// Rubik's Cube 3D simulator
// Karl Hörnell, March 11 1996
// Last modified October 6

import java.awt.*;
import java.lang.Math;
import java.lang.Character;

public final class rubik extends java.applet.Applet {
  int i,j,k,n,o,p,q,lastX,lastY,dx,dy;
  int rectX[],rectY[];
  Color colList[],bgcolor;
  final double sideVec[]={0,0,1,0,0,-1,0,-1,0,1,0,0,0,1,0,-1,0,0}; // Normal vectors
  final double corners[]={-1,-1,-1,1,-1,-1,1,1,-1,-1,1,-1,
        -1,-1,1,1,-1,1,1,1,1,-1,1,1}; // Vertex co-ordinates
  double topCorners[],botCorners[];
  final int sides[]={4,5,6,7,3,2,1,0,0,1,5,4,1,2,6,5,2,3,7,6,0,4,7,3};
  final int nextSide[]={2,3,4,5, 4,3,2,5, 1,3,0,5, 1,4,0,2, 1,5,0,3, 2,0,4,1};
  final int mainBlocks[]={0,3,0,3,0,3,0,3,0,3,0,3,0,3,0,3,0,3,0,3,0,3,0,3};
  final int twistDir[]={-1,1,-1,1, -1,1,-1,1, 1,1,1,1, 1,-1,1,-1, 1,1,1,1, -1,1,-1,1};
  final int colDir[]={-1,-1,1,-1,1,-1};
  final int circleOrder[]={0,1,2,5,8,7,6,3};
  int topBlocks[],botBlocks[];
  int sideCols[],sideW,sideH;
  int dragReg,twistSide=-1;
  int nearSide[],buffer[]; // Which side belongs to dragCorn
  double dragCorn[],dragDir[];
  double eye[]={0.3651,0.1826,-0.9129}; // Initial observer co-ordinate axes (view)
  double eX[]={0.9309,-0.0716,0.3581}; // (sideways)
  double eY[]; // (vertical)
  double Teye[],TeX[],TeY[];
  double light[],temp[]={0,0,0},temp2[]={0,0,0},newCoord[];
  double sx,sy,sdxh,sdyh,sdxv,sdyv,d,t1,t2,t3,t4,t5,t6;
  double phi,phibase=0,Cphi,Sphi,currDragDir[];

  boolean naturalState=true,twisting=false,OKtoDrag=false;
  Math m;
  Graphics offGraphics;
  Image offImage;

  public void init() {
    offImage=createImage(120,120); // Double buffer
    offGraphics=offImage.getGraphics();
    rectX=new int[4];
    rectY=new int[4];
    newCoord=new double[16]; // Projected co-ordinates (on screen)
    dragDir=new double[24];
    dragCorn=new double[96];
    topCorners=new double[24]; // Vertex co-ordinate storage
    botCorners=new double[24]; // for sub-cubes during twist
    topBlocks=new int[24];
    botBlocks=new int[24];
    buffer=new int[12];
    nearSide=new int[12];
    light=new double[3];
    Teye=new double[3];
    TeX=new double[3];
    TeY=new double[3];
    currDragDir=new double[2];
    eY=new double[3];
    vecProd(eye,0,eX,0,eY,0); // Fix y axis of observer co-ordinate system
    normalize(eY,0);
    colList=new Color[120];
    for (i=0;i<20;i++) {
      colList[i]=new Color(103+i*8,103+i*8,103+i*8);    // White
      colList[i+20]=new Color(i*6,i*6,84+i*9);          // Blue
      colList[i+40]=new Color(84+i*9,i*5,i*5);          // Red
      colList[i+60]=new Color(i*6,84+i*9,i*6);          // Green
      colList[i+80]=new Color(84+i*9,84+i*9,i*6);       // Yellow
      colList[i+100]=new Color(84+i*9,55+i*8,i*3);      // Orange    
    }
    sideCols=new int[54];
    for (i=0;i<54;i++)
      sideCols[i]=i/9;
    bgcolor=findBGColor();
    resize(125,125);
    repaint();
  }

