clc,clear all
disp('Se rezolva problema lui Dido')
% x2=3; l=4;
% x2=3.5; l=7.5;
 x2=3.5; l=5;
% x2=6; l=10*asin(3/5);
fprintf('Extremitatea de dreapta x2=%d\n',x2)
fprintf('Lungimea funiei l=%d\n',l)
s{1}='function y = MyFunc(x)';
s{2}='R=x(1); alpha=x(2); y=x;';
s{3}=['y(1)=R*alpha-(' char(sym(l)) ');'];
s{4}=['y(2)=2*R*sin(alpha/2)-(' char(sym(x2)) ');'];
filename=fullfile(pwd,'MyFunc.m');
disp(['Textul fisierului ' filename ':'])
fprintf('%s\n',s{:});
fid=fopen(filename,'w');
fprintf(fid,'%s\n',s{:});
fclose(fid);
xinit=[x2/2;pi]; % aproximatia initiala
options=optimset('fsolve'); % optiunile implicite
options=optimset(options,'Display','off','MaxIter',1000,'TolX',1e-8);
[xzero,fval,exitflag]=fsolve('MyFunc',xinit,options);
if exitflag>0,
  disp('S-a determinat solutia');
elseif exitflag<0,
  disp('Solutia nu a fost determinata - nu avem convergenta');
else
  disp(['Au fost efectuate un numar maxim admisibil de iteratii ' ...
        ' - convergenta e lenta']);
end
R=xzero(1);
alpha=xzero(2);
disp('Se determina solutia sistemului:')
fprintf('R=%12.6f\nalpha=%12.6f\n',R,alpha)
x0=x2/2; y0=(R^2-x0^2)^0.5;
if alpha<pi,
  y0=-y0;
end
disp('Centrul cercului:')
fprintf('x0=%12.6f\ny0=%12.6f\n',x0,y0)
t1=(pi-alpha)/2;  t2=(pi+alpha)/2;
disp('Valorile parametrului la frontiera:')
fprintf('t1=%12.6f\nt2=%12.6f\n',t1,t2)
t=linspace(t1,t2); 
x143=x0+R*cos(t); 
y143=y0+R*sin(t); 
x2n=2*l/pi; % problema cu extremitatea dreapta mobila
Rn=x2n/2; % raza in problema cu extremitatea mobila
tn=linspace(0,pi); x143n=Rn+Rn*cos(tn); 
y143n=Rn*sin(tn); S=R^2*alpha/2+x2*y0/2; % aria
Sm=pi*Rn^2/2; % aria maxima
fprintf('Suprafata in cazul in care e fixata extremitatea de dreapta x2: S=%12.6f\n',S)
fprintf('Suprafata in cazul in care extremitatea de dreapta x2 e mobila: S=%12.6f\n',Sm)
plot(x143,y143,'--b',x143n,y143n,'-r')
%plot(x143,y143,'--b')
set(get(gcf,'CurrentAxes'),'FontName','Times New Roman','FontSize',11)
yl=ylim; % se gasesc limitele in raport cu axa Oy
yl(1)=0; % limita de jos e 0
da=daspect; da(1:2)=min(da(1:2)); daspect(da);
ylim(yl); % se stabilesc limitele in raport cu axa Oy
title ('\bfProblema lui Dido')
xlabel ('\itx')
ylabel ('\ity')
legend('solutia problemei cu extremitatile fixate','solutia problemei cu extremitatile mobile',0)
delete(filename)
grid on, box on