Re: translation and rotation in Euclidean space
- From: "Androcles" <Headmaster@xxxxxxxxxxxxxxxx>
- Date: Sat, 25 Oct 2008 18:06:06 +0100
"John Polasek" <jpolasek@xxxxxxxxxx> wrote in message
news:b4g6g4llu7j8ssojcpiupsdrkuq89a742t@xxxxxxxxxx
On Sat, 25 Oct 2008 04:54:31 +0100, "Androcles"
<Headmaster@xxxxxxxxxxxxxxxx> wrote:
snip
which is a 2nd rank tensor, isomorphic to one axis of a gimbal set.advance for any help.Another flagrant case of the vanishing OP. He posts a poorly framed
Best...Frank
problem, confusing distance with length, introducing a, b, u, v
without defining them, and now we have a half dozen kindly experts
poring and proposing amongst themselves, with nary any evidence that I
have seen, that the OP is still there or even interested.
In the first place the rotation can only be done by multiplying the
vector by a 3x3 matrix
In the second place a single rotation only requires a 2x2 matrix.
[cos -sin]
[ sin cos]
In the third place a 3x3 matrix permits rotation in pitch, roll and yaw,
A rotation in any of pitch. roll or yaw can be done with a 2x2 if you
want to play that way.
Of course, but when you have a full database such as many computer
games like "Flight Simulator" or even Google Earth or Google Sketchup
do and wish to rotate and translate a scene it is helpful if you process
all
relevant points (vectors) with a single 4x4 matrix. That way you don't
need to recompute.
in the fourth place a 4x4 matrix can be used to include translation.I didnt notice he was stuck in 2 dimensions. But a rotation matrix is
In the fifth place your first place is wrong.
a 2d rank tensor, say Lij, a vector is a 1st rank tensor say Xi and
they cannot be combined in some kind of 4x4 and still be a tensor.
This 4x4 tensor cannot be rotated, just as the metric tensor cannot be
rotated. It's a donkey matrix.
Ok.
Be a good guy and show Frank how to write your 4x4 matrix.
That's all over the web:
http://tinyurl.com/5vsnqs
This is obviously a translation ; (-) is a dummy variable:
[ 0 0 0 0 ] [ a ] [ d ]
[ 0 0 0 0 ] * [ b ] = [ e ]
[ 0 0 0 0 ] [ c ] [ f ]
[d/a, e/b, f/c, 0 ] [ (-) ] [ 0 ]
Likewise a null rotation is obvious:
[ 1 0 0 0 ] [ a ] [ a ]
[ 0 1 0 0 ] * [ b ] = [ b ]
[ 0 0 1 0 ] [ c ] [ c ]
[ 0, 0, 0, 0 ] [ (-) ] [ 0 ]
Now the question becomes :
Do we want to translate and then rotate or
rotate first and then translate?
It's really just a question of how the scene changes as
you move or an object in the scene moves.
If you are watching a car move along a highway then
that's different to being in a car watching the world
passing by you. And you might be doing both.
http://www.androcles01.pwp.blueyonder.co.uk/Vector/RP.gif
(By the way, where is Frank/Athan anyway?)No idea. Probably cheesed off by all the cranks mumbling crap
they couldn't program a computer to do. sci.physics.relativity
is a kook NG. <shrug>
I only post here to take the piss out of them, which is why nobody
likes me.
http://www.androcles01.pwp.blueyonder.co.uk/QUESTION.htm
.
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