Error using mesh X, Y, Z., and C cannot be complex

I have this code:

*x1='Bucur',
x2='Mihai'
a=(single(uint8(x1(1)))+single(uint8(x2(2))))/2-60
%b=(numarul de ordine din grupa 92X)/4 (X=1,2,3,4,5,6,7);
b=2/4

%1.1. Sa se determine tangenta, normala si binormala la curba: [b*sin(t); b*cos(t); a*t*sin(t)*cos(t)], t=[-pi,pi],
%in punctele: t1=-2*pi/3, t2=pi/3

syms t
r=[0.5000*sin(t),0.5000*cos(t),25.5000*t.*sin(t).*cos(t)];

%Derivatele lui r:
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) %Tangenta
Bvec=cross(rprim,rsec);
Bvec2=Bvec(1)^2+Bvec(2)^2+Bvec(3)^2
k=sqrt(Bvec2/rprim2) %Curbura

N=(rprim2*rsec-rprim_rsec*rprim)/rprim2^2 %Normala

B=cross(T,N) %Binormala

tau=(r1xr2(1)*rtert(1)+r1xr2(2)*rtert(2)+r1xr2(3)*rtert(3))/rprim_rsec^2 %Torsiunea

% tangenta, normala si binormala in t1=-2*pi/3

Tangenta=[subs(T(1),t,-2*pi/3),subs(T(2),t,-2*pi/3),subs(T(3),t,-2*pi/3)]

Normala=[subs(N(1),t,-2*pi/3),subs(N(2),t,-2*pi/3),subs(N(3),t,-2*pi/3)]

Binormala=[subs(B(1),t,-2*pi/3),subs(B(2),t,-2*pi/3),subs(B(3),t,-2*pi/3)]

Curbura=subs(k,t,-2*pi/3)

Torsiunea=subs(tau,t,-2*pi/3)

%tangenta, normala si binormala in t2=pi/3

Tangenta=[subs(T(1),t,pi/3),subs(T(2),t,pi/3),subs(T(3),t,pi/3)]

Normala=[subs(N(1),t,pi/3),subs(N(2),t,pi/3),subs(N(3),t,pi/3)]

Binormala=[subs(B(1),t,pi/3),subs(B(2),t,pi/3),subs(B(3),t,pi/3)]

Curbura=subs(k,t,pi/3)

Torsiunea=subs(tau,t,pi/3)

%1.2. Sa se determine lungimea curbei intre punctele mentionate.

   %Definim elemtul de arc ce ne va da lungimea integralei

   u=[-2*pi/3:0.001:pi/3];
   elemarc=sqrt(rprim(1).^2+rprim(2).^2+rprim(3).^2)

   lungimea=trapz(u,subs(elemarc,t,u))

   %2.1. Sa se reprezinte grafic elipsoidul: 
   %  r(u,v):=[u;a/b*sqrt(b2-u2)*cos(v);a/b*sqrt(b2-u2)*sin(v)]; 
   % Observatie!
   %  sqrt(b^2-u^2)=>0. atunci -b<=u<=b.

   figure;

u=linspace(-5,5,30);
v=linspace(0,2*pi,30);

[u,v]=meshgrid(u,v);

x=u;
y= 25.5000/0.5000*sqrt(0.5000^2-u.^2).*cos(v);
z= 25.5000/0.5000*sqrt(0.5000^2-u.^2).*sin(v);

mesh(x,y,z)
 hold

   %2.2. Sa se precizeze planul tangent in punctul u:=0, v:=2*pi/3. 

% Ecuatia planului tangent intr-un punct si doua directii date.

    syms u v
     ruv=[u;36.5/4.75*sqrt(4.75^2-u.^2).*cos(v);36.5/4.75*sqrt(4.75^2-u.^2).*sin(v);];
     ru=diff(ruv,1,u)
     rv=diff(ruv,1,v)

     x=u;
     y= 25.5000/0.5000*sqrt(5^2-u.^2).*cos(v);
     z= 25.5000/0.5000*sqrt(5^2-u.^2).*sin(v);

     syms x1 y1 z1

     %Calculam determinantul urmatoarei matrici:

   A=[(x1-subs(x,{u,v},{0,2*pi/3})) (y1-subs(y,{u,v},{0,2*pi/3})) (z1-subs(z,{u,v},{0,2*pi/3}))
       (subs(ru(1),{u,v},{0,2*pi/3})) (subs(ru(2),{u,v},{0,2*pi/3})) (subs(ru(3),{u,v},{0,2*pi/3}))
       (subs(rv(1),{u,v},{0,2*pi/3})) (subs(rv(2),{u,v},{0,2*pi/3})) (subs(rv(3),{u,v},{0,2*pi/3}))]

   d=det(A)

     %(73*y1)/4 - (73*3^(1/2)*z1)/4 + 5329/4=0

%2.3 Aria elipsoidului
 % x^2/b^2+y^2/a^2+z^2/a^2=1 

% Suprafata elipsoid:
% S=2*pi*(a^2+c^2/sin(ae)*log((1+sin(ae)/cos(ae))), unde ae=arccos(c/a)

ae=acos(0.5000/25.5000)
S=2*pi*(25.5000^2+0.5000^2/sin(0.5000/25.5000)*log((1+sin(0.5000/25.5000))/cos(0.5000/25.5000)))*

and when i run it it gives me this error:

*Error using mesh X, Y, Z, and C cannot be complex.*

can you help me? Thanks

Answer 1

[Beatrice Balaceanu]

Try using the absolute value of the square root from the equation of the ellipsoid. Instead of typing sqrt(4.75^2-u.^2) , you could use abs(sqrt(4.75^2-u.^2)).

Answer 2

[Steven Lord]

Some of the code you wrote includes:

u=linspace(-5,5,30);
v=linspace(0,2*pi,30);
[u,v]=meshgrid(u,v);
x=u;
y= 25.5000/0.5000*sqrt(0.5000^2-u.^2).*cos(v);

The maximum value u can take is 5. Is sqrt(0.5^2-5^2) real or complex? That will determine whether y is real or complex in that snippet of code.

Did you intend for u to range from -0.5 to 0.5 instead of from -5 to 5?