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Trying to update the concepts definition to reflect reality

release/4.3a0
Paul Furgale 2014-12-11 12:41:16 +01:00
parent 376dec5103
commit 24e1334e5a
1 changed files with 5 additions and 5 deletions
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10
GTSAM-Concepts.md
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@ -20,14 +20,13 @@ To optimize over continuous types, we assume they are manifolds. This is central
In GTSAM we assume that a manifold type can yield such a *Chart* at any point, and we require that a functor `defaultChart` is available that, when called for any point on the manifold, returns a Chart type. Hence, the functor itself can be seen as an *Atlas*.
In detail, we ask the following are defined for a MANIFOLD type:
In detail, we ask the following are defined in the namespace `gtsam::manifold::traits` for each MANIFOLD type:
* values:
* `dimension`, an int 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.
* functors:
* `defaultChart`, returns the default chart at a point p
* types:
* `TangentVector`, type that lives in tangent space. This will almost always be an `Eigen::Matrix<double,n,1>`.
* `DefaultChart`, the default chart at a point p
* valid expressions:
* `size_t dim = getDimension(p);` free function should be defined in case the dimension is not known at compile time.
@ -39,6 +38,7 @@ A given chart is implemented using a small class that defines the chart itself (
* types:
* `ManifoldType`, a pointer back to the type
* `Jacobian`, a typedef for `gtsam::OptionalJacobian<Dimension, Dimension>` where the dimension is taken from `gtsam::maifold::traits::dimension`.
* valid expressions:
* `v = Chart::Local(p,q,Hp,Hq)`, the chart, from manifold to tangent space, think of it as *q (-) p*
* `p = Chart::Retract(p,v,Hp,Hv)`, the inverse chart, from tangent space to manifold, think of it as *p (+) v*
@ -50,8 +50,8 @@ For many differential manifolds, an obvious mapping is the `exponential map`,
which 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:
* Sometimes, most notably for *SO(3)* and *SE(3)*, the exponential map is unnecessarily expensive for use in optimization. Hence, the `defaultChart` functor returns a chart that is much cheaper to evaluate.
* While vector spaces (see below) are in principle also manifolds, it is overkill to think about charts etc. Really, we should simply think about vector addition and subtraction. Hence, while a `defaultChart` functor is defined by default for every vector space, GTSAM will never call it.
* Sometimes, most notably for *SO(3)* and *SE(3)*, the exponential map is unnecessarily expensive for use in optimization. Hence, the `DefaultChart` type refers to a chart that is much cheaper to evaluate.
* While vector spaces (see below) are in principle also manifolds, it is overkill to think about charts etc. Really, we should simply think about vector addition and subtraction. Hence, while a `DefaultChart` is defined by default for every vector space, GTSAM will never invoke it.
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