I was thinking, regarding act() in all complex groups. Maybe we could have special actions. In case e.g. of SGal3, we would have:
transform points: T+R*p
boost: see Kelly's paper
event-transform: see paper
and other possible actions only available for this group.
In SE3 we have a similar problem, in
transforming points T+R*p
and transforming vetors R*v
In manif we already have some examples on non-abstracted methods:
asSO3() <-- for SE3, SE23, SGal3
E6() <-- for the generators
so I see no fundamental impediment for act(). In fact, it is possible that act() as an abstract form is not convenient, precisely because actions are not pre-defined operations for Lie groups in their abstract form.
Complex groups are
SE(3)
,SE_2(3)
,Sgal(3)
.I was thinking, regarding
act()
in all complex groups. Maybe we could have special actions. In case e.g. ofSGal3
, we would have:T+R*p
and other possible actions only available for this group.
In SE3 we have a similar problem, in
T+R*p
R*v
In
manif
we already have some examples on non-abstracted methods:asSO3()
<-- forSE3
,SE23
,SGal3
E6()
<-- for the generatorsso I see no fundamental impediment for
act()
. In fact, it is possible thatact()
as an abstract form is not convenient, precisely because actions are not pre-defined operations for Lie groups in their abstract form.