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.effect.VertexEffectDeform;

import org.distorted.library.effect.VertexEffectMove;

import org.distorted.library.effect.VertexEffectRotate;

import org.distorted.library.effect.VertexEffectScale;

import org.distorted.library.main.DistortedEffects;

import org.distorted.library.main.DistortedTexture;

import org.distorted.library.mesh.MeshBase;

import org.distorted.library.mesh.MeshJoined;

import org.distorted.library.mesh.MeshPolygon;

import org.distorted.library.mesh.MeshSquare;

import org.distorted.library.type.Static1D;

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 RubikDino extends RubikObject

{

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

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

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

  static final Static3D[] ROT_AXIS = new Static3D[]

         {

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

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

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

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

         };

  // the six axis that determine the faces

  static final Static3D[] FACE_AXIS = new Static3D[]

         {

           new Static3D(1,0,0), new Static3D(-1,0,0),

           new Static3D(0,1,0), new Static3D(0,-1,0),

           new Static3D(0,0,1), new Static3D(0,0,-1)

         };

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

         {

           0xffffff00, 0xffffffff,   // FACE_AXIS[0] (right-YELLOW) FACE_AXIS[1] (left  -WHITE)

           0xff0000ff, 0xff00ff00,   // FACE_AXIS[2] (top  -BLUE  ) FACE_AXIS[3] (bottom-GREEN)

           0xffff0000, 0xffb5651d    // FACE_AXIS[4] (front-RED   ) FACE_AXIS[5] (back  -BROWN)

         };

  // All legal rotation quats of a RubikDino

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

         {

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

           new Static4D(  0.5f,  0.5f,  0.5f, -0.5f ),

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

           new Static4D(  0.5f, -0.5f, -0.5f, -0.5f ),

           new Static4D(  0.5f,  0.5f,  0.5f,  0.5f ),

           new Static4D(  0.5f,  0.5f, -0.5f, -0.5f ),

           new Static4D(  0.5f, -0.5f,  0.5f, -0.5f ),

           new Static4D(  0.5f, -0.5f, -0.5f,  0.5f ),

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

           new Static4D(  0.5f, -0.5f,  0.5f,  0.5f ),

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

           new Static4D(  0.5f,  0.5f, -0.5f,  0.5f )

         };

  // centers of the 12 edges. Must be in the same order like QUATs above.

  private static final Static3D[] CENTERS = new Static3D[]

         {

           new Static3D( 0.0f, 1.5f, 1.5f ),

           new Static3D( 1.5f, 0.0f, 1.5f ),

           new Static3D( 0.0f,-1.5f, 1.5f ),

           new Static3D(-1.5f, 0.0f, 1.5f ),

           new Static3D( 1.5f, 1.5f, 0.0f ),

           new Static3D( 1.5f,-1.5f, 0.0f ),

           new Static3D(-1.5f,-1.5f, 0.0f ),

           new Static3D(-1.5f, 1.5f, 0.0f ),

           new Static3D( 0.0f, 1.5f,-1.5f ),

           new Static3D( 1.5f, 0.0f,-1.5f ),

           new Static3D( 0.0f,-1.5f,-1.5f ),

           new Static3D(-1.5f, 0.0f,-1.5f )

         };

  private static final int[] mFaceMap = {4,2, 0,4, 4,3, 1,4,

                                         2,0, 3,0, 3,1, 2,1,

                                         5,2, 0,5, 5,3, 1,5 };

  private static MeshBase mMesh;

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

  RubikDino(int size, Static4D quat, DistortedTexture texture,

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

    {

    super(size, 60, quat, texture, mesh, effects, moves, RubikObjectList.DINO, res, scrWidth);

    }

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

  private void createBasicMesh()

    {

    final float ANGLE = (float)((180/Math.PI)*(Math.atan(SQ2)));

    final int MESHES=4;

    float D = 0.02f;

    float E = 0.5f*SQ2;

    float F = 0.5f;

    float[] bands0 = { 1.0f    , 0,

                       1.0f-2*D, D*0.25f,

                       1.0f-4*D, D*0.35f,

                       1.0f-8*D, D*0.6f,

                       0.60f   , D*1.0f,

                       0.30f   , D*1.375f,

                       0.0f    , D*1.4f };

    float[] vertices0 = { -F,F/3, 0,-2*F/3, +F,F/3 };

