Thanks Petr, the sign function will be of help. I was not aware of
it. Bryan
On Feb 2, 2011, at 3:21 AM, Petr Savicky wrote:
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.
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