[question] Correct order of `Mat*Mat` and `Mat*Vec` multiplications using `zmath`

[heysokam]

I'm really confused about the correct order of mul operations to create a Transformation matrix using zmath.Mat operations.

The desired goal is this order, from Left.first to Right.last:
First .scaling(by{1,2,3}) -then-> .rotation(by{quat}) -then-> .translation(to{position}) -then-> .apply_matrix(to{input}) -output-> final vector

The problem is that, as my understanding goes, row-major and column-major have different ordering of operations to achieve correct transformations:

row-major[  vec*S*R*T  ]
col-major[  T*R*S*vec  ]

So, in order to achieve an S->R->T order: How should I order my arguments for zmath.mul?

1. mul(mul(mul(vec, S), R), T)
2. mul(S, mul(R, mul(vec, T)))
3. Something else entirely

[heysokam]

// AKA needs to be ->   mul(vec3, transform)  !!
const works      = mul(loadArr3w(vector[0..3].*, 1), matFromArr(transform));
const very_wrong = mul(matFromArr(transform), loadArr4(vector));
const also_wrong = mul(matFromArr(transform), loadArr3w(vector[0..3].*, 1));

After wasting ~20h of my life to this, this is the answer on how to apply Transformations
Its mul(vec3_with_w1, TransformationMatrix{ FirstScale, ThenRotate, LastTranslate })

Vector goes on the LEFT of mul(vec, mat) !!!
-and- it must have a vec[W] == 1 (not the default, zmath sets this to 0), or else the transformation will be erased!
And the incoming matrix MUST be the right hand argument, like so:
M = (mul(M,S) * mul(M,R)) * mul(M,T) -then-> mul(vec, M)

Please add a note to the file somewhere stating these facts 🙏 🙏
Because its a major source of frustration when coming from Column major backgrounds
(aka the entire internet)

[heysokam]

Edited the above comment to add Matrix combination argument order.

[michal-z]

We have some info about this in the comment section here:
https://github.com/zig-gamedev/zmath/blob/main/src/root.zig#L10
https://github.com/zig-gamedev/zmath/blob/main/src/root.zig#L22

Could you please make a PR and add more info?