Re: [Algorithms] algorithm for calculating a circle out of three points

[Stephen J B. <sj...@li...>]

On Tue, 28 May 2002, Christian Henning wrote:

> To be honest I don't want implement an algo. for solving a set of linear
> equations. In case there is no other way, how to solve the equations?

You don't have to solve the equations in realtime.

Do that on paper (or with MathCAD or something) - symbolically - and
you'll wind up with four horrible expressions relating the (x,y,z)
of the center of the circle plus it's radius to the nine numbers that
represent the coordinates of the points.  That'll turn into four
lines of C code (which you'll then want to optimise to eliminate
common sub-expressions, things you've already computed, etc, etc).

An algorithm for solving an arbitary set of equations would be
relatively nasty - but you don't have an arbitary set - you have
a very fixed set.

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