// Call this function to generate a fake sphere from a point sprite
vec3 point_normal(in vec2 uv)
{
    vec3 n;
    n.xy = uv * 2.0 - 1.0;

    float rr = dot(n.xy, n.xy);
    if (rr > 1.0) discard;
    n.z = sqrt(1.0 - rr);

    return n;
}

// ...
// Then later, use the normal returned by `point_normal` to calculate the new frag depth
// ...

float radius = point_sprite_size * 0.5;
vec4 pixel_position = vec4(fs_in.camera_space_position + normal * radius, 1.0);
vec4 clip_space_position = projectionMatrix * pixel_position;
clip_space_position.z /= clip_space_position.w;
gl_FragDepth = clip_space_position.z;