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.graphics.Canvas;

import android.graphics.Paint;

import org.distorted.library.effect.MatrixEffect;

import org.distorted.library.effect.MatrixEffectMove;

import org.distorted.library.effect.MatrixEffectRotate;

import org.distorted.library.effect.VertexEffectSink;

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.MeshRectangles;

import org.distorted.library.type.Static1D;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

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

class RubikCube extends RubikObject

{

  // the three rotation axis of a RubikCube. Must be normalized.

  static final Static3D[] AXIS = new Static3D[]

         {

           new Static3D(1,0,0),

           new Static3D(0,1,0),

           new Static3D(0,0,1)

         };

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

         {

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

           0xff0000ff, 0xff00ff00,   // AXIS[1]right (top  -BLUE  ) AXIS[1]left (bottom-GREEN)

           0xffff0000, 0xffb5651d    // AXIS[2]right (front-RED   ) AXIS[2]left (back  -BROWN)

         };

  // All legal rotation quats of a RubikCube of any size must have all four of their components

  // equal to either 0, +-1, +-0.5 or +-sqrt(2)/2.

  // Here's how to compute this:

  // 1) compute how many rotations there are (RubikCube of any size = 24)

  // 2) take the AXIS, angles of rotation (90 in RubikCube's case) compute the basic quaternions

  // (i.e. rotations of 1 basic angle along each of the axis) and from there start semi-randomly

  // multiplying them and eventually you'll find all (24) legal rotations.

  // 3) linear scan through those shows that the only floats in those 24 quats are those 7 given

  // below.

  //

  // Example program in C, res/raw/compute_quats.c , is included.

  private static final float[] LEGALQUATS = new float[]

         {

           0.0f ,

           0.5f ,

          -0.5f ,

           1.0f ,

          -1.0f ,

           0.5f*((float)Math.sqrt(2)) ,

          -0.5f*((float)Math.sqrt(2))

         };

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

  RubikCube(int size, Static4D quatCur, Static4D quatAcc, DistortedTexture texture, MeshRectangles mesh, DistortedEffects effects, int[][] moves)

    {

    super(size, 60, quatCur,quatAcc,texture,mesh,effects,moves, RubikObjectList.CUBE);

    }

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

// paint the square with upper-right cornder at (left,top) and side length 'side' with texture

// for face 'face'.

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

    {

    final float R = side*0.10f;

    final float M = side*0.05f;

    paint.setColor(FACE_COLORS[face]);

    canvas.drawRoundRect( left+M, top+M, left+side-M, top+side-M, R, R, paint);

    }

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

  Static3D[] getCubitPositions(int size)

    {

    int numCubits = size>1 ? 6*size*size - 12*size + 8 : 1;

    Static3D[] tmp = new Static3D[numCubits];

    float diff = 0.5f*(size-1);

    int currentPosition = 0;

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

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

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

          if( x==0 || x==size-1 || y==0 || y==size-1 || z==0 || z==size-1 )

            {

            tmp[currentPosition++] = new Static3D(x-diff,y-diff,z-diff);

            }

    return tmp;

    }

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

  float[] getLegalQuats()

    {

    return LEGALQUATS;

    }

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

  int getNumFaces()

    {

    return FACE_COLORS.length;

    }

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

  float getScreenRatio()

    {

    return 0.5f;

    }

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

  VertexEffectSink getSink(int size)

    {

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

    Static4D region = new Static4D(0,0,0,0.72f);

    float strength;

    switch(size)

      {

      case 1 : strength= 1.1f; break;

      case 2 : strength= 1.5f; break;

      case 3 : strength= 1.8f; break;

      case 4 : strength= 2.0f; break;

      default: strength= 3.0f - 4.0f/size;

      }

    return new VertexEffectSink( new Static1D(strength), center, region );

    }

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

  MeshBase createCubitMesh(int cubit, int vertices)

    {

    final int MESHES=6;

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

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

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

    Static1D angle  = new Static1D(0);

    MatrixEffect[] effectsY = new MatrixEffect[2];

    effectsY[0] = new MatrixEffectMove(new Static3D(0,0,+0.5f));

    effectsY[1] = new MatrixEffectRotate( angle, axisY, center );

    MeshBase[] meshes = new MeshRectangles[MESHES];

    for(int i=0; i<MESHES; i++) meshes[i] = new MeshRectangles(vertices,vertices);

    angle.set(0);

    meshes[4].apply(effectsY);  // front

    angle.set(90);

    meshes[0].apply(effectsY);  // right

    angle.set(180);

    meshes[5].apply(effectsY);  // back

    angle.set(270);

    meshes[1].apply(effectsY);  // left

    MatrixEffect[] effectsX = new MatrixEffect[2];

    effectsX[0] = new MatrixEffectMove(new Static3D(0,0,+0.5f));

    effectsX[1] = new MatrixEffectRotate( angle, axisX, center );

    angle.set( 90);

    meshes[3].apply(effectsX);  // bottom

    angle.set(-90);

    meshes[2].apply(effectsX);  // top

    return new MeshJoined(meshes);

