Laboratorul2

figure('Name','r=(t,2*t,t^2)')
t=[0:pi/20:pi];
plot3(exp(t),sin(t).*t,t.^2)
figure('Name','r=(exp(t),sin(t)*t,t^2)')
plot3(t,2.*t,t.^2)
syms t
r=[exp(t),sin(t).*t,t.^2]; %r=(exp(t)*cos(t),exp(-t)*sin(t),sin(t)*cos(t))
rprim=diff(r);
rsec=diff(r,2);
rtert=diff(r,3);
r1xr2=cross(rprim,rsec);
rprim2=rprim(1)^2+rprim(2)^2+rprim(3)^2;
rprim_rsec=rprim(1)*rsec(1)+rprim(2)*rsec(2)+rprim(3)*rsec(3)
T=rprim./sqrt(rprim2)
Bvec=cross(rprim,rsec);
Bvec2=Bvec(1)^2+Bvec(2)^2+Bvec(3)^2
k=sqrt(Bvec2/rprim2)
N=(rprim2*rsec-rprim_rsec*rprim)/rprim2^2
B=cross(T,N)
tau=(r1xr2(1)*rtert(1)+r1xr2(2)*rtert(2)+r1xr2(3)*rtert(3))/rprim_rsec^2
r=[cos(t),sin(t),sin(t).*cos(t)]; %r=(cos(t),sin(t),sin(t)*cos(t))
rprim=diff(r);
rsec=diff(r,2);
rtert=diff(r,3);
r1xr2=cross(rprim,rsec);
rprim2=rprim(1)^2+rprim(2)^2+rprim(3)^2;
rprim_rsec=rprim(1)*rsec(1)+rprim(2)*rsec(2)+rprim(3)*rsec(3)
T=rprim./sqrt(rprim2)
Bvec=cross(rprim,rsec);
Bvec2=Bvec(1)^2+Bvec(2)^2+Bvec(3)^2
k=sqrt(Bvec2/rprim2)
N=(rprim2*rsec-rprim_rsec*rprim)/rprim2^2
B=cross(T,N)
tau=(r1xr2(1)*rtert(1)+r1xr2(2)*rtert(2)+r1xr2(3)*rtert(3))/rprim_rsec^2
r=[cos(t),sin(t),0]; %r=[cos(t), sin(t), 0]
rprim=diff(r);
rsec=diff(r,2);
rtert=diff(r,3);
r1xr2=cross(rprim,rsec);
rprim2=rprim(1)^2+rprim(2)^2+rprim(3)^2;
rprim_rsec=rprim(1)*rsec(1)+rprim(2)*rsec(2)+rprim(3)*rsec(3)
T=rprim./sqrt(rprim2)
Bvec=cross(rprim,rsec);
Bvec2=Bvec(1)^2+Bvec(2)^2+Bvec(3)^2
k=sqrt(Bvec2/rprim2)
N=(rprim2*rsec-rprim_rsec*rprim)/rprim2^2
B=cross(T,N)
tau=(r1xr2(1)*rtert(1)+r1xr2(2)*rtert(2)+r1xr2(3)*rtert(3))/rprim_rsec^2
figure('Name','Plot1')
syms u1 v1 %plotare1
ruv=[u1;v1;0.5*(u1^2-v1^2)];
[u1n,v1n]=meshgrid(-1:0.1:1,-1:0.1:1);
surf(u1n,v1n,double(subs(ruv(3),{u1,v1},{u1n,v1n})))
rprimu=diff(ruv,u1)
rprimv=diff(ruv,v1)
E=dot(rprimu,rprimu)
G=dot(rprimv,rprimv)
F=dot(rprimu,rprimv)
figure('Name','r=(u,v,u^2+v^2)')
ruv=[u1;v1;(u1^2+v1^2)];
[u1n,v1n]=meshgrid(-1:0.1:1,-1:0.1:1);
surf(u1n,v1n,double(subs(ruv(3),{u1,v1},{u1n,v1n})))
rprimu=diff(ruv,u1)
rprimv=diff(ruv,v1)
E=dot(rprimu,rprimu)
G=dot(rprimv,rprimv)
F=dot(rprimu,rprimv)
figure('Name','r=(u+v,u-v,u^3+v^3)')
ruv=[u1+v1;u1-v1;(u1^3+v1^3)];
[u1n,v1n]=meshgrid(-1:0.1:1,-1:0.1:1);
surf(u1n,v1n,double(subs(ruv(3),{u1,v1},{u1n,v1n})))
rprimu=diff(ruv,u1)
rprimv=diff(ruv,v1)
E=dot(rprimu,rprimu)
G=dot(rprimv,rprimv)
F=dot(rprimu,rprimv)