The pursuit m-file numerically calculates the pursuit curve and animates it






function varargout=pursuit(varargin);

if nargin==0
Hf=findobj(get(0,'Children'),'Tag','PursuitMainFig');
if isempty(Hf) %Check for multiple instances
status='init';
else
status='wait';
end
else
status=varargin{1};
end

%Goto correct function
switch status
case 'wait'
shg;
%Wait for user....



%Initialize
case 'init'
%Set up main figure window
s = get(0,'ScreenSize');
w=500; %Width of figure window
h=420; %Height of figure window
HfMain = figure('Units','pixels', ...
'Position',[(s(3)-w)/2 (s(4)-h)/2 w h], ...
'NumberTitle','off', ...
'Name','Pursuit Curve', ...
'Tag','PursuitMainFig');

%Set background color for ui control text
Color = get(HfMain,'Color');

%Hide Help menu and show Gallery
HmG = uimenu(HfMain,'Label','&Gallery', ...
'Tag', 'GalleryMenu');
uimenu(HmG,'Label','&Astroid', ...
'Tag', 'AstroidGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Astroid'')');
uimenu(HmG,'Label','C&ardioid', ...
'Tag', 'CardioidGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Cardioid'')');
uimenu(HmG,'Label','&Circle', ...
'Tag', 'CircleGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Circle'')');
uimenu(HmG,'Label','F&reeth''s Nephroid', ...
'Tag', 'FreethGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Freeth'')');
uimenu(HmG,'Label','&Hypocycloid', ...
'Tag', 'HypocycloidGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Hypocycloid'')');
uimenu(HmG,'Label','&Line', ...
'Tag', 'LineGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Line'')');
uimenu(HmG,'Label','&Nephroid', ...
'Tag', 'NephroidGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Nephroid'')');
uimenu(HmG,'Label','&Warren''s Curve', ...
'Tag', 'WarrenGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Warren'')');
uimenu(HmG,'Label','W&ierd', ...
'Tag', 'WierdGalleryMenu', ...
'Callback', 'pursuit(''Gallery'',''Wierd'')');

%Set up axes
HaMain=pursuit('SetAxes',HfMain);

%Set up start button
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[385 80 75 24], ...
'Callback','pursuit(''intpplot'')', ...
'String','Start', ...
'Style','pushbutton', ...
'Tag','PursuitStartButton');

%Set up close button
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[385 40 75 24], ...
'Callback','close(''Pursuit Curve'')', ...
'String','Close', ...
'Style','pushbutton', ...
'Tag','PursuitCloseButton');

%Set up edit boxes for Pursued equations
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[45 385 300 15], ...
'String','Pursued Curve''s Parametric Equations', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'PursuitCurveText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[23 362.5 25 15], ...
'String','x(t)', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'xPursuitCurveText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[45 360 130 20], ...
'String','cos(t)', ...
'BackgroundColor',[1 1 1], ...
'Style','edit', ...
'Tag','xPursuedEdit');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[193 362.5 25 15], ...
'String','y(t)', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'yPursuitCurveText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[215 360 130 20], ...
'BackgroundColor',[1 1 1], ...
'String','sin(t)', ...
'Style','edit', ...
'Tag','yPursuedEdit');

%Set up t values edit
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[370 385 105 15], ...
'String','t Values', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'tValuesText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'BackgroundColor',[1 1 1], ...
'Position',[370 360 43 20], ...
'String', '0', ...
'Style','edit', ...
'Tag','tInitEdit');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[415 362.5 15 15], ...
'String','to', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'totValuesText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'BackgroundColor',[1 1 1], ...
'Position',[432 360 42 20], ...
'String', '5*pi', ...
'Style','edit', ...
'Tag','tFinalEdit');

%Set up step size edit
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[350 300 145 15], ...
'String','Step Size', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'StepSizeText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'BackgroundColor',[1 1 1], ...
'Position',[390 275 65 20], ...
'String', '.1', ...
'Style','edit', ...
'Tag','StepSizeEdit');

