Magic Cube

import org.distorted.library.effect.MatrixEffectMove;

import org.distorted.library.effect.MatrixEffectQuaternion;

import org.distorted.library.effect.MatrixEffectScale;

import java.util.ArrayList;

  private static final double[] mBuffer = new double[3];

  private static final double[] mQuat1  = new double[4];

  private static final double[] mQuat2  = new double[4];

  private static final double[] mQuat3  = new double[4];

  private static final double[] mQuat4  = new double[4];

  private static class StickerCoords

    {

    double[] vertices;

    }

  private static class FaceTransform

    {

    int sticker;

    double vx,vy,vz;

    double scale;

    double qx,qy,qz,qw;

    boolean flip;

    }

  private static final ArrayList<FaceTransform> mFaceTransform = new ArrayList<>();

  private static final ArrayList<StickerCoords> mStickerCoords = new ArrayList<>();

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

  private boolean areColinear(double[][] vertices, int index1, int index2, int index3)

    {

    double x1 = vertices[index1][0];

    double y1 = vertices[index1][1];

    double z1 = vertices[index1][2];

    double x2 = vertices[index2][0];

    double y2 = vertices[index2][1];

    double z2 = vertices[index2][2];

    double x3 = vertices[index3][0];

    double y3 = vertices[index3][1];

    double z3 = vertices[index3][2];

    double v1x = x2-x1;

    double v1y = y2-y1;

    double v1z = z2-z1;

    double v2x = x3-x1;

    double v2y = y3-y1;

    double v2z = z3-z1;

    double A = Math.sqrt( (v1x*v1x+v1y*v1y+v1z*v1z) / (v2x*v2x+v2y*v2y+v2z*v2z) );

    return (v1x==A*v2x && v1y==A*v2y && v1z==A*v2z);

    }

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

  private void computeNormalVector(double[][] vertices, int index1, int index2, int index3)

    {

    double x1 = vertices[index1][0];

    double y1 = vertices[index1][1];

    double z1 = vertices[index1][2];

    double x2 = vertices[index2][0];

    double y2 = vertices[index2][1];

    double z2 = vertices[index2][2];

    double x3 = vertices[index3][0];

    double y3 = vertices[index3][1];

    double z3 = vertices[index3][2];

    double v1x = x2-x1;

    double v1y = y2-y1;

    double v1z = z2-z1;

    double v2x = x3-x1;

    double v2y = y3-y1;

    double v2z = z3-z1;

    mBuffer[0] = v1y*v2z - v2y*v1z;

    mBuffer[1] = v1z*v2x - v2z*v1x;

    mBuffer[2] = v1x*v2y - v2x*v1y;

    double len = mBuffer[0]*mBuffer[0] + mBuffer[1]*mBuffer[1] + mBuffer[2]*mBuffer[2];

    len = Math.sqrt(len);

    mBuffer[0] /= len;

    mBuffer[1] /= len;

    mBuffer[2] /= len;

    }

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

// return quat1*quat2

  private static void quatMultiply( double[] quat1, double[] quat2, double[] result )

    {

    double qx = quat1[0];

    double qy = quat1[1];

    double qz = quat1[2];

    double qw = quat1[3];

    double rx = quat2[0];

    double ry = quat2[1];

    double rz = quat2[2];

    double rw = quat2[3];

    result[0] = rw*qx - rz*qy + ry*qz + rx*qw;

    result[1] = rw*qy + rz*qx + ry*qw - rx*qz;

    result[2] = rw*qz + rz*qw - ry*qx + rx*qy;

    result[3] = rw*qw - rz*qz - ry*qy - rx*qx;

    }

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

  private void fitInSquare(FaceTransform info, double[][] vert3D)

    {

    double minX = Double.MAX_VALUE;

    double maxX =-Double.MAX_VALUE;

    double minY = Double.MAX_VALUE;

    double maxY =-Double.MAX_VALUE;

    for (double[] vert : vert3D)

