argument in meshgrid - confused

Hey folks!

I am trying to use -meshgrid- and use -contourf- to plot a contourp map.

The two-variable function I am interested in studying is:

for

I tried this code: Version 1

%Meshgrid Ver 1

a = -1:.2:1;

b = 0:.2:1;

[X,Y]= meshgrid(a,b);

Z = X./(Y.*(1-X)-1);

contourf(X,Y,Z);

Next, I tried a similar code, except I changed the -meshgrid- argument:

%Meshgrid Ver 2

[X,Y]= meshgrid(-1:1);

Z = X./(Y.*(1-X)-1);

contourf(X,Y,Z);

I looked at the MATLAB document here: https://www.mathworks.com/help/matlab/ref/meshgrid.html

My questions:

(1) Why are they giving different contour plots?

(2) Version 1 is the correct contour plot corresponding to the origina equation Z, right?

Thanks, guys!

Answer 1

[Bruno Luong]

You need to make finer grid, you meshgrid is too coarse.

The version 1 is the top half of version 2.

%Meshgrid Ver 1
a = -1:.01:1;
b = 0:.01:1;
[X,Y]= meshgrid(a,b);
Z = X./(Y.*(1-X)-1);
ax1 = subplot(2,1,1);
contourf(X,Y,Z);
title('Version 1')
%Meshgrid Ver 2
[X,Y]= meshgrid(-1:0.01:1);
Z = X./(Y.*(1-X)-1);
ax2 = subplot(2,1,2);
contourf(X,Y,Z);
title('Version 2')
linkaxes([ax1 ax2])

[Tatte Berklee]

Thanks for the response, Bruno! But whta I am confused is the coarser version giving the zigzag part means the function is not smooth (in a differentiable sense in calculus) or it is just because I made the points too coarse but in fact it is smooth and differentiable?

[Bruno Luong]

Because your grid is too coarse. Matlab draws the contour line as sequence of straight lines that cut the grid. The real function and contour lines are smooth.

[Tatte Berklee]

Gocha! Thanks, Bruno!!

Answer 2

[David Hill]

Your domain for X is -1:1 and your domain for Y is 0:1. The first code choses the correct domains, the second assigns the same domain to both X and Y (-1:1). If you want more data points:

a = -1:.001:1;
b = 0:.001:1;
[X,Y]= meshgrid(a,b);
Z = X./(Y.*(1-X)-1);
contourf(X,Y,Z);

[Tatte Berklee]

Thanks for the response, David!