<s>
An	O
implicit	B-Algorithm
surface	I-Algorithm
is	O
the	O
set	O
of	O
zeros	O
of	O
a	O
function	O
of	O
three	O
variables	O
.	O
</s>
<s>
Despite	O
difficulty	O
of	O
visualization	O
,	O
implicit	B-Algorithm
surfaces	I-Algorithm
provide	O
relatively	O
simple	O
techniques	O
to	O
generate	O
theoretically	O
(	O
e.g.	O
</s>
<s>
The	O
proof	O
of	O
this	O
formula	O
relies	O
(	O
as	O
in	O
the	O
case	O
of	O
an	O
implicit	B-Algorithm
curve	I-Algorithm
)	O
on	O
the	O
implicit	O
function	O
theorem	O
and	O
the	O
formula	O
for	O
the	O
normal	O
curvature	O
of	O
a	O
parametric	O
surface	O
.	O
</s>
<s>
As	O
in	O
the	O
case	O
of	O
implicit	B-Algorithm
curves	I-Algorithm
it	O
is	O
an	O
easy	O
task	O
to	O
generate	O
implicit	B-Algorithm
surfaces	I-Algorithm
with	O
desired	O
shapes	O
by	O
applying	O
algebraic	O
operations	O
(	O
addition	O
,	O
multiplication	O
)	O
on	O
simple	O
primitives	O
.	O
</s>
<s>
The	O
equipotential	O
surface	O
for	O
the	O
potential	O
value	O
is	O
the	O
implicit	B-Algorithm
surface	I-Algorithm
which	O
is	O
a	O
sphere	O
with	O
center	O
at	O
point	O
.	O
</s>
<s>
The	O
displayed	O
surface	O
is	O
the	O
equipotential	O
surface	O
(	O
implicit	B-Algorithm
surface	I-Algorithm
)	O
.	O
</s>
<s>
In	O
a	O
similar	O
way	O
implicit	B-Algorithm
surfaces	I-Algorithm
can	O
be	O
defined	O
by	O
a	O
constant	O
distance	O
product	O
to	O
several	O
fixed	O
points	O
.	O
</s>
<s>
A	O
further	O
simple	O
method	O
to	O
generate	O
new	O
implicit	B-Algorithm
surfaces	I-Algorithm
is	O
called	O
metamorphosis	O
of	O
implicit	B-Algorithm
surfaces	I-Algorithm
:	O
</s>
<s>
For	O
two	O
implicit	B-Algorithm
surfaces	I-Algorithm
(	O
in	O
the	O
diagram	O
:	O
a	O
constant	O
distance	O
product	O
surface	O
and	O
a	O
torus	O
)	O
one	O
defines	O
new	O
surfaces	O
using	O
the	O
design	O
parameter	O
:	O
</s>
<s>
There	O
are	O
various	O
algorithms	O
for	O
rendering	O
implicit	B-Algorithm
surfaces	I-Algorithm
,	O
including	O
the	O
marching	B-Algorithm
cubes	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Essentially	O
there	O
are	O
two	O
ideas	O
for	O
visualizing	O
an	O
implicit	B-Algorithm
surface	I-Algorithm
:	O
One	O
generates	O
a	O
net	O
of	O
polygons	O
which	O
is	O
visualized	O
(	O
see	O
surface	B-Algorithm
triangulation	I-Algorithm
)	O
and	O
the	O
second	O
relies	O
on	O
ray	B-Algorithm
tracing	I-Algorithm
which	O
determines	O
intersection	O
points	O
of	O
rays	O
with	O
the	O
surface	O
.	O
</s>