      {

      double x = vert[0];

      double y = vert[1];

      if (x > maxX) maxX = x;

      if (x < minX) minX = x;

      if (y > maxY) maxY = y;

      if (y < minY) minY = y;

      }

    minX = minX<0 ? -minX:minX;

    maxX = maxX<0 ? -maxX:maxX;

    minY = minY<0 ? -minY:minY;

    maxY = maxY<0 ? -maxY:maxY;

    double max1 = Math.max(minX,minY);

    double max2 = Math.max(maxX,maxY);

    double max3 = Math.max(max1,max2);

    info.scale = max3/0.5;

    int len = vert3D.length;

    StickerCoords sInfo = new StickerCoords();

    sInfo.vertices = new double[2*len];

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

      {

      sInfo.vertices[2*vertex  ] = vert3D[vertex][0] / info.scale;

      sInfo.vertices[2*vertex+1] = vert3D[vertex][1] / info.scale;

      }

    mStickerCoords.add(sInfo);

    info.sticker = mStickerCoords.size() -1;

    info.flip = false;

    }

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

  private void constructNew(FaceTransform info, final double[][] vert3D)

    {

    // compute center of gravity

    info.vx = 0.0f;

    info.vy = 0.0f;

    info.vz = 0.0f;

    int len = vert3D.length;

    for (double[] vert : vert3D)

      {

      info.vx += vert[0];

      info.vy += vert[1];

      info.vz += vert[2];

      }

    info.vx /= len;

    info.vy /= len;

    info.vz /= len;

    // move all vertices so that their center of gravity is at (0,0,0)

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

      {

      vert3D[i][0] -= info.vx;

      vert3D[i][1] -= info.vy;

      vert3D[i][2] -= info.vz;

      }

    // find 3 non-colinear vertices

    int foundIndex = -1;

    for(int vertex=2; vertex<len; vertex++)

      {

      if( !areColinear(vert3D,0,1,vertex) )

        {

        foundIndex = vertex;

        break;

        }

      }

    // compute the normal vector

    if( foundIndex==-1 )

      {

      throw new RuntimeException("all vertices colinear");

      }

    computeNormalVector(vert3D,0,1,foundIndex);

    // rotate so that the normal vector becomes (0,0,1)

    double axisX, axisY, axisZ;

    if( mBuffer[0]!=0.0f || mBuffer[1]!=0.0f )

      {

      axisX = -mBuffer[1];

      axisY =  mBuffer[0];

      axisZ = 0.0f;

      double axiLen = axisX*axisX + axisY*axisY;

      axiLen = Math.sqrt(axiLen);

      axisX /= axiLen;

      axisY /= axiLen;

      axisZ /= axiLen;

      }

    else

      {

      axisX = 0.0f;

      axisY = 1.0f;

      axisZ = 0.0f;

      }

    double cosTheta = mBuffer[2];

    double sinTheta = Math.sqrt(1-cosTheta*cosTheta);

    double sinHalfTheta = computeSinHalf(cosTheta);

    double cosHalfTheta = computeCosHalf(sinTheta,cosTheta);

    mQuat1[0] = axisX*sinHalfTheta;

    mQuat1[1] = axisY*sinHalfTheta;

    mQuat1[2] = axisZ*sinHalfTheta;

    mQuat1[3] = cosHalfTheta;

    mQuat2[0] =-axisX*sinHalfTheta;

    mQuat2[1] =-axisY*sinHalfTheta;

    mQuat2[2] =-axisZ*sinHalfTheta;

    mQuat2[3] = cosHalfTheta;

    for (double[] vert : vert3D)

      {

      quatMultiply(mQuat1, vert  , mQuat3);

      quatMultiply(mQuat3, mQuat2, vert  );

      }

    // fit the whole thing in a square and remember the scale & 2D vertices

    fitInSquare(info, vert3D);

    // remember the rotation

    info.qx =-mQuat1[0];

    info.qy =-mQuat1[1];

    info.qz =-mQuat1[2];

    info.qw = mQuat1[3];

    }

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

  private double computeCos(double oldX, double oldY, double newX, double newY, double len1, double len2)

