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Spheres under perspective projection

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The main thing I want to accomplish is the quickest way to get a screen space bounding rect of a sphere. If anyone knows a good fast method I would appreciate it. But in addition I would like to know more about why a sphere under perspective projection isn't perfectly round? More specifically I was looking at this: http://www.iquilezles.org/www/articles/sphereproj/sphereproj.htm page and in the first picture one of the spheres appear to tilted and was wondering what exactly causes that? But like I said the primary thing I would like is a quick screen space bounding rect for a given sphere and a particular MVP matrix.

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