function wp = plate_pad(w, bc)
% PLATE_PAD  Extend a displacement field by one ghost layer according to the edge condition.
%
%   wp = plate_pad(w, bc) returns the (ny+2) x (nx+2) array whose interior is w.
%   Along each edge w = 0 is imposed on the edge nodes themselves; the ghost
%   values encode the second condition:
%
%     'simply-supported'  w = 0 and w_nn = 0  ->  ghost = -(first interior value)
%                         (odd reflection: the Laplacian vanishes on the edge)
%     'clamped'           w = 0 and w_n = 0   ->  ghost = +(first interior value)
%                         (even reflection: zero slope on the edge)
%
%   Finite-difference stencils evaluated on wp are then valid at every node of
%   the original grid, including the edges.

[ny, nx] = size(w);
wp = zeros(ny + 2, nx + 2);
wp(2:ny + 1, 2:nx + 1) = w;
switch bc
    case 'simply-supported'
        sgn = -1;
    case 'clamped'
        sgn = 1;
    otherwise
        error('plate_pad: unknown boundary condition "%s"', bc);
end
wp(1, 2:nx + 1) = sgn * w(2, :);
wp(ny + 2, 2:nx + 1) = sgn * w(ny - 1, :);
wp(2:ny + 1, 1) = sgn * w(:, 2);
wp(2:ny + 1, nx + 2) = sgn * w(:, nx - 1);
% Corner ghosts: reflect twice (sgn^2 = 1 for both conditions)
wp(1, 1) = w(2, 2);
wp(1, nx + 2) = w(2, nx - 1);
wp(ny + 2, 1) = w(ny - 1, 2);
wp(ny + 2, nx + 2) = w(ny - 1, nx - 1);
end