[FT] [computer] 3D math

Hiya

I'm looking for a non-horrendous formula for calculating, given the
following facts, 

- 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>. 

B) What percentage of the volume of S2 is contained within S1? What
formula
will determine this?

This one I won't guess at. I can't think of an elegant generic solution
that
doesn't work by regions. 

B) Is point P3 within sphere S1?

<My guess here is take the magnitude of the line between the centre of
S1
and P3 and if it is <= radius r1 then P3 is inside of S1>. 

It strikes me these formula might be useful for determining moves in 3D
vector games on a computer. I'm looking at doing something in this line
of
thought sometime. The math is vaguely disturbing though. 

T. 

------------------------------------------
Thomas R. S. Barclay
Voice: (613) 722-3232 ext 349
e-mail: tomb@bitheads.com

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