# Why are vertices represented as 4f, but normals and light positions as 3f?

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I'm using GLSL specifically and attempting to reproduce the diffuse side of phone shading.  I've noticed in all example code I've seen, positions are represented as a vector of size 4, but normals and light positions are stored in vec3.  Why do positions need the fourth value but normals and lights do not?

-Nick

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I should mention that using w=0 is fine for directional lights (they are at a point at infinity, which is what w=0 means), but for normals this doesn't always work. The 4x4 matrix that describes the affine transformation has a 3x3 submatrix that describes a mapping from vectors to vectors, but in general you should apply the inverse transpose of that matrix to a normal vector. If your 3x3 matrix is a rotation, it is its own inverse transpose, so plugging in w=0 will work. But it's good to know why it works and in which circumstances it might not.

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To develop the above posts a bit, vectors can be used for positions, differences between positions, directions, and normals/tangents/bi-normals/bi-tangents.

* A position vector denotes, well, a point in space.

* A difference vector has no beginning and no end in the sense of positions, it has just a direction and a length. This may be confusing, but look at it so: It is easy to find two different pairs of positions where the difference vectors are identical; you cannot tell which one resulted from which pair of positions by looking at the vectors components.

* A direction vector is a vector with its length set to 1 (unit length), so that the vector still has a direction but no distinguishable length. A difference vector can be made to a direction vector by "normalization".

* A normal/... vector is a direction vector with the constraint to have a specific angle to a line, surface, and/or other vectors.

In a homogeneous co-ordinate system a position vector has the homogeneous co-ordinate, say w, set to a value unequal to zero, where w==1 denotes the normalized case (all cases can simply be converted to the normalized case by dividing by w). All other vector kinds have a w==0. In an affine co-ordinate system the w is implicit (you as the programmer have to remember and think of which kind of vector you're dealing with). In a homogeneous coordinate system you have w as a helper, but still need to remember and think of the special constraints on normals/tangents/... as mentioned by Álvaro.

I'm sure (not to say I'm hoping) that the examples you found on the internet do consider this in the one or other way.

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