%Set up pursuer's starting point edit
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[350 225 145 15], ...
'String','Pursuer''s Starting Point', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'PursuerStartText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[358 202.5 10 15], ...
'String','(', ...
'HorizontalAlignment','Right', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'LParPursuerStartText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'BackgroundColor',[1 1 1], ...
'Position',[370 200 43 20], ...
'String', '0', ...
'Style','edit', ...
'Tag','xPursuerInitEdit');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[415 202.5 15 15], ...
'String',',', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'CommaPursuerStartText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'BackgroundColor',[1 1 1], ...
'Position',[432 200 43 20], ...
'String', '0', ...
'Style','edit', ...
'Tag','yPursuerInitEdit');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[477 202.5 10 15], ...
'String',')', ...
'HorizontalAlignment','Left', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'RParPursuerStartText');

%Set up relative speed edit
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'Position',[350 150 145 15], ...
'String','Pursuer''s Relative Speed', ...
'Style', 'Text', ...
'BackgroundColor',Color,...
'Tag', 'tValuesText');
H = uicontrol('Parent',HfMain, ...
'Units','pixels', ...
'BackgroundColor',[1 1 1], ...
'Position',[390 125 65 20], ...
'String', '.75', ...
'Style','edit', ...
'Tag','RelativeSpeedEdit');
refresh(HfMain);


%Initialize Axes
case 'SetAxes'
SAxes=struct('Parent',varargin{2}, ...
'Units','pixels', ...
'Position',[45 45 300 300], ...
'Box','on', ...
'DataAspectRatio',[1 1 1], ...
'PlotBoxAspectRatio',[1 1 1], ...
'Tag','PursuitMainAxes');
H=gca;
set(H,SAxes);
xlabel('x-axis');
ylabel('y-axis');
varargout{1}=H;



%Plot Curves
case 'intpplot'

%Get figure handle
Hf=findobj(get(0,'Children'),'Tag','PursuitMainFig');

%Get Children
Hc=get(Hf,'Children');

%Change start to stop
%Hstart=findobj(Hf,'flat','Tag','PursuitStartButton');
%set(Hstart,'String','Stop', ...
% 'Callback', '');
%refresh(Hf);

%Get axes handle
Ha=findobj(Hc,'flat','Tag','PursuitMainAxes');

%Get parameters
H=findobj(Hc,'flat','Tag','RelativeSpeedEdit');
k=eval(get(H,'String'));
H=findobj(Hc,'flat','Tag','xPursuedEdit');
p=get(H,'String');
H=findobj(Hc,'flat','Tag','yPursuedEdit');
q=get(H,'String');
H=findobj(Hc,'flat','Tag','tInitEdit');
ti=eval(get(H,'String'));
H=findobj(Hc,'flat','Tag','tFinalEdit');
tf=eval(get(H,'String'));
H=findobj(Hc,'flat','Tag','xPursuerInitEdit');
xi=eval(get(H,'String'));
H=findobj(Hc,'flat','Tag','yPursuerInitEdit');
yi=eval(get(H,'String'));
H=findobj(Hc,'flat','Tag','StepSizeEdit');
s=eval(get(H,'String'));

%Call internal pursuit curve calculater
[pursuer,pursued]=pursuit('calc',k,p,q,[ti,tf],[xi;yi],s);

%Clear Axes
cla;

%Comet pursuit curve
pursuit('comet', Ha, ...
pursuer.x, pursuer.y, ...
pursued.x, pursued.y);

%Plot approximate pursuit curve
H = plot(pursuer.x,pursuer.y,'r', ...
pursued.x,pursued.y,'b');

%Reinitialize Axes
pursuit('SetAxes',Hf);



%Change stop to start
%set(Hstart,'String','Start', ...
% 'Callback', 'pursuit(''intpplot'')');
%refresh(Hf);



%Calculate x and y of pursuer and pursued
case 'calc'
%Set variables from input args
k=varargin{2};
pfunc=varargin{3};
qfunc=varargin{4};
bounds=varargin{5};
xyinit=varargin{6};
s=varargin{7};

