X,Y,Z} by applying appropriate Quat to mBasicCorner{X,Y,Z}

// Appropriate one: QUATS[QUAT_INDICES[corner]].

  private void computeBasicCornerVectors(int corner)

    {

    Static4D quat = QUATS[QUAT_CORNER_INDICES[corner]];

    mCurrCornerV[0] = RubikSurfaceView.rotateVectorByQuat(mBasicCornerV[0],quat);

    mCurrCornerV[1] = RubikSurfaceView.rotateVectorByQuat(mBasicCornerV[1],quat);

    mCurrCornerV[2] = RubikSurfaceView.rotateVectorByQuat(mBasicCornerV[2],quat);

    }

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

  private void computeCorner(Static3D pos, int numCubitsPerCorner, int numLayers, int corner, int part)

    {

    float D = numLayers/3.0f;

    Static3D corn = CORNERS[corner];

    if( part==0 )

      {

      pos.set( corn.get0()*D, corn.get1()*D, corn.get2()*D );

      }

    else

      {

      float E = 2.0f*(numLayers/3.0f)*(0.5f-MEGA_D)/(0.5f*(numLayers-1));

      int N = (numCubitsPerCorner-1)/3;

      int block = (part-1) % N;

      int index = (part-1) / N;

      Static4D pri = mCurrCornerV[index];

      Static4D sec = mCurrCornerV[(index+2)%3];

      int multP = (block % ((numLayers-3)/2)) + 1;

      int multS = (block / ((numLayers-3)/2));

      pos.set( corn.get0()*D + (pri.get0()*multP + sec.get0()*multS)*E,

               corn.get1()*D + (pri.get1()*multP + sec.get1()*multS)*E,

               corn.get2()*D + (pri.get2()*multP + sec.get2()*multS)*E );

      }

    }

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

  private int computeEdgeType(int cubit, int numCubitsPerCorner, int numCubitsPerEdge)

    {

    int part = (cubit - NUM_CORNERS*numCubitsPerCorner) % numCubitsPerEdge;

    return (part+1)/2;

    }

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

  private void computeEdge(Static3D pos, int numLayers, int edge, int part)

    {

    float corr = numLayers/3.0f;

    Static3D c1 = CORNERS[ mEdgeMap[edge][0] ];

    Static3D c2 = CORNERS[ mEdgeMap[edge][1] ];

    float x = corr*(c1.get0() + c2.get0())/2;

    float y = corr*(c1.get1() + c2.get1())/2;

    float z = corr*(c1.get2() + c2.get2())/2;

    if( part==0 )

      {

      pos.set(x,y,z);

      }

    else

      {

      int mult = (part+1)/2;

      int dir  = (part+1)%2;

      float[] center = mCenterCoords[ mEdgeMap[edge][dir+2] ];

      float vX = corr*center[0] - x;

      float vY = corr*center[1] - y;

      float vZ = corr*center[2] - z;

      float len = (float)Math.sqrt(vX*vX+vY*vY+vZ*vZ);

      float A = mult*corr*(0.5f-MEGA_D)*COS18/((numLayers-1)*0.5f)/len;

      pos.set( x+A*vX, y+A*vY, z+A*vZ );

      }

    }

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

  Static3D[] getCubitPositions(int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    int numCubits = NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge + NUM_CENTERS;

    int index=0;

    final Static3D[] CENTERS = new Static3D[numCubits];

    for(int corner=0; corner<NUM_CORNERS; corner++)

      {

      computeBasicCornerVectors(corner);

      for(int part=0; part<numCubitsPerCorner; part++, index++)

        {

        CENTERS[index] = new Static3D(0,0,0);

        computeCorner(CENTERS[index],numCubitsPerCorner,numLayers,corner,part);

        }

      }

    for(int edge=0; edge<NUM_EDGES; edge++)

      {

      for(int part=0; part<numCubitsPerEdge; part++, index++)

        {

        CENTERS[index] = new Static3D(0,0,0);

        computeEdge(CENTERS[index], numLayers, edge, part );

        }

      }

    for(int center=0; center<NUM_CENTERS; center++, index++)

      {

      CENTERS[index] = new Static3D(0,0,0);

      computeCenter(CENTERS[index], center, numLayers);

      }

    return CENTERS;

    }

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

  private int getQuat(int cubit, int numCubitsPerCorner, int numCubitsPerEdge)

    {

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      int corner = cubit/numCubitsPerCorner;

      return QUAT_CORNER_INDICES[corner];

      }

    if( cubit < NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int edge = (cubit-NUM_CORNERS*numCubitsPerCorner)/numCubitsPerEdge;

      return QUAT_EDGE_INDICES[edge];

      }

    int center = cubit - NUM_CORNERS*numCubitsPerCorner - NUM_EDGES*numCubitsPerEdge;

    return QUAT_CENTER_INDICES[center];

    }

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

  MeshBase createCubitMesh(int cubit, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    int index = (numLayers-3)/2;

    int[] sizes = ObjectList.MEGA.getSizes();

    int variants = sizes.length;

    MeshBase mesh;

    if( mCornerMeshes==null ) mCornerMeshes = new MeshBase[variants];

    if( mEdgeMeshes  ==null ) mEdgeMeshes   = new MeshBase[variants][(sizes[variants-1]-1)/2];

    if( mCenterMeshes==null ) mCenterMeshes = new MeshBase[variants];

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      if( mCornerMeshes[index]==null )

        {

        mCornerMeshes[index] = FactoryCubit.getInstance().createMegaminxCornerMesh(numLayers);

        }

      mesh = mCornerMeshes[index].copy(true);

      }

    else if( cubit<NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int type = computeEdgeType(cubit,numCubitsPerCorner,numCubitsPerEdge);

      if( mEdgeMeshes[index][type]==null )

