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Date: Wed, 06 Sep 2000 21:47:13 -0400

Subject: Re: [FT] [computer] 3D math

```
"Barclay, Tom" wrote:
> - in 3 space
> - a sphere we shall call S1 located at coorinates (x1,y1,z1) of radius
r1.
> - a sphere we shall call S2 located at coorinates (x2,y2,z2) of radius
r2.
> - a point we shall call P3 located at coordinates (x3,y3,z3).
>
> A) Do r1 and r2 intersect one another? What formula will determine
this?
> <My guess: Take a line between the centre of S1 and S2 and determine
if the
> length of this segment exceeds the sum of the radii r1 and r2>.
Yes, that's my take on it. Use the true distance formula.
d = sqrt( (x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2 )
where:
d = distance between the centers of the spheres
sqrt(X) = square root of X
(x)^2 = square of x
S1 and S2 intersect each other if
d < (r1 + r2)
> B) What percentage of the volume of S2 is contained within S1? What
formula
> will determine this?
You're on your own on this one. My calculus is weak.
> B) Is point P3 within sphere S1?
Same as A). Use x1,y1,z1 and x3,y3,z3 in the true
distance formula.
Point P3 is inside sphere S1 if
d < r1
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