From 63effbb43364efdc72b774dbb1bd796f239afa34 Mon Sep 17 00:00:00 2001 From: Frank Dellaert Date: Fri, 5 Dec 2014 16:26:06 +0000 Subject: [PATCH] Small changes to latest big commit --- GTSAM-Concepts.md | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/GTSAM-Concepts.md b/GTSAM-Concepts.md index 8a841e94a..683fa9619 100644 --- a/GTSAM-Concepts.md +++ b/GTSAM-Concepts.md @@ -81,7 +81,7 @@ Hence, we formalize by the following extension of the concept: * 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,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 --------- @@ -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: - * `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 ------------ -Trivial Lie Group where +Trivial Lie group where - * `identity == 0` + * `identity == 0` * `inverse(p) == -p` * `compose(p,q) == p+q` * `between(p,q) == q-p` - * `chart.retract(q) == p-q` - * `chart.retract(v) == p+v` + * `chart::retract(q) == p-q` + * `chart::retract(v) == p+v` This considerably simplifies certain operations.