🚀 go-pugleaf

In article <3123178B.7CD8@lysator.liu.se>
           zap@lysator.liu.se "Mr 'Zap' Andersson" writes:

> >    I think everyone did not understand what the original poster
> > (Jonathan Cohn) was trying ti say. I Think he was asking what is the
> > minimal amount of information you need to define a plane in 3 space.
> > Everybody's knee jerk reaction to that is to say you need three points
> > or nine numbers (x1,y1,z1) - (x2,y2,z2 ) - (x3,y3,z3).
> >   He was pointing out that you can use less numbers to give the same
> > information. Thus stating you need two points or more to the point
> > just six numbers (x1,y1,z1) (vx1,vy1,vz1).  I am sure he knows the
> > difference between a point and vector.
> >   If this is what he was trying to say then I have to correct him and
> > say you only need four numbers to define a plane, the four
> > coefficients of the planer equation Ax + By + Cz + D = 0.
> > That is the minimal amount of info needed for a plane.
> 
> Not entirely true. Assume the length of the normal vector is 1, you can leave
>  one 
> component out. I.e. C can be calculated from A and B.
> 
> So the *storage* needed is really only three numbers!
> 

I don't *think* so.  Say you give A, B and D.

I presume you are using pythag, so you get

1=A2+B2+C2                (A2 = A * A)

ie C=+/-sqrt(1-A2-B2)

I believe you now describe two possible planes.

You require 3 numbers + a sign.  Actually you could store it as the sign
for D (Distances are always positive) and keep it within 3 numbers, but that
is computer science, not mathematics.

[Correct me if I made a fatal flaw, plz...]
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