From cbb84a64360cce71ced04ba0ad5f8224ef746c53 Mon Sep 17 00:00:00 2001 From: Frank Dellaert Date: Thu, 14 Mar 2019 14:14:20 +0000 Subject: [PATCH] Added information about LieGroup helper class --- GTSAM-Concepts.md | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/GTSAM-Concepts.md b/GTSAM-Concepts.md index 366a58a09..a6cfee984 100644 --- a/GTSAM-Concepts.md +++ b/GTSAM-Concepts.md @@ -97,12 +97,24 @@ Note that in the Lie group case, the usual valid expressions for Retract and Loc For Lie groups, the `exponential map` above is the most obvious mapping: it associates straight lines in the tangent space with geodesics on the manifold -(and it's inverse, the log map). However, there are two cases in which we deviate from this: +(and it's inverse, the log map). However, there are several cases in which we deviate from this: However, the exponential map is unnecessarily expensive for use in optimization. Hence, in GTSAM there is the option to provide a cheaper chart by means of the `ChartAtOrigin` struct in a class. This is done for *SE(2)*, *SO(3)* and *SE(3)* (see `Pose2`, `Rot3`, `Pose3`) Most Lie groups we care about are *Matrix groups*, continuous sub-groups of *GL(n)*, the group of *n x n* invertible matrices. In this case, a lot of the derivatives calculations needed can be standardized, and this is done by the `LieGroup` superclass. You only need to provide an `AdjointMap` method. +A CRTP helper class `LieGroup` is available that can take a class and create some of the Lie group methods automatically. The class needs: + +* operator* : implements group operator +* inverse: implements group inverse +* AdjointMap: maps tangent vectors according to group element +* Expmap/Logmap: exponential map and its inverse +* ChartAtOrigin: struct where you define Retract/Local at origin + +To use, simply derive, but also say `using LieGroup::inverse` so you get an inverse with a derivative. + +Finally, to create the traits automatically you can use `internal::LieGroupTraits` + Vector Space ------------