MATLAB: How to get the volume of a 3D concave shape

concave shapeImage Processing Toolboxvolume

Hi smart guys,

I am wondering if anyone knows how to get the volume of a 3D concave shape? The Matlab build-in function can only calculate the volume of a convex shape. For example,

[K, V] = convhulln(shape.vertices);

V is the volume. Here the shape is defined by a mesh with vertices and faces.

Thanks very much.

Best, Aaronne.

Best Answer

I would recommend voxelizing it and then just summing the resulting three dimensional volumetric image. There are a few utilities on the FEX that do this:

Related Solutions

MATLAB: Divide a 3D shape into equal-volume subregions

Based on the comments, my original question was too open ended, so I am answering this to bring it to a close. A simple 3D division of the space inside the volume into cubes is good enough, something like,

load('seamount.mat', 'x', 'y', 'z'); % Generic data that comes with Matlab; contains 3D points
% Make the example shape less flat!
x = x*5000; 
y = y*8000; 
DT = delaunayTriangulation(x,y,z); % 3D triangulization of points
[C, volHull] = convexHull(DT); % Compute convex hull, which is cone-shaped
figure('Name', 'Convex Hull');  
hPatch = trisurf(C,DT.Points(:,1),DT.Points(:,2),DT.Points(:,3), ...
    'FaceAlpha', 0.1);
nCubesDesired = 100; 
cubeLength = range(z)/round(nCubesDesired^(1/3)); 
xGrid = min(x):cubeLength:max(x); 
yGrid = min(y):cubeLength:max(y);
zGrid = min(z):cubeLength:max(z);
% Loop through each cube and check if it is inside the volume using 
% in_polyhedreon from File Exchange
% https://www.mathworks.com/matlabcentral/fileexchange/48041-in_polyhedron
% If it is not inside the volume, throw the cube out.
set(gca, 'xtick', xGrid, 'ytick', yGrid, 'ztick', zGrid);
grid on;
% Iterate on cubeLength until you get the desired number of cubes

MATLAB: Volume of 3D data points and volume of Convex Hull of those data points

So it sounds like you have a binary three dimensional volume that you are essentially summing to get the volume of the points? If this is correct, I would first calculate an isosurface of this using isosurface:

doc isosurface

Then with vertices from the isosurface, calculate the convex volume using convhulln. To calculate the non-convex volume, you can do what you're doing now which will be an overapproximation or you could convert the mesh to convex tetrahedra and sum up their volumes.

This might help with that:

http://www.mathworks.com/matlabcentral/fileexchange/27830-mesh2tetra

Best Answer

Related Solutions

MATLAB: Divide a 3D shape into equal-volume subregions

MATLAB: Volume of 3D data points and volume of Convex Hull of those data points

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