Calculate the distance between two 3d points in screen coordinates

Question

Given the Point A with the coordinates gl_FragCoord.xy, I have to find the distance to the Center of the cube face to which it belongs in screen coordinates.

Specifically what I need is the formula to convert the Center of every face of the cube in screen coordinates, in order to compare it with gl_FragCoord.

This the fragment shader:

precision mediump float;

uniform vec2 u_resolution;

varying vec2 v_uv;

void main() {
  gl_FragColor = vec4(v_uv.x, v_uv.y, 0.0, 1.0);
}

This the vertex shader:

precision mediump float;

attribute vec3 a_position;
attribute vec2 a_uv;

uniform mat4 u_view;
uniform mat4 u_projection;

varying vec2 v_uv;

void main() {
  v_uv = a_uv;

  gl_Position = u_projection * u_view * vec4(a_position, 1.0);
}