-------- Original Message --------
Subject: Re: Volume calculations from 3D mesh
Date: Wed, 11 Jan 2012 17:59:40 -0500
From: Mauricio Torres <[email protected]>
To: [email protected]
Dear Rebecca,
if you have five points you actually have two tetrahedra. You can
calculate the volume of a tetrahedron if you know the distances between
points. If you have coordinates, these distances can be calculated using
the distance equation in 3D
(http://mathworld.wolfram.com/Distance.html). Once you have your
distances, the following function in R can calculate the volume using
the Cayley-Menger determinant
(http://mathworld.wolfram.com/Tetrahedron.html):
volume_tetrahedron<-function(d12,d13,d14,d23,d24,d34){
temp_matrix<-matrix(data=c(0,1,1,1,1, 1,0,d12^2,d13^2,d14^2,
1,d12^2,0,d23^2,d24^2,
1,d13^2,d23^2,0,d34^2,1,d14^2,d24^2,d34^2,0),nrow=5, ncol=5)
temp_det<-abs(det(temp_matrix))
temp_volume<-sqrt(temp_det/288)#I'm not sure if this should be taken as
the absolute value or not. Sometimes the determinant is negative, so I
just dit that and the results make sense.
return(temp_volume)
}
Best,
Mauricio
=================================
Mauricio Torres-Mejia
PhD Candidate
Department of Biology
University of California, Riverside, CA, 92521
USA
http://student.ucr.edu/~rtorr006/
2012/1/11 morphmet <[email protected]
<mailto:[email protected]>>
-------- Original Message --------
Subject: Volume calculations from 3D mesh
Date: Wed, 11 Jan 2012 13:51:21 -0500
From: Green, Rebecca <[email protected]
<mailto:[email protected]>>
To: [email protected] <mailto:[email protected]>
<[email protected] <mailto:[email protected]>>
Hi All,
I am working on a study to compare the development of facial shape
in mouse models who develop a cleft lip and those who do not, ie
looking at growth over time in various parts of the face and
comparing the differences between the two groups. My data from
standard geometric morphometrics seems to not account for the full
range of variance we see based on our 3D scans. To that end I am
interested in trying to calculate the volume of one area of the face
between 5 landmarks that essentially form a tetrahedron. I have used
MeshLab to landmark the images.
Does any one have any ideas of an easy way to calculate this, or a
software piece that can do this.
Best,
Rebecca
Rebecca Green
Williams Lab - Graduate Student
Program in Reproductive Sciences
303-724-4568 <tel:303-724-4568>
[email protected] <mailto:[email protected]>
