Normal vector to surface in a specific point

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Alessandro 2014-5-26

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/131171-normal-vector-to-surface-in-a-specific-point

回答： Semiha YILMAZER 2021-10-12

Hi to all!

I've some problems with my code...I'm working on a code where considering a surface z=f(x,y)and a cutting plane the code have to calculate and plot: - the equation of the curve obtained by the intersection of the plane and the surface - the minimum point - the tangent plane to the surface in the minimum point - the normal vector to the surface in the minimum point

I would like to do all the procedures with symbolic expressions...here is my code:

clc
  close all
  clear all
a=0;
b=0;
c=1
syms x y z x1 y1 z1 t
f(x,y)=2*(x)^2-(y)^2 %surface
f2=a*x+b*y+c %plane
f3=f(x, f2) %trajectory
xt=x
yt=f2
zt=f3
dy=diff(yt,x)
dz=diff(zt,x)
X=solve(dz)
Y=subs(yt, x, X)
Z=subs(zt, x, X)
P=double ([X Y Z])
g = z-f; 
subs(g,[x,y,z],[X,Y,Z])
gradg=jacobian(g, [x,y,z])
grad1=gradient(g)
planenormal=subs(gradg, [x,y,z], [X,Y,Z])
realdot = @(u, v) u*transpose(v);
planeq = realdot(planenormal, [x-X,y-Y,z-Z])
planefun=solve(planeq,z)
grad_point=subs(gradg, [x,y],[X,Y])
grad_point_arr =double((grad_point))
norm=[X+grad_point_arr(1)*t, Y+grad_point_arr(2)*t, Z+grad_point_arr(3)*t]
view(74,34)
hold on
ezsurf(x,y,f,[-10,10,-10,10])
ezsurf(x,f2,z,[-10,10,-10,10])
ezplot3 (x,yt,zt,[-10,10,-10,10])
scatter3(X,Y,Z, 'MarkerEdgeColor','k','MarkerFaceColor',[0 .75 .75])
ezplot3(norm(1), norm(2), norm(3))
ezsurf(planefun)
figure(2)
view(74,34)
hold on
ezplot3 (x,f2,f3,[-10,10,-10,10])
scatter3(X,Y,Z, 'MarkerEdgeColor','k','MarkerFaceColor',[0 .75 .75])
ezplot3(norm(1), norm(2), norm(3))
ezsurf(planefun)