    {

    double ret= (oldX*newX+oldY*newY) / (len1*len2);

    if( ret<-1.0 ) return -1.0;

    if( ret> 1.0 ) return  1.0;

    return ret;

    }

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

// sin of (signed!) angle between vectors 'old' and 'new', counterclockwise!

  private double computeSin(double oldX, double oldY, double newX, double newY, double len1, double len2)

    {

    double ret= (newX*oldY-oldX*newY) / (len1*len2);

    if( ret<-1.0 ) return -1.0;

    if( ret> 1.0 ) return  1.0;

    return ret;

    }

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

  private void rotateAllVertices(double[] result, int len, double[] vertices, double sin, double cos)

    {

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

      {

      result[2*i  ] = vertices[2*i  ]*cos - vertices[2*i+1]*sin;

      result[2*i+1] = vertices[2*i  ]*sin + vertices[2*i+1]*cos;

      }

    }

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

  private double computeScale(double[] v1, double[] v2)

    {

    double lenSq1 = v1[0]*v1[0] + v1[1]*v1[1];

    double lenSq2 = v2[0]*v2[0] + v2[1]*v2[1];

    return Math.sqrt(lenSq2/lenSq1);

    }

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

  private double computeSinHalf(double cos)

    {

    return Math.sqrt((1-cos)/2);

    }

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

  private double computeCosHalf(double sin, double cos)

    {

    double cosHalf = Math.sqrt((1+cos)/2);

    return sin<0 ? -cosHalf : cosHalf;

    }

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

  private int computeRotatedIndex(int oldVertex, int len, int rotatedVertex, boolean inverted)

    {

    int v = (rotatedVertex + (inverted? -oldVertex : oldVertex));

    if( v>=len ) v-=len;

    if( v< 0   ) v+=len;

    return v;

    }

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

  private boolean isScaledVersionOf(double[] newVert, double[] oldVert, int len, int vertex, boolean inverted)

    {

    double EPSILON = 0.001;

    double scale = computeScale(newVert,oldVert);

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

      {

      int index = computeRotatedIndex(i,len,vertex,inverted);

      double horz = oldVert[2*i  ] - scale*newVert[2*index  ];

      double vert = oldVert[2*i+1] - scale*newVert[2*index+1];

      if( horz>EPSILON || horz<-EPSILON || vert>EPSILON || vert<-EPSILON ) return false;

      }

    return true;

    }

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

  private void mirrorAllVertices(double[] output, int len, double[] input)

    {

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

      {

      output[2*vertex  ] = input[2*vertex  ];

      output[2*vertex+1] =-input[2*vertex+1];

      }

    }

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

  private void correctInfo(FaceTransform info, double scale, double sin, double cos, int oldSticker, boolean flip)

    {

    mStickerCoords.remove(info.sticker);

    info.flip    = flip;

    info.sticker = oldSticker;

    info.scale  *= scale;

    mQuat1[0] = info.qx;

    mQuat1[1] = info.qy;

    mQuat1[2] = info.qz;

    mQuat1[3] = info.qw;

    double sinHalf = computeSinHalf(cos);

    double cosHalf = computeCosHalf(sin,cos);

    if( flip )

      {

      mQuat3[0] = 0.0f;

      mQuat3[1] = 0.0f;

      mQuat3[2] = sinHalf;

      mQuat3[3] = cosHalf;

      mQuat4[0] = 1.0;

      mQuat4[1] = 0.0;

      mQuat4[2] = 0.0;

      mQuat4[3] = 0.0;

      quatMultiply( mQuat3, mQuat4, mQuat2 );

      }

    else

      {

      mQuat2[0] = 0.0f;

      mQuat2[1] = 0.0f;

      mQuat2[2] = sinHalf;

      mQuat2[3] = cosHalf;

      }

    quatMultiply( mQuat1, mQuat2, mQuat3 );

    info.qx = mQuat3[0];

    info.qy = mQuat3[1];

    info.qz = mQuat3[2];

    info.qw = mQuat3[3];

