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 sampled tangent vector field.
%   Samples one arrow per patch at the patch center. The vector field is the
%   tangential projection of (1, 0, 0) onto the surface — a smooth "wind"
%   field that vanishes near the poles and is strongest near the equator.

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

% Sample one tangent vector at the center of each patch.
vx = zeros(1, np);
vy = zeros(1, np);
vz = zeros(1, np);
uu = zeros(1, np);
vv = zeros(1, np);
ww = zeros(1, np);

for k = 1:np
    n = size(dom.x{k}, 1);
    mid = ceil(n / 2);
    cx = real(dom.x{k}(mid, mid));
    cy = real(dom.y{k}(mid, mid));
    cz = real(dom.z{k}(mid, mid));

    % Outward unit normal (sphere: normal = normalised position)
    r = sqrt(cx^2 + cy^2 + cz^2);
    nx = cx / r;  ny = cy / r;  nz = cz / r;

    % Tangential projection of (1, 0, 0)
    dot_val = nx;          % (1,0,0) · normal
    tu = 1 - dot_val * nx;
    tv =   - dot_val * ny;
    tw =   - dot_val * nz;

    % Normalise so all arrows have the same base length
    tmag = sqrt(tu^2 + tv^2 + tw^2);
    if tmag > 1e-10
        tu = tu / tmag;
        tv = tv / tmag;
        tw = tw / tmag;
    end

    vx(k) = cx;  vy(k) = cy;  vz(k) = cz;
    uu(k) = tu;  vv(k) = tv;  ww(k) = tw;
end

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', vx, 'y', vy, 'z', vz, 'u', uu, 'v', vv, 'w', ww);
end