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I have a parametric representation of a cylindrical shape (well, it's like a cone, but its spike is trimmed). I would like to have an analytic expression for its silhouette lines in terms of the shape's parameters. The parameters I use are:

  • Top circle center
  • Bottom circle center
  • Top circle radius
  • Bottom circle radius

Note that the choice of top/bottom is arbitrary. I just call one side top and the other one bottom.

Thanks!

Update:

The silhouette, of course, is dependent on the viewpoint of the viewer. I assume an orthographic projection, and I know the viewer's position, look direction and up direction.

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    @Alex That doesn't really answer my question. I asked about *how* the projection was being made. But no worries. (Incidentally, this does not jibe with http://www.thefreedictionary.com/silhouette.)2011-03-31

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The top and bottom circles project to ellipses. If one ellipse is entirely inside the other, the silhouette is just the outer ellipse. If not, the silhouette consists of portions of the two ellipses plus two line segments that are tangent to both ellipses.