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.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.RubikSurfaceView;

import java.util.Random;

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

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

public class TwistyPyraminx extends TwistyObject

{

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

  private static final float SQ3 = (float)Math.sqrt(3);

  private static final float SQ6 = (float)Math.sqrt(6);

  static final Static3D[] ROT_AXIS = new Static3D[]

         {

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

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

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

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

         };

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

         {

           COLOR_GREEN , COLOR_YELLOW,

           COLOR_BLUE  , COLOR_RED

         };

  // computed with res/raw/compute_quats.c

  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,   0.5f,   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),

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

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

         };

  private static MeshBase mOctaMesh, mTetraMesh;

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

  TwistyPyraminx(int size, Static4D quat, DistortedTexture texture, MeshSquare mesh,

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

    {

    super(size, 30, quat, texture, mesh, effects, moves, ObjectList.PYRA, res, scrWidth);

    }

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

  private void addTetrahedralLattice(int size, int index, Static3D[] pos)

    {

    final float DX = 1.0f;

    final float DY = SQ2/2;

    final float DZ = 1.0f;

    float startX = 0.0f;

    float startY =-DY*(size-1)/2;

    float startZ = DZ*(size-1)/2;

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

      {

      float currX = startX;

      float currY = startY;

      for(int x=0; x<layer+1; x++)

        {

        float currZ = startZ;

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

          {

          pos[index] = new Static3D(currX,currY,currZ);

          index++;

          currZ -= DZ;

          }

        currX += DX;

        }

      startX-=DX/2;

      startY+=DY;

      startZ-=DZ/2;

      }

    }

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

// there are (n^3-n)/6 octahedrons and ((n+1)^3 - (n+1))/6 tetrahedrons

  Static3D[] getCubitPositions(int size)

    {

    int numOcta = (size-1)*size*(size+1)/6;

    int numTetra= size*(size+1)*(size+2)/6;

    Static3D[] ret = new Static3D[numOcta+numTetra];

    addTetrahedralLattice(size-1,      0,ret);

    addTetrahedralLattice(size  ,numOcta,ret);

    return ret;

    }

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

  Static4D[] getQuats()

    {

    return QUATS;

    }

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

  int getNumFaces()

    {

    return FACE_COLORS.length;

    }

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

  int getNumStickerTypes()

    {

    return 1;

    }

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

  float getBasicStep()

    {

    return SQ6/3;

    }

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

  int getNumCubitFaces()

    {

    return 8;

    }

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

  float getScreenRatio()

    {

    return 0.82f;

    }

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

  boolean shouldResetTextureMaps()

    {

    return false;

    }

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

  private int faceColor(int cubit, int axis)

    {

    float row = CUBITS[cubit].mRotationRow[axis];

    return row*row < 0.1f ? axis : NUM_FACES;

    }

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

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

    {

    if( cubit< (size-1)*size*(size+1)/6 )

      {

      switch( cubitface )

        {

        case 0: return faceColor(cubit,0);

        case 2: return faceColor(cubit,1);

        case 5: return faceColor(cubit,3);

        case 7: return faceColor(cubit,2);

        default:return NUM_FACES;

        }

      }

    else

      {

      return cubitface<NUM_FACES ? faceColor(cubit,cubitface) : NUM_FACES;

      }

    }

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

  MeshBase createCubitMesh(int cubit)

    {

    int size = getSize();

    if( cubit< (size-1)*size*(size+1)/6 )

      {

      if( mOctaMesh==null ) mOctaMesh = CubitFactory.getInstance().createOctaMesh();

      return mOctaMesh.copy(true);

      }

    else

      {

      if( mTetraMesh==null ) mTetraMesh = CubitFactory.getInstance().createTetraMesh();

      return mTetraMesh.copy(true);

      }

    }

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

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

    {

    float STROKE = 0.044f*side;

    float OFF = STROKE/2 -1;

    float OFF2 = 0.5f*side + OFF;

    float HEIGHT = side - OFF;

    float RADIUS = side/12.0f;

    float ARC1_H = 0.2f*side;

    float ARC1_W = side*0.5f;

    float ARC2_W = 0.153f*side;

    float ARC2_H = 0.905f*side;

    float ARC3_W = side-ARC2_W;

    float M = SQ3/2;

    float D = (M/2 - 0.51f)*side;

    paint.setAntiAlias(true);

    paint.setStrokeWidth(STROKE);

    paint.setColor(FACE_COLORS[face]);

    paint.setStyle(Paint.Style.FILL);

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

    paint.setColor(INTERIOR_COLOR);

    paint.setStyle(Paint.Style.STROKE);

    canvas.drawLine(           left, M*HEIGHT+D,  side       +left, M*HEIGHT+D, paint);

    canvas.drawLine(      OFF +left, M*side  +D,       OFF2  +left,          D, paint);

    canvas.drawLine((side-OFF)+left, M*side  +D, (side-OFF2) +left,          D, paint);

    canvas.drawArc( ARC1_W-RADIUS+left, M*(ARC1_H-RADIUS)+D, ARC1_W+RADIUS+left, M*(ARC1_H+RADIUS)+D, 225, 90, false, paint);

    canvas.drawArc( ARC2_W-RADIUS+left, M*(ARC2_H-RADIUS)+D, ARC2_W+RADIUS+left, M*(ARC2_H+RADIUS)+D, 105, 90, false, paint);

    canvas.drawArc( ARC3_W-RADIUS+left, M*(ARC2_H-RADIUS)+D, ARC3_W+RADIUS+left, M*(ARC2_H+RADIUS)+D, 345, 90, false, paint);

    }

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

// SQ6/3 = height of the tetrahedron

  float returnMultiplier()

    {

    return getSize()/(SQ6/3);

    }

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

  float[] getRowChances()

    {

    int size = getSize();

    int total = size*(size+1)/2;

    float running=0.0f;

    float[] chances = new float[size];

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

      {

      running += (size-i);

      chances[i] = running / total;

      }

    return chances;

    }

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

// PUBLIC API

  public Static3D[] getRotationAxis()

    {

    return ROT_AXIS;

    }

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

  public int getBasicAngle()

    {

    return 3;

    }

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

  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

      }

    }

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

// only needed for solvers - there are no Pyraminx solvers ATM)

  public String retObjectString()

    {

    return "";

    }

}