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More manifold stuff

release/4.3a0
dellaert 2014-12-03 17:53:56 +01:00
parent c05f43ab51
commit 079d1b122d
1 changed files with 6 additions and 4 deletions
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GTSAM-Concepts.md
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@ -23,11 +23,13 @@ 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 the vector space. [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 the vector space.
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 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.
* values: `dimension` * values: `dimension`
* functors `defaultChart` * types: `Vector`, type that lives in tangent space
* types: `DefaultChart` is the *type* of chart returned by the functor `defaultChart` *
* `DefaultChart` is the *type* of the chart returned by the functor `defaultChart`
* functor `defaultChart`, returns a `DefaultChart`
* invariants: `defaultChart::result_type == DefaultChart::type` * invariants: `defaultChart::result_type == DefaultChart::type`
Anything else? Anything else?
@ -35,7 +37,7 @@ Anything else?
Chart Chart
----- -----
* types: `Manifold`, `Vector` * types: `Manifold`, a pointer back to the type
* values: `retract`, `local` * values: `retract`, `local`
Are these values? They are just methods. Anything else? Are these values? They are just methods. Anything else?