sclass IIPureQuad extends Meta implements IIntegralImage {
  int imageSizeInBits; // e.g. 8 = 256*256
  int[] pixelSumsByChannel; // average color of whole image stored as pixel sum
  IIntegralImage[] quadrants = new[4]; // in scan line order
  
  int imageSize() { ret 1 << imageSizeInBits; }
  int halfSize() { ret 1 << (imageSizeInBits-1); }
  public int getWidth() { ret imageSize(); }
  public int getHeight() { ret imageSize(); }
  int pixelCount() { ret 1 << (imageSizeInBits*2); }

  public double getIntegralValue(int x, int y, int channel) {
    int quadX = x >> (imageSizeInBits-1);  // 0 or 1
    int quadY = y >> (imageSizeInBits-1);  // 0 or 1
    int quadrant = quadX | (quadY << 1); // 0 to 3
    int xLo = x & ~halfSize(); // clear topmost bit
    int yLo = y & ~halfSize(); // clear topmost bit
    
    // first query quadrant we landed in
    
    double pixelSum = quadrants[quadrant].getIntegralValue(xLo, yLo, channel);
    
    // add quadrant to the left
    
    if (quadX != 0)
      pixelSum += quadrants[quadrant-1].getIntegralValue(halfSize(), yLo, channel);
      
    // add quadrant above
      
    if (quadY != 0)
      pixelSum += quadrants[quadrant-2].getIntegralValue(xLo, halfSize(), channel);
      
    // add full top left quadrant
    
    if (quadrant == 3)
      pixelSum += quadrants[0].getIntegralValue(halfSize(), halfSize(), channel);
      
    ret pixelSum;
  }
}