Lens Demo Effect by luis2048.

A picture is shown and it looks like a magnifying glass is drawn over the picture. One of the most famous demos that has a lens effect is 2nd reality by future crew. The trick is to precalculate the entire effect. Just make an array that for each pixel in the destination picture tells which pixel to take from the source picture. This array is called the transformation array. The tricky part is to calculate the transformation array to make the destination look like a lens is beeing held over the source picture. Based on lens formula by on Abe Racadabra.

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, P2D);

  // 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, P2D);
  lensImage2 = createGraphics(lensD, lensD, P2D);

  // 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, P2D);

  // 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); 

}