How do I plot a 3D function characterized by 2 equations?

So far, I've been plotting 3d functions like so:

[X,Y]=meshgrid(-3:0.5:3,-3:0.5:3);

Z=2-X-Y;

surf(X,Y,Z)

but that is for functions that can be characterized by a single equation.

However, if I want to plot a 3d function characterized by a system of two equations, such as

Z=2*arctan(Y/X)

and

Z=.2*sqrt(X^2+Y^2)

How would I go about plotting the function?

[Walter Roberson]

You want the intersection of the two functions?

You used arctan(Y/X). Do you want quandrant adjustment, atan2(Y, X) ?

Answer 1

[Walter Roberson]

If you rewrite in polar coordinates, 2*arctan(Y/X) is 2*theta, and .2*sqrt(X^2+Y^2) is r/5. If you equate the two and solve for r in terms of theta, you get r = 10*theta which is easily plotted:

theta = linspace(0, 2*pi);
r = 10*theta;
[x,y] = pol2cart(theta, r);
plot(x, y)

[Jett Marcos]

Doing this would only take into account one of the two equations of the system. I could change coordinate system, but I would still need to plot the system characterized by the ff: r=10*theta: z=2*theta: Going back to my original question, how do I plot the intersection of these two equations on the same 3d plot?

[Walter Roberson]

No, this takes into account both equations. You can proceed from here to

theta = linspace(-pi/2, pi/2);
r = 10*theta;
[x,y] = pol2cart(theta, r);

Z1a = 2 * theta;
Z2a = .2 * r;

Z1b = 2 * atan(y./x);
Z2b = .2 * sqrt(x.^2 + y.^2);

max(Z1a - Z1b)   %zero to within round-off, so they are computing the same thing -- the polar form is the same as the cartesian form
max(Z2a - Z2b)   %zero to within round-off, so they are computing the same thing -- the polar form is the same as the cartesian form

max(Z1a - Z2a)   %zero to within round-off, so they are computing the same thing -- the intersection has been successful when calculated in polar
max(Z1b - Z2b)   %zero to within round-off, so they are computing the same thing -- the intersection has been successful when calculated in cartesian

plot3(x, y, Z1a)