untabify
Mike Bosse
parent
409214e165
commit
6f992e623e
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@ -22,28 +22,28 @@ In GTSAM, all properties and operations needed to use a type must be defined thr
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In detail, we ask the following are defined in the traits object:
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* values:
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* `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.
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* `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.
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* types:
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* `TangentVector`, type that lives in tangent space. This will almost always be an `Eigen::Matrix<double,n,1>`.
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* `ChartJacobian`, a typedef for `OptionalJacobian<dimension, dimension>`.
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* `ManifoldType`, a pointer back to the type.
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* `structure_category`, a tag type that defines what requirements the type fulfills, and therefore what requirements this traits class must fulfill. It should be defined to be one of the following:
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* `gtsam::traits::manifold_tag` -- Everything in this list is expected
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* `gtsam::traits::group_tag` -- Everything in this list is expected, plus the functions defined under **Groups** below.
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* `gtsam::traits::lie_group_tag` -- Everything in this list is expected, plus the functions defined under **Groups**, and **Lie Groups** below.
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* `gtsam::traits::vector_space_tag` -- Everything in this list is expected, plus the functions defined under **Groups**, and **Lie Groups** below.
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* `ChartJacobian`, a typedef for `OptionalJacobian<dimension, dimension>`.
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* `ManifoldType`, a pointer back to the type.
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* `structure_category`, a tag type that defines what requirements the type fulfills, and therefore what requirements this traits class must fulfill. It should be defined to be one of the following:
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* `gtsam::traits::manifold_tag` -- Everything in this list is expected
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* `gtsam::traits::group_tag` -- Everything in this list is expected, plus the functions defined under **Groups** below.
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* `gtsam::traits::lie_group_tag` -- Everything in this list is expected, plus the functions defined under **Groups**, and **Lie Groups** below.
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* `gtsam::traits::vector_space_tag` -- Everything in this list is expected, plus the functions defined under **Groups**, and **Lie Groups** below.
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* valid expressions:
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* `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.
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* `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.
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* `v = traits<T>::Local(p,q, Hp, Hq)`.
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* `v = traits<T>::Local(p,q, Hp, Hq)`.
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* `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.
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* `p = traits<T>::Retract(p,v, Hp, Hv)`.
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In the functions above, the `H` arguments stand for optional Jacobians. When provided, it is assumed
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that the function will return the derivatives of the chart (and inverse) with respect to its arguments.
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* invariants
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* `Retract(p, Local(p,q)) == q`
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* `Local(p, Retract(p, v)) == v`
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* `Retract(p, Local(p,q)) == q`
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* `Local(p, Retract(p, v)) == v`
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For many differential manifolds, an obvious mapping is the `exponential map`,
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which associates straight lines in the tangent space with geodesics on the manifold
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@ -61,17 +61,17 @@ A [group](http://en.wikipedia.org/wiki/Group_(mathematics)) should be well known
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* `q = traits<M>::Inverse(p)`, where *p* and*q* are elements of the manifold.
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* `r = traits<M>::Between(p,q)`, where *p*, *q*, and *r* are elements of the manifold.
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* static members:
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* `traits<M>::Identity`, a static const member that represents the group's identity element.
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* `traits<M>::Identity`, a static const member that represents the group's identity element.
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* invariants:
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* `Compose(p,Inverse(p)) == Identity`
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* `Compose(p,Between(p,q)) == q`
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* `Between(p,q) == Compose(Inverse(p),q)`
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The `gtsam::group::traits` namespace defines the following:
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* values:
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* `traits<M>::Identity` -- The identity element for this group stored as a static const.
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* `traits<M>::group_flavor` -- the flavor of this group's `compose()` operator, either:
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* `gtsam::traits::group_multiplicative_tag` for multiplicative operator syntax ,or
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* `gtsam::traits::group_additive_tag` for additive operator syntax.
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* `traits<M>::Identity` -- The identity element for this group stored as a static const.
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* `traits<M>::group_flavor` -- the flavor of this group's `compose()` operator, either:
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* `gtsam::traits::group_multiplicative_tag` for multiplicative operator syntax ,or
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* `gtsam::traits::group_additive_tag` for additive operator syntax.
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We do *not* at this time support more than one composition operator per type. Although mathematically possible, it is hardly ever needed, and the machinery to support it would be burdensome and counter-intuitive.
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@ -125,12 +125,14 @@ In addition, a Lie group has a Lie algebra, which affords two extra valid expres
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Note that in the Lie group case, the usual valid expressions for Retract and Local can be generated automatically, e.g.
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```
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T Retract(p,v,Hp,Hv) {
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T q = Exp(v,Hqv);
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T r = Compose(p,q,Hrp,Hrq);
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Hv = Hrq * Hqv; // chain rule
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return r;
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}
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```
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Lie Group Action
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----------------
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@ -212,10 +214,10 @@ An example of implementing a Manifold type is here:
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#!c++
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// GTSAM type
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class Rot2 {
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typedef Vector2 TangentVector; // internal typedef, not required
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typedef Vector2 TangentVector; // internal typedef, not required
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class Chart : gtsam::Chart<Rot2,Chart>{
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static TangentVector local(const Rot2& R1, const Rot2& R2);
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static Rot2 retract(const Rot2& R, const TangentVector& v);
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static TangentVector local(const Rot2& R1, const Rot2& R2);
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static Rot2 retract(const Rot2& R, const TangentVector& v);
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}
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Rot2 operator*(const Rot2&) const;
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Rot2 transpose() const;
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@ -359,16 +361,16 @@ Providing the Vector space concept is easier:
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Point2 operator-() const;
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// Still needs to be defined, unless Point2 *is* Vector2
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class Chart {
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static Vector2 local(const Point2& p, const Point2& q) const;
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static Rot2 retract(const Point2& p, const Point2& v) const;
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static Vector2 local(const Point2& p, const Point2& q) const;
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static Rot2 retract(const Point2& p, const Point2& v) const;
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}
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}
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```
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The following macro, called inside the gtsam namespace,
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DEFINE_VECTOR_SPACE_TRAITS(Point2)
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DEFINE_VECTOR_SPACE_TRAITS(Point2)
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should automatically define
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```
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