# How to perform a coordinate transformation in a function?

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##### 3 Comments

John D'Errico
on 24 Dec 2023

This is not a question about knowing MATLAB, but a question of understanding what a coordinate transform means, and how you would "apply" such a thing.

For example, suppose you have coordinates, (x,y). Then you might wish to convert to polar coordinates. That is a coordinate transform. You can do so by a simple set of equations, or you can use the cart2pol function in MATLAB.

Even more simply, given coordinates (x,y), then the pair (x+1,y+2) is a coordinate transform, a simple translational one.

The problem is, we have no idea what you are doing, what transformation you would employ, or how you would use it in code. I could see cases where you might use the coordinate transform in a purely mathematical way, so before you write any code at all. Or it might become an essential part of your code.

You need to be far more clear if you want a useful answer.

### Accepted Answer

David Goodmanson
on 24 Dec 2023

Hi Kovacs

Here is one way. Clearly

x^2 + t^2 = xi^2

by inspection, so that factor, which is common to both terms, can be saved till the end.

syms x t xi lam dxi dlam

x = xi*cos(lam)

t = xi*sin(lam)

dx = diff(x,lam)*dlam + diff(x,xi)*dxi

dt = diff(t,lam)*dlam + diff(t,xi)*dxi

ds2 = simplify((1/xi^2)*((-dt^2+dx^2)*(x^2-t^2) +4*x*t*(dx*dt)))

ds2 = - dlam^2*xi^2 + dxi^2

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