@techreport{TR-IC-09-29,
   number = {IC-09-29},
   author  =  {Anamaria  Gomide and Danillo Roberto. Pereira and Jorge
                   Stolfi},
   title = {Comparison of Finite Element Bases for Global Illumination
                   in Image Synthesis},
   month = {September},
   year = {2009},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 17 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       Finite  element  bases  defined by sampling points were used by
       J.~Lehtinen  in  2008  for  the efficient computation of global
       illumination  in  virtual  scenes.  The  bases  provide  smooth 
       approximations  for  the  radiosity  and  spontaneous  emission 
       functions,  leading to a discrete version of Kajiya's rendering
       equation. Unlike methods that are based on surface subdivision,
       Lehtinen's method can cope with arbitrarily complex geometries.
       In   this  paper  we  present  an  experimental  validation  of 
       Lehtinen's  meshless  method  by  comparing its results with an
       independent  numerical  solution of the rendering equation on a
       simple  three-dimensional  scene.  We  also  compare Lehtinen's
       special  finite-element basis with two other similar bases that
       are often used for meshless data interpolation, namely a radial
       basis   with   a   Gaussian   mother  function,  and  Shepard's 
       inverse-square-distance  weighted  interpolation.  The  results 
       confirm the superiority of Lehtinen's basis and clarify why the
       other two bases provide inferior-looking results.
  }
}