How can I plot Polyhedra

Let and . if , How can I plot H when or ?

Answer 1

[Tejas]

Hello Ali,

To plot a Polyhedron, the 'fimplicit' function can be utilized. More details about this function are available in this documentation: https://www.mathworks.com/help/matlab/ref/fimplicit.html.

Here is an example demonstrating how to plot a Polyhedron using the 'fimplicit' function for 'n'=2:

• Start by initializing the matrix 'A' and 'b'.

    A = [1, 2; -1, 2; 0, -1]; 
    b = [3; 1; 0];            
    figure;
    hold on;

• Use the 'fimplicit' function to plot the inequality equations.

    fimplicit(@(x, y) A(1,1)*x + A(1,2)*y - b(1), 'r', 'LineWidth', 1);
    fimplicit(@(x, y) A(2,1)*x + A(2,2)*y - b(2), 'g', 'LineWidth', 1);
    fimplicit(@(x, y) A(3,1)*x + A(3,2)*y - b(3), 'b', 'LineWidth', 1); 

• Finally, plot the Polyhedron, as shown in below code snippet.

    xlim([-5, 5]);
    ylim([-5, 5]);
    xlabel('x');
    ylabel('y');
    title('Feasible Region for Ax \geq b');
    grid on;
    hold off;

Similarly, for 'n'=3, the inequalities can be plotted using the 'fimplicit3' function, as illustrated in the code snippet below. For more information on this function, refer to this documentation: https://www.mathworks.com/help/matlab/ref/fimplicit3.html.

fimplicit3(@(x, y, z) A(1,1)*x + A(1,2)*y + A(1,3)*z - b(1), 'r', 'FaceAlpha', 0.5);
fimplicit3(@(x, y, z) A(2,1)*x + A(2,2)*y + A(2,3)*z - b(2), 'g', 'FaceAlpha', 0.5);
fimplicit3(@(x, y, z) A(3,1)*x + A(3,2)*y + A(3,3)*z - b(3), 'b', 'FaceAlpha', 0.5);