MATLAB Central Newsreader - Vectors

Vectors

M K — Wed, 12 Nov 2008 12:56:02 -0500

I have 4 points of a plane, ABCD .Can i calculate the normal vector,n of it?

Is it n= cross(AB,CD)?

Re: Vectors

M K — Wed, 12 Nov 2008 13:10:04 -0500

Can the Dot product of two vectors, A and B in Matlab be written as

dot(A,B)/norm(A)*norm(B)=cos(teta)

"M K"

<maha_k@mathworks.com> wrote in message <gfejp2$od9$1@fred.mathworks.com>...
> I have 4 points of a plane, ABCD .Can i calculate the normal vector,n of it?
>
> Is it n= cross(AB,CD)?

Re: Vectors

M K — Wed, 12 Nov 2008 13:23:02 -0500

Sorry I should re-phrase that.

Calculating the aangle between two vectors. I did a search on this forum and found another thread which gave two ways of calculating it

1) the usual acos(dot(A,B)/(norm(A)*norm(B))

2) angle = atan2(norm(cross(a,b)),dot(a,b));

I get different answers when I use these two ... Any help will be appreciated!

Re: Vectors

John D'Errico — Wed, 12 Nov 2008 13:28:01 -0500

"M K" <maha_k@mathworks.com> wrote in message <gfejp2$od9$1@fred.mathworks.com>...
> I have 4 points of a plane, ABCD .Can i calculate the normal vector,n of it?
>
> Is it n= cross(AB,CD)?

Are these 4 points that lie in a plane in how many
dimensions?

In 3-d, only 3 points determine a plane. Are all 4
points known to lie in the same plane? (If they are
not coplanar, then you cannot determine a normal
vector.)

So what do you have? Perhaps the simplest solution
to your question is to use null. Assuming that A,B,C,D
are all row vectors, then do this:

N = null([B-A;C-A;D-A]);

John

Re: Vectors

John D'Errico — Wed, 12 Nov 2008 13:31:49 -0500

"M K" <maha_k@mathworks.com> wrote in message <gfekjc$46l$1@fred.mathworks.com>...
> Can the Dot product of two vectors, A and B in Matlab be written as
>
> dot(A,B)/norm(A)*norm(B)=cos(teta)
>

First of all, if you have a new question, put it in a
new thread!

What is your question anyway?

The dot product of two vectors is just

dot(A,B)

or if A and B are row vectors, then just

A*B'

Are you trying to compute the cosine of the
angle between the vectors? Why not say it?

John

Re: Vectors

Roger Stafford — Wed, 12 Nov 2008 18:02:01 -0500

"M K" <maha_k@mathworks.com> wrote in message <gfelbm$cc9$1@fred.mathworks.com>...
> Sorry I should re-phrase that.
>
> Calculating the aangle between two vectors. I did a search on this forum and found another thread which gave two ways of calculating it
>
> 1) the usual acos(dot(A,B)/(norm(A)*norm(B))
>
> 2) angle = atan2(norm(cross(a,b)),dot(a,b));
>
> I get different answers when I use these two ... Any help will be appreciated!
-----------
I assume that you are dealing with three-element vectors in three-dimensional space, with the angle between vectors being regarded as lying somewhere between 0 and pi. In theory the two formulas you mention should give exactly the same answers. However, in terms of computational robustness the first formula suffers a loss of accuracy for angles that lie very near either 0 or pi. The derivative of the 'acos' function approaches infinity at such values and this results in excessive computational errors. The 'atan2' function avoids this difficulty for all angles in the range. That might account for the differences you allude to.

It would help if you could give a concrete example of the a and b vector values and the differences you are seeing between the two formulas' results.

Roger Stafford