Bill Baxter wrote: > 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
Ah, thanks for the explanation!
