**A perspective
is a central projection** : the transformation of points and lines in
the 3D space onto a plane by connecting corresponding points with conccurent
lines (the common point is the perspective centre (if this point is at
the infiniy, all the lines become parallel and we have a projection. The
branch of geometry dealing with the properties and invariants of geometric
figures under perspective is called **projective geometry**.

**The perspectives
of a circle** (in red, in the light green plane) on the light blue plane
(using the red point which can be moved with the mouse) is** a conic**
(in green).

The intersection
line of the circle's plane with the plane parallel to the perspective plane
and going through the perspective centre is "send to the infinity". The
tangents at the point(s) of the circle in that plane (in yellow) become
the "tangents at infinity" :

- a parabola
is tangent to the "line at infinity,

- the asymptotes
(in blue) of an hyperbola are the tangents at infinity.