  public Color findBGColor() {
    int hex[];
    String s,h="0123456789abcdef";
    Color c;
    hex=new int[6];
    s=getParameter("bgcolor");
    if ((s!=null)&&(s.length()==6))
    {
      for (i=0;i<6;i++)
        for (j=0;j<16;j++)
          if (Character.toLowerCase(s.charAt(i))==h.charAt(j))
            hex[i]=j;
      c=new Color(hex[0]*16+hex[1],hex[2]*16+hex[3],hex[4]*16+hex[5]);
    }
    else c=Color.white;
    return c;
  }

  public double scalProd(double v1[],int ix1,double v2[],int ix2) {
    return v1[ix1]*v2[ix2]+v1[ix1+1]*v2[ix2+1]+v1[ix1+2]*v2[ix2+2];
  }

  public double vNorm(double v[],int ix) {
    return m.sqrt(v[ix]*v[ix]+v[ix+1]*v[ix+1]+v[ix+2]*v[ix+2]);
  }

  public double cosAng(double v1[],int ix1,double v2[],int ix2) {
    return scalProd(v1,ix1,v2,ix2)/(vNorm(v1,ix1)*vNorm(v2,ix2));
  }

  public void normalize(double v[], int ix) {
    double t=vNorm(v,ix);
    v[ix]=v[ix]/t;
    v[ix+1]=v[ix+1]/t;
    v[ix+2]=v[ix+2]/t;
  }

  public void scalMult(double v[], int ix,double a) {
    v[ix]=v[ix]*a;
    v[ix+1]=v[ix+1]*a;
    v[ix+2]=v[ix+2]*a;
  }

  public void addVec(double v1[], int ix1,double v2[],int ix2) {
    v2[ix2]+=v1[ix1];
    v2[ix2+1]+=v1[ix1+1];
    v2[ix2+2]+=v1[ix1+2];
  }

  public void subVec(double v1[], int ix1,double v2[],int ix2) {
    v2[ix2]-=v1[ix1];
    v2[ix2+1]-=v1[ix1+1];
    v2[ix2+2]-=v1[ix1+2];
  }

  public void copyVec(double v1[], int ix1,double v2[],int ix2) {
    v2[ix2]=v1[ix1];
    v2[ix2+1]=v1[ix1+1];
    v2[ix2+2]=v1[ix1+2];
  }

  public void vecProd(double v1[],int ix1,double v2[],int ix2, double v3[],int ix3) {
    v3[ix3]=v1[ix1+1]*v2[ix2+2]-v1[ix1+2]*v2[ix2+1];
    v3[ix3+1]=v1[ix1+2]*v2[ix2]-v1[ix1]*v2[ix2+2];
    v3[ix3+2]=v1[ix1]*v2[ix2+1]-v1[ix1+1]*v2[ix2];
  }

  public void cutUpCube() {
    boolean check;
    for (i=0;i<24;i++) {
      topCorners[i]=corners[i];
      botCorners[i]=corners[i];
    }
    copyVec(sideVec,3*twistSide,temp,0); 
    copyVec(temp,0,temp2,0); 
    scalMult(temp,0,1.3333);
    scalMult(temp2,0,0.6667);
    for (i=0;i<8;i++) {
      check=false;
      for (j=0;j<4;j++) if (i==sides[twistSide*4+j]) check=true;
      if (check) subVec(temp2,0,botCorners,i*3); else addVec(temp,0,topCorners,i*3);
    }

    for (i=0;i<24;i++) {
      topBlocks[i]=mainBlocks[i]; // Large sub-cube data
      botBlocks[i]=mainBlocks[i]; // Small sub-cube data
    }
    for (i=0;i<6;i++) {
      if (i==twistSide) {
        botBlocks[i*4+1]=0; 
        botBlocks[i*4+3]=0;
      }
      else {
        k=-1;
        for (j=0;j<4;j++)
          if (nextSide[i*4+j]==twistSide)
            k=j;
        switch (k) {

