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I know that in perspective projection the circle turns into an ellipse. but does it convert to ellipse and ellipsoid to ellipse in perspective projection?

Especially in perspective ellipse is still ellipse?. I read here that this is so in orthographic but is it so in perspective projection?

Rodrigo de Azevedo
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Edi
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1 Answers1

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Yes -- it's surprisingly simple:

  1. a circle turns into an ellipse under any perspective projection
  2. Combined perspective projections are still perspective projections
  3. Every ellipse is a circle in some perspective projection

That means that we can turn a projection $P$ into $(PT^{-1})T$ where $T$ is a projection that turns the given ellipse into a circle.

I think there are some degenerate cases where this breaks down.

Alex K
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  • But you don't establish that an ellipsoid lighted by a source point has an elliptic shadow on any plane (the source of light being either at finite distance or at infinity). – Jean Marie Jan 26 '23 at 18:12
  • @JeanMarie you're correct; I forgot about that part of the question -- and I don't have a ready answer. – Alex K Jan 26 '23 at 19:42
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    In fact an explanation can be extracted from here but it necessitates some familarity with quadratic forms... – Jean Marie Jan 26 '23 at 21:40
  • A more accessible approach in an answer to this question with a reference as well to an answer of mine using Schur's complement. – Jean Marie Jan 27 '23 at 09:12