lab10

syms u v;

x = @(u,v) u;
y = @(u,v) v;
z = @(u,v) sin(u)^2 + cos(v);
f = @(u,v) [x(u,v),y(u,v),z(u,v)];
ezsurf(x,y,z);

du = diff(f(u,v),u);
dv = diff(f(u,v),v);

dudv = diff(f(u,v),u,v);
ddu = diff(f(u,v),u,2);
ddv = diff(f(u,v),v,2);

disp('Coeficientii formei intai fundamentale');

E = dot(du,du);
F = dot(du,dv);
G = dot(dv,dv);

disp(E);
disp(F);
disp(G);

disp('Matricea formei intai fundamentale');
I = [E,F;F,G];
disp(I);

disp('Aplicatia Gauss:');
NG = cross(du,dv)/sqrt(sum(cross(du,dv).^2));
disp(NG);

disp('Coeficientii formei a doua fundamentale')

L = dot(NG,ddu);
M = dot(NG,dudv);
N = dot(NG,ddv);

disp(L);
disp(M);
disp(N);

disp('Matricea formei a doua fundamentale');
II = [L,M;M,N];
disp(II);

disp('Curbura totala a suprafetei');
K = (L*N-M^2)/(E*G-F^2);
disp(K);

disp('Operatorul Weingarten');
W = I' * II;
disp(W);

u = 1;
v = pi/2;
KF = function_handle(K);

disp(KF(u,v));
if(KF(u,v) > 0)
  disp('Punct eliptic');
elseif(KF(u,v) < 0)
  disp('Punct hiperbolid');
else
  disp('Punct parabolic sau planar');
endif