surface area of a 3D surface

I have data for 3D points and I have made a surface using these points. Is there a way to get surface area of this 3D surface.

Thanks

Answer 1

[Roger Stafford]

If you know the 3D coordinates of each of the three vertices for each triangle in your diagram, then just take the sum of all the triangles' areas.

For example, if P1, P2, and P3 are 3D coordinate vectors of the three respective vertices of some particular triangle, then its area is given by:

   AreaP1P2P3 = 1/2*norm(cross(P2-P1,P3-P1));

[M.S. Khan]

Hi Rogar, if P1, P2............................Pn, then how will we proceed. Please i have shared same question in the forum. Could you please guide me how to proceed. Regards

[Jerry Campbell]

Hi M. S.

I created a simple Cube with sides of 100mm in AutoCad then exported the STL file

I then used the following code to calculate the volume and surface area of the cube.

% Create PDE Model

UnitCubeModel = createpde();

% Import STL file into Geometry of Model

UnitCubeModelGeometry = importGeometry(UnitCubeModel,'Unit Cube 100mm v1.stl');

% Generate Mesh for Model

UnitCubeMesh = generateMesh(UnitCubeModel);

% V for vertices and F for the facets

% allDisplayFaces is backward compatible method of the Geometry Object

[F, V] = UnitCubeModelGeometry.allDisplayFaces();

% Perform cross product across all the Facets and Vertices in the Model

a = V(F(:, 2), :) - V(F(:, 1), :);

b = V(F(:, 3), :) - V(F(:, 1), :);

c = cross(a, b, 2);

% Calculate Surface Area and Volume of Model

modelSurfaceArea = 1/2 * sum(sqrt(sum(c.^2, 2)));

modelVolume = volume(UnitCubeMesh);

% Plot the PDE Model

pdegplot(UnitCubeModel,'FaceLabels','on','FaceAlpha',0.5);

% Display the Volume and Surface Area

disp("Volume of Model = " + modelVolume);

disp("The surface area of the Model = " + modelSurfaceArea);