Re: Question about Pluecker coordinates

On 30 Lug, 08:26, Kaba <n...@xxxxxxxx> wrote:
mike wrote:
Isn't that just because a plane has no orientation. If you want a plane
to have a distinguishable side (lets say it is red on one side and green
on the other) then it needs one extra bit to 'orient' it. But it is no
longer a simple mathematical plane. Likewise, if the plane has a

I agree. Oriented planes and lines are different and require that extra
bit of information. It's a nice advantage of the 5 and 6 parameter
versions of being able to encode it in.

--http://kaba.hilvi.org

I think you don't need extra bits to record the orientation.

Take as an instance a straight line on a 2D plane and its
representation with two real numbers: distance d from the origin and
angle theta of its normal (with respect to the X axis :))

-oo < d < +oo
-Pi <= theta < Pi

Then eg (d=1, theta=Pi/4) and (d=-1, theta=-3Pi/4) are the same line
with opposite orientations.
No extra bit (unless you consider so the sign bit :))

.

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