title: Concentration of potentially active microfacets in a Normal Distribution Function
body: <p>I'm trying to understand the Cook-Torrance Microfacet Model and am currently stuck on the Normal Distribution function <em>D</em> (being either Beckmann, Blinn-Phong or GGX).
  Several online resources claim that <em>D</em> is the fraction of microfacets normals <strong>M</strong> that allign with the surface normal <strong>N</strong> and D being a fraction it would lie between [0,1]. <a href="https://graphicscompendium.com/theory/07-cook-torrance" rel="nofollow noreferrer">1</a>, <a href="http://www.codinglabs.net/article_physically_based_rendering_cook_torrance.aspx" rel="nofollow noreferrer">2</a></p>
  
  <p>After some research however I learned that D is the concentration of <strong>M</strong> aligned with <strong>N</strong>. <a href="https://blog.selfshadow.com/publications/s2012-shading-course/hoffman/s2012_pbs_physics_math_notes.pdf" rel="nofollow noreferrer">3</a>, 
  <a href="https://stackoverflow.com/questions/23177878/how-to-properly-clamp-beckmann-distribution">4</a></p>
  
  <p>This concentration value (which after some testing can go up to 32 and even higher) is kind of ominous to me. </p>
  
  <p>What exactly can one read from such an unnormalized value? </p>
  
  <p>Can it be related to the fraction of aligned <strong>M</strong> to <strong>N</strong>?</p>
  
  <p>Or is there something simple I'm overlooking?</p>