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 org.distorted.helpers.FactoryCubit;

import org.distorted.helpers.ObjectShape;

import org.distorted.helpers.ObjectSticker;

import org.distorted.helpers.QuatHelper;

import org.distorted.library.effect.MatrixEffectQuaternion;

import org.distorted.library.main.DistortedEffects;

import org.distorted.library.main.DistortedTexture;

import org.distorted.library.mesh.MeshBase;

import org.distorted.library.mesh.MeshSquare;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

import org.distorted.main.R;

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

public class TwistyMegaminx extends TwistyMinx

{

  static final float MEGA_D = 0.04f;

  private static final int[] QUAT_CENTER_INDICES =

      {

        16, 18, 22,  1, 20, 13, 14, 15,  0, 12,  2,  3

      };

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

      {

        { -0.36327127f, -0.5f, 0.36327127f, -0.26393202f, 0.36327127f, 0.5f, -0.36327127f, 0.26393202f },

        { -0.5f, -0.0914315f, 0.5f, -0.4163512f, 0.5f, 0.4163512f, -0.5f, 0.0914315f },

        { -0.49233657f, -0.18006028f, 0.49233657f, -0.5f, 0.49233657f, 0.5f, -0.49233657f, 0.18006028f },

        { -0.3002273f, -0.30490047f, 0.3002273f, -0.5f, 0.3002273f, 0.5f, -0.3002273f, 0.30490047f },

        { -0.29389262f, 0.4045085f, -0.47552824f, -0.1545085f, 0.0f, -0.5f, 0.47552824f, -0.1545085f, 0.29389262f, 0.4045085f }

      };

  private static final ObjectSticker[] mStickers;

  static

    {

    mStickers = new ObjectSticker[STICKERS.length];

    final float R0 = 0.08f;

    final float R1 = 0.12f;

    final float R2 = 0.12f;

    final float R3 = 0.08f;

    final float R4 = 0.10f;

    final float[][] radii = { {R0,R0,R0,R0},{R1,R1,R1,R1},{R2,R2,R2,R2},{R3,R3,R3,R3},{R4,R4,R4,R4,R4} };

    final float[] strokes = { 0.10f,0.12f,0.12f,0.08f,0.07f };

    for(int s=0; s<STICKERS.length; s++)

      {

      mStickers[s] = new ObjectSticker(STICKERS[s],null,radii[s],strokes[s]);

      }

    }

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

  TwistyMegaminx(int size, Static4D quat, DistortedTexture texture, MeshSquare mesh,

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

    {

    super(size, size, quat, texture, mesh, effects, moves, ObjectList.MEGA, res, scrWidth);

    }

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

  private int numCubitsPerCorner(int numLayers)

    {

    return 3*((numLayers-1)/2)*((numLayers-3)/2) + 1;

    }

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

  private int numCubitsPerEdge(int numLayers)

    {

    return numLayers-2;

    }

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

  float getScreenRatio()

    {

    return 1.07f;

    }

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

  int getNumStickerTypes(int numLayers)

    {

    return (numLayers+3)/2;

    }

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

  float[][] getCuts(int numLayers)

    {

    float[][] cuts = new float[6][numLayers-1];

    float D = numLayers*MovementMinx.DIST3D;

    float E = 2*SIN54;

    float X = 2*D*E/(1+2*E);  // height of the 'upper' part of a dodecahedron, i.e. put it on a table,

                              // its height is then D*2*DIST3D, it has one 'lower' part of height X, one

                              // 'middle' part of height Y and one upper part of height X again.

                              // It's edge length = numLayers/3.0f.

    int num = (numLayers-1)/2;

    float G = X*(0.5f-MEGA_D)/num; // height of one Layer

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

      {

      float cut = -D + (i+0.5f)*G;

      int j = 2*num-1-i;

      cuts[0][i] = +cut;

      cuts[0][j] = -cut;

      cuts[1][i] = +cut;

      cuts[1][j] = -cut;

      cuts[2][i] = +cut;

      cuts[2][j] = -cut;

      cuts[3][i] = +cut;

      cuts[3][j] = -cut;

      cuts[4][i] = +cut;

      cuts[4][j] = -cut;

      cuts[5][i] = +cut;

      cuts[5][j] = -cut;

