Ellipsoids rotation or plot in order to intersect at the top

Hello to all,

Here is my problem: I need to plot three ellipsoids in 3D in such way that one end of each ellipsoid is placed on the x, y, z axis and the other three ends intersect in order to show me the region of intersection.

So far all of my attempts have ended in failure: i have tried rotating the ellipsoids with no results. I ave tried to modify the centers with no results. I am using the ellipsoid function to generate the x, y, z, matrix and the surf function to plot them.

Best regards, Jean

Answer 1

[nick]

Hello Jean,

Kindly clarify whether no result implies there is a mismatch between expected ouptut and obtained output or the figure is empty.

You can utlise 'FaceAlpha' property in 'surf' function to make the ellipsoids semi-transparent, allowing you to visualize the intersection region, as shown:

a = 2; 
b = 1; 
c = 1; 

[x1, y1, z1] = ellipsoid(a, 0, 0, a, b, c, 30); % Centered on x-axis
[x2, y2, z2] = ellipsoid(0, b, 0, a, b, c, 30); % Centered on y-axis
[x3, y3, z3] = ellipsoid(0, 0, c, a, b, c, 30); % Centered on z-axis


figure;
hold on;

% Ellipsoid along x-axis
surf(x1, y1, z1, 'FaceAlpha', 0.2, 'EdgeColor', 'none', 'FaceColor', 'r');

% Ellipsoid along y-axis
surf(x2, y2, z2, 'FaceAlpha', 0.2, 'EdgeColor', 'none', 'FaceColor', 'g');

% Ellipsoid along z-axis
surf(x3, y3, z3, 'FaceAlpha', 0.2, 'EdgeColor', 'none', 'FaceColor', 'b');

axis equal;
xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');
title('Intersecting Ellipsoids');
grid on;
view(3);
hold off;

You can refer to the documentation by executing the following command in MATLAB Command Window to know more about properties in 'surf' function :

doc surf