MATLAB: Plot quiver onto the base of a 3D plot

Question

hi there,

I'm was looking at an issue on gradient, and I came across an example of a great plot in wikipedia. this is the link to it here https://en.wikipedia.org/wiki/Gradient and direct to plot working towards

I can get to a point, by using the following code, but I cant seem to find how I can shift or move or plot the quiver plot onto the base of 3d plot. ie, the quiver plot would be on the xy axis at a z value of -4.

I've found that contour has a handle handle called ContourZLevel property is a hidden property at https://undocumentedmatlab.com/blog/customizing-contour-plots-part-2 but I dont see such functionality with quiver.

any help appreciated.

many thanks

[x,y] = meshgrid(-80:80, -80:80);

z = -(cosd(x).^2 + cosd(y).^2).^2;

plot3(x,y,z)

grid

% planeimg = min(z,[],"all")

[xx,yy] = meshgrid(-80:10:80, -80:10:80);

zz = -(cosd(xx).^2 + cosd(yy).^2).^2;

[U,V] = gradient(zz);

hold on

h = quiver(xx,yy,U,V);

hold off

Answer 1

This seems to approximate what I believe you want:

[x,y] = meshgrid(-80:80, -80:80);
z = -(cosd(x).^2 + cosd(y).^2).^2;
mesh(x,y,z)
grid
[xx,yy] = meshgrid(-80:10:80, -80:10:80);
zz = -(cosd(xx).^2 + cosd(yy).^2).^2;
[U,V] = gradient(zz);
hold on
h = quiver3(xx,yy,ones(size(zz))*min(zlim),U,V,zeros(size(zz)));
hold off
grid on
view(-30,30)

producing:

To plot it along the surface itself:

[x,y] = meshgrid(-80:80, -80:80);
z = -(cosd(x).^2 + cosd(y).^2).^2;
mesh(x,y,z)
grid
[xx,yy] = meshgrid(-80:10:80, -80:10:80);
zz = -(cosd(xx).^2 + cosd(yy).^2).^2;
[U,V,W] = surfnorm(xx,yy,zz);                           % Calculate Surface Normals
dW = gradient(W);                                       % Gradient Of ‘W’
hold on
h = quiver3(xx,yy,zz,U,V,dW);
hold off
grid on
view(-30,60)

(There may be better mathematical expressions for the same idea.)

producing: