Plotting multiple inequalities in 3D Space

Hi, I wanted to plot a set of points in 3d space in Matlab subject to multiple inequalities. I tried doing this:

[x,y,x] = meshgrid(-10:0.1:10);

ineq = [0<=y, y<=3, 9-y.^2<=x, x<=9, 0<=z, z<=9-x]

x(~ineq) = NaN;

y(~ineq) = NaN;

z(~ineq) = NaN;

surf(x,y,z)

But I am told that I "Attempted to grow array along ambiguous dimension." I was wondering what the correct way to do this would be.

Answer 1

[John D'Errico]

First,

[x,y,x] = meshgrid(-10:0.1:10);

Correct code is important in MATLAB. Else it will not know that you really intended to write [x,y,z] and not [x,y,x].

Next, what do you think this does?

ineq = [0<=y, y<=3, 9-y.^2<=x, x<=9, 0<=z, z<=9-x]

It does not create something that is "and"ed across those inequaities. Instead, it creates a larger array.

Next, is the result of that operation actually a surface, or just something that you want to interpret as a surface?

surf(x,y,z)

So how can surf possibly interpret what it will see as a set of scattered points, some of which are NaNs, and know what you intend?

You MIGHT try this:

[x,y,z] = meshgrid(-10:0.1:10,-10:0.1:10,-10:0.1:10); 
ineq = (0<=y) & (y<=3) & (9-y.^2<=x) & (x<=9) & (0<=z) & (z<=9-x);
x(~ineq) = NaN;
y(~ineq) = NaN;
z(~ineq) = NaN;
plot3(x(:),y(:),z(:),'.')
view(-15,65)
box on
grid on

But all that does is show a non-convex domain, represented by scattered data points that lie inside the domain. Surf is not designed to do what you want.