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Godot @programming.dev Ti_Ka @lemmy.blahaj.zone

Are Transform3D's commutative?

As in, for any two Transform3D objects A and B i might encounter does Godot (4.1) always return A * B == B * A as true? Alternatively is it approximately commutative, ie (A * B).is_equal_approx(B * A), in case there are situations where floating point imprecision messes the exact equality up.

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7 comments

  • No.

    If you rotate 180 degrees about the x axis and then 180 degrees about the line y=x, you get a rotation anticlockwise by 90 degrees about the z axis.

    If you do it the other way round, the rotation is the opposite direction (clockwise).

    They only commute in quite specific circumstances.

  • Ok so it seems like they don't commute? I asked the question in part because i wanted to do something like:

    const base_transform : Transform3D = <some transform>

func get_base_transform(node : Node3D) -> Transform3D:
    return node.transform * base_transform

func set_base_transform(node : Node3D, transform : Transform3D) -> void:
    node.transform = base_transform.affine_inverse() * node.transform

    and i wanted to be sure that if i do set_base_transform(some_node, some_transform) i'd be guaranteed to get that get_base_transform(some_node) == some_transform afterwards. But when i tried it the above code did not work out, at least i didnt get the result i expected. But when i flipped it so that set_base_transform did node.transform = node.transform * base_transform.affine_inverse() instead it did work out. Its still not hard proof though, maybe something else was messed up the first time, or it only looks like it works now and i'll discover the transform still isn't what i wanted it to be. Or they do commute but only under some constriction like no scale on any axis or something and i just happened to fulfill it with all the ones i used in my test.

    So it would still be good to know for sure whether/when Transform3D's commute.

    EDIT: I accidentally wrote the first line wrong, it said that they do commute. When actually the experience i had with it working only after both functions did their multiplications in a compatible order should indicate that they don't commute.

7 comments