demo1.m

% DEMO1
%
% Description
%     Move an interface in a "pinching" velocity field. Phi is kept relatively
%     close to a signed distance function. 
%     
%     This demo shows the merging and separation of two interfaces, as well as
%     the interfaces leaving the grid.

% Print out help message.
help demo1

    %
    % Initialize grid.
    %

lset_grid([80 80]);


    % 
    % Construct the initial structure/interface.
    %

phi = lset_circle([-10 0], 3);
phi = lset_union(phi, lset_circle([10 0], 3));


    % 
    % Construct the signed distance function for the interface.
    %

[phi, err] = signed_distance(phi, 1e-1);


    % 
    % Construct a "pinching" velocity field.
    %

V = lset_velfield(@(x, y) -(x+0.1).^-1 .* (abs(y)+1).^-1, @(x, y) 0.2*sign(y));


    %
    % Move the surface within the velocity field, keep phi "close" to a
    % signed distance function.
    %

while (true)
    lset_plot(phi); drawnow; % Visualize.
    phi = update_interface(phi, V, 0, 0); % Move the interface.
    try
        [phi, err] = signed_distance(phi, 1e-3); % Make phi more sdf-like.
    catch
        lset_plot(phi); % Visualize.
        break; % If signed_distance failed, we have no more interfaces.
    end
end