<s>
In	O
Euclidean	O
geometry	O
,	O
oblique	B-Algorithm
reflections	I-Algorithm
generalize	O
ordinary	O
reflections	B-Algorithm
by	O
not	O
requiring	O
that	O
reflection	O
be	O
done	O
using	O
perpendiculars	O
.	O
</s>
<s>
If	O
two	O
points	O
are	O
oblique	B-Algorithm
reflections	I-Algorithm
of	O
each	O
other	O
,	O
they	O
will	O
still	O
stay	O
so	O
under	O
affine	B-Algorithm
transformations	I-Algorithm
.	O
</s>
<s>
For	O
an	O
oblique	B-Algorithm
reflection	I-Algorithm
,	O
one	O
requires	O
instead	O
of	O
perpendicularity	O
that	O
AB	O
be	O
parallel	O
to	O
a	O
given	O
reference	O
line	O
.	O
</s>
<s>
Formally	O
,	O
let	O
there	O
be	O
a	O
plane	O
P	O
in	O
the	O
three-dimensional	O
space	O
,	O
and	O
a	O
line	O
L	O
in	O
space	O
not	O
parallel	O
to	O
P	O
.	O
To	O
obtain	O
the	O
oblique	B-Algorithm
reflection	I-Algorithm
of	O
a	O
point	O
A	O
in	O
space	O
in	O
respect	O
to	O
the	O
plane	O
P	O
,	O
one	O
draws	O
through	O
A	O
a	O
line	O
parallel	O
to	O
L	O
,	O
and	O
lets	O
the	O
oblique	B-Algorithm
reflection	I-Algorithm
of	O
A	O
be	O
the	O
point	O
B	O
on	O
that	O
line	O
on	O
the	O
other	O
side	O
of	O
the	O
plane	O
such	O
that	O
the	O
midpoint	O
of	O
AB	O
is	O
in	O
P	O
.	O
If	O
the	O
reference	O
line	O
L	O
is	O
perpendicular	O
to	O
the	O
plane	O
,	O
one	O
obtains	O
the	O
usual	O
reflection	O
.	O
</s>
<s>
The	O
concept	O
of	O
oblique	B-Algorithm
reflection	I-Algorithm
is	O
easily	O
generalizable	O
to	O
oblique	B-Algorithm
reflection	I-Algorithm
in	O
respect	O
to	O
an	O
affine	O
hyperplane	O
in	O
Rn	O
with	O
a	O
line	O
again	O
serving	O
as	O
a	O
reference	O
,	O
or	O
even	O
more	O
generally	O
,	O
oblique	B-Algorithm
reflection	I-Algorithm
in	O
respect	O
to	O
a	O
k-dimensional	O
affine	O
subspace	O
,	O
with	O
a	O
nk-dimensional	O
affine	O
subspace	O
serving	O
as	O
a	O
reference	O
.	O
</s>
<s>
Back	O
to	O
three	O
dimensions	O
,	O
one	O
can	O
then	O
define	O
oblique	B-Algorithm
reflection	I-Algorithm
in	O
respect	O
to	O
a	O
line	O
,	O
with	O
a	O
plane	O
serving	O
as	O
a	O
reference	O
.	O
</s>
<s>
An	O
oblique	B-Algorithm
reflection	I-Algorithm
is	O
an	O
affine	B-Algorithm
transformation	I-Algorithm
,	O
and	O
it	O
is	O
an	O
involution	B-Algorithm
,	O
meaning	O
that	O
the	O
reflection	O
of	O
the	O
reflection	O
of	O
a	O
point	O
is	O
the	O
point	O
itself	O
.	O
</s>
