Back in March I was able to successfully recreate galaga style
enemy patterns using pattern tables and some custom motion code.
But there was one problem with the implementation: dual side-by-
side formations were wrong--at certain points the inner and
outer formation paths intersect. Why do the formations
intersect? Each formation is following the same pattern table
commands but the outer formation adds an additional offset to
the (x, y) position of outer formation ship to keep the
formations apart. Now, imagine two formations following the same
circular path where the outer path (in this case the red circle)
is offset by some (x, y) position. Eventually at some time t (or
some radian theta) the two circular paths will intersect as
demonstrated below: It is pretty obvious that the inner and
outer formations can not use the same circle. But what if we
increase the radius of the outer circular path by a few units
keeping the two paths separated by some distance D defined by D
= | R1 - R0 | (where R0 and R1 are