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## -*- texinfo -*-
## @deftypefn  {} {} specular (@var{sx}, @var{sy}, @var{sz}, @var{lv}, @var{vv})
## @deftypefnx {} {} specular (@var{sx}, @var{sy}, @var{sz}, @var{lv}, @var{vv}, @var{se})
## Calculate the specular reflection strength of a surface defined by the
## normal vector elements @var{sx}, @var{sy}, @var{sz} using Phong's
## approximation.
##
## The light source location and viewer location vectors are specified using
## parameters @var{lv} and @var{vv} respectively.  The location vectors can
## given as 2-element vectors [azimuth, elevation] in degrees or as 3-element
## vectors [x, y, z].
##
## An optional sixth argument specifies the specular exponent (spread)
## @var{se}.  If not given, @var{se} defaults to 10.
## @seealso{diffuse, surfl}
## @end deftypefn

function retval = specular (sx, sy, sz, lv, vv, se)

  if (nargin < 5 || nargin > 6)
    print_usage ();
  endif

  ## Check normal vectors
  if (! size_equal (sx, sy, sz))
    error ("specular: SX, SY, and SZ must be the same size");
  endif

  ## Check light vector (lv) argument
  if (! isvector (lv) || length (lv) < 2 || length (lv) > 3)
    error ("specular: light vector LV must be a 2- or 3-element vector");
  elseif (length (lv) == 2)
    [lv(1), lv(2), lv(3)] = sph2cart (lv(1) * pi/180, lv(2) * pi/180, 1.0);
  endif

  ## Check view vector (vv) argument
  if (! isvector (vv) || length (vv) < 2 || length (lv) > 3)
    error ("specular: view vector VV must be a 2- or 3-element vector");
  elseif (length (vv) == 2)
    [vv(1), vv(2), vv(3)] = sph2cart (vv(1) * pi / 180, vv(2) * pi / 180, 1.0);
  endif

  ## Check specular exponent (se) argument
  if (nargin < 6)
    se = 10;
  elseif (! (isnumeric (se) && numel (se) == 1 && se > 0))
    error ("specular: exponent SE must be a positive scalar");
  endif

  ## Normalize view and light vectors
  if (sum (abs (lv)) > 0)
    lv /= norm (lv);
  endif
  if (sum (abs (vv)) > 0)
    vv /= norm (vv);
  endif

  ## Calculate normal vector lengths and dot-products
  ns = sqrt (sx.^2 + sy.^2 + sz.^2);
  l_dot_n = (sx * lv(1) + sy * lv(2) + sz * lv(3)) ./ ns;
  v_dot_n = (sx * vv(1) + sy * vv(2) + sz * vv(3)) ./ ns;

  ## Calculate specular reflection using Phong's approximation
  retval = 2 * l_dot_n .* v_dot_n - dot (lv, vv);

  ## Set reflectance to zero if light is on the other side
  retval(l_dot_n < 0) = 0;

  ## Allow positive values only
  retval(retval < 0) = 0;
  retval .^= se;

endfunction