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Topic: circle intersections...
Replies: 26   Last Post: Sep 1, 2013 10:49 PM

 Messages: [ Previous | Next ]
 Chris M. Thomasson Posts: 191 Registered: 8/29/13
Re: circle intersections...
Posted: Aug 30, 2013 3:50 AM

> "Ken Pledger" wrote in message
> news:ken.pledger-BBFD52.16002730082013@news.eternal-september.org...

> In article <kvok88\$gf8\$1@speranza.aioe.org>,
> "Chris M. Thomasson" <no@spam.invalid> wrote:

> > [cross-posted to {alt.math, sci.math}]
> >
> > "Chris M. Thomasson" wrote in message
> > news:kvoe76\$155\$2@speranza.aioe.org...
> >
> > I was wondering where I could find some programming
> > methods of clever circle intersection algorithms that use
> > a single square root operation....

> Your code is hard to read, but here's a standard trick to do what you
> want. Consider the circles

> x^2 + y^2 + 2x - 4y - 4 = 0

> x^2 + y^2 - 6x + 2y + 6 = 0.

> Subtract one equation from the other to get

> 8x - 6y - 10 = 0.

[...]

I came up with the following equations from your example:

((3y+5) / 4)^2 + y^2 + 2((3y + 5) / 4) - 4y - 4 = 0

x^2 + ((4x - 5) / 3)^2 + 2x - 4((4x - 5)/3) - 4 = 0

Which does indeed mean that:

x = 1.4
y = 0.2

Which is the same answer you got here:

> The circles in my example actually touch, so the line is their common
> tangent. The same solution method finds their point of contact (7/5,
> 1/5).

Okay, now I am getting somewhere. Thanks again Ken!

:^)