          case 0: // Up side?
          {
            topBlocks[i*4+3]=1;
            botBlocks[i*4+2]=1;
            break;
          }
          case 1: // Right side?
          {
            topBlocks[i*4]=2;
            botBlocks[i*4+1]=2;
            break;
          }
          case 2: // Down side?
          {
            topBlocks[i*4+2]=2;
            botBlocks[i*4+3]=2;
            break;
          }
          case 3: // Left side?
          {
            topBlocks[i*4+1]=1;
            botBlocks[i*4]=1;
            break;
          }
          case -1: // None
          {
            topBlocks[i*4+1]=0; // Small sub-cube is blank on bottom
            topBlocks[i*4+3]=0;
            break;
          }
        }
      }
    }    
  }

  public boolean keyDown(java.awt.Event evt, int key)
  {
    if (key==114) // Restore
    {
      twisting=false;
      naturalState=true;
      for (i=0;i<54;i++)
        sideCols[i]=i/9;
      repaint();
    }
    else if (key==115) // Scramble
    {
      twisting=false;
      naturalState=true;
      for (i=0;i<20;i++)
        colorTwist((int)(m.random()*6),(int)(m.random()*3+1));
      repaint();
    }
    return false;
  }

  public boolean mouseDrag(java.awt.Event evt, int x, int y)
  {
    boolean check;
    double x1,x2,y1,y2,alpha,beta;

    if ((!twisting)&&(OKtoDrag))
    {
      OKtoDrag=false;
      check=false;
      for (i=0;i<dragReg;i++) // Check if inside a drag region
      {
        x1=dragCorn[i*8+1]-dragCorn[i*8];
        x2=dragCorn[i*8+5]-dragCorn[i*8+4];
        y1=dragCorn[i*8+3]-dragCorn[i*8];
        y2=dragCorn[i*8+7]-dragCorn[i*8+4];
        alpha=(y2*(lastX-dragCorn[i*8])-y1*(lastY-dragCorn[i*8+4]))/
          (x1*y2-y1*x2);
        beta=(-x2*(lastX-dragCorn[i*8])+x1*(lastY-dragCorn[i*8+4]))/
          (x1*y2-y1*x2);
        if ((alpha>0)&&(alpha<1)&&(beta>0)&&(beta<1)) // We're in
        {
          currDragDir[0]=dragDir[i*2];
          currDragDir[1]=dragDir[i*2+1];
          d=currDragDir[0]*(x-lastX)+currDragDir[1]*(y-lastY);
          d=d*d/((currDragDir[0]*currDragDir[0]+currDragDir[1]*currDragDir[1])*
            ((x-lastX)*(x-lastX)+(y-lastY)*(y-lastY)));
          if (d>0.6)
          {
            check=true;
            twistSide=nearSide[i];
            i=100;
          }
        }
      }
      if (check) // We're twisting
      {
        if (naturalState) // The cube still hasn't been split up
        {
          cutUpCube();
          naturalState=false;
        }
        twisting=true;
        phi=0.02*(currDragDir[0]*(x-lastX)+currDragDir[1]*(y-lastY))/
          m.sqrt(currDragDir[0]*currDragDir[0]+currDragDir[1]*currDragDir[1]);
        repaint();
        return false;
      }
    }
    
    OKtoDrag=false;
    if (!twisting) // Normal rotation
    {
      dx=lastX-x; // Vertical shift
      copyVec(eX,0,temp,0);
      scalMult(temp,0,((double)dx)*0.016);
      addVec(temp,0,eye,0);
      vecProd(eY,0,eye,0,eX,0);
      normalize(eX,0);
      normalize(eye,0);
      dy=y-lastY; // Horizontal shift
      copyVec(eY,0,temp,0);
      scalMult(temp,0,((double)dy)*0.016);
      addVec(temp,0,eye,0);
      vecProd(eye,0,eX,0,eY,0);
      normalize(eY,0);
      normalize(eye,0);
      lastX=x;
      lastY=y;
      repaint();
    }
    else // Twist, compute twisting angle phi
    {
      phi=0.02*(currDragDir[0]*(x-lastX)+currDragDir[1]*(y-lastY))/
        m.sqrt(currDragDir[0]*currDragDir[0]+currDragDir[1]*currDragDir[1]);
      repaint();
    }
    return false;
  }

