Magic Cube

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// 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.SharedPreferences;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

import org.distorted.main.RubikSurfaceView;

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

class Cubit

  {

  private final Static3D mOrigPosition;

  private RubikObject mParent;

  private Static3D mCurrentPosition;

  private int mNumAxis;

  int mQuatIndex;

  float[] mRotationRow;

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

  Cubit(RubikObject parent, Static3D position)

    {

    float x = position.get0();

    float y = position.get1();

    float z = position.get2();

    mParent          = parent;

    mOrigPosition    = new Static3D(x,y,z);

    mCurrentPosition = new Static3D(x,y,z);

    mQuatIndex       = 0;

    mNumAxis     = mParent.ROTATION_AXIS.length;

    mRotationRow = new float[mNumAxis];

    computeRotationRow();

    }

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

// Because of quatMultiplication, errors can accumulate - so to avoid this, we

// correct the value of the 'scramble' quat to what it should be - one of the legal quats from the

// list QUATS.

//

// We also have to remember that the group of unit quaternions is a double-cover of rotations

// in 3D ( q represents the same rotation as -q ) - so invert if needed.

  private int normalizeScrambleQuat(Static4D quat)

    {

    float x = quat.get0();

    float y = quat.get1();

    float z = quat.get2();

    float w = quat.get3();

    float xd,yd,zd,wd;

    float diff, mindiff = Float.MAX_VALUE;

    int ret=0;

    int num_quats = mParent.QUATS.length;

    Static4D qt;

    for(int q=0; q<num_quats; q++)

      {

      qt = mParent.QUATS[q];

      xd = x - qt.get0();

      yd = y - qt.get1();

      zd = z - qt.get2();

      wd = w - qt.get3();

      diff = xd*xd + yd*yd + zd*zd + wd*wd;

      if( diff < mindiff )

        {

        ret = q;

        mindiff = diff;

        }

      xd = x + qt.get0();

      yd = y + qt.get1();

      zd = z + qt.get2();

      wd = w + qt.get3();

      diff = xd*xd + yd*yd + zd*zd + wd*wd;

      if( diff < mindiff )

        {

        ret = q;

        mindiff = diff;

        }

      }

    return ret;

    }

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

  private void modifyCurrentPosition(Static4D quat)

    {

    float cubitCenterX = mCurrentPosition.get0();

    float cubitCenterY = mCurrentPosition.get1();

    float cubitCenterZ = mCurrentPosition.get2();

    Static4D cubitCenter =  new Static4D(cubitCenterX, cubitCenterY, cubitCenterZ, 0);

    Static4D rotatedCenter = RubikSurfaceView.rotateVectorByQuat( cubitCenter, quat);

    float rotatedX = rotatedCenter.get0();

    float rotatedY = rotatedCenter.get1();

    float rotatedZ = rotatedCenter.get2();

    mCurrentPosition.set(rotatedX, rotatedY, rotatedZ);

    mParent.clampPos(mCurrentPosition);

    computeRotationRow();

    }

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

// cast current position on axis; use mStart and mStep to compute the rotation row for each axis.

  private void computeRotationRow()

    {

    float tmp;

    Static3D axis;

    float x = mCurrentPosition.get0();

    float y = mCurrentPosition.get1();

    float z = mCurrentPosition.get2();

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

      {

      axis = mParent.ROTATION_AXIS[i];

      tmp = x*axis.get0() + y*axis.get1() + z*axis.get2();

      mRotationRow[i] = (tmp-mParent.mStart)/mParent.mStep;

      }

    }

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

  int computeAssociation()

    {

    int row, result = 0, accumulativeShift = 0;

    for(int axis=0; axis<mNumAxis; axis++)

      {

      row = (int)(mRotationRow[axis]+0.5f);

      result += (1<<(row+accumulativeShift));

      accumulativeShift += RubikObjectList.MAX_OBJECT_SIZE;

      }

    return result;

    }

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

  void savePreferences(SharedPreferences.Editor editor)

    {

    String number = mOrigPosition.get0()+"_"+mOrigPosition.get1()+"_"+mOrigPosition.get2();

    editor.putInt("q_"+number, mQuatIndex);

    }

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

  int restorePreferences(SharedPreferences preferences)

    {

    String number = mOrigPosition.get0()+"_"+mOrigPosition.get1()+"_"+mOrigPosition.get2();

    mQuatIndex = preferences.getInt("q_"+number, 0);

    modifyCurrentPosition(mParent.QUATS[mQuatIndex]);

    return mQuatIndex;

    }

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

// 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.

  boolean thereIsNoVisibleDifference(int quatIndex)

    {

    if ( mQuatIndex == quatIndex ) return true;

    int belongsToHowManyFaces = 0;

    int size = mParent.getSize()-1;

    float row;

    final float MAX_ERROR = 0.01f;

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

      {

      row = 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

               float cubitCenterX = mOrigPosition.get0();

               float cubitCenterY = mOrigPosition.get1();

               float cubitCenterZ = mOrigPosition.get2();

               Static4D quat1 = mParent.QUATS[quatIndex];

               Static4D quat2 = mParent.QUATS[mQuatIndex];

               Static4D cubitCenter = new Static4D(cubitCenterX, cubitCenterY, cubitCenterZ, 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<mNumAxis; i++)

                 {

                 axis = mParent.ROTATION_AXIS[i];

                 ax = axis.get0();

                 ay = axis.get1();

                 az = axis.get2();

                 row1 = ((x1*ax + y1*ay + z1*az) - mParent.mStart) / mParent.mStep;

                 row2 = ((x2*ax + y2*ay + z2*az) - mParent.mStart) / mParent.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

      }

    }

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

  int removeRotationNow(Static4D quat)

    {

    Static4D q = RubikSurfaceView.quatMultiply(quat,mParent.QUATS[mQuatIndex]);

    mQuatIndex = normalizeScrambleQuat(q);

    modifyCurrentPosition(quat);

    return mQuatIndex;

    }

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

  void solve()

    {

    mQuatIndex = 0;

    mCurrentPosition.set(mOrigPosition);

    computeRotationRow();

    }

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

  float getDistSquared(float[] point)

    {

    float dx = mCurrentPosition.get0() - point[0];

    float dy = mCurrentPosition.get1() - point[1];

    float dz = mCurrentPosition.get2() - point[2];

    return dx*dx + dy*dy + dz*dz;

    }

}