What do you know about yhe relationship between world coordinates and device coordinates?

Solved

Posted on 1998-09-11

I have a figure that I need to slide to a point. The problem is this figure slides in its local corsys. So the point in world coordinates may be (4,-7) away but I need to slide the device (2,8) in its coordinates. My question is how do I find that local translation? All this is done in 4x4 matrices. I guess it has to do with get the destination point into the devices coordinate system, which I am also not sure how to do. Below is a diagram that might help

y

10

09

08 x

07 /

06 p

05 \

04 y

03

02

01 X goal poin

00

1 2 3 4 5 6 7 8 9 10 x

So you can see that in world all I need to do is slide p 8 in X and -5 in Y. But I need to use p local coordinates and slide it in x or y. So it should be something like 7 in y and 2 in x. All the values I am working with are in 4x4 matrices.

Thanks

y

10

09

08 x

07 /

06 p

05 \

04 y

03

02

01 X goal poin

00

1 2 3 4 5 6 7 8 9 10 x

So you can see that in world all I need to do is slide p 8 in X and -5 in Y. But I need to use p local coordinates and slide it in x or y. So it should be something like 7 in y and 2 in x. All the values I am working with are in 4x4 matrices.

Thanks

2 Comments

If everything is right you have one matrix to convert from local coords to world coords [W]. (The inverse of the matrix converts back).

Seeing that you use 4x4 matrices means you are working in 3D right?

[ 1 0 0 tx ] [x] [ x + tx ]

[ 0 1 0 ty ] [y] = [ y + ty ]

[ 0 0 1 tz ] [z] [ z + tz ]

[ 0 0 0 1 ] [1] [ 1 ]

This is the translation matrix [T]

If you want to convert your local vars to world vars and then translate you can use

[x]

[M][T] [y]

[z]

[1]

(You understand how to multiply matrices?)

The other way around would be first translating the converting:

[x]

[T][M][y]

[z]

[1]

You can also multiply the matrixes and use the new matrix as the conversion from model to world.

Regards Jacco

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