%Make p and q vector safe
pfunc = strrep(pfunc,'.','');
qfunc = strrep(qfunc,'.','');
pfunc = strrep(pfunc,'*','.*');
qfunc = strrep(qfunc,'*','.*');
pfunc = strrep(pfunc,'/','./');
qfunc = strrep(qfunc,'/','./');
pfunc = strrep(pfunc,'^','.^');
qfunc = strrep(qfunc,'^','.^');

%Calculate t based on bounds and step size.
ns=round(100/abs(s));
t=linspace(bounds(1),bounds(2),ns);

%Delcare more variables
x=zeros(size(t));
y=zeros(size(t));
p=zeros(size(t));
q=zeros(size(t));
d=0;
u=0;

%Set intitial conditions
x(1)=xyinit(1);
y(1)=xyinit(2);

%Evaluate p(t) and q(t)
p=eval(pfunc).*ones(size(t));
q=eval(qfunc).*ones(size(t));

%Approximate x and y
for n=1:ns-1
d = sqrt( (p(n+1)-p(n))^2 + (q(n+1)-q(n))^2 );
pn=p(n); %+ (p(n+1)-p(n))/2;
qn=q(n); %+ (q(n+1)-q(n))/2;
u = sqrt( (pn-x(n))^2 + (qn-y(n))^2 );
x(n+1) = x(n) + k*d*(pn-x(n))/u;
y(n+1) = y(n) + k*d*(qn-y(n))/u;
end

%If no arguments out, plot curves, arrange figure window
if nargout == 0
h=plot(p,q,'b',x,y,'r',x(1),y(1),'*r');
legend(h,'Pursued','Pursuer');
set(gcf,'NumberTitle','off','Name','Pursuit Curves in MATLAB');
xlabel('x-axis');
ylabel('y-axis');
axis equal;
shg;

%Else return calculations
else
varargout{1} = struct('t',t, ...
'x', x, ...
'y', y);
varargout{2} = struct('t',t, ...
'x', p, ...
'y', q);
end




case 'comet'
%(h,x1,y1,x2,y2,p)
if nargin == 1, error('Not enough input arguments.'); end
if nargin < 7
p = 0.05;
end

ax = varargin{2};
x1=varargin{3};
y1=varargin{4};
x2=varargin{5};
y2=varargin{6};

if ~ishold,
xmax = max( [x1(isfinite(x1)), x2(isfinite(x2))] );
xmin = min( [x1(isfinite(x1)), x2(isfinite(x2))] );
ymax = max( [y1(isfinite(y1)), y2(isfinite(y2))] );
ymin = min( [y1(isfinite(y1)), y2(isfinite(y2))] );
if (xmax-xmin) > (ymax-ymin)
xdiff = ( xmax-xmin - (ymax-ymin) )/2;
ymax = ymax + xdiff;
ymin = ymin - xdiff;
elseif (xmax-xmin) < (ymax-ymin)
ydiff = ( ymax-ymin - (xmax-xmin) )/2;
xmax = xmax + ydiff;
xmin = xmin - ydiff;
end
axis([xmin xmax ymin ymax]);
end

% Choose first three colors for head, body, and tail
head1 = line('color','m','marker','o','erase','xor', ...
'xdata',x1(1),'ydata',y1(1));
body1 = line('color','m','linestyle','-','erase','none', ...
'xdata',[],'ydata',[]);
tail1 = line('color','r','linestyle','-','erase','none', ...
'xdata',[],'ydata',[]);
head2 = line('color','k','marker','o','erase','xor', ...
'xdata',x2(1),'ydata',y2(1));
body2 = line('color','k','linestyle','-','erase','none', ...
'xdata',[],'ydata',[]);
tail2 = line('color','b','linestyle','-','erase','none', ...
'xdata',[],'ydata',[]);

m = length(x1);
k = round(p*m);

