I didn't know this about ellipses

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  1. #1
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    I didn't know this about ellipses

    I've was studying from "Creative Illustration for Artists and Illustrators" by Ernest W. Watson, when I came upon something interesting.

    To quote the author:

    " Always we must remember that the long diameter of the ellipse is not a structural line of the object: it is merely an imaginary line - useful only for drawing purposes. It is never the same as the geometric diameter of the circle which the ellipse represents "

    Also:

    " Many beginners, especially those who are mechanically minded, are quite surprised to be told that the diameter of a circle and the long diameter of its elliptical appearance are never the same lines; and to discover that the long diameter of the ellipse is always in front of (ie nearer the spectator) the circle's structural diameter. "

    I've always been under the assumption that the true diameter of the circle naturally ended up as the long-side-line of the ellipse. Anyways, I'm sure that this only information for the beginners (like myself), but I figured it couldn't hurt to post it.

    I looked back through a lot of my perspective studies of ellipses, and I've noticed a lot of mistakes due to my lack of understanding in this regard.

    PS: The image attached shows an example of what I am talking about.

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  4. #2
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    I am one of those technically minded beginners:
    ''In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the LONGEST chords of the circle.''
    So this is the technical explanation. What would the artistic one be. I would like to understand what you are quoting. I'm suggesting the imaginary diameter is the dashed line. But why is it behind the real diameter. I ques it is about perspective. Can you explain, please.

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  5. #3
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    I am not near the book right now, so I can't give you the full written out explanation. But I recall the explanation being something like: the diameter ends up being behind the long side of ellipse because the long side is CLOSER to your eyes.

    I'm not totally sure how much this applies to the average situation when rendering ellipses (circles in perspective), because I think it's only useful information depending on the angle that you are viewing the ellipse (circle in perspective); I think that some angles cause the true diameter and long side of the ellipse to be so close together that the difference is negligible.

    I'm sure someone else here can manage a much less confusing answer than the one I just gave...

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    Also, to prove this, the author put forth an experiment to try:

    Cut out a large cardboard circle and draw a thick black line indicating the true diameter. Then, place the circle at random distances and elevations from your eyes, and observe this phenomenon taking place.

    I tried this out ^ and it definitely messed with my head. The thing I'm having trouble with right now is properly judging the difference in space between the true diameter, and the imaginary/long-side-of-the-ellipse lines.

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    Inscribe the ellipse inside a square in perspective. Where the square's diagonals cross is the perspective center of the circle. The further the circle is from the viewer, the closer the actual center of the ellipse will approach the perspective center of the circle.

    Last edited by Elwell; November 13th, 2011 at 08:19 PM.

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  9. #6
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    Quote Originally Posted by Elwell View Post
    Inscribe the ellipse inside a square in perspective. Where the square's diagonals cross is the perspective center of the circle. The further the circle is from the viewer, the closer the actual center of the ellipse will approach the perspective center of the circle.
    Bam. There we go.

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    See Syle, there was a good reason for you post - to educate me

    Thanks for the info Elwell.

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    It's explained with a lot more clarity in Norling's "Perspective made easy" book.

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    Quote Originally Posted by arenhaus View Post
    It's explained with a lot more clarity in Norling's "Perspective made easy" book.
    This book is highly recommended, explanations are very easy to grasp plus the book is dirt-cheap.

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    Quote Originally Posted by LORD M View Post
    This book is highly recommended, explanations are very easy to grasp plus the book is dirt-cheap.
    I'll have to get that one. I have the same book as OP and it's not so easy to get through {at least for me}.

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  15. #11
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    I kept going.. Whaaaat?
    Till I finally noticed the 'perspective' keyword.

    Yes, there is a difference between mathematical or pure geometric ellipse construction (in orthogonal view), where the diameter coincides with the long axis, and artistically drawn ellipse in perspective.

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    Download sketchup and draw a square with a circle in it. Move it around and render it as a jpeg. Study what's happening.

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  17. #13
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    Perspective's a bitch, ain't it?

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