Assuming I have infinite vertices to represent the sphere, if I project the sphere from any position/scale in 3D to 2D, will it be a circle?

I know it will not be a circle on the screen, because of scaling and different resolutions. But do field of view and aspect ratio effect the results?

Edit: Sorry yes, I am talking about perspective projection. Seems the answer is no then, perspective will distort the sphere. Thanks!

  • \$\begingroup\$ Are you talking about perspective projection? Orthographic projection? \$\endgroup\$ – Laurent Couvidou Nov 9 '12 at 11:13

If we're talking about any projection, this is quite obviously not the case. After all, Cahill's Butterfly is a valid projection of a sphere onto a 2D surface:

enter image description here

Non-uniform parallel projections will also tend to distort the shape. Perspective projections on the other hand won't distort the shape as long as the projection surface has zero curvature (that is, it's "flat" in respect to the space embedding it).


In a perspective projection, not necessarily - in fact, the further the sphere is from center of projection, the more distorted it will be. Example: old picture of a distorted sphere.

  • \$\begingroup\$ That picture is very helpful, sorry I can't select two answers \$\endgroup\$ – ashleysmithgpu Nov 9 '12 at 11:20
  • \$\begingroup\$ Note though that if the sphere is directly along the view vector, it will be a circle. \$\endgroup\$ – Sean Middleditch Nov 2 '15 at 17:18

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