How to Scale Gradient Field for large z-values?

I want to plot a function R^2 -> R with gradient Field beneath:

f2 = @(x,y) 1./sqrt(x.^2+y.^2);
[u2,v2] = meshgrid(-1:0.01:1);
[du2,dv2] = gradient(f2(u2,v2));
s = surf(u2,v2,f2(u2,v2));
hold on

contour(u2,v2,f2(u2,v2))
hold on

norm = 1./sqrt(du2.^2+dv2.^2);
quiver(u2,v2,du2./norm,dv2./norm,'LineWidth',2)
axis([-1 1 -1 1 0 10])

caxis([0,10])
colormap(cool)
alpha(s,0.95)
shading flat

Sadly the gradient field is not visible. Probably because it's too small, f2 get's too large and I'm lacking of the mathmatical knowledge to adjust it properly

Answer 1

[Anurag Ojha]

Hello Niklas

One way to adjust it is by normalizing the gradient vectors before plotting them.

Here's an updated version of your code:

f2 = @(x,y) 1./sqrt(x.^2+y.^2);
[u2,v2] = meshgrid(-1:0.01:1);
[du2,dv2] = gradient(f2(u2,v2));

% Normalize the gradient vectors
norm = sqrt(du2.^2+dv2.^2);
du2_norm = du2./norm;
dv2_norm = dv2./norm;

s = surf(u2,v2,f2(u2,v2));
hold on

contour(u2,v2,f2(u2,v2))
hold on

quiver(u2,v2,du2_norm,dv2_norm,'LineWidth',2)
axis([-1 1 -1 1 0 10])
caxis([0,10])
colormap(cool)
alpha(s,0.95)
shading flat

This code normalizes the gradient vectors by dividing the du2 and dv2 components by their magnitude (norm). This ensures that the length of each vector is 1, making them visible in the plot.

[Niklas Kurz]

Thanks for cleaning up open questions like this one that I have asked long ago x) Today I'd probably know better and woud have done it similar to you.