I agree. Howerever you still have to adjust your feet (angle of plane) to walk the circle, even if it is a extremely slight.if you walk around a maypole with a taut 10 foot rope and keep your left shoulder exactly parallel to the maypole, would your perspective change? no. your body would be in the same relation to the pole as it was 45degrees earlier. your view (the scenery) would change.
Me watching you walk around the Maypole has nothing to do with the position of YOUR body in space compared to the maypole.
edited persons to ease visual
Otherwise you could draw a perfect circle using just a ruler.