# Converting vectors to tangent or world space. (Explanation please?)

Hi, in the tutorial I’m watching, the Vector Transform node is used to change a vector from tangent to world space. I’ve taken a look at the documentation for this “Transform” node:

“The Transform expression converts a three-channel vector value from one reference coordinate system to another.
By default, all shader calculations in a material are done in tangent space. The vector constants, camera vector, light vector, etc are all transformed to tangent space before being used in a material. The Transform expression allows these vectors to be transformed from tangent space to world-space, local-space, or view-space coordinate systems. In addition, it allows world-space and local-space vectors to be transformed to any of the other reference coordinate systems.”

Here’s the example picture that can be found on the wiki page.

https://docs.unrealengine.com/latest/images/Engine/Rendering/Materials/ExpressionReference/VectorOps/TransformExample1.jpg

Can anyone walk me through exactly what is going on here? I understand that tangent space is “up and down” while world space can be in any number of directions, but I don’t understand how it could be applied to something like a flat material. And I don’t understand how you could just take an arbitrary constant vector and convert it to world space- it seems like just a number, it doesn’t actually /exist/ anywhere. Are the “tangent / world” spaces based on the flat material themselves or the object instance they’re applied to?

Maybe someone could carefully walk me through exactly what is happening in this example. I don’t have a lot of experience with higher-level math terms so forgive me.