On Thu, Jan 29, 2009 at 9:44 AM, Chad J <gamerc...@__spam.is.bad__gmail.com> wrote: > Sandeep Kakarlapudi wrote: >> Other mistakes that still irritate quite a few: >> C++ vector vs a mathematical vector >> In real time computer graphics, using binormal inplace of the bitangent. >> Curves have a binormal and surfaces have bitangents! >> No matter how many times binormal is used it still is wrong and sounds >> counter intiutive! > > I don't know if those are right or not, but curves having binormals and > surfaces having bitangents seems inconsistent with other mathematical > terminology, since curves tend to have tangents and surfaces tend to > have normals.
The classic "Frenet frame" used to describe differential properties of spatial curves include a tangent, normal, and binormal. Note that with a curve in 3-space there are two independent directions which are normal to the curve. With a surface in 3D this is not the case. There are two independent directions which are tangent to the surface (which you could call tangent and bi-tangent), and a single normal. I have O'Neill's book on differential geometry, and while it mentions binormals of curves, it says nothing about binormals or bitangents for surfaces. So I think the problem is there was just a terminology vacuum that the graphics guys needed filled, and they filled it in a somewhat illogical way. --bb