    }

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

// PUBLIC API

  public Static3D[] getRotationAxis()

    {

    return AXIS;

    }

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

  public int getBasicAngle()

    {

    return 4;

    }

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

  public float returnMultiplier()

    {

    return getSize();

    }

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

  public float[] getRowChances()

    {

    int size = getSize();

    float[] chances = new float[size];

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

      {

      chances[i] = (i+1.0f) / size;

      }

    return chances;

    }

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

  public float returnRotationFactor(float offset)

    {

    return 1.0f;

    }

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

// order: Up --> Right --> Front --> Down --> Left --> Back

// (because the first implemented Solver - the two-phase Cube3 one - expects such order)

//

// Solved 3x3x3 Cube maps to "UUUUUUUUURRRRRRRRRFFFFFFFFFDDDDDDDDDLLLLLLLLLBBBBBBBBB"

//

// s : size of the cube; let index = a*s + b    (i.e. a,b = row,column)

//

// Up    :   index --> b<s-1 ? (s-1)*(s+4b)+a : 6*s*s -13*s +8 +a

// Right :   index --> 6*s*s - 12*s + 7 - index

// Front :   index --> if b==0  : s*s - 1 - index

//                     if b==s-1: 6*s*s -11*s +6 - index

//                     else

//                         a==0: s*s + s-1 + 4*(b-1)*(s-1) + 2*(s-2) + s

//                         else: s*s + s-1 + 4*(b-1)*(s-1) + 2*(s-1-a)

// Down  :   index --> b==0 ? (s-1-a) : s*s + s-1 + 4*(b-1)*(s-1) - a

// Left  :   index --> (s-1-a)*s + b

// Back  :   index --> if b==s-1: s*(s-1-a)

//                     if b==0  : 5*s*s -12*s + 8 + (s-1-a)*s

//                     else

//                        if a==s-1: s*s + 4*(s-2-b)*(s-1)

//                        else     : s*s + 4*(s-2-b)*(s-1) + s + (s-2-a)*2

  public String retObjectString()

    {

    StringBuilder objectString = new StringBuilder();

    int size = getSize();

    int len = size*size;

    int cubitIndex, row, col;

    int color;

    final int RIGHT= 0;

    final int LEFT = 1;

    final int UP   = 2;

    final int DOWN = 3;

    final int FRONT= 4;

    final int BACK = 5;

    final char[] FACE_NAMES = { 'R', 'L', 'U', 'D', 'F', 'B'};

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

      {

      row = i/size;

      col = i%size;

      cubitIndex = col<size-1 ? (size-1)*(size+4*col) + row : 6*size*size - 13*size + 8 + row;

      color = getCubitFaceColorIndex(cubitIndex,UP);

      objectString.append(FACE_NAMES[color]);

      }

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

      {

      cubitIndex = 6*size*size - 12*size +7 - i;

      color = getCubitFaceColorIndex(cubitIndex,RIGHT);

      objectString.append(FACE_NAMES[color]);

      }

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

      {

      row = i/size;

      col = i%size;

      if( col==size-1 ) cubitIndex = 6*size*size - 11*size + 6 -i;

      else if( col==0 ) cubitIndex = size*size - 1 - i;

      else

        {

        if( row==0 ) cubitIndex = size*size + size-1 + 4*(col-1)*(size-1) + 2*(size-2) + size;

        else         cubitIndex = size*size + size-1 + 4*(col-1)*(size-1) + 2*(size-1-row);

        }

      color = getCubitFaceColorIndex(cubitIndex,FRONT);

      objectString.append(FACE_NAMES[color]);

      }

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

      {

      row = i/size;

      col = i%size;

      cubitIndex = col==0 ? size-1-row : size*size + size-1 + 4*(col-1)*(size-1) - row;

      color = getCubitFaceColorIndex(cubitIndex,DOWN);

      objectString.append(FACE_NAMES[color]);

      }

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

      {

      row = i/size;

      col = i%size;

      cubitIndex = (size-1-row)*size + col;

      color = getCubitFaceColorIndex(cubitIndex,LEFT);

      objectString.append(FACE_NAMES[color]);

      }

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

      {

      row = i/size;

      col = i%size;

      if( col==size-1 ) cubitIndex = size*(size-1-row);

      else if( col==0 ) cubitIndex = 5*size*size - 12*size + 8 + (size-1-row)*size;

      else

        {

        if( row==size-1 ) cubitIndex = size*size + 4*(size-2-col)*(size-1);

        else              cubitIndex = size*size + 4*(size-2-col)*(size-1) + size + 2*(size-2-row);

        }

      color = getCubitFaceColorIndex(cubitIndex,BACK);

      objectString.append(FACE_NAMES[color]);

      }

    return objectString.toString();

    }

}