function vector_field_viewer(dom)
%VECTOR_FIELD_VIEWER  Interactive figure showing a tangent vector field on a surface.
%   VECTOR_FIELD_VIEWER(DOM) opens a figure that renders a tangent vector
%   field on the surfacemesh DOM. The arrow scale can be adjusted with a
%   slider in the figure (purely client-side; no MATLAB callback needed).

html = fileread(fullfile('app', 'dist', 'index.html'));
data = build_data(dom);

fig = figure;
gl = uigridlayout(fig, [1 1], 'Padding', [0 0 0 0], ...
                  'RowHeight', {'1x'}, 'ColumnWidth', {'1x'});
uihtml(gl, 'HTMLSource', html, 'Data', data);
end

function data = build_data(dom)
%BUILD_DATA  Pack surface patches and a dense divergence-free tangent vector field.
%   Samples every collocation point across all patches. The field is the
%   stream-function field for F = xyz:
%       v = (x(y^2-z^2),  y(z^2-x^2),  z(x^2-y^2))
%   It is automatically tangent to the unit sphere (v·n = 0) and
%   divergence-free. The flow has 8 vortex centres at the cube vertices and
%   6 saddle points at the cube-face centres, producing eight distinct
%   swirling regions whose index sum satisfies the Poincare-Hopf theorem.

np = length(dom);
px = cell(1, np);
py = cell(1, np);
pz = cell(1, np);
for k = 1:np
    px{k} = real(dom.x{k}(:).');
    py{k} = real(dom.y{k}(:).');
    pz{k} = real(dom.z{k}(:).');
end

% Collect ALL collocation points across every patch.
all_x = horzcat(px{:});
all_y = horzcat(py{:});
all_z = horzcat(pz{:});

% Stream-function vector field v = n x grad_S(xyz) on the unit sphere.
uu = all_x .* (all_y.^2 - all_z.^2);
vv = all_y .* (all_z.^2 - all_x.^2);
ww = all_z .* (all_x.^2 - all_y.^2);

data = struct();
data.type = 'vectorfield';
data.n = size(dom.x{1}, 1);
data.x = px;
data.y = py;
data.z = pz;
data.npatches = np;
data.vectors = struct('x', all_x, 'y', all_y, 'z', all_z, 'u', uu, 'v', vv, 'w', ww);
end