Plotting surface tangent to surface plot

clc

clear

f=@(x,y)-38+19.*x-62.*y+5.*x.^2-14.*x.*y-3*y.^2;

dfdx=@(x,y)10.*x+19-14.*y;

dfdy=@(x,y)14.*x-6.*y-62;

L=@(x,y,a,b)f(a,b)+dfdx(a,b)*(x-a)+dfdy(a,b)*(y-b);

n=@(x,y)[dfdx(x,y);dfdy(x,y);-1];

a=-4;

b=-2;

p0=[a;b;f(a,b)];

n0=n(a,b);

x=linspace(-9,0.5,1);

y=linspace(-7,0.5,3);

[X,Y]=meshgrid(x,y);

Z=f(X,Y);

T=L(X,Y,a,b);

surf(x,y,Z)

hold on

surf(x,y,T,'FaceColor','b','FaceAlpha',0.4) % Tangentplanet

s=[-1 1];

plot3(p0(1)+s*n0(1),p0(2)+s*n0(2),p0(3)+s*n0(3),'m','linewidth',2)

hold off

xlabel('x'), ylabel('y'), zlabel('z'), box on

axis equal, axis vis3d, rotate3d on 2

clc

clear

f=@(x,y)-38+19.*x-62.*y+5.*x.^2-14.*x.*y-3*y.^2;

dfdx=@(x,y)10.*x+19-14.*y;

dfdy=@(x,y)14.*x-6.*y-62;

L=@(x,y,a,b)f(a,b)+dfdx(a,b)*(x-a)+dfdy(a,b)*(y-b);

n=@(x,y)[dfdx(x,y);dfdy(x,y);-1];

a=-4;

b=-2;

p0=[a;b;f(a,b)];

n0=n(a,b);

x=linspace(-9,0.5,1);

y=linspace(-7,0.5,3);

[X,Y]=meshgrid(x,y);

Z=f(X,Y);

T=L(X,Y,a,b);

surf(x,y,Z)

hold on

surf(x,y,T,'FaceColor','b','FaceAlpha',0.4) % Tangentplanet

s=[-1 1];

plot3(p0(1)+s*n0(1),p0(2)+s*n0(2),p0(3)+s*n0(3),'m','linewidth',2)

hold off

xlabel('x'), ylabel('y'), zlabel('z'), box on

axis equal, axis vis3d, rotate3d on 2

Hi, I have a problem with this code. I gives this error in the console

Error using surf

Z must be a matrix, not a scalar or vector.

Error in studio22 (line 21)

surf(x,y,Z)

How should I go about solving this?

Answer 1

[Star Strider]

The code defines ‘x’ as a scalar:

x=linspace(-9,0.5,1);

with one element equal to 0.5.

That creates ‘X’ and ‘Y’ as vectors, and makes ‘Z’ a vector as well.

.

Answer 2

[MarKf]

You should use a matrix, not a scalar or vector, as the error says.

Z (and T) are vectors, probably an issue with how you define x and y with linspace (x being a scalar), which then makes meshgrid not create a grid, which is why then the 2 functions don't return matrices. Not sure what you meant to do, but for example this works:

f=@(x,y)-38+19.*x-62.*y+5.*x.^2-14.*x.*y-3*y.^2;
dfdx=@(x,y)10.*x+19-14.*y;
dfdy=@(x,y)14.*x-6.*y-62;
L=@(x,y,a,b)f(a,b)+dfdx(a,b)*(x-a)+dfdy(a,b)*(y-b); 
n=@(x,y)[dfdx(x,y);dfdy(x,y);-1]; 
a=-4;
b=-2;
p0=[a;b;f(a,b)]; 
n0=n(a,b);
x=-9:0.5:1; % or x=linspace(-9,0.5,10);
y=-7:0.5:3; % or y=linspace(-7,0.5,10);
[X,Y]=meshgrid(x,y);
Z=f(X,Y);
T=L(X,Y,a,b); 
surf(x,y,Z); 
hold on  
surf(x,y,T,'FaceColor','b','FaceAlpha',0.4) % Tangentplanet 
s=[-1 1]; 
plot3(p0(1)+s*n0(1),p0(2)+s*n0(2),p0(3)+s*n0(3),'m','linewidth',2) 
hold off 
xlabel('x'), ylabel('y'), zlabel('z'), box on
axis equal, axis vis3d