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release/4.3a0
Frank Dellaert 2014-12-05 16:26:06 +00:00
parent c975382b59
commit 63effbb433
1 changed files with 8 additions and 6 deletions
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14
GTSAM-Concepts.md
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@ -81,7 +81,7 @@ Hence, we formalize by the following extension of the concept:
* valid expressions: * valid expressions:
* `group::act(g,t)`, for some instance of a space T, that can be acted upon by the group * `group::act(g,t)`, for some instance of a space T, that can be acted upon by the group
* `group::act(g,t,H)`, if the group acted upon is a continuous differentiable manifold * `group::act(g,t,H)`, if the space acted upon is a continuous differentiable manifold
Lie Group Lie Group
--------- ---------
@ -96,19 +96,21 @@ where above the `H` arguments stand for optional Jacobian arguments. That makes
when a Lie group acts on a space, we have two derivatives to care about: when a Lie group acts on a space, we have two derivatives to care about:
* `group::act(g,t,Hg,Ht)`, if the group acted upon is a continuous differentiable manifold * `group::act(g,t,Hg,Ht)`, if the space acted upon is a continuous differentiable manifold
For now, we won't care about Lie groups acting on non-manifolds.
Vector Space Vector Space
------------ ------------
Trivial Lie Group where Trivial Lie group where
* `identity == 0` * `identity<T> == 0`
* `inverse(p) == -p` * `inverse(p) == -p`
* `compose(p,q) == p+q` * `compose(p,q) == p+q`
* `between(p,q) == q-p` * `between(p,q) == q-p`
* `chart.retract(q) == p-q` * `chart::retract(q) == p-q`
* `chart.retract(v) == p+v` * `chart::retract(v) == p+v`
This considerably simplifies certain operations. This considerably simplifies certain operations.