    MeshBase[] meshes = new MeshPolygon[MESHES];

    meshes[0] = new MeshPolygon(vertices0, bands0, 2, 5);

    meshes[0].setEffectAssociation(0,1,0);

    meshes[1] = meshes[0].copy(true);

    meshes[1].setEffectAssociation(0,2,0);

    float[] bands1 = { 1.0f    , 0,

                       0.50f   , 0.10f,

                       0.0f    , 0.20f };

    float[] vertices1 = { -E/2,-E*(SQ3/6), E/2,-E*(SQ3/6), 0,E*(SQ3/3) };

    meshes[2] = new MeshPolygon(vertices1, bands1, 1, 2);

    meshes[2].setEffectAssociation(0,4,0);

    meshes[3] = meshes[2].copy(true);

    meshes[3].setEffectAssociation(0,8,0);

    mMesh = new MeshJoined(meshes);

    Static3D a0 = new Static3D(     0,-3*F,    0 );

    Static3D a1 = new Static3D(     0,   0, -3*F );

    Static3D a2 = new Static3D(  -3*F,   0,    0 );

    Static3D a3 = new Static3D(  +3*F,   0,    0 );

    Static3D v0 = new Static3D(     0,-3*F/2, 3*F/2 );

    Static3D v1 = new Static3D(     0, 3*F/2,-3*F/2 );

    Static3D v2 = new Static3D(  -3*F, 3*F/2, 3*F/2 );

    Static3D v3 = new Static3D(  +3*F, 3*F/2, 3*F/2 );

    float d1 = 1.0f;

    float d2 =-0.10f;

    float d3 =-0.10f;

    float d4 = 0.40f;

    Static3D dCen0 = new Static3D( d1*a0.get0(), d1*a0.get1(), d1*a0.get2() );

    Static3D dCen1 = new Static3D( d1*a1.get0(), d1*a1.get1(), d1*a1.get2() );

    Static3D dCen2 = new Static3D( d1*a2.get0(), d1*a2.get1(), d1*a2.get2() );

    Static3D dCen3 = new Static3D( d1*a3.get0(), d1*a3.get1(), d1*a3.get2() );

    Static3D dVec0 = new Static3D( d3*v0.get0(), d3*v0.get1(), d3*v0.get2() );

    Static3D dVec1 = new Static3D( d3*v1.get0(), d3*v1.get1(), d3*v1.get2() );

    Static3D dVec2 = new Static3D( d2*v2.get0(), d2*v2.get1(), d2*v2.get2() );

    Static3D dVec3 = new Static3D( d2*v3.get0(), d2*v3.get1(), d2*v3.get2() );

    Static4D dReg  = new Static4D(0,0,0,d4);

    Static1D dRad  = new Static1D(1);

    Static1D angle1 = new Static1D(+ANGLE);

    Static1D angle2 = new Static1D(-ANGLE);

    Static3D axisX  = new Static3D(1,0,0);

    Static3D axisY  = new Static3D(0,1,0);

    Static3D axisZ  = new Static3D(0,-1,1);

    Static3D center0= new Static3D(0,0,0);

    Static3D center1= new Static3D(0,-3*F,0);

    VertexEffectScale   effect0 = new VertexEffectScale ( new Static3D(3,3,3) );

    VertexEffectMove    effect1 = new VertexEffectMove  ( new Static3D(0,-F,0) );

    VertexEffectRotate  effect2 = new VertexEffectRotate( new Static1D(90), axisX, center0 );

    VertexEffectScale   effect3 = new VertexEffectScale ( new Static3D(1,-1,1) );

    VertexEffectMove    effect4 = new VertexEffectMove  ( new Static3D(3*E/2,E*(SQ3/2)-3*F,0) );

    VertexEffectRotate  effect5 = new VertexEffectRotate( new Static1D(+90), axisY, center1 );

    VertexEffectScale   effect6 = new VertexEffectScale ( new Static3D(-1,1,1) );

