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3.2.1
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3.2.1
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Concept check class for Manifold types Requires a mapping between a linear tangent space and the underlying manifold, of which Lie is a specialization.
The necessary functions to implement for Manifold are defined below with additional details as to the interface. The concept checking function in class Manifold will check whether or not the function exists and throw compile-time errors.
A manifold defines a space in which there is a notion of a linear tangent space that can be centered around a given point on the manifold. These nonlinear spaces may have such properties as wrapping around (as is the case with rotations), which might make linear operations on parameters not return a viable element of the manifold.
We perform optimization by computing a linear delta in the tangent space of the current estimate, and then apply this change using a retraction operation, which maps the change in tangent space back to the manifold itself.
There may be multiple possible retractions for a given manifold, which can be chosen between depending on the computational complexity. The important criteria for the creation for the retract and localCoordinates functions is that they be inverse operations.
Returns dimensionality of the tangent space, which may be smaller than the number of nonlinear parameters. size_t dim() const;
Returns a new T that is a result of updating *this with the delta v after pulling the updated value back to the manifold T. T retract(const Vector& v) const;
Returns the linear coordinates of lp in the tangent space centered around *this. Vector localCoordinates(const T& lp) const;
By convention, we use capital letters to designate a static function
1.8.6 
