Guide to Creating a Group

This guide explains the minimal requirements for creating a class that satisfies the Group concept in GTSAM. The Group is a foundational algebraic concept that precedes the geometric Manifold concept. It defines types that have a binary operation (composition), an identity element, and an inverse for every element.

Like other GTSAM concepts, this is achieved through traits-based metaprogramming, not class inheritance, see GTSAM-Concepts.

1. Group Operations¶

At its heart, a group is defined by four abstract operations: Identity, Compose, Between, and Inverse. GTSAM distinguishes between two “flavors” of groups based on the C++ syntax used to implement these operations.

2. Implementation Requirements: Choose a Flavor¶

You must implement the methods for one of the two flavors.

A) MultiplicativeGroup Flavor¶

This is for groups that use operator* for composition, like rotation or pose types. Your class must provide:

• A static Identity method.

• An operator* for composition.

• An inverse method.

B) AdditiveGroup Flavor¶

This is for groups that behave like vector spaces, using operator+ for composition. Your class must provide:

• A static Identity method.

• An operator+ for composition.

• A binary operator- for the Between operation.

• A unary operator- for the Inverse operation.

3. Prerequisite: The Testable Concept¶

The Group concept requires the Testable concept. Before satisfying the group requirements, your class must also implement:

• A print method.

• An equals method.

4. Linking Your Class to GTSAM (The traits Specialization)¶

This is the crucial step that registers your class with GTSAM. You must specialize the gtsam::traits struct for your class. This specialization should inherit from one of the helpers provided in Group.h. The helper automatically maps your chosen C++ operators to the abstract Compose, Between, and Inverse operations.

To do this, you will add a specialization of traits<MyGroup> in the gtsam namespace. If your group is multiplicative, this specialization will inherit from internal::MultiplicativeGroup<MyGroup>. If your group is additive, it will inherit from internal::AdditiveGroup<MyGroup>.

5. Concept Checking¶

To verify that your implementation is correct, add the GTSAM_CONCEPT_GROUP_INST macro, followed by your class name in parentheses, to your unit test file. This will cause a compile-time error if any of the requirements for a Group (including Testable) are not met.