[R] Function to locate points in 3d octants or points on twoaxes

[Bryan Hanson]

Thanks Dan for pointing that out.  My question really arose from the  
need to draw splines between arbitrary 3d pairs of points, so I posted  
a new question to the list addressing that more specifically.  While  
the issue of 3d splines must have been dealt with in graphics/ 
animation oriented programs/languages, I think I may have to "grow my  
own" and I'll need the suggestions offered by you and Petr.  Thanks,  
Bryan

On Feb 2, 2011, at 11:55 AM, Daniel Nordlund wrote:

>> -----Original Message-----
>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org 
>> ]
>> On Behalf Of Bryan Hanson
>> Sent: Wednesday, February 02, 2011 5:23 AM
>> To: Petr Savicky
>> Cc: r-help at r-project.org
>> Subject: Re: [R] Function to locate points in 3d octants or points on
>> twoaxes
>>
>> 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.
>>>
>
> For a general solution you also need to consider how you want to  
> deal with "boundary" conditions.  For example, if the x and y  
> coordinates are zero for both points then the points lie in both the  
> xz and yz planes.  And if one of the coordinates of a point is zero,  
> then how do you decide which quadrant it is in?
>
> Dan
>
> Daniel Nordlund
> Bothell, WA USA
>
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