ml84.m

%% options
clear_frames_after = 5;
segment = "c"; % can be 'a', 'b', or 'c'.

%% diff eqs
%because r=1
px = @(t,x) cos(t)-x;
py = @(t,y) sin(t)-y;

p = @(t,x,y) [px(t,x),py(t,y)];
p_hat = @(t,x,y) 1./norm(p(t,x,y)) * p(t,x,y);
%% a
if segment=="a"
    q = @(t) 0.3;
end
%% b
if segment=="b"
    lambda = 30; %[s]
    q = @(t) 0.50 * exp(-t./lambda);
end
%% a+b
%small dog
if segment=="a" || segment=="b"
    v = @(t,x,y) q(t)*p_hat(t,x,y);
    vpos = @(t,pos) v(t,pos(1),pos(2));
    dpdt = @(t,p) transpose(vpos(t,p));

    [ts,ps]=ode45(dpdt,[0,14 * pi],[0,-3]);
    draw_global_frames(ts, ps, clear_frames_after)
end
%% c
if segment=="c"
    q = @(t) 0.32;
    v = @(t,x,y) q(t) ./ norm(p(t,x,y))  * p_hat(t,x,y);

    %small dog
    vpos = @(t,pos) v(t,pos(1),pos(2));
    dpdt = @(t,p) transpose(vpos(t,p));

    events = odeset('Events',@early_stopping);
    [ts,ps]=ode45(dpdt,[0,14 * pi],[0,-3], events);

    draw_global_frames(ts, ps, clear_frames_after)
end
%% drawables
function draw_global_frames(ts, ps, clear_after_frames)
    xs = ps(:,1);
    ys = ps(:,2);
    for i=1:length(ts) 
        if clear_after_frames ~= -1
            if mod(i,clear_after_frames) == 0
                clf
            end
        end
        hold on
        
        xlim([-3,3])
        ylim([-3,3])
        
        t = ts(i);
        % draw circle
        draw_circle(0,0,1);
    
        % draw small dog pos
        draw_point(xs(i), ys(i));
        
        % draw large dog pos
        draw_cpoint(1,t);
        hold off
        pause(0.05)
    end
    
end

function [x,y] = radial_to_linear(r, angle)
    x = r * cos(angle);
    y = r * sin(angle);
end

function fig = draw_cpoint(r,angle)    
    [x,y] = radial_to_linear(r, angle);
    fig = plot(x,y,'Marker','O',"MarkerFaceColor", "red");
end

function fig = draw_point(x,y)
    fig = plot(x,y,'Marker','O',"MarkerFaceColor", "blue");
end

function fig = draw_circle(x,y,r)
    th = 0:pi/50:2*pi;
    xunit = r * cos(th) + x;
    yunit = r * sin(th) + y;
    fig = plot(xunit, yunit);
end

%% helper funcs
function [value, stop, d] = early_stopping(t,p)
    % position of the big dog 
    % this exploits r=1.
    P = [cos(t); sin(t)];

    eps = 0.1;
    value = norm(P-p)-eps;
    stop = 1;
    d = 0;
end