Each point casts a ray to the camera, that is in the center of a lens. The lens is modeled as an ellipsoid.
At the intersection of the ray and the lens, the point is then drawn on the surface of the lens.
Finally, the lens gets rendered in the view box by casting parallel lines through the lens' surface onto the viewbox (seen as green box in the lens rendering).
You can model the lens' axes by selecting a preset or by moving the sliders.
Move around with WASD, space and left shift.
Look around by dragging the mouse inside the view box.