  public boolean mouseDown(java.awt.Event evt, int x, int y)
  {
    lastX=x;
    lastY=y;
    OKtoDrag=true;
    return false;
  }

  public boolean mouseUp(java.awt.Event evt, int x, int y)
  {
    int quads;
    double qu;
    if (twisting) // We have let go of the mouse when twisting
    {
      twisting=false;
      phibase+=phi; // Save twist angle
      phi=0;
      qu=phibase;
      while (qu<0)
        qu+=125.662;
      quads=((int)(qu*3.183));
      if (((quads % 5)==0)||((quads % 5)==4)) // Close enough to a corner?
      {
        quads=((quads+1)/5) % 4;
        if (colDir[twistSide]<0)
          quads=(4-quads) % 4;
        phibase=0;
        naturalState=true; // Return the cube to its natural state
        colorTwist(twistSide,quads); // and shift the colored fields
      }
      repaint();
    }
    return false;    
  }

  public void colorTwist(int sideNum, int quads) // Shift colored fields
  {
    int i,j,k,l=0;
    k=quads*2; // quads = number of 90-degree multiples
    for (i=0;i<8;i++)
    {
      buffer[k]=sideCols[sideNum*9+circleOrder[i]];
      k=(k+1) % 8;
    }
    for (i=0;i<8;i++)
      sideCols[sideNum*9+circleOrder[i]]=buffer[i];
    k=quads*3;
    for (i=0;i<4;i++)
    {
      for (j=0;j<4;j++)
        if (nextSide[nextSide[sideNum*4+i]*4+j]==sideNum)
          l=j;
      for (j=0;j<3;j++)
      {
        switch(l)
        {
          case 0:
            buffer[k]=sideCols[nextSide[sideNum*4+i]*9+j];
            break;
          case 1:
            buffer[k]=sideCols[nextSide[sideNum*4+i]*9+2+3*j];
            break;
          case 2:
            buffer[k]=sideCols[nextSide[sideNum*4+i]*9+8-j];
            break;
          case 3:
            buffer[k]=sideCols[nextSide[sideNum*4+i]*9+6-3*j];
            break;
          default:
            break;
        }
        k=(k+1) % 12;
      }
    }
    k=0;
    for (i=0;i<4;i++)
    {
      for (j=0;j<4;j++)
        if (nextSide[nextSide[sideNum*4+i]*4+j]==sideNum)
          l=j;
      for (j=0;j<3;j++)
      {
        switch(l)
        {
          case 0:
            sideCols[nextSide[sideNum*4+i]*9+j]=buffer[k];
            break;
          case 1:
            sideCols[nextSide[sideNum*4+i]*9+2+3*j]=buffer[k];
            break;
          case 2:
            sideCols[nextSide[sideNum*4+i]*9+8-j]=buffer[k];
            break;
          case 3:
            sideCols[nextSide[sideNum*4+i]*9+6-3*j]=buffer[k];
            break;
          default:
            break;
        }
        k++;
      }
    }
  }

