R help - Feb 2011 - Function to locate points in 3d octants or points on two axes

[Sorry, resending with a proper subject line!]

Hi Guru's...

I have a set of points that may lie along any of the x, y and z axes  
in a Cartesian coordinate system.  I am hoping that a function exists  
which will determine if any two selected points are on different axes,  
i.e, if the one of the points is on x and the other on y or z, not  
elsewhere on the x axis.  Put another way, I need to determine if the  
triangle formed by the two points and the origin lies in the xy, xz or  
yz planes.  This might be as simple as testing if any particular value  
is zero, i.e. if the x coordinate is zero, then the points must be on  
the z and y axes and the triangle in the yz plane.  But, I'm looking  
for a fairly general solution, one that also returns the appropriate  
plane as the answer.  Very closely related to this, I could use a  
function that determines which of the 8 octants a point lies in. Seems  
like the cross product might be part of this, but I'm a little rusty  
on how to apply it.

I hope this is clear enough, and someone has a suggestion to point me  
in the right direction.  Before writing my own klunky version, I  
thought I'd ask.

Thanks, Bryan
****************
Prof. Bryan Hanson
Dept of Chemistry & Biochemistry
DePauw University
602 S. College Ave
Greencastle IN 46135 USA

On Tue, Feb 01, 2011 at 08:30:22PM -0500, Bryan Hanson
wrote:
> [Sorry, resending with a proper subject line!]
> 
> Hi Guru's...
> 
> I have a set of points that may lie along any of the x, y and z axes  
> in a Cartesian coordinate system.  I am hoping that a function exists  
> which will determine if any two selected points are on different axes,  
> i.e, if the one of the points is on x and the other on y or z, not  
> elsewhere on the x axis.  Put another way, I need to determine if the  
> triangle formed by the two points and the origin lies in the xy, xz or  
> yz planes.  This might be as simple as testing if any particular value  
> is zero, i.e. if the x coordinate is zero, then the points must be on  
> the z and y axes and the triangle in the yz plane.  But, I'm looking  
> for a fairly general solution, one that also returns the appropriate  
> plane as the answer.  Very closely related to this, I could use a  
> function that determines which of the 8 octants a point lies in. Seems  
> like the cross product might be part of this, but I'm a little rusty  
> on how to apply it.
> 
> I hope this is clear enough, and someone has a suggestion to point me  
> in the right direction.  Before writing my own klunky version, I  
> thought I'd ask.
Hi.

I think that for suggesting an appropriate solution it may be needed
to know, which data structure is used for the input pairs of points. For
example, it may a single matrix n times 3 with points as rows and a pair
is represented by two indices of the points. Alternatively, the input
may be a single matrix n times 6, where rows are pairs of points.

In any case, the input may be simplified using sign() function. For example

  a <- as.matrix(expand.grid(x=c(-1.1, 0, 1.1), y=c(0, 1.2), z=c(0, 1.3)))
  a

           x   y   z
   [1,] -1.1 0.0 0.0
   [2,]  0.0 0.0 0.0
   [3,]  1.1 0.0 0.0
   [4,] -1.1 1.2 0.0
   [5,]  0.0 1.2 0.0
   [6,]  1.1 1.2 0.0
   [7,] -1.1 0.0 1.3
   [8,]  0.0 0.0 1.3
   [9,]  1.1 0.0 1.3
  [10,] -1.1 1.2 1.3
  [11,]  0.0 1.2 1.3
  [12,]  1.1 1.2 1.3

  sign(a)

         x y z
   [1,] -1 0 0
   [2,]  0 0 0
   [3,]  1 0 0
   [4,] -1 1 0
   [5,]  0 1 0
   [6,]  1 1 0
   [7,] -1 0 1
   [8,]  0 0 1
   [9,]  1 0 1
  [10,] -1 1 1
  [11,]  0 1 1
  [12,]  1 1 1

This output represents a classification of the points into a finite
number of regions and keeps the information needed for any of the
tasks, which you mention.

Hope this helps.

Petr Savicky.