2
$\begingroup$

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.

  • 1
    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
  • 0
    I am not seeking a shadow. I am seeking the silhouette from a given viewpoint. I will update the question.2011-03-31
  • 1
    @Ross: is it "frustrum" or "frustum"?2011-03-31
  • 0
    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
  • 0
    @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
  • 0
    @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
  • 0
    @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
  • 0
    @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

1 Answers 1