> On 12/02/2013 8:22 PM, Christian Froeschlin wrote:
>> Stephen wrote:
>>
>>>> Since you are dealing with lines in 3-space (x,y,z), the lines will
>>>> only
>>>> intersect if they lie on the same plane.
>>
>>> Can that be right?
>>
>> take two pens, and you will find you can easily hold them
>> so that they do not intersect, are not parallel, and with the
>> point of closest approach clearly within the physical pen
>> boundaries (and not just their projection to infinity).
>>
>
> Yes, that is true.
>
>>> What about the lines of the three axis?
>>
>> any two axes lie within a plane and intersect at the origin.
>
> And is the third axis, in 3D space, in the same plane as the plane of
> the first two axis?
>
>
The X and Y axis are coplanar, so are X and Z and Y and Z, it's just 
that they don't share the same planes.

Any 2 lines that intersect are always coplanar, but any 3 or more 
intersecting lines are not always coplanar relative to the same plane. 
Each pair of lines can define different planes.

Next, any pair of parallel lines are also always coplanar.

Finaly, you have non-parallel lines that don't intersect.

The mention of using a very thin cylinder to represent one line and 
using the trace function is interesting. A returned normal of <0,0,0> 
indicating non-intersecting lines that MAY be parallel. Replacing the 
target line by a plane WILL result in false positives in the case of 
non-coplanar lines.



Alain

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