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.object;

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.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.

  private 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)

    {

    super(size,quatCur,quatAcc,texture,mesh,effects);

    }

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

  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;

    }

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

  Static3D[] getRotationAxis()

    {

    return AXIS;

    }

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

// paint only the square with lower-left corner at (face*TEX_H,0) and side length TEX_H

  void createFaceTexture(Canvas canvas, Paint paint, int face)

    {

    final int S = TEXTURE_HEIGHT;

    final int R = TEXTURE_HEIGHT/10;

    final int M = TEXTURE_HEIGHT/20;

    paint.setColor(FACE_COLORS[face]);

    canvas.drawRoundRect( (face*S+M), M, (face*S+M) + (S-2*M), M + (S-2*M), R, R, paint);

    }

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

  MeshBase createCubitMesh(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 int getBasicAngle()

    {

    return 4;

    }

}