    }

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

  private void printVert(double[] buffer)

    {

    int len = buffer.length/2;

    String str = "";

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

      {

      str += (" ("+buffer[2*i]+" , "+buffer[2*i+1]+" ) ");

      }

    android.util.Log.d("D", str);

    }

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

  private boolean foundVertex(FaceTransform info, double[] buffer, int len, double[] newVert,

                              double[] oldVert, double lenFirstOld, int oldSticker, boolean inverted)

    {

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

      {

      double newX = newVert[2*vertex  ];

      double newY = newVert[2*vertex+1];

      double lenIthNew = Math.sqrt(newX*newX + newY*newY);

      double cos = computeCos( oldVert[0], oldVert[1], newX, newY, lenIthNew, lenFirstOld);

      double sin = computeSin( oldVert[0], oldVert[1], newX, newY, lenIthNew, lenFirstOld);

      rotateAllVertices(buffer,len,newVert,sin,cos);

      if( isScaledVersionOf(buffer,oldVert,len,vertex,inverted) )

        {

        double scale = computeScale(oldVert,newVert);

        correctInfo(info,scale,sin,cos,oldSticker,inverted);

        return true;

        }

      }

    return false;

    }

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

  private boolean successfullyCollapsedStickers(final FaceTransform newInfo, final FaceTransform oldInfo)

    {

    StickerCoords sNewInfo = mStickerCoords.get(newInfo.sticker);

    StickerCoords sOldInfo = mStickerCoords.get(oldInfo.sticker);

    double[] newVert = sNewInfo.vertices;

    double[] oldVert = sOldInfo.vertices;

    int oldLen = oldVert.length;

    int newLen = newVert.length;

    if( oldLen == newLen )

      {

      int oldSticker = oldInfo.sticker;

      double[] buffer1 = new double[oldLen];

      double lenFirstOld = Math.sqrt(oldVert[0]*oldVert[0] + oldVert[1]*oldVert[1]);

      if( foundVertex(newInfo, buffer1, oldLen/2, newVert, oldVert, lenFirstOld, oldSticker, false) ) return true;

      double[] buffer2 = new double[oldLen];

      mirrorAllVertices(buffer2, newLen/2, newVert);

      if( foundVertex(newInfo, buffer1, oldLen/2, buffer2, oldVert, lenFirstOld, oldSticker, true ) ) return true;

      }

    return false;

    }

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

  private double[][] constructVert(double[][] vertices, int[] index)

    {

    int len = index.length;

    double[][] ret = new double[len][4];

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

      {

      ret[i][0] = vertices[index[i]][0];

      ret[i][1] = vertices[index[i]][1];

      ret[i][2] = vertices[index[i]][2];

      ret[i][3] = 1.0f;

      }

    return ret;

    }

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

  private void prepareAndRoundCorners(MeshBase mesh, double[][] vertices, int[][] vertIndexes,

                                      float[][] corners, int[] cornerIndexes )

    {

    int numNeig, lenFV;

    int lenV = vertices.length;

    int[] verts = new int[2*(lenV-1)];

    Static3D[] staticVert = new Static3D[1];

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

    double cx, cy, cz;

    double[] singleV;

    for(int v=0; v<lenV; v++)

      {

      // prepare verts[]

      numNeig = 0;

      for (int[] vertIndex : vertIndexes)

        {

        lenFV = vertIndex.length;

        for (int fv = 0; fv < lenFV; fv++)

          if (vertIndex[fv] == v)

            {

            int prev = fv > 0 ? fv - 1 : lenFV - 1;

            int next = fv < lenFV - 1 ? fv + 1 : 0;

            verts[numNeig++] = vertIndex[prev];

            verts[numNeig++] = vertIndex[next];

            }

        }

      cx=cy=cz=0.0f;

      // from verts[] prepare center

      for(int n=0; n<numNeig; n++)

        {

        singleV = vertices[verts[n]];

        cx += singleV[0];

        cy += singleV[1];

        cz += singleV[2];

