Here’s a simple Matlab example to help you visualize how the intersection of your two regions changes as you adjust the parameters α and β. You can use this template with your own functions and parameter values.
% Step 1: Define the grid for X and Y
x = linspace(-10, 10, 400);
y = linspace(-10, 10, 400);
[X, Y] = meshgrid(x, y);
% Step 2: Set example values for alpha and beta
alpha = 1.5; % You can change this value
beta = -2; % You can change this value
% Step 3: Define example functions f and g
% Example: f(X, Y, alpha) = X + alpha*Y - 2
% g(X, Y, beta) = Y.^2 + beta*X - 5
F = X + alpha * Y - 2;
G = Y.^2 + beta * X - 5;
% Step 4: Define the regions using logical indexing
region_f = F > 0; % Region where f > 0
region_g = G > 0; % Region where g > 0
% Step 5: Find the intersection of the two regions
intersection = region_f & region_g;
% Step 6: Plot the results
figure;
subplot(1,3,1);
imagesc(x, y, region_f);
axis xy;
title('Region: f(X, Y, \alpha) > 0');
xlabel('X'); ylabel('Y');
colormap([1 1 1; 0 0.7 1]); % white and blue
subplot(1,3,2);
imagesc(x, y, region_g);
axis xy;
title('Region: g(X, Y, \beta) > 0');
xlabel('X'); ylabel('Y');
colormap([1 1 1; 1 0.7 0]); % white and orange
subplot(1,3,3);
imagesc(x, y, intersection);
axis xy;
title('Intersection');
xlabel('X'); ylabel('Y');
colormap([1 1 1; 0 1 0]); % white and green
Here's the attached screenshot of the plot I have received when the above code is run:
PFA the links for further reference :
Hope this helps!
