# How to use isosurface to measure volume of the cone??

조회 수: 6(최근 30일)
M.S. Khan 2020년 8월 30일
편집: M.S. Khan 2020년 8월 31일
Using code below , i have measure volume of a cone but i want to measure it using isosuface() i.e. using voxels. Can anyone help me please. I will be very thankful.
Thanks in advance for all help.
Regards
R = 10;
h = 20;
N = 10000;
% Generate points in cone
dx = (pi*R^2*h/3/N)^(1/3);
rvec = linspace(-R,R,ceil(2*R/dx));
hvec = linspace(0,h,ceil(h/dx));
[X,Y,Z] = ndgrid(rvec,rvec,hvec);
is_in_cone = (X.^2+Y.^2) <= (R/h*(h-Z)).^2;
x = X(is_in_cone);
y = Y(is_in_cone);
z = Z(is_in_cone);
% Estimate the volume of the 3D object assuming the object is convex
tri = delaunay(x,y,z);
trisurf(tri,x,y,z)
% indices of triangle
i1 = tri(:,1);
i2 = tri(:,2);
i3 = tri(:,3);
i4 = tri(:,4);
%Volume by summing tetrahedron
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)];
v3 = [x(i1)-x(i4) y(i1)-y(i4) z(i1)-z(i4)];
A = 1/2*cross(v1,v2,2); % surface of a triangle
V = 1/3*dot(A,v3,2); % volume of a tetrahedron
format long
V = sum(abs(V))

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### 채택된 답변

Bruno Luong 2020년 8월 30일
편집: Bruno Luong 2020년 8월 31일
Theoretical volume = 2094.4, Isosurface estimation = 2092.4.
Pretty good to me.
R = 10;
h = 20;
N = 1e5;
% Theoretical volume
Vol = pi*R^2*h/3
% Generate points in cone
dx = (pi*R^2*h/3/N)^(1/3);
margin = 1e-3;
rmin = -(1+margin)*R;
rmax = +(1+margin)*R;
rvec = linspace(rmin,rmax,ceil((rmax-rmin)/dx));
zmin = -0.5*margin*h;
zmax = (1+0.5*margin)*h;
hvec = linspace(zmin,zmax,ceil((zmax-zmin)/dx));
[X,Y,Z] = meshgrid(rvec,rvec,hvec);
Vcone = sqrt(X.^2+Y.^2) - abs(R/h*(h-Z));
Vcone = max(Vcone,-Z);
Vcone = max(Vcone,Z-h);
[F,V] = isosurface(X,Y,Z,Vcone,0);
% Volume estimated from isosurface
VF = permute(reshape(V(F,:),[size(F) 3]),[3 1 2]);
Vol = 1/6*sum(dot(cross(VF(:,:,1),VF(:,:,2),1),VF(:,:,3),1))
% close all
% isosurface(X,Y,Z,Vcone,0)
% axis equal
% axis([-20 20 -20 20 -10 30])
##### 댓글 수: 1표시숨기기 없음
M.S. Khan 2020년 8월 31일
편집: M.S. Khan 2020년 8월 31일
Dear Bruno, Thank you so much. you are shining star. If possible, please help me how to measure its volume layer by layer. i have added this question of layers in the new thread also. Warmest regards.

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### 추가 답변(1개)

Walter Roberson 2020년 8월 30일
I absolutely positively would not use isosurface() to measure volumes. It makes the task into a Computer Vision task, requiring that you take screen captures of the surface from several different angles (6 different angles at absolute minimum), and use Stereo Vision techniques to try to reconstruct depths. It is too many unnecessary complications for too low an accuracy.
Do not do this. Find a different approach.
##### 댓글 수: 4표시숨기기 이전 댓글 수: 3
M.S. Khan 2020년 8월 31일
Dear Bruno, i need one more favor. Using these methods, we measured volume of whole object. Now, if we want to divide this object into layers and then we measure volume layer by layer of the object. so, the sum of volume of all layers will give us volume of the object. Is it possible? Sorry for asking again and again. i know i am taking your valuable time.

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