If f1(x,y)≤z≤f2(x,y), how to draw the range of z?

x=-5:0.1:5;

y=-5:0.1:5;

for m=1:101

for n=1:101

z1(m,n)=x(m)^2+y(n)^2;

z2(m,n)=3*x(m)^3+y(n)^2+1;

end

end

surf(x,y,z1,"EdgeColor","none")

hold on

surf(x,y,z2,"EdgeColor","none")

If the upper and lower limits of z are described by separate functions, how to plot the range of the z function in the direction of the z-axis instead of two surfaces?

Answer 1

[KSSV]

x=-5:0.1:5;
y=-5:0.1:5;

[m,n] = meshgrid(x,y) ; 

z1 = m.^2+n.^2;
z2 = 3*m.^3+n.^2+1 ;

surf(x,y,z1,"EdgeColor","none")
hold on
surf(x,y,z2,"EdgeColor","none")

Answer 2

[Shivam]

Hi @xin,

As per my understanding, you are given an inequality f1(x,y) <= z <= f2(x,y) describing the upper and lower limit for z on defined arrays x and y and you want to see the region of z satisfiying the inequality given.

In the workaround provided below, the points z1 and z2, corresponding to f1(x,y) and f2(x,y) respectively, are identified where z1 <= z2. The points that satisfy this condition are plotted in different colors using surface plot.

x = -5:0.1:5;
y = -5:0.1:5;

% Create meshgrid for x and y
[m, n] = meshgrid(x, y);

% Calculate z1 and z2
z1 = m.^2 + n.^2;
z2 = 3*m.^3 + n.^2 + 1;

% Logical mask for the region where z1 <= z2
mask = z2 >= z1;

% Set the values of z1 and z2 to NaN where the condition is not met
% This effectively removes these points from the plot
z1(~mask) = NaN;
z2(~mask) = NaN;

% Plot the region where z1 <= z2
figure;
surf(x, y, z2, 'EdgeColor', 'none', 'FaceAlpha', 0.7, 'FaceColor', 'r');
hold on;
surf(x, y, z1, 'EdgeColor', 'none', 'FaceAlpha', 0.7, 'FaceColor', 'b');

% Add labels and title
xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');
title('Region where z1 <= z2');
grid on;
hold off;

The region between red and blue surface is technically the preferred region for z as per the given equality.

I hope it helps.

Answer 3

[Image Analyst]

Do you want just the magnitude of the range, without visualizing the starting and stopping points? If so you can just subtract the functions:

x=-5:0.1:5;
y=-5:0.1:5;
for m=1:101
    for n=1:101
        z1(m,n)=x(m)^2+y(n)^2;
        z2(m,n)=3*x(m)^3+y(n)^2+1;
    end
end
rangeMagnitude = abs(z1-z2);
imshow(rangeMagnitude, []);
axis('on', 'image')
colorbar

[xin]

No, I want to fill the area between two surfaces. Is there a function that does something similar to fill or patch?