Talk:Bitangent

Isn't a Bitangent by this definition the same as a secant line? How does it differ mathematically? Also, I've heard "bitangent" and "binormal" used interchangeably in the context of a graphics programming applications (such as parallax mapping). Is this idea at all related to the definition provided here? --Tim Ambrogi


 * Secant lines, in general, cross a curve twice. Bitangents have two points where they touch the curve but do not cross it. The article could do a better job of making this more clear; I will work on rewording it and linking to secant. —David Eppstein 21:54, 22 February 2007 (UTC)

Apparently, the graphics programming application refers to the fact that you need a surface normal and a surface tangent to represent a three-dimensional surface. However, there is a third vector generated through the cross-product of the normal and the tangent (called the binormal or bitangent, depending on your point of view). Perhaps there is another term for this binormal/bitangent vector? In any case, this other common use of the term "bitangent" probably warrants some disambiguation, unless there is some connection that I am unaware of. --Tim Ambrogi

Issue with diagram
The caption on the diagram is somewhat unclear, especially the phrase 'symmetric with respect to the origin'. To me, symmetric with respect to the origin means symmetric with respect to a 180 degree rotation about the origin. Since 4 of the tangents pass through the origin, 16 lines would be needed to include all 28 as either in the diagram or in the diagram's symmetric image. If any rotation about the origin is meant, then 8 lines are needed. If the full symmetry group D4 is meant then only 6 lines are needed. Would the diagram be too complicated if all 28 lines were included? Maybe a simpler curve with a single bitangent would be clearer (if less cool).--RDBury (talk) 17:00, 3 July 2008 (UTC)


 * I changed it to "symmetric with respect to 90° rotations through the origin." Does that help? —David Eppstein (talk) 17:13, 3 July 2008 (UTC)