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In perspective view (a projection), when you look at the circle from different angles, it becomes an ellipse. (also in the world). Most things make sense with perspective, but I don't see why the center of the circle doesn't match the center of the ellipse (just the fact of geometric intersection?). I like to draw, so I'm curious.

kirismasdada
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    It does.${}{}{}$ – TonyK Dec 24 '22 at 22:12
  • but no same place, perspective view – kirismasdada Dec 24 '22 at 22:13
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    When things are further away, they appear closer together. The centre lies equidistant between the point on the circle closest to you and the point furthest away. Because the centre and the further point are the same distance, but further away from you, than the centre and the closer point, naturally, the centre will appear closer to the further point. – Theo Bendit Dec 24 '22 at 22:14
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    @TheoBendit: The OP specifically mentioned a projection. In this case, the two centres coincide. – TonyK Dec 24 '22 at 22:15
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    @TonyK It depends on the type of projection, but regardless, I suspect that the argument in my comment is the sort of thing that the OP will be interested in. – Theo Bendit Dec 24 '22 at 22:18
  • i know perspective rule. ok but ellipse center Isn't it related to anything? – kirismasdada Dec 24 '22 at 22:19
  • I read somewhere that the image of the ellipse cannot be restored to the circle. – kirismasdada Dec 24 '22 at 22:22
  • Similar question: why a set of equidistant parallel lines do not appear equidistant in perspective? – Jean-Claude Arbaut Dec 24 '22 at 22:23
  • As I understand it, the circle looks like an ellipse in perspective.very symmetrical ellipse, the midpoints cannot intersect for perspective reasons. – kirismasdada Dec 24 '22 at 22:31
  • Unless you clarify what perspective and/or projection you mean, this is unanswerable. As it is, for a natural orthogonal projection, the answer is that you're wrong, they do intersect, so you must have more conditions not included here. – Nij Dec 24 '22 at 22:38

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This is explained without words in the following schematic where the bottom black line segment is the circle lying horizontally, and projection plane is shown in green. Point O is where all the rays converge. It can be seen that the projection of the center of the circle is not halfway between the two extremities of the projection of the circle.

enter image description here

Hosam Hajeer
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