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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 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: * 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. * `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: * types:
* `TangentVector`, type that lives in tangent space. This will almost always be an `Eigen::Matrix<double,n,1>`. * `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: * valid expressions:
* `size_t dim = getDimension(p);` free function should be defined in case the dimension is not known at compile time. * `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: * types:
* `ManifoldType`, a pointer back to the type * `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: * valid expressions:
* `v = Chart::Local(p,q,Hp,Hq)`, the chart, from manifold to tangent space, think of it as *q (-) p* * `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* * `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 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: (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. * 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` functor is defined by default for every vector space, GTSAM will never call it. * 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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