int lensD = 256;  // Lens diameter
  int[] lensArray = new int[lensD*lensD];  // Height and width of lens
  
  PGraphics lensEffect;
  PImage lensImage;
  PImage lensImage2;
  
  int xx = 0;
  int yy = 0; 
  int dx = 1;
  int dy = 1;
  
  void setup() {
  
    size(640, 360);
  
    // Create buffered image for lens effect
    lensEffect = createGraphics(width, height, JAVA2D);
  
    // Load background image 
    lensEffect.beginDraw();
    lensEffect.image(loadImage("red_smoke.jpg"), 0, 0, 
                     lensEffect.width, lensEffect.height);
    lensEffect.endDraw();
  
    // Create buffered image for image to warp
    lensImage = createGraphics(lensD, lensD, JAVA2D);
    lensImage2 = createGraphics(lensD, lensD, JAVA2D);
  
    // Lens algorithm (transformation array)
    int magFactor = 40;  // Magnification factor
    int m, a, b;
  
    int r = lensD / 2;
    float s = sqrt(r*r - magFactor*magFactor);
  
    for (int y = -r; y < r; y++) {
      for (int x = -r ;x < r; x++) {
        if(x*x + y*y >= s*s) {
          a = x;
          b = y;
        }
        else {
          float z = sqrt(r*r - x*x - y*y);
          a = int(x * magFactor / z + 0.5);
          b = int(y * magFactor / z + 0.5);
        }
        lensArray[(y + r)*lensD + (x + r)] = (b + r) * lensD + (a + r);
      }
    }
  }
  
  void draw() {
  
    // Bounce lens around the screen
    if((xx+dx+lensD > lensEffect.width) || (xx+dx < 0)) {
      dx =- dx;
    } 
    if((yy+dy+lensD > lensEffect.height) || (yy+dy < 0)) {
      dy =- dy;
    }
    xx += dx;
    yy += dy;
  
    lensImage = createGraphics(lensD, lensD, JAVA2D);
  
    // save the backgrounlensD of lensHeight*lensWilensDth pixels rectangle at the coorlensDinates 
    // where the lens effect will be applielensD.
    lensImage2.copy(lensEffect, xx, yy, lensD, lensD, 0, 0, lensD, lensD);
  
    // output into a bufferelensD image for reuse
    lensImage.loadPixels();
  
    // For each pixel in the destination rectangle, apply the color
    // from the appropriate pixel in the saved background. The lensArray
    // array tells the offset into the saved background.
    for (int i = 0; i < lensImage.pixels.length; i++)  {
      lensImage.pixels[i] = lensImage2.pixels[lensArray[i]]; 
    } 
    lensImage.updatePixels();
  
    // Restore the original picture
    image(lensEffect, 0, 0, width, height); 
  
    // Overlay the lens square
    image(lensImage, xx, yy, lensD, lensD); 
  
  }