# Why does GLM only have a translate function that returns a 4x4 matrix, and not a 3x3 matrix?

I'm working on a 2D game engine project, and I want to implement matrices for my transformations. I'm going to use the GLM library.

Since my game is only 2D, I figured I only need a 3x3 matrix to combine the translation, rotation and scale operations. However, glm::translation is only overloaded to return a 4x4 matrix, and never a 3x3.

I thought a translation could be performed by using a 3x3 matrix; why does GLM only have a translate function that returns a 4x4 matrix, and not a 3x3 matrix?

• You should use 4*4 matrices, just convert the vectors to 4d ones – Bálint Feb 18 '17 at 20:50
• So most of my vectors should have default W coordinate values of 1? In order to work with 4x4 matrices? – Jason Feb 18 '17 at 20:53
• If you ask for a vec4 in the shader, but you pass a vec3, then it'll automatically fill it up – Bálint Feb 18 '17 at 21:03
• I dont feel I know enough about this to properly answer, but the "w" axis (i.e. the fourth coordinate) has always been a point of confusion for me, and many sources fail to explain it without over explaining it. A recent tutorial I completed finally explained it clearly; we sometimes need a 4th coordinate to allow for matrix multiplication. The 4th coordinate is often 1 or 0 - because 0 cancels out the translation matrix, and 1 retains it. In other words, if the last coordinate is 0, we do not have an actual position applied to the final result, commonly used to convey a direction. – Gnemlock Mar 22 '17 at 3:40
• When a vector conveys a direction, actual position is ultimately irrelevant. – Gnemlock Mar 22 '17 at 3:41

You still need 4x4 for the projection matrix, even in 2D.

Typically you will use a combined MVP matrix in your shaders rather than separate matrices, so the calculations are easier (and faster - 4x4 is SIMD-friendly whereas 3x3 is not) throughout the pipeline if you just use 4x4 matrices everywhere.

Because GLM (as well as OpenGL) is designed to work for 3D graphics in the first place, and you need mat4 to perform translations in 3D.

You could write a 2D translation function yourself. It's as simple as returning the following matrix:

1 0 x
0 1 y
0 0 1


Keep in mind that to use it you will need to have a 1 as the last component of your vectors (you don't need to actually store it, you may just add it temporarily before doing multiplication).