Thread Subject: Finding volumes of tetrahedron?

Hey guys I know that finding the cross product of two
vectors can give you areas of parallelogram.

But if I had VERtices of (1,2,3) (4,5,6) (7,8,9) (2,5,1) how
would I find the volume of a tetrahedron with mat lab?
Thanks

"Rufus Worrell" <hollywoodbatez@AOL.com> wrote in message
<fofn40$agb$1@fred.mathworks.com>...
> Hey guys I know that finding the cross product of two
> vectors can give you areas of parallelogram.
>
> But if I had VERtices of (1,2,3) (4,5,6) (7,8,9) (2,5,1) how
> would I find the volume of a tetrahedron with mat lab?
> Thanks

V = 1/6 *|det(V1,V2,V3)|

with
V1 := P2-P1
V2 := P3-P2
V3 := P4-P3

Bruno

In article <fofn40$agb$1@fred.mathworks.com>,
Rufus Worrell <hollywoodbatez@AOL.com> wrote:
>Hey guys I know that finding the cross product of two
>vectors can give you areas of parallelogram.

>But if I had VERtices of (1,2,3) (4,5,6) (7,8,9) (2,5,1) how
>would I find the volume of a tetrahedron with mat lab?

http://en.wikipedia.org/wiki/Tetrahedron#Volume_of_any_tetrahedron

  For a tetrahedron with vertices [...] the volume is [...]
  This can be rewritten using dot product and a cross product, yielding
  V = |(a-d) . ((b-d) x (c-d))| / 6
--
   "I was very young in those days, but I was also rather dim."
   -- Christopher Priest

"Bruno Luong" <b.luong@fogale.fr> wrote in message <fofnh3
$h5m$1@fred.mathworks.com>...
> "Rufus Worrell" <hollywoodbatez@AOL.com> wrote in message
> <fofn40$agb$1@fred.mathworks.com>...
> > Hey guys I know that finding the cross product of two
> > vectors can give you areas of parallelogram.
> >
> > But if I had VERtices of (1,2,3) (4,5,6) (7,8,9)
(2,5,1) how
> > would I find the volume of a tetrahedron with mat lab?
> > Thanks
>
> V = 1/6 *|det(V1,V2,V3)|
>
> with
> V1 := P2-P1
> V2 := P3-P2
> V3 := P4-P3
>
> Bruno

ok for another question i put this in mat lab >> P1 = [1 2
1]
P2 = [1 -3 4]
P3 = [2 3 5]
P4 = [2 -3 5]

V1 := P2-P1
V2 := P3-P2
V3 := P4-P3

V = 1/6 *|det(V1,V2,V3)|


V1 := P2-P1
V2 := P3-P2
V3 := P4-P3

P1 =

     1 2 1


P2 =

     1 -3 4


P3 =

     2 3 5


P4 =

     2 -3 5

but i get the error Undefined function or method 'V1' for
input arguments of type 'char'.

Why you are using := for a vector subtraction in Matlab. I
would use only =.
I think that this could be your error.




"Rufus Worrell" <hollywoodbatez@AOL.com> wrote in message
<fohiqh$cks$1@fred.mathworks.com>...
> "Bruno Luong" <b.luong@fogale.fr> wrote in message <fofnh3
> $h5m$1@fred.mathworks.com>...
> > "Rufus Worrell" <hollywoodbatez@AOL.com> wrote in message
> > <fofn40$agb$1@fred.mathworks.com>...
> > > Hey guys I know that finding the cross product of two
> > > vectors can give you areas of parallelogram.
> > >
> > > But if I had VERtices of (1,2,3) (4,5,6) (7,8,9)
> (2,5,1) how
> > > would I find the volume of a tetrahedron with mat lab?
> > > Thanks
> >
> > V = 1/6 *|det(V1,V2,V3)|
> >
> > with
> > V1 := P2-P1
> > V2 := P3-P2
> > V3 := P4-P3
> >
> > Bruno
>
> ok for another question i put this in mat lab >> P1 = [1 2
> 1]
> P2 = [1 -3 4]
> P3 = [2 3 5]
> P4 = [2 -3 5]
>
> V1 := P2-P1
> V2 := P3-P2
> V3 := P4-P3
>
> V = 1/6 *|det(V1,V2,V3)|
>
>
> V1 := P2-P1
> V2 := P3-P2
> V3 := P4-P3
>
> P1 =
>
> 1 2 1
>
>
> P2 =
>
> 1 -3 4
>
>
> P3 =
>
> 2 3 5
>
>
> P4 =
>
> 2 -3 5
>
> but i get the error Undefined function or method 'V1' for
> input arguments of type 'char'.
>

"Rufus Worrell" <hollywoodbatez@AOL.com> wrote in message
<fohiqh$cks$1@fred.mathworks.com>...

> but i get the error Undefined function or method 'V1' for
> input arguments of type 'char'.
>

Sorry, I wrote a mathematical formula. You should of course
adapt it with correct MATLAB syntax like this:

V1=P2-P1;
V2=P3-P2;
V3=P4-P3;

V = abs(det([V1(:) V2(:) V3(:)]))/6

Bruno