3D plotting of five inequalities

I'm looking to make a 3D plot of the following inequalities and was wondering how to implement it:

x.*y - x - y + 1 > 0;

z < 1;

x.*y - x - y - 4.*z + 1 >0;

z.^2 - 1 > z.*(x + y - 2);

z.^4 - (x.^2 + y.^2 + 2.*x.*y - 4.*x - 4.*y + 6).*z.^2 +1 > z.^4 + (2.*x + 2.*y - .*y - 3).*z.^3 - (x.*y + 1).*z.^2 - (x.^2 + y.^2 + x.*y - 2.*x - 2.*y +1).*z + x.*y)

with them both being on the same plot. How would I go about doing this please? Or any other similar example is fine.

Thanks in advance

Answer 1

[Massimo Zanetti]

Hi Matthew. If you are looking for the portion of 3D space where points satisfy all the inequalities at the same time, then one way can be the following. Notice that I have just considered three of the inequalities you mentioned, but you can easily add them to the piece of code.

%define the range of x,y,z coordinates
step=.5;
x=-10:step:10;
y=-10:step:10;
z=-10:step:10;
%generate a grid with all triplets (x,y,z)
[X,Y,Z] = meshgrid(x,y,z);
%intersection of inequalities in a logical matrix
I = (X.*Y-X-Y+1>0) & (Z<1) & (X.*Y-X-Y-4*Z+1>0);
%plot of the points (x,y,z) that verify all inequalities
scatter3(X(I),Y(I),Z(I),'.');
xlabel('X'); ylabel('Y'); zlabel('Z');

Is this what you need? Max