How can I plot the region for two inequalities?

I'm looking to plot the two inequalities for the formula: abs(x+y+x.^2<3) and abs(y+x+y.^2<3)

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

[Walter Roberson]

You should restore the original question here, and open a new question about fonts.

[Rena Berman]

(Answers dev) restored the original question

Answer 1

[Karan Gill]

Here's how to numerically evaluate the conditions and visualize them.

v = -5:0.01:5;  % plotting range from -5 to 5
[x y] = meshgrid(v);  % get 2-D mesh for x and y
cond1 = x+y+x.^2 < 3;  % check conditions for these values
cond2 = y+x+y.^2 < 3;
cond1 = double(cond1);  % convert to double for plotting
cond2 = double(cond2);
cond1(cond1 == 0) = NaN;  % set the 0s to NaN so they are not plotted
cond2(cond2 == 0) = NaN;
cond = cond1.*cond2;  % multiply the two condaces to keep only the common points
surf(x,y,cond)
view(0,90)    % change to top view

[Image Analyst]

Or, more directly:

v = -5:0.01:5;  % plotting range from -5 to 5
[x, y] = meshgrid(v);  % get 2-D mesh for x and y
conditions = (x + y + x.^2 < 3) & (y + x + y.^2 < 3);
cond = zeros(length(v)); % Initialize
cond(conditions) = NaN;
surf(x, y, cond)
view(0,90)

[TARIQ MOUSSAMIH]

I'm looking to plot a system of inequalities in 3-D (ax+by+cz<d). How would I go about doing this please? Thanks in advance

[Mai Le]

please let me know why z is always equal to 1. If I want z=0 what should I do

[Image Analyst]

@Mai Le, I don't see any z in the code.

[Mai Le]

when I delete the view (0,90) the graph is shown in Oxyz coordinates and z is always 1

[Walter Roberson]

v = -5:0.01:5;  % plotting range from -5 to 5
[x y] = meshgrid(v);  % get 2-D mesh for x and y
cond1 = x+y+x.^2 < 3;  % check conditions for these values
cond2 = y+x+y.^2 < 3;
cond1 = double(cond1);  % convert to double for plotting
cond2 = double(cond2);
cond1(cond1 == 0) = NaN;  % set the 0s to NaN so they are not plotted
cond2(cond2 == 0) = NaN;
cond = cond1.*cond2.*0;  % multiply the two condaces to keep only the common points
surf(x,y,cond)

[Image Analyst]

The "cond" matrix is either 0 or nan, so why does it look curved/warped instead of flat?

Answer 2

[Image Analyst]

You could do this:

r = -5:0.01:5;  % plotting range from -5 to 5
[x, y] = meshgrid(r);  % Get 2-D mesh for x and y based on r
condition1 = x+y+x.^2 < 3;
condition2 = y+x+y.^2 < 3;
output = ones(length(r)); % Initialize to 1
output(~(condition1 & condition2)) = 0; % Zero out coordinates not meeting conditions.
imshow(output, 'xdata', r, 'ydata', r); % Display
axis on;

[Ming Zhen Ellis Tiew]

Good afternoon, I was wonder is that possible to let the y-axis start form -5 to 5 (because the picture is 5 to -5)? Thank you!

[Image Analyst]

Try

axis ij;

after you've called imshow().

Answer 3

[Anna]

Is it possible to draw the region with a different color than black?

[Ayka]

There are various ways. The most directy way is to construct the third dimension as the RGB color space and multiply the output by different values as the RGB value. For example, if you want to color the white center area to RGB(64,128,192), you can manipulate as

l = length(r);
colored_output = zeros(l,l,3);
colored_output(:,:,1) = output * 64;  % 0 remains 0, 1 is amplified to 64
colored_output(:,:,2) = output * 128;
colored_output(:,:,3) = output * 192;
colored_output = uint8(colored_output);  % Convert double to uint8 values
imshow(colored_output, 'xdata', r, 'ydata', r);
axis on

If you want to color the surrounding black area, you can just add values to the zero values like

output1 = output;
output1(output1 == 0) = 64;
colored_output(:,:,1) = output1;