        }

      center.set( (float)(cx/numNeig - vertices[v][0]),

                  (float)(cy/numNeig - vertices[v][1]),

                  (float)(cz/numNeig - vertices[v][2]));

android.util.Log.e("D", "vertex: "+v+" CENTER: "+center.get0()+" "+center.get1()+" "+center.get2());

      // round Corners

      staticVert[0] = new Static3D( (float)vertices[v][0], (float)vertices[v][1], (float)vertices[v][2]);

      int corn = cornerIndexes[v];

      float strength = corners[corn][0];

      float radius   = corners[corn][1];

      roundCorners(mesh, center, staticVert, strength, radius);

      }

    }

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

  private void correctComponents(MeshBase mesh, int numComponents)

    {

    int numTexToBeAdded = numComponents-mesh.getNumTexComponents();

    mesh.mergeEffComponents();

    for(int i=0; i<numTexToBeAdded; i++ ) mesh.addEmptyTexComponent();

    }

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

// PUBLIC

  public void printStickerCoords()

    {

    int stickers = mStickerCoords.size();

    android.util.Log.d("D", "---- STICKER COORDS ----");

    for(int s=0; s<stickers; s++)

      {

      String ver = "{ ";

      StickerCoords info = mStickerCoords.get(s);

      int len = info.vertices.length/2;

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

        {

        if( i!=0 ) ver += ", ";

        ver += ( (float)info.vertices[2*i]+"f, "+(float)info.vertices[2*i+1]+"f");

        }

      ver += " }";

      android.util.Log.d("D", ver);

      }

    android.util.Log.d("D", "---- END STICKER COORDS ----");

    }

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

  public void printFaceTransform()

    {

    android.util.Log.d("D", "---- FACE TRANSFORM ---");

    int faces = mFaceTransform.size();

    for(int f=0; f<faces; f++)

      {

      FaceTransform info = mFaceTransform.get(f);

      android.util.Log.e("D", "q=("+info.qx+", "+info.qy+", "+info.qz+", "+info.qw+") v=("

                       +info.vx+", "+info.vy+", "+info.vz+") scale="+info.scale+" sticker="+info.sticker);

      }

    }

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

  public void clear()

    {

    mStickerCoords.clear();

    mFaceTransform.clear();

    }

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

  public void createNewFaceTransform( final double[][] vertices, final int[][] indexes)

    {

    mFaceTransform.clear();

    int numFaces = indexes.length;

    FaceTransform oldInfo;

    for(int face=0; face<numFaces; face++)

      {

      FaceTransform newInfo = new FaceTransform();

      int[] index = indexes[face];

      double[][] vert = constructVert(vertices,index);

      constructNew(newInfo,vert);

      for(int previous=0; previous<face; previous++)

        {

        oldInfo = mFaceTransform.get(previous);

        if( successfullyCollapsedStickers(newInfo,oldInfo) ) break;

        }

      mFaceTransform.add(newInfo);

      }

    }

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

  public MeshBase createRoundedSolid(final double[][] vertices, final int[][] vertIndexes,

                                     final float[][] bands    , final int[]   bandIndexes,

                                     final float[][] corners  , final int[]   cornerIndexes,

                                     final int numComponents )

    {

    int numFaces = vertIndexes.length;

    float[] band, bandsComputed;

    MeshBase[] meshes = new MeshBase[numFaces];

    FaceTransform fInfo;

    StickerCoords sInfo;

    for(int face=0; face<numFaces; face++)

      {

      fInfo = mFaceTransform.get(face);

      sInfo = mStickerCoords.get(fInfo.sticker);

      double[] verts = sInfo.vertices;

      int lenVerts = verts.length;

      float[] vertsFloat = new float[lenVerts];

      for(int i=0; i<lenVerts; i++) vertsFloat[i] = (float)verts[i];

      band = bands[bandIndexes[face]];

      bandsComputed = computeBands( band[0], (int)band[1], band[2], band[3], (int)band[4]);

      meshes[face] = new MeshPolygon(vertsFloat,bandsComputed,(int)band[5],(int)band[6]);

