protected void drawToolTipOutline(
      DrawContext dc, double width, double height, ToolTipAttributes attributes) {
    GL2 gl = dc.getGL().getGL2(); // GL initialization checks for GL2 compatibility.

    this.applyColor(dc, attributes.getOutlineColor(), attributes.getOutlineOpacity());
    gl.glLineWidth((float) getOutlineWidth());

    // Draw a line loop around the background rectangle. Inset the lines slightly to compensate for
    // OpenGL's line
    // rasterization algorithm. We want the line to straddle the rectangle pixels.
    double inset = 0.5;
    gl.glBegin(GL2.GL_LINE_LOOP);
    gl.glVertex2d(inset, inset);
    gl.glVertex2d(width - inset, inset);
    gl.glVertex2d(width - inset, height - inset);
    gl.glVertex2d(inset, height - inset);
    gl.glEnd();
  }
  private void recursiveDraw(
      int level, double x1, double y1, double x2, double y2, double x3, double y3) {
    if (level < 1) {
      return;
    }

    gl.glBegin(GL2.GL_LINE_LOOP);
    gl.glVertex2d(x1, y1);
    gl.glVertex2d(x2, y2);
    gl.glVertex2d(x3, y3);
    gl.glEnd();

    for (int i = 0; i < transitions; i += 1) {
      x1 = rotate_scale_xx[i] * x1 + rotate_scale_xy[i] * y1 + trans_x[i];
      y1 = rotate_scale_yx[i] * x1 + rotate_scale_yy[i] * y1 + trans_y[i];
      x2 = rotate_scale_xx[i] * x2 + rotate_scale_xy[i] * y2 + trans_x[i];
      y2 = rotate_scale_yx[i] * x2 + rotate_scale_yy[i] * y2 + trans_y[i];
      x3 = rotate_scale_xx[i] * x3 + rotate_scale_xy[i] * y3 + trans_x[i];
      y3 = rotate_scale_yx[i] * x3 + rotate_scale_yy[i] * y3 + trans_y[i];

      recursiveDraw(level - 1, x1, y1, x2, y2, x3, y3);
    }
  }
  /** Called back by the animator to perform rendering. */
  @Override
  public void display(GLAutoDrawable drawable) {
    GL2 gl = drawable.getGL().getGL2(); // get the OpenGL 2 graphics context
    gl.glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); // clear color and depth buffers

    for (int i = 0; i < stars.length; i++) {
      // Reset the view (x, y, z axes back to normal)
      gl.glLoadIdentity();
      gl.glTranslatef(0.0f, 0.0f, z);

      // The stars are texture quad square drawn on x-y plane and
      // distributed on on x-z plane around the y-axis

      // Initial 90 degree tile in the x-axis, y-axis pointing out of screen
      gl.glRotatef(tilt, 1.0f, 0.0f, 0.0f);
      // Rotate about y-axis (pointing out of screen), initial angle is 0
      gl.glRotatef(stars[i].angle, 0.0f, 1.0f, 0.0f);
      // Translate about the x-axis (pointing right) to its current distance
      gl.glTranslatef(stars[i].distance, 0.0f, 0.0f);

      // The stars have initial angle of 0, and initial distance linearly
      // distributed between 0 and 5.0f

      // Rotate the axes back, so that z-axis is again facing us, to ensure that
      // the quad (with texture) on x-y plane is facing us
      gl.glRotatef(-stars[i].angle, 0.0f, 1.0f, 0.0f);
      gl.glRotatef(-tilt, 1.0f, 0.0f, 0.0f);

      // Take note that without the two rotations and undo, there is only one
      // translation along the x-axis
      // Matrix operation is non-commutative. That is, AB != BA.
      // Hence, ABCB'A' != C

      // Draw the star, which spins on the z axis (pointing out of the screen)
      gl.glRotatef(starSpinAngle, 0.0f, 0.0f, 1.0f);
      // Set the star's color using bytes (why bytes? not float or int?)
      gl.glColor4ub(stars[i].r, stars[i].g, stars[i].b, (byte) 255);
      gl.glBegin(GL_QUADS);
      // draw a square on x-y plane
      gl.glTexCoord2f(textureCoordLeft, textureCoordBottom);
      gl.glVertex3f(-1.0f, -1.0f, 0.0f);
      gl.glTexCoord2f(textureCoordRight, textureCoordBottom);
      gl.glVertex3f(1.0f, -1.0f, 0.0f);
      gl.glTexCoord2f(textureCoordRight, textureCoordTop);
      gl.glVertex3f(1.0f, 1.0f, 0.0f);
      gl.glTexCoord2f(textureCoordLeft, textureCoordTop);
      gl.glVertex3f(-1.0f, 1.0f, 0.0f);
      gl.glEnd();

      // If twinkling, overlay with another drawing of an arbitrary color
      if (twinkleOn) {
        // Assign a color using bytes
        gl.glColor4ub(
            stars[(numStars - i) - 1].r,
            stars[(numStars - i) - 1].g,
            stars[(numStars - i) - 1].b,
            (byte) 255);
        gl.glBegin(GL_QUADS);
        // draw a square on x-y plane
        gl.glTexCoord2f(textureCoordLeft, textureCoordBottom);
        gl.glVertex3f(-1.0f, -1.0f, 0.0f);
        gl.glTexCoord2f(textureCoordRight, textureCoordBottom);
        gl.glVertex3f(1.0f, -1.0f, 0.0f);
        gl.glTexCoord2f(textureCoordRight, textureCoordTop);
        gl.glVertex3f(1.0f, 1.0f, 0.0f);
        gl.glTexCoord2f(textureCoordLeft, textureCoordTop);
        gl.glVertex3f(-1.0f, 1.0f, 0.0f);
        gl.glEnd();
      }

      // Update for the next refresh
      // The star spins about the z-axis (pointing out of the screen), and spiral
      // inwards and collapse towards the center, by increasing the angle on x-y
      // plane and reducing the distance.

      starSpinAngle += 0.01f; // used to spin the stars about the z-axis
      // spiral pattern
      stars[i].angle += (float) i / numStars; // changes the angle of a star
      // collapsing the star to the center
      stars[i].distance -= 0.01f; // changes the distance of a star
      // re-bone at the edge
      if (stars[i].distance < 0.0f) { // Is the star collapsed to the center?
        stars[i].distance += 5.0f; // move to the outer ring
        stars[i].setRandomRGB(); // choose a random color for the star
      }
    }
  }