Question

Concerning translation matrices.....




How do you find a translation matrix to begin with??

Answer 1

Let's make sure we are talking about the same thing.

Like, say, translate a line right and down, that sort of thing?

Answer 2

Yeah. The picture I'm supposed to be doing it for is this

Answer 3

OK, translate the triangle somewhere?

Answer 4

Pretty much

Answer 5

Say you have a point (x,y), to translate it with t(a,b) you just put (x+a,y+b)

So point A (-1-2), say you want to translate t(2,2) (2 up and 2 right) is (-1 +2 ,- 2 +2)

You can write it in matrix notation if you want to

Answer 6

there is more here http://en.wikipedia.org/wiki/Translation_matrix

Answer 7

Well, it has to look like this;

Answer 8

I don't see a B' or C' on your picture, so that makes no sense...

Answer 9

are we to assume they all change in the same way A translates to A' ??

Answer 10

It's just overkill, every point is being specified even with repetition.....

Answer 11

It's just t(a,b) written 3 times....

Answer 12

I don't see your meaning @estudier i see A, A', B, C, D' and E'

Answer 13

It's a straight linear transformation t(a,b)

Answer 14

left 3 and up 2 you mean, right?

Answer 15

He just wants to write the transformation in matrices (that's what they asked him to do)

Answer 16

x-3, y+2

Answer 17

Yes, we've been there, done that....

Answer 18

I see that

Answer 19

We don't know what the actual transform is ....

Answer 20

Can I go now?

Answer 21

well that's what I'm saying, I suppose we must assume that for every point
so what is the transform\[A\binom xy=\binom{x-3}{x+2}\]is the question, right?

Answer 22

no @estudier you must stay or I will ban you forever :P
nah, what's keeping you here?, I'll try it out

Answer 23

y+2

Answer 24

My computer's about to die and we lost power from this storm so I'm going to have to get back you in a little while

Answer 25

my bad...

Answer 26

then to be continued...

Answer 27

Yes, to be continued

Answer 28

Your teacher has made this unnecessarily difficult.....

Answer 29

I agree

Answer 30

I don't have a teacher. That's the problem

Answer 31

Ah!

Answer 32

Yup

Answer 33

I'll be back on later guys

Answer 34

Ok, it is actually very easy once you see it,......

Answer 35

I'm back!

Answer 36

I guess what you need is represent translation by multiplication? Tell me if I am right.

Answer 37

@cerabear

Answer 38

I think so. I'm not entirely sure

Answer 39

if that is so: imagin the point you trying to translate as a position vector p:

Answer 40

now, you whant to translte it by vector V(a,b)

Answer 41

then your matrix is:
\[\left[\begin{matrix}1 & 0 & a\\0&1 &b\\ 0 & 0 & 1\end{matrix}\right]\left(\begin{matrix}x\\ y\\ 1\end{matrix}\right)\]

Answer 42

Oh. Well it's all pretty straight forward now lol

Answer 43

:)

Answer 44

just to make it clear: x and y that apear in the column matrix are the coordinates of mpoint P. So P(x,y)

Answer 45

@estudier
@TuringTest

Answer 46

Okay, cool. Thanks!

Answer 47

you wellcome