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

      }

    MeshBase mesh = new MeshJoined(meshes);

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

    for(int face=0; face<numFaces; face++)

      {

      int assoc = (1<<face);

      fInfo = mFaceTransform.get(face);

      float vx = (float)fInfo.vx;

      float vy = (float)fInfo.vy;

      float vz = (float)fInfo.vz;

      float sc = (float)fInfo.scale;

      float qx = (float)fInfo.qx;

      float qy = (float)fInfo.qy;

      float qz = (float)fInfo.qz;

      float qw = (float)fInfo.qw;

      Static3D scale = new Static3D(sc,sc, fInfo.flip ? -sc : sc);

      Static3D move3D= new Static3D(vx,vy,vz);

      Static4D quat  = new Static4D(qx,qy,qz,qw);

      mesh.apply(new MatrixEffectScale(scale)           ,assoc,-1);

      mesh.apply(new MatrixEffectQuaternion(quat,center),assoc,-1);

      mesh.apply(new MatrixEffectMove(move3D)           ,assoc,-1);

      }

    prepareAndRoundCorners(mesh, vertices, vertIndexes, corners, cornerIndexes);

    correctComponents(mesh,numComponents);

    return mesh;

    }

  private final double[][] VERTICES_SMALL = new double[][]

          {

              { 0.5, 0.5, 0.5 },

              { 0.5, 0.5,-0.5 },

              { 0.5,-0.5, 0.5 },

              { 0.5,-0.5,-0.5 },

              {-0.5, 0.5, 0.5 },

              {-0.5, 0.5,-0.5 },

              {-0.5,-0.5, 0.5 },

              {-0.5,-0.5,-0.5 },

          };

  private final double[][] VERTICES_BIG = new double[][]

          {

              // TODO

          };

  private final int[][] VERT_INDEXES = new int[][]

          {

              {2,3,1,0},   // counterclockwise!

              {7,6,4,5},

              {4,0,1,5},

              {7,3,2,6},

              {6,2,0,4},

              {3,7,5,1}

          };

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

  double[][] getVertices(int cubitType)

    {

     if( cubitType==0 )  // Small cubit

      {

      return VERTICES_SMALL;

      }

    if( cubitType==1 )  // Big cubit

      {

      return VERTICES_BIG;

      }

    return null;

    }

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

  int[][] getVertIndexes(int cubitType)

    {

    return VERT_INDEXES;

    }

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

  int getNumCubitTypes(int numLayers)

    {

    return 2;

    }

  private final double[][] VERTICES_SMALL = new double[][]

          {

              { 0.5, 0.5, 0.5 },

              { 0.5, 0.5,-0.5 },

              { 0.5,-0.5, 0.5 },

              { 0.5,-0.5,-0.5 },

              {-0.5, 0.5, 0.5 },

              {-0.5, 0.5,-0.5 },

              {-0.5,-0.5, 0.5 },

              {-0.5,-0.5,-0.5 },

          };

  private final double[][] VERTICES_BIG = new double[][]

          {

              // TODO

          };

  private final int[][] VERT_INDEXES = new int[][]

          {

              {2,3,1,0},   // counterclockwise!

              {7,6,4,5},

              {4,0,1,5},

              {7,3,2,6},

              {6,2,0,4},

              {3,7,5,1}

          };

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

  double[][] getVertices(int cubitType)

    {

     if( cubitType==0 )  // Small cubit

      {

      return VERTICES_SMALL;

      }

    if( cubitType==1 )  // Big cubit

      {

      return VERTICES_BIG;

      }

    return null;

    }

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

  int[][] getVertIndexes(int cubitType)

    {

    return VERT_INDEXES;

    }

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

  int getNumCubitTypes(int numLayers)

    {

    return 2;

    }

  private final double[][] VERTICES_SMALL = new double[][]

          {

              { 0.5, 0.5, 0.5 },

              { 0.5, 0.5,-0.5 },

              { 0.5,-0.5, 0.5 },

              { 0.5,-0.5,-0.5 },

              {-0.5, 0.5, 0.5 },

              {-0.5, 0.5,-0.5 },

              {-0.5,-0.5, 0.5 },

              {-0.5,-0.5,-0.5 },

          };

  private final double[][] VERTICES_MEDIUM = new double[][]

          {

              // TODO

          };

  private final double[][] VERTICES_BIG = new double[][]

          {

              // TODO

          };

  private final int[][] VERT_INDEXES = new int[][]

          {

              {2,3,1,0},   // counterclockwise!