    VertexEffectRotate  effect7 = new VertexEffectRotate( new Static1D( 45), axisX, center1 );

    VertexEffectRotate  effect8 = new VertexEffectRotate( angle1           , axisZ, center1 );

    VertexEffectRotate  effect9 = new VertexEffectRotate( angle2           , axisZ, center1 );

    VertexEffectDeform  effect10= new VertexEffectDeform(dVec0, dRad, dCen0, dReg);

    VertexEffectDeform  effect11= new VertexEffectDeform(dVec1, dRad, dCen1, dReg);

    VertexEffectDeform  effect12= new VertexEffectDeform(dVec2, dRad, dCen2, dReg);

    VertexEffectDeform  effect13= new VertexEffectDeform(dVec3, dRad, dCen3, dReg);

    effect0.setMeshAssociation(15,-1);  // apply to meshes 0,1,2,3

    effect1.setMeshAssociation( 3,-1);  // apply to meshes 0,1

    effect2.setMeshAssociation( 2,-1);  // apply to mesh 1

    effect3.setMeshAssociation( 2,-1);  // apply to mesh 0

    effect4.setMeshAssociation(12,-1);  // apply to meshes 2,3

    effect5.setMeshAssociation(12,-1);  // apply to meshes 2,3

    effect6.setMeshAssociation( 8,-1);  // apply to mesh 3

    effect7.setMeshAssociation(12,-1);  // apply to meshes 2,3

    effect8.setMeshAssociation( 4,-1);  // apply to mesh 2

    effect9.setMeshAssociation( 8,-1);  // apply to mesh 3

    effect10.setMeshAssociation(15,-1); // apply to meshes 0,1,2,3

    effect11.setMeshAssociation(15,-1); // apply to meshes 0,1,2,3

    effect12.setMeshAssociation(15,-1); // apply to meshes 0,1,2,3

    effect13.setMeshAssociation(15,-1); // apply to meshes 0,1,2,3

    mMesh.apply(effect0);

    mMesh.apply(effect1);

    mMesh.apply(effect2);

    mMesh.apply(effect3);

    mMesh.apply(effect4);

    mMesh.apply(effect5);

    mMesh.apply(effect6);

    mMesh.apply(effect7);

    mMesh.apply(effect8);

    mMesh.apply(effect9);

    mMesh.apply(effect10);

    mMesh.apply(effect11);

    mMesh.apply(effect12);

    mMesh.apply(effect13);

    mMesh.mergeEffComponents();

    }

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

  float getScreenRatio()

    {

    return 0.5f;

    }

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

  Static4D[] getQuats()

    {

    return QUATS;

    }

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

  int getNumFaces()

    {

    return FACE_COLORS.length;

    }

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

  int getNumStickerTypes()

    {

    return 1;

    }

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

  int getNumCubitFaces()

    {

    return 4;

    }

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

  Static3D[] getCubitPositions(int size)

    {

    return CENTERS;

    }

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

  MeshBase createCubitMesh(int cubit)

    {

    if( mMesh==null ) createBasicMesh();

    MeshBase mesh = mMesh.copy(true);

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

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

    return mesh;

    }

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

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

    {

    switch(cubitface)

      {

      case 0 : return mFaceMap[2*cubit];

      case 1 : return mFaceMap[2*cubit+1];

      default: return NUM_FACES;

      }

    }

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

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

    {

    float STROKE = 0.04f*side;

    float L= left;

    float H= 0.333f*side;

    float LEN = 0.5f*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( L      , H,  L+2*LEN, H    , paint);

    canvas.drawLine( L      , H,  L+  LEN, H+LEN, paint);

    canvas.drawLine( L+2*LEN, H,  L+  LEN, H+LEN, paint);

    float S1 = 0.150f*side;

    float S2 = 0.090f*side;

    float X  = 0.7f*S2;

    float Y  = 0.2f*S1;

    float LA = left+0.500f*side;

    float RA = left;

    float TA = 0.333f*side;

    float BA = 0.833f*side;

    canvas.drawArc( RA+X        , TA     , RA+X+S2  , TA+S2, 135,135, false, paint);

    canvas.drawArc( RA+side-S2-X, TA     , RA+side-X, TA+S2, 270,135, false, paint);

    canvas.drawArc( LA-S1/2     , BA-S1-Y, LA+S1/2  , BA-Y ,  45, 90, false, paint);

