Re: Generating Two Unit Orthogonal Vectors to a 3D Vector
- To: mathgroup at smc.vnet.net
- Subject: [mg36360] Re: Generating Two Unit Orthogonal Vectors to a 3D Vector
- From: Tom Burton <tburton at brahea.com>
- Date: Tue, 3 Sep 2002 01:41:02 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Adding my two cents to:
On 9/2/02 1:30 AM, in article akv7s5$fl8$1 at smc.vnet.net, "David Park"
<djmp at earthlink.net> wrote:
> There are many cases in graphics, and otherwise, where it is useful to
> obtain two orthogonal unit vectors to a given vector. I know a number of
> ways to do it, but they all seem to be slightly inelegant. I thought I would
> pose the problem to MathGroup. Who has the most elegant Mathematica
> routine...
To this I would like to add a criterion of smoothness. Armed with a second
vector b not parallel to the given vector a, it's a trivial matter to
orthogonalize b WRT a by Gram-Schmidt and then form the third vector c = a x
b. (Normalize as needed.)
I don't need more elegance that this, but I would like a scheme to select
the vector b that results in a triad {a,b,c} that various smoothly as "a"
varies over all possible directions. Each of my attempts to date involve a
branched algorithm and jumps in the resulting triad for certain small
changes in "a".
To David's call for elegance I add a call for smoothness.
Tom Burton