sinterface IBWIntegralImage extends MakesBufferedImage, IBWImage, IMeta {

  public int getWidth();

  public int getHeight();

  // implement one of the following two methods!

  // integer version (both coordinates & brightnesses are ints)

  public default int getIIValue(int x, int y) {

    ret iround(getIIValue((double) x, (double) y));

  }

  // floating point version (both coordinates & brightnesses are doubles)

  public default double getIIValue(double x, double y) {

    ret getIIValue(ifloor(x), ifloor(y));

  }

  // 0.0 to 255.0

  default public double getPixelAverage(int x1, int y1, int x2, int y2) {

    int area = (x2-x1)*(y2-y1);

    ret doubleRatio(getPixelSum(x1, y1, x2, y2), area);

  }

  default public dbl getPixelAverage(dbl x1, dbl y1, dbl x2, dbl y2) {

    dbl area = (x2-x1)*(y2-y1);

    ret doubleRatio(getPixelSum(x1, y1, x2, y2), area);

  }

  default public double getPixelAverage(Rect r) {

    ret getPixelAverage(r.x, r.y, r.x2(), r.y2());

  }

  default public int getPixelSum(int x1, int y1, int x2, int y2) {

    ret bwIntegralImage_sumRect(this, x1, y1, x2, y2);

  }

  default public double getPixelSum(double x1, double y1, double x2, double y2) {

    ret bwIntegralImage_sumRect(this, x1, y1, x2, y2);

  }

  default public int getPixelBrightness aka getInt(int x, int y) {

    ret getPixelSum(x, y, x+1, y+1);

  }

  default public int getPixelBrightness(Pt p) { ret getPixelBrightness(p.x, p.y); }

  public default BufferedImage getBufferedImage() {

    //ret scaleDownUsingIntegralImageBW(this, w).getBufferedImage();

    ret grayImageFromIBWIntegralImage(this);

  }

  // implementing IBWImage

  public default float getFloatPixel(int x, int y) {

    ret getPixelBrightness(x, y)/255f;

  }

}