int side=35; 
int sx=side+1; 
int sy=side+1; 
int sz=side+1; 
int hsx=int(sx/2.0f); 
int hsy=int(sy/2.0f); 
int hsz=int(sz/2.0f); 
int nc=52; 
float[][][] points=new float[sx][sy][sz]; 
float[][] transDown=new float[sx][sz]; 
float[][] transUp=new float[sx][sz]; 
float[][] transLeft=new float[sy][sz]; 
float[][] transRight=new float[sy][sz];
float[][] transFront=new float[sx][sy]; 
float[][] transBack=new float[sx][sy]; 
int[][][] volumes=new int[nc][2][3]; 
float ct=0.5; 
float ay=0.50; 
float ry=0.005; 
float ax=0.2; 
float factor=1.0; 
float scx=350.0/sx;
float scy=350.0/sy; 
float scz=350.0/sz; 
int count;


void setup(){
  size(623,420);
  noFill();
  setupVolume(); 

}

void draw(){
  background(255);
  if (count<nc+1){
    calculate(); 
  }
  drawProj();
  factor=1.0;
  count++;
  
}

void keyReleased(){
  
  setupVolume();
  count=0;
}

void setupVolume(){
  volumes[0][0][0]=1;
  volumes[0][1][0]= side;
  volumes[0][0][1]=side-1;
  volumes[0][1][1]= side;
  volumes[0][0][2]=1;
  volumes[0][1][2]= side;
  volumes[1][0][0]=1;
  volumes[1][1][0]= side;
  volumes[1][0][1]=1;
  volumes[1][1][1]= 2;
  volumes[1][0][2]=1;
  volumes[1][1][2]= side;
  for(int c=2; c<nc; c++){
    for(int i=0;i<3;i++){
      volumes[c][0][i]=1+int(random(side));
      volumes[c][1][i]= volumes[c][0][i]+int(random(side-volumes[c][0][i]));
    }
  }
}

void calculate(){
  for(int i=0;i<sx;i++){
    for(int j=0;j<sy;j++){
      for(int k=0;k<sz;k++){
        points[i][j][k]=0.0f;
        transDown[i][k]=0.0f;
        transUp[i][k]=0.0f;
        transLeft[j][k]=0.0f;
        transRight[j][k]=0.0f;
        transFront[i][j]=0.0f;
        transBack[i][j]=0.0f;
      }
    }
  }

  for(int c=0;c<min(count,nc);c++){ 
    for(int i=volumes[c][0][0];i<volumes[c][1][0];i++){
      for(int j=volumes[c][0][1];j<volumes[c][1][1];j++){
        for(int k=volumes[c][0][2];k<volumes[c][1][2];k++){
          points[i][j][k]+=factor;
        }
      }
    }
    factor*=-1.0;
  }

  for(int i=0;i<sx;i++){
    for(int j=2;j<sy-2;j++){
      for(int k=0;k<sz;k++){
        if (points[i][j][k]>0) transDown[i][k]+=points[i][j][k] ;
        if (points[i][j][k]<0) transUp[i][k]-=points[i][j][k] ;
        if (points[i][j][k]>0) transLeft[j][k]+=points[i][j][k] ;
        if (points[i][j][k]<0) transRight[j][k]-=points[i][j][k] ;
        if (points[i][j][k]>0) transFront[i][j]+=points[i][j][k] ;
        if (points[i][j][k]<0) transBack[i][j]-=points[i][j][k] ;
      }
    }
  }
}

void drawProj(){//draw projections on bottom or top platform 
  noStroke();
  fill(230,60);
  rect(14,14,189,189);
  rect(217,14,189,189);
  rect(420,14,189,189);
  rect(14,217,189,189);
  rect(217,217,189,189);
  rect(420,217,189,189);
  
  
    beginShape(QUADS);
    for(int k=1;k<sz-1;k++){
      for(int i=1;i<sx-1;i++){
        fill(120,0,0,transDown[i][k]*4);
        vertex(21+5*i,21+5*k);
        vertex(21+5*i+5,21+5*k);
        vertex(21+5*i+5,21+5*k+5);
        vertex(21+5*i,21+5*k+5);
      }
    }
    endShape();
  
    beginShape(QUADS);
    for(int k=1;k<sz-1;k++){
      for(int i=1;i<sx-1;i++){
        fill(120,0,0,int(transUp[i][k]*4));
        vertex(21+5*i,224+5*k);
        vertex(21+5*i+5,224+5*k);
        vertex(21+5*i+5,224+5*k+5);
        vertex(21+5*i,224+5*k+5);
      }
    }
    endShape();
  
 
    beginShape(QUADS);
    for(int k=1;k<sz-1;k++){
      for(int j=1;j<sy-1;j++){
        fill(120,0,0,int(transLeft[j][k]*4));
        vertex(224+5*k,21+5*j);
        vertex(224+5*k+5,21+5*j);
        vertex(224+5*k+5,21+5*j+5);
        vertex(224+5*k,21+5*j+5);
      }
    }
    endShape();
  
    beginShape(QUADS);
    for(int k=1;k<sz-1;k++){
      for(int j=1;j<sy-1;j++){
        fill(120,0,0,int(transRight[j][k]*4));
        vertex(224+5*j,224+5*k);
        vertex(224+5*j+5,224+5*k);
        vertex(224+5*j+5,224+5*k+5);
        vertex(224+5*j,224+5*k+5);
      }
    }
    endShape();
  
  
    beginShape(QUADS);
    for(int j=1;j<sy-1;j++){
      for(int i=1;i<sx-1;i++){
        fill(120,0,0,int(transFront[i][j]*4));
        vertex(427+5*i,21+5*j);
        vertex(427+5*i+5,21+5*j);
        vertex(427+5*i+5,21+5*j+5);
        vertex(427+5*i,21+5*j+5);
      }
    }
    endShape();
  
    beginShape(QUADS);
    for(int j=1;j<sy-1;j++){
      for(int i=1;i<sx-1;i++){
        fill(120,0,0,int(transBack[i][j]*4));
        vertex(427+5*i,224+5*j);
        vertex(427+5*i+5,224+5*j);
        vertex(427+5*i+5,224+5*j+5);
        vertex(427+5*i,224+5*j+5);
      }
    }
    endShape();
  
}


boolean between(float value, float limit1, float limit2){
  return (((value<=limit1)&&(value>limit2))||((value<=limit2)&&(value>limit1)));
}

float ruleOfThree(float x1, float x2, float x3, float y1, float y2){// if x1 maps to y1, and x2 maps to y2, find y3 linearly corresponding to x3
  return(y1 + (y2-y1)/(x2-x1)*(x3-x1));
}