<p>Would someone be able to explain why a sphere when projected with the pinhole projection model has its projected 2D image be an ellipsis. IN particular when the sphere is not directly in front of the center of projections why is the image of the sphere skewed? Any diagrams explaining this or formula would be greatly appreciated.</p>

CC BY-SA 4.0
2021-01-27T19:59:51.560Z
Actually it is not always an ellipse. It can be a hyperbola parabola or a circle too. See [this near duplicate](https://computergraphics.stackexchange.com/questions/1493/does-a-sphere-projected-into-2d-space-always-result-in-an-ellipse/)
joojaa
CC BY-SA 4.0
2021-01-28T13:22:09.423Z
Does this answer your question? [Does a sphere projected into 2D space always result in an ellipse?](https://computergraphics.stackexchange.com/questions/1493/does-a-sphere-projected-into-2d-space-always-result-in-an-ellipse)
Kaan E.
CC BY-SA 4.0
2021-01-29T08:03:58.187Z
Even though this is not a 100% duplicate of the question linked by @joojaa [I vote to close this question](https://computergraphics.meta.stackexchange.com/questions/314/lowering-the-vote-threshold-to-close-reopen-a-question-from-5-to-3). The real good answers in the linked question also answer this one and I don't think it makes sense to repeat everything here.
wychmaster
<image-processing><computational-geometry>
Pinhole Projection & Spheres
gmjasonx
# Pinhole Projection & Spheres

(Asked by: username_0 on 2021-01-26)

Would someone be able to explain why a sphere when projected with the pinhole projection model has its projected 2D image be an ellipsis. IN particular when the sphere is not directly in front of the center of projections why is the image of the sphere skewed? Any diagrams explaining this or formula would be greatly appreciated.

**Tags:** image-processing, computational-geometry

> **Comments:**
> **username_1**: Actually it is not always an ellipse. It can be a hyperbola parabola or a circle too. See [this near duplicate](https://computergraphics.stackexchange.com/questions/1493/does-a-sphere-projected-into-2d-space-always-result-in-an-ellipse/)  
> **username_2**: Does this answer your question? [Does a sphere projected into 2D space always result in an ellipse?](https://computergraphics.stackexchange.com/questions/1493/does-a-sphere-projected-into-2d-space-always-result-in-an-ellipse)  
> **username_3**: Even though this is not a 100% duplicate of the question linked by @username_1 [I vote to close this question](https://computergraphics.meta.stackexchange.com/questions/314/lowering-the-vote-threshold-to-close-reopen-a-question-from-5-to-3). The real good answers in the linked question also answer this one and I don't think it makes sense to repeat everything here.  

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