              {7,6,4,5},

              {4,0,1,5},

              {7,3,2,6},

              {6,2,0,4},

              {3,7,5,1}

          };

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

  double[][] getVertices(int cubitType)

    {

     if( cubitType==0 )  // Small cubit

      {

      return VERTICES_SMALL;

      }

    if( cubitType==1 )  // Medium cubit

      {

      return VERTICES_MEDIUM;

      }

    if( cubitType==2 )  // Big cubit

      {

      return VERTICES_BIG;

      }

    return null;

    }

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

  int[][] getVertIndexes(int cubitType)

    {

    return VERT_INDEXES;

    }

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

  int getNumCubitTypes(int numLayers)

    {

    return 3;

    }

  private final double[][] VERTICES_SMALL = new double[][]

          {

              { 0.5, 0.5, 0.5 },

              { 0.5, 0.5,-0.5 },

              { 0.5,-0.5, 0.5 },

              { 0.5,-0.5,-0.5 },

              {-0.5, 0.5, 0.5 },

              {-0.5, 0.5,-0.5 },

              {-0.5,-0.5, 0.5 },

              {-0.5,-0.5,-0.5 },

          };

  private final double[][] VERTICES_BIG = new double[][]

          {

              // TODO

          };

  private final int[][] VERT_INDEXES = new int[][]

          {

              {2,3,1,0},   // counterclockwise!

              {7,6,4,5},

              {4,0,1,5},

              {7,3,2,6},

              {6,2,0,4},

              {3,7,5,1}

          };

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

  double[][] getVertices(int cubitType)

    {

     if( cubitType==0 )  // Small cubit

      {

      return VERTICES_SMALL;

      }

    if( cubitType==1 )  // Big cubit

      {

      return VERTICES_BIG;

      }

    return null;

    }

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

  int[][] getVertIndexes(int cubitType)

    {

    return VERT_INDEXES;

    }

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

  int getNumCubitTypes(int numLayers)

    {

    return 2;

    }

  private static final double[][] VERTICES = new double[][]

          {

              { 0.5, 0.5, 0.5 },

              { 0.5, 0.5,-0.5 },

              { 0.5,-0.5, 0.5 },

              { 0.5,-0.5,-0.5 },

              {-0.5, 0.5, 0.5 },

              {-0.5, 0.5,-0.5 },

              {-0.5,-0.5, 0.5 },

              {-0.5,-0.5,-0.5 },

          };

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

          {

              {2,3,1,0},   // counterclockwise!

              {7,6,4,5},

              {4,0,1,5},

              {7,3,2,6},

              {6,2,0,4},

              {3,7,5,1}

          };

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

          {

              { -0.5f, -0.5f, 0.5f, -0.5f, 0.5f, 0.5f, -0.5f, 0.5f }

          };

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

  double[][] getVertices(int cubitType)

    {

    return VERTICES;

    }

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

  int[][] getVertIndexes(int cubitType)

    {

    return VERT_INDEXES;

    }

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

// in the sense of shape, there's always only 1 cubit type.

  int getNumCubitTypes(int numLayers)

    {

    return 1;

    }

      FactoryCubit factory = FactoryCubit.getInstance();

      factory.clear();

      int extraI, extraV, num;

      switch(numLayers)

        {

        case 2 : num = 6; extraI = 2; extraV = 2; break;

        case 3 : num = 5; extraI = 2; extraV = 2; break;

        case 4 : num = 5; extraI = 1; extraV = 2; break;

        default: num = 5; extraI = 1; extraV = 0; break;

