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Subject: Re: common point of two planes



jindra wrote:
> I need to compute a common point of two planes which are given by
>
Two planes in 3D (usually) intersect in a line. Never just in
a single point.

> 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 ?
>
Without parametric form - sure: just use Gaussian elimination and
you get the generic equation of the intersection line.

Without any kind of solving a system of equation - no.
Any algorithm solving your problem *is* a solver for a system
of equations, by the very definition of your problem.

Przemek

--
"Beauty is the first test: there is no permanent place
in the world for ugly mathematics." G.H. Hardy

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