ch-ch-changes

[Chad J]

Bill Baxter wrote:
> On Thu, Jan 29, 2009 at 9:44 AM, Chad J
> <gamerchad at __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!