      }

    return cuts;

    }

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

  private float[] computeCenter(int center, int numLayers)

    {

    float[] coords = mCenterCoords[center];

    float A = numLayers/3.0f;

    return new float[] { A*coords[0], A*coords[1], A*coords[2] };

    }

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

// Fill out mCurrCorner{X,Y,Z} by applying appropriate Quat to mBasicCorner{X,Y,Z}

// Appropriate one: QUATS[QUAT_INDICES[corner]].

  private void computeBasicCornerVectors(int corner)

    {

    Static4D quat = QUATS[QUAT_CORNER_INDICES[corner]];

    mCurrCornerV[0] = QuatHelper.rotateVectorByQuat(mBasicCornerV[0],quat);

    mCurrCornerV[1] = QuatHelper.rotateVectorByQuat(mBasicCornerV[1],quat);

    mCurrCornerV[2] = QuatHelper.rotateVectorByQuat(mBasicCornerV[2],quat);

    }

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

  private float[] computeCorner(int numCubitsPerCorner, int numLayers, int corner, int part)

    {

    float D = numLayers/3.0f;

    float[] corn = CORNERS[corner];

    if( part==0 )

      {

      return new float[] { corn[0]*D, corn[1]*D, corn[2]*D };

      }

    else

      {

      float E = 2.0f*D*(0.5f-MEGA_D)/(0.5f*(numLayers-1));

      int N = (numCubitsPerCorner-1)/3;

      int block = (part-1) % N;

      int index = (part-1) / N;

      Static4D pri = mCurrCornerV[index];

      Static4D sec = mCurrCornerV[(index+2)%3];

      int layers= (numLayers-3)/2;

      int multP = (block % layers) + 1;

      int multS = (block / layers);

      return new float[] {

                          corn[0]*D + (pri.get0()*multP + sec.get0()*multS)*E,

                          corn[1]*D + (pri.get1()*multP + sec.get1()*multS)*E,

                          corn[2]*D + (pri.get2()*multP + sec.get2()*multS)*E

                         };

      }

    }

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

  private int computeEdgeType(int cubit, int numCubitsPerCorner, int numCubitsPerEdge)

    {

    int part = (cubit - NUM_CORNERS*numCubitsPerCorner) % numCubitsPerEdge;

    return (part+1)/2;

    }

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

  private float[] computeEdge(int numLayers, int edge, int part)

    {

    float D = numLayers/3.0f;

    float[] c1 = CORNERS[ mEdgeMap[edge][0] ];

    float[] c2 = CORNERS[ mEdgeMap[edge][1] ];

    float x = D * (c1[0]+c2[0]) / 2;

    float y = D * (c1[1]+c2[1]) / 2;

    float z = D * (c1[2]+c2[2]) / 2;

    if( part==0 )

      {

      return new float[] { x, y, z };

      }

    else

      {

      int mult = (part+1)/2;

      int dir  = (part+1)%2;

      float[] center = mCenterCoords[ mEdgeMap[edge][dir+2] ];

      float vX = D*center[0] - x;

      float vY = D*center[1] - y;

      float vZ = D*center[2] - z;

      float A = mult*D*(0.5f-MEGA_D)*COS18/((numLayers-1)*0.5f);

      A /= (float)Math.sqrt(vX*vX+vY*vY+vZ*vZ);

      return new float[] { x+A*vX, y+A*vY, z+A*vZ };

      }

    }

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

  float[][] getCubitPositions(int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    int numCubits = NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge + NUM_CENTERS;

    int index=0;

    final float[][] CENTERS = new float[numCubits][];

    for(int corner=0; corner<NUM_CORNERS; corner++)

      {

      computeBasicCornerVectors(corner);

      for(int part=0; part<numCubitsPerCorner; part++, index++)

        {

        CENTERS[index] = computeCorner(numCubitsPerCorner,numLayers,corner,part);

        }

      }

    for(int edge=0; edge<NUM_EDGES; edge++)

      {

      for(int part=0; part<numCubitsPerEdge; part++, index++)

        {

        CENTERS[index] = computeEdge(numLayers, edge, part );

