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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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    Your shape is called a frustrum of a cone. Some information (but not the silhouette you are seeking) is at http://en.wikipedia.org/wiki/Frustrum.2011-03-31
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    I am not seeking a shadow. I am seeking the silhouette from a given viewpoint. I will update the question.2011-03-31
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    @Ross: is it "frustrum" or "frustum"?2011-03-31
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    Alex, what is the difference between your silhouette and your shadow? An orthographic projection is not *really* either, unless the light source (or viewpoint) is at infinity. Otherwise the beams of light (or "rays to the observer") will not be parallel.2011-03-31
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    @Isaac: You are right. I've been mistaken all these years and so is whoever named the file in Wikipedia (tho the Wikipedia page title is correct)2011-03-31
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    @Ross: It's one of those word/spelling things where I'm never entirely sure. I suspect that both words will work to get the article in Wikipedia (i.e. the link you posted is transparently redirected to the other spelling).2011-03-31
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    @Glen Wheeler: Imagine your draw the shape with black color on a white image. You will get some kind of a black blob on your white image. The silhouette are the points on the surface which are projected to the contour of this blob.2011-03-31
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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.