Gyroid Surface Area & Volume Calculation from existing code

The following code is to generate the shape of gyroid. From the code I want to calculate the surface area and volume. Instead of exporting the file and imprt in 3D design software could a potential solution, I want to get the surface area and volume from the code below:

clc
clear
close all

SizeL = 20;
Def = 40;

SFact = (SizeL/2)/pi;

A = SFact*pi;
D = A/Def;

[X,Y,Z] = meshgrid(-A:D:A);

    OBJ = cos(X/SFact).*sin(Y/SFact) + cos(Y/SFact).*sin(Z/SFact) + cos(Z/SFact).*sin(X/SFact);
    T = 0.5;
    OBJ = (OBJ - T) .* (OBJ + T);

    [F1,V1] = isosurface(X,Y,Z,OBJ,0);
    [F2,V2] = isocaps(X,Y,Z,OBJ,0,'below');

    F3 = [F1; F2+length(V1(:,1))];
    V3 = [V1;V2];

    p = patch('Vertices',V3,'Faces', F3, 'FaceColor', 'red', 'EdgeColor', 'none');
    view(3);
    camlight

Code Source: https://www.youtube.com/watch?v=uvCfVsFAcSw

Answer 1

[AKennedy]

Hi Syed,

As I understand, you would like to calculate the surface area and volume of a gyroid by adding to the code you have provided. Here is one possible way of obtaining it.

% Surface Area Calculation
SA = 0;
for i = 1:size(F3, 1)
    v1 = V3(F3(i, 1), :);
    v2 = V3(F3(i, 2), :);
    v3 = V3(F3(i, 3), :);
    edge1 = v2 - v1;
    edge2 = v3 - v1;
    area = 0.5 * norm(cross(edge1, edge2));
    SA = SA + area;
end

% Volume Calculation
Volume = 0;
centroid = mean(V3, 1);
for i = 1:size(F3, 1)
    v1 = V3(F3(i, 1), :);
    v2 = V3(F3(i, 2), :);
    v3 = V3(F3(i, 3), :);
    Volume = Volume + abs(dot(v1 - centroid, cross(v2 - centroid, v3 - centroid))) / 6;
end

% Displaying the results
disp(['Surface Area: ', num2str(SA)]);
disp(['Volume: ', num2str(Volume)]);   

This will output the required information.

Hope this helps!

[jixiong fei]

can you please tell me what the following mean?

abs(dot(v1 - centroid, cross(v2 - centroid, v3 - centroid))) / 6;