- lines:
- Let
be a set of points on a line
and
consider the action of a
projective transformation
on the the points. Since the points lie on the line we have
One can easily verify that
Thus the points
all lie on the line
.
Hence, if points are transformed as
, lines are transformed
as
.
- conics:
- Note that a conic is represented (homogeneously) as
Under a point transformation
the
conic becomes
which is the quadratic form of
with
. This gives the transformation rule for a conic.
Subhashis Banerjee
2008-01-20