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.

  • 133arc585English
    2•1 year ago

    I’m writing this as someone who has not done much with Godot, but from the mathematical standpoint, two Transform3Ds do not commute in general. There are situations in which they will commute, though. If they are both pure rotations, they will commute if their rotation axes are the same.

    Edit to add: This was based on thinking about a Transform3D as a transformation matrix acting on R3.

    • @o11cEnglish
      2•1 year ago

      I likewise don’t really use Godot, but for graphics in general, the 4th coordinate is important, even if it is “usually” 1. It’s most obvious to correctly interpolate near the poles of a sphere with a single rectangular texture, but think for a minute what “near” means.

      Back to the main point though: the important things we normally rely on for matrix math are associativity (particularly, for exponentiation!) and anticommutativity (beware definitions that are sloppy about “inverse”).

      • 133arc585English
        -1•1 year ago

        but for graphics in general, the 4th coordinate is important, even if it is “usually” 1.

        Who said it isn’t? Transformation matrices acting on R3 are 4x4 (since transformation matrices acting on Rn are of dimension n+1 in general), whether they’re full rank or not.