MATLAB: Fsurf: interval from parameters

fsurf interval parametricMATLAB

hello. when plotting this surface

syms u v
x = u;
y = v;
z = 4 - u^2 - v^2;
%fsurf(x, y, z, [-4 4 -4 4])
fsurf(x, y, z)

I was wondering if there is a way to specify the interval in terms of the u and v parameters?

for example, when u^2 + v^2 must be <= 4, something like

fsurf(x, y, z, [ u^2 + v^2 <= 4])

regards, Danny.

Best Answer

If i plot something round i usually use polar coordinates

t = linspace(0,2*pi,30);    % angle array
r = 0:5;                    % radius array
[T,R] = meshgrid(t,r);      % create grid
z = 4 - R.^2;
[x,y] = pol2cart(T,R);      % convert to cartesian
surf(x, y, z)

Related Solutions

MATLAB: Double integration of parametric function

Hi Danny,

You can find the surface area by finding the vectors Du and Dv that are parallel to the surface when you vary u and v respectively. Taking their cross product gives the the normal unit vector n, times the area element dS of a parallelogram whose area is proportional to dudv. Integrating the area elements give the total area. Since the area element does not depend on v, you can multiply by 4*pi and just do the u integral.

This procedure is analogous to finding the Jacobian. It's almost easier to do this by hand than to use syms, but

syms u v a real
x = u * cos(v);
y = u * sin(v);
z = a*v;         % in case you want to vary the pitch
zplot = v;
fsurf(x, y, zplot, [0 5 0 4*pi])
Du = diff([x,y,z],u)     % Du is diff() times du
Dv = diff([x,y,z],v)     % Dv is diff() times dv
dS = simplify(norm(cross(Du,Dv)))
Area = 4*pi*int(dS,0,5)
double(subs(Area,a,1))
% results
Du = [ cos(v), sin(v), 0]
Dv = [ -u*sin(v), u*cos(v), a]
dS = (a^2 + u^2)^(1/2)
Area =  4*pi*((a^2*log((a^2 + 25)^(1/2) + 5))/2 - (a^2*log(a^2))/4 + (5*(a^2 + 25)^(1/2))/2)
ans =  174.7199

MATLAB: How to shift a fsurf plot

r = @(u,v) 2 + sin(7.*u + 5.*v);
funx = @(u,v) r(u,v).*cos(u).*sin(v);
funy = @(u,v) r(u,v).*sin(u).*sin(v);
funz = @(u,v) r(u,v).*cos(v);
% fsurf(funx,funy,funz,[0 2*pi 0 pi]); % This plot should be shifted
xshift = 2; yshift = -2;
% fsurf( @(u,v)funx(u-xshift,v-yshift), @(u,v)funy(u-xshift,v-yshift), @(u,v)funz(u-xshift,v-yshift), [0 2*pi 0 pi])
M = 100 ; N =100 ;
u = linspace(0,2*pi,M) ;
v = linspace(0,pi,N) ;
[U,V] = meshgrid(u,v) ;
X = funx(U,V)-2 ;
Y = funy(U,V)+2 ;
Z = funz(U,V) ;
surf(X,Y,Z)

Best Answer

Related Solutions

MATLAB: Double integration of parametric function

MATLAB: How to shift a fsurf plot

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