MATLAB: How to find the extremum search curve of a parametric surface

differential equationsMATLABode

I have a parametric surface S(u,v). Can anybody help me solve the differential equation to find the extremum search curve like the pictures below?

These curves passe the local maxima and minima of the surface (z direction).

The extremum search curve is represented as:

Example:

syms u v;
x=u;
y=v;
z=sin(u).*cos(v)-1/8*u*v;
figure; fsurf(x,y,z,[0 2*pi 0 2*pi]);axis equal

Thank you so much!

Best Answer

If you have specific point (local max or min) you can substitute (x0,y0) in your function

- first search curve (any x)

- second search curve (any y)

Related Solutions

MATLAB: Duplicate plot in 4

[x,y] = meshgrid(-2:.2:2);
z = exp(-(x.^2 +y.^2));
% Part 1
surf(x,y,z);
colormap(hot)
hold on
% 

x2 = x+4 ;
y2 = y ;
z2 = z ;
surf(x2,y2,z2);
% 
x3 = x ;
y3 = y+4 ;
z3 = z ;
surf(x3,y3,z3);
%
x4 = x2 ;
y4 = y3 ;
z4 = z ;
surf(x4,y4,z4);

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: Duplicate plot in 4

MATLAB: How to shift a fsurf plot

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