Collision detection through f(x,y,z)

I've been wondering whether or not it would be possible for a 3 dimensional game to use a 3 dimensional function as collision detection, meaning that instead of checking vertices, you would simply check them to a single equation. This equation would, of course, be determined by the vertices of the model and calculated during design time, making calculation time irrelevant. If possible, how could the function be derived (approximately, the model would have a "width" anyway)?

PS: Sorry if I'm a bit incoherent, its after midnight here.

What shaped objects, are they moving, are they accelerating, is the detection to be during an time interval or instantaneously?

I'm guessing using a system like this...

(this is in Basic)

VB Code:

type thing
x as integer
y as integer
z as integer
end type
dim stuff (0 to 9) as thing
dim mover as thing
dim area(0 to 99, 0 to 99, 0 to 99)
for a = 0 to 9
stuff(a).x = int(rnd*100)
stuff(a).y=int(rnd*100)
stuff(a).z=int(rnd*100)
next a
for a = 0 to 9
area(stuff(a).x,stuff(a).y,stuff(a).z) = 1
next a
do until 'you are happy with it
'Code that changes variable MOVER around here
if area(mover.x,mover.y,mover.z) = 1 then print "AHHH ASTEROID"
loop

Basicly you wouldn't want to use this on moving objects cause it would take more time the it saves... uses up alot of memory too..