Transformation matrix for matrix indices to cartesian coordinates(1,1) (1,2) (1,3)(2,1) (2,2) (2,3)(3,1) (3,2) (3,3)This is an example 3x3 matrix. In corresponding cartesian coordinate system, the representation would be:(-1,1) (0,1) (1,1)(-1,0) (0,0) (1,0)(-1,1) (0,-1) (1,-1)Say, I have any square matrix with dimension-N, where N is odd. I need a generic transformation matrix such that I can get a vector as cartesian coordinates from matrix indices. Does such a function already exist? How should I go ahead in implementing this?

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nuvolor8 · Accepted Answer

The transformation of indices is the following:  (  x  ,  y  )  =  f  (  i  ,  j  )  =      (    j    −                  n        +        1            2        ,    −    i    +                  n        +        1            2        )       .Here   i is the index for the rows,   j the one for the columns and   n the order of your square matrix.

glycleWogry · Accepted Answer

Interchange indices   i and   j in initial matrix, then flip it upside down to get the same orientation like a usual coordinate system and then subtract   (  2  ,  2  ) or   (            n      +      1        2    ,            n      +      1        2    ) in general to shift the center.

Transformation matrix for matrix indices to cartesian coordinates (1,1) (1,2) (1,3) (2,1) (2,2) (2

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