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About projection

  1. Apr 28, 2009 #1
    Draw a circle in a paper, if the line of sight perpendular to the paper , we see a circle ,but if the line of sight is not perpendular to the paper, must we see an ellipse ? how to prove it ? how to find out the major axis or minor axis ? It seem that when we observe the circle ,it should be wide in near place and narrow in far place and should look like a chicken egg ,but it is not true ,how to explain the contradiction. When we view by eyes,we make an affine transformation or a projective transformation ? Whether the relation is true below : parallel projection = affine transformation, central projection = Perspective projection?
     
  2. jcsd
  3. Apr 28, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi redoxes! Welcome to PF! :smile:

    Proof that a circle viewed obliquely is an ellipse depends on how you define an ellipse.

    The easiest way is to define it as a conic section, that is as the intersection of a plane and an upright circular cone …

    then you can prove it using Dandelin spheres …

    see the PF LIbrary on https://www.physicsforums.com/library.php?do=view_item&itemid=98" :wink:
     
    Last edited by a moderator: Apr 24, 2017
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