comp.graphics.algorithms

Subject: Re: common point of two planes

On 20 Apr 2006 23:53:47 -0700, "jindra" wrote:
>I need to compute a common point of two planes which are given by
>general equations a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 =
>0. Is there some easy way how to compute it without converting into
>parametric form and solving some system of equations ?

Yes, but do you want a common point or the common line? The simplest
technology is probably Pluecker coordinates, described briefly in the
cga FAQ,

and more extensively in the links, especially this one.

Quoting from the latter:

L={E×F:fE-eF}, for [E:e] and [F:f] distinct planes containing L.

and

(V×U:U·U) is the point of L closest to the origin.
Pnt(t)=(V×U+tU:U·U) parameterizes points on L.

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