        {

        float height= (numLayers/3.0f)*(0.5f-MEGA_D)*COS18/((numLayers-1)*0.5f);

        float width = (numLayers/3.0f)*2*MEGA_D + 2*type*height*SIN18/COS18;

        mEdgeMeshes[index][type] = FactoryCubit.getInstance().createMegaminxEdgeMesh(width,height);

        }

      mesh = mEdgeMeshes[index][type].copy(true);

      }

    else

      {

      if( mCenterMeshes[index]==null )

        {

        float width = 2 * (numLayers/3.0f) * (MEGA_D+(0.5f-MEGA_D)*SIN18);

        mCenterMeshes[index] = FactoryCubit.getInstance().createMegaminxCenterMesh(width);

        }

      mesh = mCenterMeshes[index].copy(true);

      }

    Static4D q = QUATS[getQuat(cubit,numCubitsPerCorner,numCubitsPerEdge)];

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

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

    return mesh;

    }

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

  int getCornerColor(int cubit, int cubitface, int numLayers, int numCubitsPerCorner)

    {

    if( cubitface<0 || cubitface>2 ) return NUM_TEXTURES;

    int part  = cubit % numCubitsPerCorner;

    int corner= cubit / numCubitsPerCorner;

    if( part==0 )

      {

      return mCornerFaceMap[corner][cubitface];

      }

    else

      {

      int N = (numCubitsPerCorner-1)/3;

      int block = (part-1) % N;

      int index = (part-1) / N;

      if( block< (numLayers-3)/2 )

        {

        switch(index)

          {

          case 0: return cubitface==1 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          case 1: return cubitface==0 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          case 2: return cubitface==2 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          }

        }

      else

        {

        switch(index)

          {

          case 0: return cubitface==0 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          case 1: return cubitface==2 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          case 2: return cubitface==1 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          }

        }

      }

    return NUM_TEXTURES;

    }

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

  int getEdgeColor(int edge, int cubitface, int numCubitsPerEdge)

    {

    if( cubitface<0 || cubitface>1 ) return NUM_TEXTURES;

    int part    = edge % numCubitsPerEdge;

    int variant = edge / numCubitsPerEdge;

    return (part==0 || cubitface==((part+1)%2)) ? mEdgeMap[variant][cubitface+2] + ((part+3)/2)*NUM_FACES : NUM_TEXTURES;

    }

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

  int getCenterColor(int center, int cubitface, int numLayers)

    {

    return cubitface>0 ? NUM_TEXTURES : center + NUM_FACES*(numLayers+1)/2;

    }

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

  int getFaceColor(int cubit, int cubitface, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      return getCornerColor(cubit,cubitface,numLayers,numCubitsPerCorner);

      }

    else if( cubit<NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int edge = cubit - NUM_CORNERS*numCubitsPerCorner;

      return getEdgeColor(edge,cubitface,numCubitsPerEdge);

      }

    else

      {

      int center = cubit-NUM_CORNERS*numCubitsPerCorner-NUM_EDGES*numCubitsPerEdge;

      return getCenterColor( center, cubitface, numLayers);

      }

    }

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

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

    {

    int COLORS = FACE_COLORS.length;

    float R,S;

    float[] vertices;

    int variant = face/COLORS;

    if( variant==0 )

      {

      float Y = COS54/(2*SIN54);

      R = 0.06f;

      S = 0.065f;

      vertices = new float[] { -0.5f, 0.0f, 0.0f, -Y, 0.5f, 0.0f, 0.0f, Y };

      }

    else

      {

      int numLayers = getNumLayers();

      float height= (numLayers/3.0f)*(0.5f-MEGA_D)*COS18/((numLayers-1)*0.5f);

      float W = height*SIN18/COS18;

      float width = (numLayers/3.0f)*2*MEGA_D + 2*(variant-1)*W;

      if( variant < (numLayers+1)/2 )

        {

        float X1 = 0.5f*height;

        float Y1 = 0.5f*width;

        float Y2 = 0.5f*width + W;

        R = 0.04f;

        S = 0.05f;

        vertices = new float[] { -X1, Y1, -X1, -Y1, X1, -Y2, X1, Y2 };

        }

      else

        {

        float Z = width/(2*COS54);

        float X1 = 0.5f*width;

        float Y1 = Z*SIN54;

        float X2 = Z*COS18;

        float Y2 = Z*SIN18;

        R = 0.05f;

        S = 0.05f;

        vertices = new float[] { -X1,+Y1, -X2,-Y2, 0.0f,-Z, +X2,-Y2, +X1,+Y1 };

        }

      }

    FactorySticker factory = FactorySticker.getInstance();

    factory.drawRoundedPolygon(canvas, paint, left, top, vertices, S, FACE_COLORS[face%COLORS], R);

    }

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

// PUBLIC API

  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 lastLayer = getNumLayers()-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-lastLayer<MAX_ERROR && row-lastLayer>-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;

               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++)

                 {

                 row1 = computeRow(x1,y1,z1,i);

                 row2 = computeRow(x2,y2,z2,i);

                 if( (row1==0 && row2==0) || (row1==lastLayer && row2==lastLayer) ) return true;

                 }

               return false;

      default: return false;  // edge or corner

      }

    }

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

  public int getObjectName(int numLayers)

    {

    if( numLayers==3 ) return R.string.minx3;

    if( numLayers==5 ) return R.string.minx4;

    return 0;

    }

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

  public int getInventor(int numLayers)

    {

    if( numLayers==3 ) return R.string.minx3_inventor;

    if( numLayers==5 ) return R.string.minx4_inventor;

    return 0;

    }

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

  public int getComplexity(int numLayers)

    {

    if( numLayers==3 ) return 4;

    return 5;

    }

}