        }

      }

    for(int center=0; center<NUM_CENTERS; center++, index++)

      {

      CENTERS[index] = computeCenter(center, numLayers);

      }

    return CENTERS;

    }

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

  private int getQuat(int cubit, int numCubitsPerCorner, int numCubitsPerEdge)

    {

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      int corner = cubit/numCubitsPerCorner;

      return QUAT_CORNER_INDICES[corner];

      }

    if( cubit < NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int edge = (cubit-NUM_CORNERS*numCubitsPerCorner)/numCubitsPerEdge;

      return QUAT_EDGE_INDICES[edge];

      }

    int center = cubit - NUM_CORNERS*numCubitsPerCorner - NUM_EDGES*numCubitsPerEdge;

    return QUAT_CENTER_INDICES[center];

    }

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

  ObjectShape getObjectShape(int cubit, int numLayers)

    {

    int variant = getCubitVariant(cubit,numLayers);

    int numVariants = getNumCubitVariants(numLayers);

    if( variant==0 )

      {

      float width = (numLayers/3.0f)*(0.5f-MEGA_D)/(0.5f*(numLayers-1));

      float A = (2*SQ3/3)*SIN54;

      float B = 0.4f;

      double X = width*COS18*SIN_HALFD;

      double Y = width*SIN18;

      double Z = width*COS18*COS_HALFD;

      int N = numLayers==3 ? 1:0;

      double[][] vertices = new double[][]

        {

            { 0.0, 0.0      , 0.0 },

            {   X,   Y      ,  -Z },

            { 0.0, 2*Y      ,-2*Z },

            {  -X,   Y      ,  -Z },

            { 0.0, 0.0-width, 0.0 },

            {   X,   Y-width,  -Z },

            { 0.0, 2*Y-width,-2*Z },

            {  -X,   Y-width,  -Z },

        };

      int[][] vertIndexes = new int[][]

        {

            {4,5,1,0},

            {7,4,0,3},

            {0,1,2,3},

            {4,5,6,7},

            {6,5,1,2},

            {7,6,2,3}

        };

      float[][] bands    = new float[][]

        {

         {0.04f,34,0.3f,0.2f, 3, N, 0},

         {0.00f, 0,0.0f,0.0f, 2, N, 0}

        };

      int[] bandIndices   = new int[] { 0,0,0,1,1,1};

      float[][] corners   = new float[][] { {0.04f,0.10f} };

      int[] cornerIndices = new int[] { 0,-1,-1,-1,-1,-1,-1,-1 };

      float[][] centers   = new float[][] { {0.0f, -(float)Math.sqrt(1-A*A)*B,-A*B} };

      int[] centerIndices = new int[] { 0,-1,-1,-1,-1,-1,-1,-1 };

      return new ObjectShape(vertices,vertIndexes,bands,bandIndices,corners,cornerIndices,centers,centerIndices,getNumCubitFaces(), null);

      }

    if( variant<numVariants-1 )

      {

      int numCubitsPerCorner = numCubitsPerCorner(numLayers);

      int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

      int type = computeEdgeType(cubit,numCubitsPerCorner,numCubitsPerEdge);

      float height= (numLayers/3.0f)*(0.5f-MEGA_D)*COS18/((numLayers-1)*0.5f);

      float width = (numLayers/3.0f)*2*MEGA_D + 2*type*height*SIN18/COS18;

      double W = width/2;

      double X = height*SIN_HALFD;

      double Y = height*SIN18/COS18;

      double Z = height*COS_HALFD;

      double[][] vertices = new double[][]

        {

            { 0.0,   W   , 0.0 },

            {   X, W+Y   ,  -Z },

            { 0.0, W+2*Y ,-2*Z },

            {  -X, W+Y   ,  -Z },

            { 0.0,  -W   , 0.0 },

            {   X,-W-Y   ,  -Z },

            { 0.0,-W-2*Y ,-2*Z },

            {  -X,-W-Y   ,  -Z },

        };

      int[][] vertIndexes = new int[][]

        {

            {4,5,1,0},

            {7,4,0,3},

            {7,6,2,3},

            {6,5,1,2},

            {0,1,2,3},

            {4,5,6,7}

        };

      int N = numLayers<=5 ? 5 : 3;

      float[][] bands     = new float[][]

