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GTSAM-Concepts.md edited online with Bitbucket

release/4.3a0
Frank Dellaert 2016-02-13 18:58:03 +00:00
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GTSAM-Concepts.md
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@ -19,10 +19,10 @@ To optimize over continuous types, we assume they are manifolds. This is central
[Manifolds](http://en.wikipedia.org/wiki/Manifold#Charts.2C_atlases.2C_and_transition_maps) and [charts](http://en.wikipedia.org/wiki/Manifold#Charts.2C_atlases.2C_and_transition_maps) are intimately linked concepts. We are only interested here in [differentiable manifolds](http://en.wikipedia.org/wiki/Differentiable_manifold#Definition), continuous spaces that can be locally approximated *at any point* using a local vector space, called the [tangent space](http://en.wikipedia.org/wiki/Tangent_space). A *chart* is an invertible map from the manifold to that tangent space.
In GTSAM, all properties and operations needed to use a type must be defined through template specialization of the struct `gtsam::traits`. Concept checks are used to check that all required functions are implemented.
In detail, we ask the following are defined in the traits object:
In detail, we ask the following are defined in the traits object (although, not all are needed for optimization):
* values:
* `enum { dimension = D};`, an enum that indicates the dimensionality *n* of the manifold. In Eigen-fashion, we also support manifolds whose dimenionality is only defined at runtime, by specifying the value -1.
* `enum { dimension = D};`, an enum that indicates the dimensionality *n* of the manifold. In Eigen-fashion, we also support manifolds whose dimensionality is only defined at runtime, by specifying the value -1.
* types:
* `TangentVector`, type that lives in tangent space. This will almost always be an `Eigen::Matrix<double,n,1>`.
* `ChartJacobian`, a typedef for `OptionalJacobian<dimension, dimension>`.
@ -33,7 +33,7 @@ In detail, we ask the following are defined in the traits object:
* `gtsam::traits::lie_group_tag` -- Everything in this list is expected, plus the functions defined under **Groups**, and **Lie Groups** below.
* `gtsam::traits::vector_space_tag` -- Everything in this list is expected, plus the functions defined under **Groups**, and **Lie Groups** below.
* valid expressions:
* `size_t dim = traits<T>::getDimension(p);` static function should be defined. This is mostly useful if the size is not known at compile time.
* `size_t dim = traits<T>::GetDimension(p);` static function should be defined. This is mostly useful if the size is not known at compile time.
* `v = traits<T>::Local(p,q)`, the chart, from manifold to tangent space, think of it as *q (-) p*, where *p* and *q* are elements of the manifold and the result, *v* is an element of the vector space.
* `p = traits<T>::Retract(p,v)`, the inverse chart, from tangent space to manifold, think of it as *p (+) v*, where *p* is an element of the manifold and the result, *v* is an element of the vector space.
* invariants