# Sliver triangle

Reading through geometric algorithms and code, I've encountered a term I'm not familiar with, and even the mighty google has not been that helpful:

What is a sliver triangle ?

From what i understand it's a triangle that is almost flat (ie its minimum height is small). But i didn't find a valid information source.

In terms of mesh generation slivers can cause problems, in particular when applying Delaunay triangulation in 3D (with tetrahedrons instead of triangles), you most likely end up with many slivers.

In this setting, slivers are usually defined by having much smaller area/volume than its circumcircle. In 2D this would be equivalent to having a small angle between two edges, but this doesn't hold for tetrahedrons.

• Thanks for the reply ! It's not only a flat triangle, it's a large and flat triangle, am i right ? Commented Aug 10, 2011 at 11:42
• @Clodéric: Remember to accept the answer if you think it answers the question. Commented Aug 10, 2011 at 11:44
• @Clodéric: I somehow missed the second part of your comment. It would be a sharp triangle, or a nearly flat or pointy tetrahedron (small internal angle). I don't understand what you mean by large, since its just a matter of scaling Commented Aug 10, 2011 at 17:44

According to Computer graphics dictionary by Roger T. Stevens (Google books link):

"A sliver polygon is a polygon whose area is so thin that its interior does not contain a distinct span for each scan line. In other words, instead of each scan line having a beginning and and ending pixel, each of which defines one side of the polygon, each scan line has only one pixel that may be the beginning or ending pixel."

As an additional example of situations where a "sliver triangle" might cause trouble, Velvel Kahan shows in this article (he uses "needle" instead of "sliver" though) how Heron's usual formula for computing the area of a triangle from side lengths can give bad results in inexact arithmetic when implemented naïvely (as well as other neat stuff I won't get into here).