Hello Rui,
To address your questions, let's break them down into two parts: finding the center point of a geometry defined by surfaces and plotting the geometry given the surfaces' equations.
To find the center point of a geometry defined by surface equations, you can use the concept of the centroid. Here is a simple MATLAB approach to calculate the centroid of a polyhedron defined by its vertices:
% Example vertices of a polyhedron (replace with your data)
vertices = [0 0 0; 1 0 0; 1 1 0; 0 1 0; 0 0 1; 1 0 1; 1 1 1; 0 1 1];
% Calculate the centroid
centroid = mean(vertices, 1);
disp('Centroid of the geometry:');
disp(centroid);
To plot the geometry given the surface equations, you can use MATLAB's plotting functions. If you have implicit equations of surfaces, such as planes, you can plot them using meshgrid and surf. Here is a general approach:
% Define the range for x and y
[x, y] = meshgrid(-10:1:10, -10:1:10);
% Example plane equation: z = ax + by + c
a = 1; b = 2; c = 3; % Example coefficients
z = a * x + b * y + c;
% Plot the surface
figure;
surf(x, y, z);
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Plane Surface');
grid on;
If your geometry is complex and consists of multiple surfaces, you may need to plot each surface separately and ensure they are correctly positioned relative to each other. You can use hold on to plot multiple surfaces in the same figure:
% Example of plotting multiple surfaces
figure;
hold on;
% Plot surface 1
z1 = a1 * x + b1 * y + c1;
surf(x, y, z1, 'FaceAlpha', 0.5);
% Plot surface 2
z2 = a2 * x + b2 * y + c2;
surf(x, y, z2, 'FaceAlpha', 0.5);
% Continue plotting other surfaces...
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Geometry Plot');
grid on;
hold off;
I hope this helps!
