Given a point light source, a eye position, we can find the silhouette (outline) of the given model. We can first find the silhouette edge, project the model into a 2-D plane, then traverse all silhouette edges. But when it comes to concave model, some part of the silhouette edges should not be included in the model outline. How to find those parts? Also, can we do this without projecting the model into a 2-D plane?

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    $\begingroup$ By talking about traversing edges, it sounds like you don't simply want a bitmap of the silhouette, but some vector description. Is that right? What kind of output are you trying to generate? $\endgroup$
    – Dan Hulme
    Commented Oct 19, 2016 at 14:22
  • $\begingroup$ Actually, all kinds of description is OK. For example, a sequence of edges, or start with one point then a path. And my confusion is that is there any method through which I can get the description of silhouette without project the model into a 2-D plane? $\endgroup$
    – zfb
    Commented Oct 19, 2016 at 16:37
  • $\begingroup$ If you just use GL to render it into a framebuffer with a fragment shader that outputs a constant colour, you'll get a bitmap of the silhouette that's correct regardless of concavity. It's so easy that I don't think I've correctly understood what you're trying to do, which is why I'm trying to clarify. $\endgroup$
    – Dan Hulme
    Commented Oct 19, 2016 at 16:48
  • $\begingroup$ well, I think rendering it into a frambuffer is same as project the model on a 2D plane right? And I want algorithms Or method other than projection to find silhouette for concave model. $\endgroup$
    – zfb
    Commented Oct 20, 2016 at 3:22

1 Answer 1


I'll explain the "geometric way" of solving the problem since that's the solution you seem to be after, instead of using rasterization that Dan suggested in the comments.

You can get the list of potential silhouette edges without 2D projection by first iterating through all edges and taking dot product of the normal of the attached two triangles against the eye->edge vector (any point on the edge will do, e.g. one of the end-points). If the dot products for the two triangles on the edge have different signs, then it's a potential silhouette edge. If the object is convex, then you are done and got the list of silhouette edges.

For concave objects it gets more complicated. For concave objects it could be that an edge is only partially a silhouette edge and can be potentially split to N fragments that all belong to the silhouette. So you need to process the list of potential edges and clip them with the geometry. The way you can do the clipping is to extrude every triangle in the geometry away from eye and use this volume to clip the list of potential silhouette edges. The remaining edge fragments that are not clipped away are your silhouette.


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