MATLAB: Volume under the surface of a 3-D plot: pdetool box

pdetoolvolume under surface of a 3-d plot

I used matlab pdetool box to model 2-D diffusion equation. 3-D plot was generated for the distrbution of concentration at a given time. Now I want to calculate the volume under the surface to get the total mass. I can export solution, u , and mesh parameters, p, t, e, to workspace. How do I calculate volume using these parameters?

Thank you

kodi

Best Answer

I found a way to do this at:

http://web.mit.edu/2.51/matlab/bredq.m

More methos are welcome.

Thank you

Related Solutions

MATLAB: How to convert a triangulation object into volume and create a BITMAP image

Below code is a good example for creating a STL file for 3D geometry, read the STL as traingulation object, save it as bitmap image and calculate the volume:

Script to create a STL file for 3D geometry. eg: cylinder

[X,Y,Z] = cylinder(r,100);
DT = delaunayTriangulation(X(:),Y(:),Z(:));
TR = triangulation(DT.ConnectivityList,DT.Points);
[F,P]=freeBoundary(TR);
TR = triangulation(F,P);
stlwrite(TR,'stl_test000.stl');

Method 1: may not be accurate for complicated shapes

%read the stl as a triangulation
gm = stlread('stl_test000.stl');
% use alphashape to create a bounding volume
shp=alphaShape(gm.Points);
plot(shp)
% If the plot does not look like the shape that you are expecting, change
% the critical radius for the alphashape
shp.Alpha = 5;
plot(shp); % this should plot the cylinder. the plot can be saved as a bitmap
% Get the volume value
shp.volume

Method 2: more accurate. Needs PDE Toolbox

pdem = createpde;
importGeometry(pdem,'stl_test000.stl');
% plot the geometry (3D)
pdegplot(pdem); % the plot can be saved as a bitmap
% mesh the geometry. For more accuracy, adjust the Hmax
msh = generateMesh(pdem,'Hmax',0.1);
% calculate the volume
msh.volume()

MATLAB: How to set space-varying boundary conditions

You can use applyBoundaryCondition. You just have to create a mesh for the geometry.

% Create a 3-dimensional PDE Model
model = createpde(3);
% Construct the Geometry
[x,y,z] = meshgrid([-3:0.25:3],[-2:0.25:2],[-1:0.25:1]);
% Create the convex hull.
x = x(:);
y = y(:);
z = z(:);
K = convhull(x,y,z);
% Put the data in the correct shape for |geometryFromMesh|.
nodes = [x';y';z'];
elements = K';
% Create a PDE model and import the mesh.
geometryFromMesh(model,nodes,elements);
% Plot geometry
figure
pdegplot(model,'FaceLabels','on')
title('Bracket with Face Labels')
% Now the new stuff
generateMesh(model)
ufun = @(region,state)[region.x.^2;region.x.^2 + region.y.^2;region.x.^2 + region.y.^2 - region.z]
applyBoundaryCondition(model,'dirichlet','Face',6,'u',ufun,'Vectorized','on')
specifyCoefficients(model,'m',0,'d',0,'c',1,'a',0,'f',[1;2;3]);
results = solvepde(model);
pdeplot3D(model,'ColorMapData',results.NodalSolution(:,1))

Alan Weiss

MATLAB mathematical toolbox documentation

Best Answer

Related Solutions

MATLAB: How to convert a triangulation object into volume and create a BITMAP image

MATLAB: How to set space-varying boundary conditions

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