Explain please what is to_local()

[ndbn]

Godot Version

4.3

Question

Hello. Can someone explain what Node2D.to_local() and how it work, may be with a picture.

For example,
I have Node2D with position (global and local) Vector2(0,0)
I have some point
var point: Vector2 = Vector2(3.5, 30)
So,
node.to_local(point) returns (28.50028, -9.999864)
My naive representation says it must be point - node.global_position, but it not.
Yes, I’ve seen what inside to_local():

return get_global_transform().affine_inverse().xform(p_global);

But do not understand why it looks like node have offset.

[soapspangledgames]

Local coordinates are relative to the origin of some object, and global coordinates are relative to the world’s origin.

Node.to_local() will convert global coordinates to coordinates that are relative to the Node.

[ndbn]

Did more tests and now understand, it affected by rotation

    var n: Node2D = Node2D.new()
    var p: Vector2 = Vector2(3.0, 5.0)    
    var p_local: Vector2 = n.to_local(p)
    n.rotate(0.5)
    var p_local_rotated: Vector2 = n.to_local(p)
    var p_calc = (p - n.global_position).rotated(-n.rotation)    
    print("p_local = ", p_local) # p_local = (3, 5), same as p
    print("p_local_rotated = ", p_local_rotated)   # p_local_rotated = (5.029875, 2.949636)     
    print("p_calc = ", p_calc) # p_calc = (5.029875, 2.949636)