Projective geometry - circles

[Starman]

If you take a circle, say 12ft in diameter, and mark it out like a clock face, standing face on to it, it will appear circular. If you then rotate the circle 45 degrees about the 6 – 12 axis it will appear elliptical, but is this a regular ellipse?

Viewing the circle at this angle, the chord distance between the 8 o’clock and 10 o’clock marks will appear greater than the chord distance between the 4 o’clock and 2 o’clock marks as the 4 – 2 chord is further away.

This means that the curve length 12 – 3 – 6, appears less than the curve 12 – 9 – 6 so the ‘ellipse’ has one side shorter than the other.

Can anyone explain this to me please?

[Guv]

I do not have an analog clock in my apartment, so I cannot experimentally decide by looking at a rotated clock face.

It seems to me that the shape is not a true ellipse. The nearer half is longer than the farther half.

I suspect that the human perceptual system would view a rotated real life clock as a circle. Unless asked some leading questions and directed to study it carefully, a human is likely to view the near and far halves as equal in length. I also suspect that it would similarly view a realistic perspective drawing as a circle, with the far and near halves equal in length.

I know that the human perceptual system creates images which do not match what is in the real world. There have been a lot of experiments done by clinical psychologists which verify this.

I first became aware of such perceptual processing when I got interested in color photography. At dawn and dusk, colors of familiar objects are adjusted to seem to be the same colors seen between 10 AM & 2 PM on a bright day. Also, familiar objects viewed under incandescent light appear to be the same color as when viewed outdoors. Any photographer familiar with color film will tell you that these perceptions are contrary to what a camera records. To compensate for incandescent lighting, special indoor film is usually used. To compensate for dawn and dusk, filters are often used. Oddly enough, a small print made from a color slide created with incorrect lighting, will appear to have incorrect colors, but the color slide projected on a large screen in a darkened room will appear to have normal colors. The human perceptual system will adjust colors of the projected image, but will not make similar adjustments to the small print due to being able to compare it with surrounding context.

Adjusted perceptual images were important to human survival in the world of 50,000 to 200,000 years ago. It would be dangerous to not immediately recognize the color of a small part of a tiger or leopard seen at dawn or dusk. Similarly, one should be able to recognize edible and poisonous plants or berries at any time of the day. It was similarly important to know the true shape of an object viewed from various angles. Evolutionary pressure resulted in our making such adjustments to the objects we see.