🚀 go-pugleaf

>    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!

>   By the way (A,B,C) is the normal vector to the plane and D is the
> distance from the origin to the plane along that normal.

Yep. And since the magnitude of the vector is of no importance to the correctness of 
the function, assuming that magnitude is 1 eases things a lot...
 
-- 
Hakan "Zap" Andersson | http://www.lysator.liu.se/~zap | Q: 0x2b | ~0x2B
Job:  GCS Scandinavia | Fax:   +46 16 96014            | A: 42
zap@lysator.liu.se    | Voice: +46 16 96460            | "Whirled Peas"
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GENIUS - Mechanical Design for AutoCAD - http://www.kuai.se/~zap/genius
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