sorry for my english, I need to know, that, given a set of points x, y in a M x N cartesian system, how can I calculate the same set of point in another system I x J, being M > I and N > J? Is this possible? If it is, which is the name of the method?
Example:
Being a plane with 100 units of width and 150 units of height, and a set of point A= {(30, 20), (78, 56), (56, 18)}, is there a method that given a plane of 20 x 60, get a set of points equivalent with A in this second plane?
Thanks and sorry about my english.
I don't know what you mean by an $M\times N$ coordinate system, but I suggest the following: Draw in black a horizontal and a vertical axis, make a few ticks and label these with the values they should denote in your "$M\times N$-system". Then draw in red another pair of axes offset $1$mm with respect to the black axes, make a few ticks and label these with the values they should denote in the "$I\times J$-system". This means that now any point $x$ on a virtual horizontal axis has an $M$-value $x_M$ and an $I$-value $x_I$ assigned, and there is a certain relationship between the numbers $x_M$ and $x_I$ which is independent of the chosen point $x$. In the same way any point $y$ on a virtual vertical axis has an $N$-value $y_N$ and a $J$-value $y_J$ assigned, and there is a certain relationship between the numbers $y_N$ and $y_J$ which is independent of the chosen point $y$. Finally, if you have an arbitrary point $P$ in the plane then it has a vertical projection to the horizontal axis whereby two numbers $x_M$ and $x_I$ are generated, and a horizontal projection onto the vertical axis whereby two numbers $y_N$ and $y_J$ are generated. It now should be easy to write down the formulas by which the pairs $(x_M,y_N)$ and $(x_I,y_J)$ are related.