  public void paint(Graphics g)
  {
    dragReg=0;
    offGraphics.setColor(bgcolor); // Clear drawing buffer
    offGraphics.fillRect(0,0,120,120);
    if (naturalState)
      fixBlock(eye,eX,eY,corners,mainBlocks,0); // Draw cube
    else
    {
      copyVec(eye,0,Teye,0); // In twisted state? Compute top observer
      copyVec(eX,0,TeX,0);
      Cphi=m.cos(phi+phibase);
      Sphi=-m.sin(phi+phibase);
      switch(twistSide) // Twist around which axis?
      {
        case 0: // z
          Teye[0]=Cphi*eye[0]+Sphi*eye[1];
          TeX[0]=Cphi*eX[0]+Sphi*eX[1];
          Teye[1]=-Sphi*eye[0]+Cphi*eye[1];
          TeX[1]=-Sphi*eX[0]+Cphi*eX[1];
          break;
        case 1: // -z
          Teye[0]=Cphi*eye[0]-Sphi*eye[1];
          TeX[0]=Cphi*eX[0]-Sphi*eX[1];
          Teye[1]=Sphi*eye[0]+Cphi*eye[1];
          TeX[1]=Sphi*eX[0]+Cphi*eX[1];
          break;
        case 2: // -y
          Teye[0]=Cphi*eye[0]-Sphi*eye[2];
          TeX[0]=Cphi*eX[0]-Sphi*eX[2];
          Teye[2]=Sphi*eye[0]+Cphi*eye[2];
          TeX[2]=Sphi*eX[0]+Cphi*eX[2];
          break;
        case 3: // x
          Teye[1]=Cphi*eye[1]+Sphi*eye[2];
          TeX[1]=Cphi*eX[1]+Sphi*eX[2];
          Teye[2]=-Sphi*eye[1]+Cphi*eye[2];
          TeX[2]=-Sphi*eX[1]+Cphi*eX[2];
          break;
        case 4: // y
          Teye[0]=Cphi*eye[0]+Sphi*eye[2];
          TeX[0]=Cphi*eX[0]+Sphi*eX[2];
          Teye[2]=-Sphi*eye[0]+Cphi*eye[2];
          TeX[2]=-Sphi*eX[0]+Cphi*eX[2];
          break;
        case 5: // -x
          Teye[1]=Cphi*eye[1]-Sphi*eye[2];
          TeX[1]=Cphi*eX[1]-Sphi*eX[2];
          Teye[2]=Sphi*eye[1]+Cphi*eye[2];
          TeX[2]=Sphi*eX[1]+Cphi*eX[2];
          break;
        default:
          break;
      }
      vecProd(Teye,0,TeX,0,TeY,0);
      if (scalProd(eye,0,sideVec,twistSide*3)<0) // Top facing away? Draw it first
      {
        fixBlock(Teye,TeX,TeY,topCorners,topBlocks,2);
        fixBlock(eye,eX,eY,botCorners,botBlocks,1);
      }
      else
      {
        fixBlock(eye,eX,eY,botCorners,botBlocks,1);
        fixBlock(Teye,TeX,TeY,topCorners,topBlocks,2);
      }
    }
    g.drawImage(offImage,0,0,this);
  }

  public void update(Graphics g)
  {
    paint(g);
  }

// Draw cube or sub-cube
  public void fixBlock(double beye[],double beX[],double beY[],
            double bcorners[],int bblocks[],int mode)
  {
    copyVec(beye,0,light,0);
    scalMult(light,0,-3);
    addVec(beX,0,light,0);
    subVec(beY,0,light,0);

    for (i=0;i<8;i++) // Project 3D co-ordinates into 2D screen ones
    {
      newCoord[i*2]=(60+35.1*scalProd(bcorners,i*3,beX,0));
      newCoord[i*2+1]=(60-35.1*scalProd(bcorners,i*3,beY,0));
    }

