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.MatrixEffectMove;

import org.distorted.library.effect.MatrixEffectQuaternion;

import org.distorted.library.effect.MatrixEffectRotate;

import org.distorted.library.effect.MatrixEffectScale;

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);

  private static final float ANGLE_FACES = (float)((180/Math.PI)*(2*Math.asin(SQ3/3))); // angle between two faces of a tetrahedron

  // 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 = {2,4, 4,0, 3,4, 4,1,

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

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

  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 MeshBase createTetrahedronMesh()

    {

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

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

    final int MESHES=4;

    int association = 1;

    float D = 0.005f;

    float E = 0.5f - D*SQ2;

    float F = 0.5f - D*SQ2*SQ3;

    float G = 0.005f;

    float[] bands = { 1.0f    ,-G,

                      1.0f-G/2,-G*0.55f,

                      1.0f-G  ,-G*0.25f,

                      1.0f-2*G,+G*0.25f,

                      0.50f, 0.040f,

                      0.0f, 0.045f };

    float[] vertices = { -F,-E, +F,-E, 0.0f,E-D*SQ2};

    MeshBase[] meshes = new MeshPolygon[MESHES];

    meshes[0] = new MeshPolygon(vertices, bands, 2, 3);

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

    for(int i=1; i<MESHES; i++)

      {

      association <<= 1;

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

      meshes[i].setEffectAssociation(0,association,0);

      }

    MeshBase result = new MeshJoined(meshes);

    Static3D a0 = new Static3D(         0,        1,       0 );

    Static3D a1 = new Static3D(         0,  -1.0f/3, 2*SQ2/3 );

    Static3D a2 = new Static3D(-SQ2*SQ3/3,  -1.0f/3,  -SQ2/3 );

    Static3D a3 = new Static3D( SQ2*SQ3/3,  -1.0f/3,  -SQ2/3 );

    float tetraHeight = SQ2*SQ3/3;

    float d1 = 0.75f*tetraHeight;

    float d2 =-0.10f*tetraHeight;

    float d3 =-0.05f*tetraHeight;

    float d4 = 0.15f*tetraHeight;

    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*a0.get0(), d3*a0.get1(), d3*a0.get2() );

    Static3D dVec1 = new Static3D( d3*a1.get0(), d3*a1.get1(), d3*a1.get2() );

    Static3D dVec2 = new Static3D( d2*a2.get0(), d2*a2.get1(), d2*a2.get2() );

    Static3D dVec3 = new Static3D( d2*a3.get0(), d2*a3.get1(), d2*a3.get2() );

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

    Static1D dRad  = new Static1D(1);

    Static1D angle  = new Static1D(ANGLE_FACES);

    Static3D axis1  = new Static3D(  -1, 0,      0);

    Static3D axis2  = new Static3D(0.5f, 0, -SQ3/2);

    Static3D axis3  = new Static3D(0.5f, 0, +SQ3/2);

    Static3D center1= new Static3D(0,-SQ3*SQ2/12,-SQ3/6);

    Static3D center2= new Static3D(0,-SQ3*SQ2/12,+SQ3/3);

    VertexEffectScale   effect1 = new VertexEffectScale ( new Static3D(1,SQ3/2,1) );

    VertexEffectRotate  effect2 = new VertexEffectRotate( new Static1D(90), new Static3D(1,0,0), new Static3D(0,0,0) );

    VertexEffectMove    effect3 = new VertexEffectMove  ( new Static3D(0,-SQ3*SQ2/12,SQ3/12) );

    VertexEffectRotate  effect4 = new VertexEffectRotate( new Static1D(180), new Static3D(0,0,1), center1 );

    VertexEffectRotate  effect5 = new VertexEffectRotate( angle, axis1, center1 );

    VertexEffectRotate  effect6 = new VertexEffectRotate( angle, axis2, center2 );

    VertexEffectRotate  effect7 = new VertexEffectRotate( angle, axis3, center2 );

    VertexEffectDeform  effect8 = new VertexEffectDeform(dVec0, dRad, dCen0, dReg);

    VertexEffectDeform  effect9 = new VertexEffectDeform(dVec1, dRad, dCen1, dReg);

    VertexEffectDeform  effect10= new VertexEffectDeform(dVec2, dRad, dCen2, dReg);

    VertexEffectDeform  effect11= new VertexEffectDeform(dVec3, dRad, dCen3, dReg);

    effect4.setMeshAssociation(14,-1);  // apply to mesh[1], [2] and [3]

    effect5.setMeshAssociation( 2,-1);  // apply only to mesh[1]

    effect6.setMeshAssociation( 4,-1);  // apply only to mesh[2]

    effect7.setMeshAssociation( 8,-1);  // apply only to mesh[3]

    result.apply(effect1);

    result.apply(effect2);

    result.apply(effect3);

    result.apply(effect4);

    result.apply(effect5);

    result.apply(effect6);

    result.apply(effect7);

    result.apply(effect8);

    result.apply(effect9);

    result.apply(effect10);

    result.apply(effect11);

    result.mergeEffComponents();

    return result;

    }

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

  private void createBasicMesh()

    {

    mMesh = createTetrahedronMesh();

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

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

    MatrixEffectMove   moveEffect = new MatrixEffectMove  ( new Static3D(0.0f,SQ3*SQ2/12,SQ3/6) );

    MatrixEffectRotate rot1Effect = new MatrixEffectRotate( new Static1D(180+ANGLE_FACES/2), axis, cent);

    MatrixEffectScale  scalEffect = new MatrixEffectScale ( new Static3D(3.0f, 3*SQ2/2, 1.5f) );

    MatrixEffectRotate rot2Effect = new MatrixEffectRotate( new Static1D(-45), axis, cent);

    mMesh.apply(moveEffect, 0xffffffff, 0);

    mMesh.apply(rot1Effect, 0xffffffff, 0);

    mMesh.apply(scalEffect, 0xffffffff, 0);

    mMesh.apply(rot2Effect, 0xffffffff, 0);

    }

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

  float getScreenRatio()

    {

    return 0.5f;

    }

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

  Static4D[] getQuats()

    {

    return QUATS;

    }

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

  int getNumFaces()

    {

    return FACE_COLORS.length;

    }

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

  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 = 0.044f*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;

    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, HEIGHT,  side       +left, HEIGHT, paint);

    canvas.drawLine(      OFF +left, side  ,       OFF2  +left,      0, paint);

    canvas.drawLine((side-OFF)+left, side  , (side-OFF2) +left,      0, paint);

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

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

    canvas.drawArc( ARC3_W-RADIUS+left, ARC2_H-RADIUS, ARC3_W+RADIUS+left, ARC2_H+RADIUS, 345, 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 "";

    }

}