        }

      float[][] bands     = new float[][] { {0.038f,35,0.5f,0.7f,num,extraI,extraV} };

      int[] bandIndexes   = new int[] { 0,0,0,0,0,0};

      float[][] corners   = new float[][] { {0.036f,0.12f} };

      int[] cornerIndexes = new int[] { 0,0,0,0,0,0,0,0 };

      FactoryCubit factory = FactoryCubit.getInstance();

      factory.createNewFaceTransform(VERTICES,VERT_INDEXES);

      mMeshes[index] = factory.createRoundedSolid(VERTICES, VERT_INDEXES,

                                                  bands, bandIndexes,

                                                  corners, cornerIndexes,

                                                  getNumCubitFaces() );

    factory.drawRoundedPolygon(canvas, paint, left, top, STICKERS[0], S, FACE_COLORS[face], R);

  float[][] getCubitPositions(int numLayers)

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

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

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

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

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

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

    return STICKERS.length;

  private final double[][] VERTICES_TETRA = new double[][]

          {

             {-0.5, SQ2/4, 0.0},

             { 0.5, SQ2/4, 0.0},

             { 0.0,-SQ2/4, 0.5},

             { 0.0,-SQ2/4,-0.5}

          };

  private final int[][] VERT_INDEXES_TETRA = new int[][]

          {

             {2,1,0},   // counterclockwise!

             {2,3,1},

             {3,2,0},

             {3,0,1}

          };

  private final double[][] VERTICES_OCTA = new double[][]

          {

             { 0.5,   0.0, 0.5},

             { 0.5,   0.0,-0.5},

             {-0.5,   0.0,-0.5},

             {-0.5,   0.0, 0.5},

             { 0.0, SQ2/2, 0.0},

             { 0.0,-SQ2/2, 0.0}

          };

  private final int[][] VERT_INDEXES_OCTA = new int[][]

          {

             {3,0,4},   // counterclockwise!

             {0,1,4},

             {1,2,4},

             {2,3,4},

             {5,0,3},

             {5,1,0},

             {5,2,1},

             {5,3,2}

          };

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

  double[][] getVertices(int cubitType)

    {

    if( cubitType==0 )  // Tetrahedron

      {

      return VERTICES_TETRA;

      }

    if( cubitType==1 )  // Octahedron

      {

      return VERTICES_OCTA;

      }

    return null;

    }

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

  int[][] getVertIndexes(int cubitType)

    {

    if( cubitType==0 )  // Tetrahedron

      {

      return VERT_INDEXES_TETRA;

      }

    if( cubitType==1 )  // Octahedron

      {

      return VERT_INDEXES_OCTA;

      }

    return null;

    }

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

  int getNumCubitTypes(int numLayers)

    {

    return 2;

    }

  private final double[][] VERTICES = new double[][]

          {

             {-0.5, 0.0, 0.0},

             { 0.5, 0.0, 0.0},

             { 0.0,-0.5, 0.0},

             { 0.0, 0.0,-0.5}

          };

  private final int[][] VERT_INDEXES = new int[][]

          {

             {2,1,0},   // counterclockwise!

             {2,3,1},

             {3,2,0},

             {3,0,1}

          };

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

  double[][] getVertices(int cubitType)

    {

    return VERTICES;

    }

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

  int[][] getVertIndexes(int cubitType)

    {

    return VERT_INDEXES;

    }

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

  int getNumCubitTypes(int numLayers)

    {

    return 1;

    }

  private final double[][] VERTICES_CORNER = new double[][]

          {

            // TODO

          };

  private final int[][] VERT_INDEXES_CORNER = new int[][]

          {

            // TODO

          };

  private final double[][] VERTICES_FACE = new double[][]

          {

            // TODO

          };

  private final int[][] VERT_INDEXES_FACE = new int[][]

          {

            // TODO

          };

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

  double[][] getVertices(int cubitType)

    {