    for (i=0;i<6;i++)
    {
      if (scalProd(beye,0,sideVec,3*i)>0.001) // Face towards us? Draw it.
      {
        k=(int)(9.6*(1-cosAng(light,0,sideVec,3*i)));
        offGraphics.setColor(Color.black);
        for (j=0;j<4;j++) // Find corner co-ordinates
        {
          rectX[j]=(int)newCoord[2*sides[i*4+j]];
          rectY[j]=(int)newCoord[2*sides[i*4+j]+1];
        }
        offGraphics.fillPolygon(rectX,rectY,4); // First draw black
        sideW=bblocks[i*4+1]-bblocks[i*4];
        sideH=bblocks[i*4+3]-bblocks[i*4+2];
        if (sideW>0)
        {
          sx=newCoord[2*sides[i*4]];
          sy=newCoord[2*sides[i*4]+1];
          sdxh=(newCoord[2*sides[i*4+1]]-sx)/sideW;
          sdxv=(newCoord[2*sides[i*4+3]]-sx)/sideH;
          sdyh=(newCoord[2*sides[i*4+1]+1]-sy)/sideW;
          sdyv=(newCoord[2*sides[i*4+3]+1]-sy)/sideH;
          p=bblocks[i*4+2];
          for (n=0;n<sideH;n++) // Then draw colored fields
          {
            q=bblocks[i*4];
            for (o=0;o<sideW;o++)
            {
              rectX[0]=(int)(sx+(o+0.1)*sdxh+(n+0.1)*sdxv);
              rectX[1]=(int)(sx+(o+0.9)*sdxh+(n+0.1)*sdxv);
              rectX[2]=(int)(sx+(o+0.9)*sdxh+(n+0.9)*sdxv);
              rectX[3]=(int)(sx+(o+0.1)*sdxh+(n+0.9)*sdxv);
              rectY[0]=(int)(sy+(o+0.1)*sdyh+(n+0.1)*sdyv);
              rectY[1]=(int)(sy+(o+0.9)*sdyh+(n+0.1)*sdyv);
              rectY[2]=(int)(sy+(o+0.9)*sdyh+(n+0.9)*sdyv);
              rectY[3]=(int)(sy+(o+0.1)*sdyh+(n+0.9)*sdyv);
              offGraphics.setColor(colList[20*sideCols[i*9+p*3+q]+k]);
              offGraphics.fillPolygon(rectX,rectY,4);
              q++;
            }
            p++;
          }
        }
        switch (mode) // Determine allowed drag regions and directions
        {
          case 0: // Just the normal cube
            t1=sx;
            t2=sy;
            t3=sdxh;
            t4=sdyh;
            t5=sdxv;
            t6=sdyv;
            for (j=0;j<4;j++)
            {
              dragCorn[8*dragReg]=t1;
              dragCorn[8*dragReg+4]=t2;
              dragCorn[8*dragReg+3]=t1+t5;
              dragCorn[8*dragReg+7]=t2+t6;
              t1=t1+t3*3;
              t2=t2+t4*3;
              dragCorn[8*dragReg+1]=t1;
              dragCorn[8*dragReg+5]=t2;
              dragCorn[8*dragReg+2]=t1+t5;
              dragCorn[8*dragReg+6]=t2+t6;
              dragDir[dragReg*2]=t3*twistDir[i*4+j];
              dragDir[dragReg*2+1]=t4*twistDir[i*4+j];
              d=t3;
              t3=t5;
              t5=-d;
              d=t4;
              t4=t6;
              t6=-d;
              nearSide[dragReg]=nextSide[i*4+j];
              dragReg++;
            }
            break;
          case 1: // The large sub-cube
            break;
          case 2: // The small sub-cube (twistable part)
            if ((i!=twistSide)&&(sideW>0))
            {
              if (sideW==3) // Determine positive drag direction
                if (bblocks[i*4+2]==0)
                {
                  dragDir[dragReg*2]=sdxh*twistDir[i*4];
                  dragDir[dragReg*2+1]=sdyh*twistDir[i*4];
                }
                else
                {
                  dragDir[dragReg*2]=-sdxh*twistDir[i*4+2];
                  dragDir[dragReg*2+1]=-sdyh*twistDir[i*4+2];
                }
              else
                if (bblocks[i*4]==0)
                {
                  dragDir[dragReg*2]=-sdxv*twistDir[i*4+3];
                  dragDir[dragReg*2+1]=-sdyv*twistDir[i*4+3];
                }
                else
                {
                  dragDir[dragReg*2]=sdxv*twistDir[i*4+1];
                  dragDir[dragReg*2+1]=sdyv*twistDir[i*4+1];
                }
              for (j=0;j<4;j++)
              {
                dragCorn[dragReg*8+j]=newCoord[2*sides[i*4+j]];
                dragCorn[dragReg*8+4+j]=newCoord[2*sides[i*4+j]+1];
              }
              nearSide[dragReg]=twistSide;
              dragReg++;
            }
            break;
          default:
            break;
        }
      }
    }
  }
}