% Grow the body
for i = 2:k+1
j = i-1:i;
set(head1,'xdata',x1(i),'ydata',y1(i))
set(body1,'xdata',x1(j),'ydata',y1(j))
set(head2,'xdata',x2(i),'ydata',y2(i))
set(body2,'xdata',x2(j),'ydata',y2(j))
drawnow
end

% Primary loop
for i = k+2:m
j = i-1:i;
set(head1,'xdata',x1(i),'ydata',y1(i))
set(body1,'xdata',x1(j),'ydata',y1(j))
set(tail1,'xdata',x1(j-k),'ydata',y1(j-k))
set(head2,'xdata',x2(i),'ydata',y2(i))
set(body2,'xdata',x2(j),'ydata',y2(j))
set(tail2,'xdata',x2(j-k),'ydata',y2(j-k))
drawnow
end

% Clean up the tail
for i = m+1:m+k
j = i-1:i;
set(tail1,'xdata',x1(j-k),'ydata',y1(j-k))
set(tail2,'xdata',x2(j-k),'ydata',y2(j-k))
drawnow
end

%Gallery Menu
case 'Gallery'

%Get handles
Hf=findobj(get(0,'Children'),'Tag','PursuitMainFig');
Hc=get(Hf,'Children');
Hp=findobj(Hc,'flat','Tag','xPursuedEdit');
Hq=findobj(Hc,'flat','Tag','yPursuedEdit');
HtInit=findobj(Hc,'flat','Tag','tInitEdit');
HtFinal=findobj(Hc,'flat','Tag','tFinalEdit');
Hspeed=findobj(Hc,'flat','Tag','RelativeSpeedEdit');
HxInit=findobj(Hc,'flat','Tag','xPursuerInitEdit');
HyInit=findobj(Hc,'flat','Tag','yPursuerInitEdit');
HStep=findobj(Hc,'flat','Tag','StepSizeEdit');

%Set values used to change edit boxes
switch varargin{2}
case 'Astroid'
pstring = 'cos(t)^3';
qstring = 'sin(t)^3';
ti = '0'; tf = '5*pi';
xi = '0'; yi = '0';
case 'Cardioid'
pstring = '2*cos(t)+cos(2*t)';
qstring = '2*sin(t)+sin(2*t)';
ti = '0'; tf = '5*pi';
xi = '.8'; yi = '.9';
case 'Circle'
pstring = 'cos(t)';
qstring = 'sin(t)';
ti = '0'; tf = '5*pi';
xi = '0'; yi = '0';
case 'Freeth'
pstring = 'cos(t)+cos(2*t)+cos(3*t)';
qstring = 'sin(t)+sin(2*t)+sin(3*t)';
ti = '0'; tf = '5*pi';
xi = '0'; yi = '0';
case 'Hypocycloid'
pstring = '(3-2)*cos(t)+cos((3-2)*t/2)';
qstring = '(3-2)*sin(t)-sin((3-2)*t/2)';
ti = '0'; tf = '5*pi';
xi = '0'; yi = '0';
case 'Line'
pstring = '5';
qstring = 't';
ti = '0'; tf = '7';
xi = '0'; yi = '0';
case 'Nephroid'
pstring = '3*cos(t)-cos(3*t)';
qstring = '3*sin(t)-sin(3*t)';
ti = '0'; tf = '5*pi';
xi = '0'; yi = '0';
case 'Warren'
pstring = '3*cos(t)-cos(3*t)';
qstring = '5*sin(t)-sin(7*t)';
ti = '0'; tf = '5*pi';
xi = '0'; yi = '0';
case 'Wierd'
pstring = '7*cos(t)-cos(7*t)';
qstring = '5*sin(5*t)+1';
ti = '0'; tf = '5*pi';
xi = '0'; yi = '0';
otherwise
error('An error has been found in the code!');
end

%Change edit box
set(Hp,'string',pstring);
set(Hq,'string',qstring);
set(HtInit,'string',ti);
set(HtFinal,'string',tf);
set(HxInit,'string',xi);
set(HyInit,'string',yi);



%Case of Incorrect input arguments
otherwise
error('Invalid Argument');
end