Everything about Circular Points At Infinity totally explained
In
projective geometry, the
circular points at infinity in the
complex projective plane (also called
cyclic points or
isotropic points) are
» (1: i: 0) and (1: −i: 0).
Here the coordinates are
homogeneous coordinates (
x:
y:
z); so that the
line at infinity is defined by
z = 0. These points are called
circular points at infinity because they lie at infinity, on that line, and they also lie on all circles. In other words, both points satisfy the homogeneous equations of the type
»
The case where the coefficients are all real gives the equation of a general circle (of the
real projective plane).
The circular points at infinity are the
points at infinity of the
isotropic lines.
The
cyclic points are
invariant under
translation and
rotation.
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