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########################################################################
##
## Copyright (C) 2009-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{refl} =} specular (@var{sx}, @var{sy}, @var{sz}, @var{lv}, @var{vv})
## @deftypefnx {} {@var{refl} =} 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 refl = specular (sx, sy, sz, lv, vv, se)
if (nargin < 5)
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
refl = 2 * l_dot_n .* v_dot_n - dot (lv, vv);
## Set reflectance to zero if light is on the other side
refl(l_dot_n < 0) = 0;
## Allow positive values only
refl(refl < 0) = 0;
refl .^= se;
endfunction
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