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

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Chris M. Thomasson

Posts: 191
Registered: 8/29/13
Re: circle intersections...
Posted: Aug 29, 2013 7:07 PM
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[cross-posted to {alt.math, sci.math}]

"Chris M. Thomasson" wrote in message

I was wondering where I could find some programming
methods of clever circle intersection algorithms that use
a single square root operation. So far, all of the examples
I can find use more than one sqrt. Therefore, I have come
up with the following formula:

R=G*J+L, {G,H,Q,J,K,L,M,R}]

That discovers intersection(s) for circles c0(A, B, C) and c1(O, P, F)
where A, B, C, O, P and F are the respective x, y center and
radius components of circles c0 and c1. A point of intersection
is contained in M and R, which represent its x, y coordinates.

Here is a solve command for a concrete example:

M=K-H*J,R=G*J+L, {A,B,C,O,P,F,G,H,Q,J,K,L,M,R}]

These examples work with Mathics Online (just copy and paste

They should also work with Mathematica.

Anyway, I was wondering if somebody could help me find any
references to existing formulas that are equal to or better
than this one.

Also, I am looking for clever approximation techniques for
lengths of right triangles. Something like:

This is all for a fractal I created based on circle intersections; here
is a link:

I think I could run the approximation throughout the iteration of
the fractal, then episodically run an actual sqrt in order and/or
correct a set of error levels in a set of heuristics.

I have implemented the formula and put it online here:


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