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;

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

public class TwistyMegaminx extends TwistyMinx

{

  static final float MEGA_D = 0.05f;

  private static final int NUM_CORNERS = 20;

  private static final int NUM_CENTERS = 12;

  private static final int NUM_EDGES   = 30;

  private static final int[][] mFaceVertexMap =

         {

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

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

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

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

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

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

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

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

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

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

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

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

         };

  private static MeshBase[] mCenterMeshes, mCornerMeshes, mEdgeMeshes;

  private static final Static4D[] mBasicV, mCurrV;

  static

    {

    mBasicV = new Static4D[3];

    mCurrV  = new Static4D[3];

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

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

    mBasicV[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 1; //numLayers;

    }

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

  float[] getCuts(int numLayers)

    {

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

    float D = (numLayers/3.0f)*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 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] = -MovementMinx.DIST3D + (i+0.5f)*G;

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

      }

    return cuts;

    }

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

  private void computeCenter(Static3D[] array, int center)

    {

    int[] map = mFaceVertexMap[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() ;

    array[center].set(x/5,y/5,z/5);

    }

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

// Fill out mCurr{X,Y,Z} by applying appropriate Quat to mBasic{X,Y,Z}

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

  private void computeBasicVectors(int corner)

    {

    Static4D quat = QUATS[QUAT_INDICES[corner]];

    mCurrV[0] = RubikSurfaceView.rotateVectorByQuat(mBasicV[0],quat);

    mCurrV[1] = RubikSurfaceView.rotateVectorByQuat(mBasicV[1],quat);

    mCurrV[2] = RubikSurfaceView.rotateVectorByQuat(mBasicV[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/6.0f - MEGA_D)/(0.5f*(numLayers-1));

      int N = (numCubitsPerCorner-1)/3;

      int block = (part-1) % N;

      int index = (part-1) / N;

      Static4D pri = mCurrV[index];

      Static4D sec = mCurrV[(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 );

      }

    }

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

// TODO

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

    {

    }

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

  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++)

      {

      computeBasicVectors(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++)

        {

        computeEdge(CENTERS,index, edge, part );

        }

      }

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

      {

      computeCenter(CENTERS,index);

      }

*/

    return CENTERS;

    }

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

  private int getQuat(int cubit, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      int corner = cubit/numCubitsPerCorner;

      return QUAT_INDICES[corner];

      }

/*

    if( cubit < NUM_CENTERS + NUM_CORNERS*numCubitsPerCorner )

      {

      switch(cubit-NUM_CORNERS*numCubitsPerCorner)

        {

        case  0: return  0;

        case  1: return 52;

        case  2: return  3;

        case  3: return 53;

        case  4: return 59;

        case  5: return 20;

        case  6: return 22;

        case  7: return 58;

        case  8: return 55;

        case  9: return 13;

        case 10: return  1;

        case 11: return 14;

        }

      }

    int numCubitsPerEdge = numCubitsPerEdge(numLayers);

    // TODO: edges

*/

    return 0;

    }

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

  MeshBase createCubitMesh(int cubit, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    int index = (numLayers-3)/2;

    MeshBase mesh;

    if( mCornerMeshes==null ) mCornerMeshes = new MeshBase[ObjectList.MEGA.getNumVariants()];

//    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

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

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

      }

/*

    else if( cubit<NUM_CENTERS + NUM_CORNERS*numCubitsPerCorner )

      {

      if( mCornerMesh==null ) mCornerMesh = FactoryCubit.getInstance().createMegaminxCenterMesh();

      mesh = mCornerMesh.copy(true);

      }

    else

      {

      if( mEdgeMesh==null ) mEdgeMesh = new MeshBase[(numLayers-1)/2];

      // TODO

      }

*/

    MatrixEffectQuaternion quat = new MatrixEffectQuaternion( QUATS[getQuat(cubit,numLayers)], new Static3D(0,0,0) );

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

    return mesh;

    }

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

// TODO

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

    {

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

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    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-1)/2 )

        {

        switch(index)

          {

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

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

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

          }

        }

      else

        {

        switch(index)

          {

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

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

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

          }

        }

      }

    return NUM_TEXTURES*NUM_FACES;

    }

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

// TODO

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

    {

    paint.setColor(FACE_COLORS[face]);

    paint.setStyle(Paint.Style.FILL);

    canvas.drawRect(left,top,left+TEXTURE_HEIGHT,top+TEXTURE_HEIGHT,paint);

    }

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

// 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;

    }

}