    }

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

  float returnMultiplier()

    {

    return 2.0f;

    }

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

  float[] getRowChances()

    {

    float[] chances = new float[3];

    chances[0] = 0.5f;

    chances[1] = 0.5f;

    chances[2] = 1.0f;

    return chances;

    }

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

// PUBLIC API

  public Static3D[] getRotationAxis()

    {

    return ROT_AXIS;

    }

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

  public int getBasicAngle()

    {

    return 3;

    }

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

  public int computeRowFromOffset(float offset)

    {

    return offset<0.5f ? 0:2;

    }

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

  public float returnRotationFactor(float offset)

    {

    return 1.0f;

    }

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

  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();

    switch(oldRotAxis)

      {

      case 0 : switch(newRotAxis)

                 {

                 case 1:

                 case 2: return oldRow;

                 case 3: return 2-oldRow;

                 default: android.util.Log.e("dino", "error: oldRotAxis="+oldRotAxis+" newRotAxis:"+newRotAxis);

                 }

      case 1 : switch(newRotAxis)

                 {

                 case 0:

                 case 3: return oldRow;

                 case 2: return 2-oldRow;

                 default: android.util.Log.e("dino", "error: oldRotAxis="+oldRotAxis+" newRotAxis:"+newRotAxis);

                 }

      case 2 : switch(newRotAxis)

                 {

                 case 0:

                 case 3: return oldRow;

                 case 1: return 2-oldRow;

                 default: android.util.Log.e("dino", "error: oldRotAxis="+oldRotAxis+" newRotAxis:"+newRotAxis);

                 }

      case 3 : switch(newRotAxis)

                 {

                 case 1:

                 case 2: return oldRow;

                 case 0: return 2-oldRow;

                 default: android.util.Log.e("dino", "error: oldRotAxis="+oldRotAxis+" newRotAxis:"+newRotAxis);

                 }

      default: return rowFloat<=0.5f ? 0:2;

      }

    }

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

// remember about the double cover or unit quaternions!

  private 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;

    }

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

// Dino is solved if and only if:

//

// All four 'X' cubits (i.e. those whose longest edge goes along the X axis) are rotated

// by the same quaternion qX, similarly all four 'Y' cubits by the same qY and all four 'Z'

// by the same qZ, and then either:

//

// a) qX = qY = qZ

// b) qY = qX*Q2 and qZ = qX*Q8  (i.e. swap of WHITE and YELLOW faces)

// c) qX = qY*Q2 and qZ = qY*Q10 (i.e. swap of BLUE and GREEN faces)

// d) qX = qZ*Q8 and qY = qZ*Q10 (i.e. swap of RED and BROWN faces)

//

// BUT: cases b), c) and d) are really the same - it's all just a mirror image of the original.

//

// X cubits: 0, 2, 8, 10

// Y cubits: 1, 3, 9, 11

// Z cubits: 4, 5, 6, 7

  public boolean isSolved()

    {

    int qX = CUBITS[0].mQuatIndex;

    int qY = CUBITS[1].mQuatIndex;

    int qZ = CUBITS[4].mQuatIndex;

    if( CUBITS[2].mQuatIndex != qX || CUBITS[8].mQuatIndex != qX || CUBITS[10].mQuatIndex != qX ||

        CUBITS[3].mQuatIndex != qY || CUBITS[9].mQuatIndex != qY || CUBITS[11].mQuatIndex != qY ||

        CUBITS[5].mQuatIndex != qZ || CUBITS[6].mQuatIndex != qZ || CUBITS[ 7].mQuatIndex != qZ  )

      {

      return false;

      }

    return ( qX==qY && qX==qZ ) || ( qY==mulQuat(qX,2) && qZ==mulQuat(qX,8) );

    }

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

// TODO  (only needed for solvers - there are no Dino solvers ATM)

  public String retObjectString()

    {

    return "";

    }

}