how to determine the trace of the graph.

Let's say i have plotted a cylinder in the matlab graph. Code is given below.

r = 4;
[X,Y,Z] = cylinder(r);
h = 20;
Z = Z*h;
surf(X,Y,Z);

I want to cut this cylinder with a plane (x+y+z=1) and determine the shape of the trace. I know it will be an ellipse but can we do it in matlab?

Answer 1

[Nithin]

Hi Chandrabhan,

I understand that you want to cut the cylinder with a plane (x+y+z=1) and determine the shape of the trace.

To implement this, kindly refer to the following code snippet-

syms x y z

% Define the equation of the plane
plane_eq = x + y + z - 1;

% Solve the equation of the plane with respect to z to get the equation of the trace
trace_eq = solve(plane_eq, z);

% Plot the original cylinder
r = 4;
[X, Y, Z] = cylinder(r);
h = 20;
Z = Z * h;
surf(X, Y, Z);
hold on;

% Plot the trace on the cylinder
fimplicit3(trace_eq, [-r, r, -r, r, 0, h]);

% Plot the graph
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Cylinder Cut with Plane');
legend('Cylinder', 'Trace');
hold off;

For more information regarding “fimplicit3” function, kindly refer to the following documentation:

https://in.mathworks.com/help/matlab/ref/fimplicit3.html

I hope this answer helps you.

Regards,

Nithin Kumar.