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Hello,

I am in need of calculating the volume of a shape that is given as a cloud of points. I thought a first step would be to triangulate using delaunay but the results are not satisfactory. I have attached some images to show what is unsatisfactory. I zoomed in to look at a part of the cloud that is kind of shaped like the cone of an airplane. I have provided two angles so a sense can be gotten. The super elongated triangles do not seem like they will be useful in getting me surface area and volume.

Does anyone know of alternatives that would produce better results?

Thanks.

Richard Brown
on 7 Nov 2019

Edited: Richard Brown
on 7 Nov 2019

As David Wilson suggested, use alphashape:

U = csvread('Coords.txt');

shp = alphashape(U(:, 1), U(:, 2), U(:, 3));

plot(shp)

disp(shp.vol)

I get a volume of 3.59e-8. The picture is here:

Or, I just noticed that the commands are different in R2019a (I did the previous with R2018a by accident):

U = csvread('Coords.txt');

shp = alphaShape(U(:, 1), U(:, 2), U(:, 3));

plot(shp)

disp(shp.volume)

darova
on 6 Nov 2019

Volume can be found as summation volume of pyramids. Here is an idea:

clc,clear

load Coords.txt

x = Coords(:,1);

y = Coords(:,2);

z = Coords(:,3);

% move to origin

x = x-mean(x);

y = y-mean(y);

z = z-mean(z);

% convert to spherical system

[t,p,r] = cart2sph(x,y,z);

tri = delaunay(t,p);

trisurf(tri,x,y,z)

% indices of triangle

i1 = tri(:,1);

i2 = tri(:,2);

i3 = tri(:,3);

% vectors of triangle base

v1 = [x(i1)-x(i2) y(i1)-y(i2) z(i1)-z(i2)];

v2 = [x(i1)-x(i3) y(i1)-y(i3) z(i1)-z(i3)];

A = 1/2*cross(v1,v2,2); % surface of a triangle

V = 1/3*dot(A,[x(i1) y(i1) z(i1)],2); % volume of a triangle

V = sum(abs(V));

darova
on 7 Nov 2019

It's because of converting cartesian coordinates to spherical

[t,p,r] = cart2sph(x,y,z);

Geometrically -pi and +pi are the same, but delaunay interprets it as different numbers.

That is why there is a gap between -pi and +pi

Don't know how to resolve it

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