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manhattan example

release/4.3a0
dellaert 2014-12-03 21:48:17 +01:00
parent b5f64fe1b4
commit dae420e38f
1 changed files with 9 additions and 9 deletions
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GTSAM-Concepts.md
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@ -42,7 +42,7 @@ A given chart is implemented using a small class that defines the chart itself (
* `v = chart.local(q)`, the chart, from manifold to tangent space, think of it as *p (-) q* * `v = chart.local(q)`, the chart, from manifold to tangent space, think of it as *p (-) q*
* `p = chart.retract(v)`, the inverse chart, from tangent space to manifold, think of it as *p (+) v* * `p = chart.retract(v)`, the inverse chart, from tangent space to manifold, think of it as *p (+) v*
For many differential manifolds, an obvious mapping is the `exponential map`, which associates staright 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: 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. * 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. * 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.
@ -125,21 +125,21 @@ The conventions for `gtsam::traits` are as follows:
typedef const int value_type; // const ? typedef const int value_type; // const ?
} }
* Functors: `gtsam::traits::someFunctor<T>::type`, i.e., they are mixedCase starting with a lowercase letter and define a functor (i.e., no *type*). The functor itself should define a `result_type`. Example * Functors: `gtsam::traits::someFunctor<T>::type`, i.e., they are mixedCase starting with a lowercase letter and define a functor (i.e., no *type*). The functor itself should define a `result_type`. A contrived example
struct Point2::retract { struct Point2::manhattan {
typedef Point2 result_type; typedef double result_type;
Point2 p_; Point2 p_;
retract(const Point2& p) : p_(p) {} manhattan(const Point2& p) : p_(p) {}
Point2 operator()(const Vector2& v) { Point2 operator()(const Point2& q) {
return Point2(p_.x()+v[0], p_.y()+v[1]); return abs(p_.x()-q.x()) + abs(p_.y()-q.x());
} }
} }
template<> template<>
gtsam::traits::retract<Point2> : Point2::retract {} gtsam::traits::manhattan<Point2> : Point2::manhattan {}
By *inherting* the trait from the functor, we can just use the [currying](http://en.wikipedia.org/wiki/Currying) style `gtsam::traits::retract<Point2>(p)(v)`. Note that, although technically a functor is a type, in spirit it is a free function and hence starts with a lowercase letter. By *inherting* the trait from the functor, we can just use the [currying](http://en.wikipedia.org/wiki/Currying) style `gtsam::traits::manhattan<Point2>℗(q)`. Note that, although technically a functor is a type, in spirit it is a free function and hence starts with a lowercase letter.
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