Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook