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## -*- texinfo -*-
## @deftypefn {} {[@var{xr}, @var{yr}, @var{zr}] =} __rotate_around_axis__ (@var{x}, @var{y}, @var{z}, @var{angle}, @var{dir}, @var{origin})
## Rotate the points given by @var{x}, @var{y}, @var{z} about an axis by
## @var{angle} degrees.
##
## The axis is specified by the vector @var{dir} and the point @var{origin}.
## @end deftypefn

function [xr, yr, zr] = __rotate_around_axis__ (x, y, z, angle, dir, origin)

  dir /= norm (dir);
  u = dir(1);
  v = dir(2);
  w = dir(3);

  a = origin(1);
  b = origin(2);
  c = origin(3);

  sa = sind (angle);
  ca = cosd (angle);

  if (a == 0 && b == 0 && c == 0)
    tmp = (u*x + v*y + w*z) * (1 - ca);

    xr = u*tmp + x*ca + (-w*y + v*z)*sa;
    yr = v*tmp + y*ca + (w*x - u*z)*sa;
    zr = w*tmp + z*ca + (-v*x + u*y)*sa;
  else
    one_m_ca = 1 - ca;
    tmp = u*x + v*y + w*z;

    xr = ((a*(v^2 + w^2) - u*(b*v + c*w - tmp))*one_m_ca
          + x*ca + (-c*v + b*w - w*y + v*z)*sa);
    yr = ((b*(u^2 + w^2) - v*(a*u + c*w - tmp))*one_m_ca
          + y*ca + (c*u - a*w + w*x - u*z)*sa);
    zr = ((c*(u^2 + v^2) - w*(a*u + b*v - tmp))*one_m_ca
          + z*ca + (-b*u + a*v - v*x + u*y)*sa);
  endif

endfunction


## No test needed for internal helper function.
%!assert (1)
