how does GLM handle translation

Question

The OpenGL maths library(GLM) uses the following algorithm to compute the translation matrix:

//taken from source code
template

        

Answer 1

The technical details of as to how the math is done is magnificiently done in @Rabbid76's answer, but if anyone would like to understand why m*t is computed instead of t*m then here's the answer: Computing the matrix tm like this:

here, you're taking the standard basis as the basis vectors for linear combination, so, essentially you're transforming in world space coordinates. but

doing it the other way around and computing mt means now you're essentially taking the basis as the m[0], m[1] and m[2] respectively, so you're transforming in the local space given by the basis, and since this is essentially a model matrix, we just call it model space.

That is probably one way to view it if you're only considering translation, but what if you're handling composite transformations like below:

M=glm::translate(M,T);
R=glm::rotate(M,angle,Rot_axis);  

Here the model matrix is M(initialized to identity at first), T is the translation matrix, R the rotation matrix and others are straightforward above.

So the transformation sequence that happens in the above code is:
M.T.R
and say this is applied to the vector v=[x, y, z, 1], the vector undergoes first a rotation, then a translation and then only the model transformation is done, if it helps, you may see it like this:
M.(T.R.v)