        {

         {0.04f,34,0.2f,0.2f,N,0,0},

         {0.00f, 0,0.3f,0.2f,2,0,0}

        };

      int[] bandIndices   = new int[] { 0,0,1,1,1,1};

      float[][] corners   = new float[][] { {0.04f,0.10f} };

      int[] cornerIndices = new int[] { -1,-1,-1,-1, -1,-1,-1,-1 };

      float[][] centers   = new float[][] { {0.0f, 0.0f, (float)(-2*Z)} };

      int[] centerIndices = new int[] { -1,-1,-1,-1, -1,-1,-1,-1 };

      return new ObjectShape(vertices,vertIndexes,bands,bandIndices,corners,cornerIndices,centers,centerIndices,getNumCubitFaces(), null);

      }

    else

      {

      float width = 2 * (numLayers/3.0f) * (MEGA_D+(0.5f-MEGA_D)*SIN18);

      final double V = 0.83;   // ??

      final double ANGLE = V*Math.PI;

      final double cosA  = Math.cos(ANGLE);

      final double sinA  = Math.sin(ANGLE);

      float R  = 0.5f*width/COS54;

      float X1 = R*COS54;

      float Y1 = R*SIN54;

      float X2 = R*COS18;

      float Y2 = R*SIN18;

      double[][] vertices = new double[][]

        {

          {-X1,+Y1*sinA, Y1*cosA},

          {-X2,-Y2*sinA,-Y2*cosA},

          {0.0f,-R*sinA, -R*cosA},

          {+X2,-Y2*sinA,-Y2*cosA},

          {+X1,+Y1*sinA, Y1*cosA}

        };

      int[][] vertIndexes = new int[][]

        {

          {0,1,2,3,4},

          {0,1,2,3,4}

        };

      int N = numLayers==3 ? 4 : 3;

      float[][] bands = new float[][]

        {

         {0.04f,45, R/3,0.2f,N,0,0},

         {0.00f, 0, R/3,0.2f,2,0,0}

        };

      int[] bandIndices   = new int[] { 0,1 };

      float[][] corners   = new float[][] { {0.04f,0.10f} };

      int[] cornerIndices = new int[] { -1,-1,-1,-1, -1 };

      float[][] centers   = new float[][] { {0.0f, 0.0f, 0.0f} };

      int[] centerIndices = new int[] { -1,-1,-1,-1, -1 };

      return new ObjectShape(vertices,vertIndexes,bands,bandIndices,corners,cornerIndices,centers,centerIndices,getNumCubitFaces(), null);

      }

    }

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

  private Static4D getQuat(int cubit, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    return QUATS[getQuat(cubit,numCubitsPerCorner,numCubitsPerEdge)];

    }

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

  private int getNumCubitVariants(int numLayers)

    {

    int[] sizes = ObjectList.MEGA.getSizes();

    int variants = sizes.length;

    return 2+(sizes[variants-1]-1)/2;

    }

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

  int getCubitVariant(int cubit, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    if( cubit<NUM_CORNERS*numCubitsPerCorner ) return 0;

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    if( cubit<NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int type = computeEdgeType(cubit,numCubitsPerCorner,numCubitsPerEdge);

      return type+1;

      }

    int[] sizes = ObjectList.MEGA.getSizes();

    int variants = sizes.length;

    int numShapes = 2+(sizes[variants-1]-1)/2;

    return numShapes-1;

    }

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

  MeshBase createCubitMesh(int cubit, int numLayers)

    {

    int variant = getCubitVariant(cubit,numLayers);

    if( mMeshes==null )

      {

      FactoryCubit factory = FactoryCubit.getInstance();

      factory.clear();

      mMeshes = new MeshBase[getNumCubitVariants(numLayers)];

      }

    if( mMeshes[variant]==null )

      {

      ObjectShape shape = getObjectShape(cubit,numLayers);

      FactoryCubit factory = FactoryCubit.getInstance();

      factory.createNewFaceTransform(shape);

      mMeshes[variant] = factory.createRoundedSolid(shape);

      }

    MeshBase mesh = mMeshes[variant].copy(true);

