ch-ch-changes

[Bill Baxter]

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