using local translations to move to a point in global space

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
micahAsked:
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JaccoConnect With a Mentor Commented:
Transformations are always reversible

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