    MatrixEffectQuaternion quat = new MatrixEffectQuaternion( getQuat(cubit,numLayers), new Static3D(0,0,0) );

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

    return mesh;

    }

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

  int getCornerColor(int cubit, int cubitface, int numLayers, int numCubitsPerCorner)

    {

    if( cubitface<0 || cubitface>2 ) return NUM_TEXTURES;

    int part  = cubit % numCubitsPerCorner;

    int corner= cubit / numCubitsPerCorner;

    if( part==0 )

      {

      return mCornerFaceMap[corner][cubitface];

      }

    else

      {

      int N = (numCubitsPerCorner-1)/3;

      int block = (part-1) % N;

      int index = (part-1) / N;

      if( block< (numLayers-3)/2 )

        {

        switch(index)

          {

          case 0: return cubitface==1 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          case 1: return cubitface==0 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          case 2: return cubitface==2 ? NUM_TEXTURES : mCornerFaceMap[corner][cubitface];

          }

        }

      else

        {

        switch(index)

          {

          case 0: return cubitface==0 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          case 1: return cubitface==2 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          case 2: return cubitface==1 ? mCornerFaceMap[corner][cubitface] : NUM_TEXTURES;

          }

        }

      }

    return NUM_TEXTURES;

    }

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

  int getEdgeColor(int edge, int cubitface, int numCubitsPerEdge)

    {

    if( cubitface<0 || cubitface>1 ) return NUM_TEXTURES;

    int part    = edge % numCubitsPerEdge;

    int variant = edge / numCubitsPerEdge;

    return (part==0 || cubitface==((part+1)%2)) ? mEdgeMap[variant][cubitface+2] + ((part+3)/2)*NUM_FACES : NUM_TEXTURES;

    }

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

  int getCenterColor(int center, int cubitface, int numLayers)

    {

    return cubitface>0 ? NUM_TEXTURES : center + NUM_FACES*(numLayers+1)/2;

    }

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

  int getFaceColor(int cubit, int cubitface, int numLayers)

    {

    int numCubitsPerCorner = numCubitsPerCorner(numLayers);

    int numCubitsPerEdge   = numCubitsPerEdge(numLayers);

    if( cubit < NUM_CORNERS*numCubitsPerCorner )

      {

      return getCornerColor(cubit,cubitface,numLayers,numCubitsPerCorner);

      }

    else if( cubit<NUM_CORNERS*numCubitsPerCorner + NUM_EDGES*numCubitsPerEdge )

      {

      int edge = cubit - NUM_CORNERS*numCubitsPerCorner;

      return getEdgeColor(edge,cubitface,numCubitsPerEdge);

      }

    else

      {

      int center = cubit-NUM_CORNERS*numCubitsPerCorner-NUM_EDGES*numCubitsPerEdge;

      return getCenterColor( center, cubitface, numLayers);

      }

    }

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

  int getColor(int face)

    {

    return FACE_COLORS[face];

    }

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

  ObjectSticker retSticker(int face)

    {

    return mStickers[getStickerIndex(face)];

    }

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

  private int getStickerIndex(int face)

    {

    int variant = face/NUM_FACES;

    if( variant==0 ) return 0;

    int numLayers = getNumLayers();

    if( variant < (numLayers+1)/2 )

      {

      if( numLayers==3 ) return 1;

      else

        {

        if( variant==1 ) return 2;

        else             return 3;

        }

      }

    return 4;

    }

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

// PUBLIC API

  public boolean isSolved()

    {

    int index = CUBITS[0].mQuatIndex;

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

      {

      if( thereIsVisibleDifference(CUBITS[i], index) ) return false;

      }

    return true;

    }

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

  public int getObjectName(int numLayers)

    {

    if( numLayers==3 ) return R.string.minx3;

    if( numLayers==5 ) return R.string.minx5;

    return 0;

    }

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

  public int getInventor(int numLayers)

    {

    if( numLayers==3 ) return R.string.minx3_inventor;

    if( numLayers==5 ) return R.string.minx5_inventor;

    return 0;

    }

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

  public int getComplexity(int numLayers)

    {

    if( numLayers==3 ) return 4;

    return 5;

    }

}