matrices and cartesians 
Author Message
 matrices and cartesians

Hi.
Can anyone tell me the formula to derive a cartesian
coordinate from a matrix?

Thanks,
Johann



Mon, 27 Jun 2005 16:37:46 GMT  
 matrices and cartesians
Hi,

For a translation matrix?

[ T ]   =         1  0   0  0
                     0  1  0  0
                     0  0  1  0
                     x   y  z  1

so, you can read the translation "offset" in the fourth row.

That is valid only for Translation matrix. For a rotation matrix,

            1  0    0    0
            0  cos sin 0
            0  -sin cos 0
            0  0    0    1

as example, for a rotation around x, there is no "coordinate" stored in the "matrix".

So, in other word, you have to know in advance what the matrix "stores". In the last example, you
would wrongly conclude that <x y z>  = < 0  0  0>  is you would have just read the fourth row.

In general, the matrix TRANSFORM something, they transform the vector with which you multiply them
and that is that vector that hold real "data", real "position".

        < New Vector >  =  < Old Vector >  [  Matrix ]

as in

          < a  b  c   1> [ Translation ]

will result into
        <  a+x,   b+y,   c+z,    1>

if we use the first matrix, and we can see it is a position < a b c>  shifted by the amount < x  y
z> to supply a new position, < a+x, b+y, c+z  >

Vanderghast, Access MVP


Quote:
> Hi.
> Can anyone tell me the formula to derive a cartesian
> coordinate from a matrix?

> Thanks,
> Johann



Tue, 28 Jun 2005 01:12:35 GMT  
 
 [ 2 post ] 

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