eye-space pixel width in GLSL vertex shader

Question

I want to compute the eye-space width of a pixel's projected pyramid at the current vertex location in a glsl vertex shader, but I can't seem to get the math right. Here is an obviously incorrect example:

// GLSL VERTEX SHADER
#version 410 compatibility

uniform vec4 viewport; // same as glViewport​
in vec4 gl_Vertex;

void main ()
{
    gl_Position = gl_ModelViewProjectionMatrix * gl_Vertex;
    float pixelWidth = gl_Position.z / viewport.z;
<snip>

But this does not account for the FOV or clipping planes.

Answer 1

I worked through the math and figured it out. :) As I had hoped there are no additional matrix transformations required, just one divide:

// GLSL VERTEX SHADER
#version 410 compatibility

uniform vec4 viewport; // same as glViewport​
in vec4 gl_Vertex;

float pixelWidthRatio = 2. / (viewport.z * gl_ProjectionMatrix[0][0]);

void main ()
{
    gl_Position = gl_ModelViewProjectionMatrix * gl_Vertex;
    float pixelWidth = gl_Position.w * pixelWidthRatio;
    <snip>

Or alternatively:

<snip>
float pixelHeightRatio = 2. / (viewport.w * gl_ProjectionMatrix[1][1]);

void main ()
{
    gl_Position = gl_ModelViewProjectionMatrix * gl_Vertex;
    float pixelHeight = gl_Position.w * pixelHeightRatio;
<snip>

As expected, pixelWidth and pixelHeight are the same if the pixels are square.