There are a couple of reasons why it is not often the
best solution. One reason has to do with an assumption
made about geometry within a perspective projection that
does not hold for the projections discussed here, namely
that we can draw a straight line between two points in a
perspective projection. In a fisheye and many other
projections one cannot draw a “straight” line between the
end points of a line segments. The solution is to split a
line segment into many smaller sections and draw each
one, the more segments the better the approximation to
what the true appearance of the line segment should be
This introduces more geometry into the rendering
pipeline and while modest for a line segment it is much
more significant for planes. A plane needs to be
tessellated into many smaller plane segments and due to
the two dimensional nature the increase in geometry rises
as the product of the number of tessellations along each
axis. There are algorithms one can imagine that tessellate
only when necessary and to an acceptable degree but
these are not trivial and can quickly overwhelm the gains
made by this approach over the cubic map algorithm.