Plotting surface tangent to surface plot

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Kevin Abdul
Kevin Abdul 2023-2-6
编辑： MarKf 2023-2-6
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?

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回答（2 个）

Star Strider
Star Strider 2023-2-6
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.
.
MarKf
MarKf 2023-2-6
编辑：MarKf 2023-2-6
Ran in:
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

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