MRPT  1.9.9
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mrpt::poses::Lie::SO< 2 > Struct Template Reference

Detailed Description

template<>
struct mrpt::poses::Lie::SO< 2 >

Traits for SO(2), rotations in R^2 space.

Definition at line 88 of file SO.h.

#include <mrpt/poses/Lie/SO.h>

Public Types

using tangent_vector = mrpt::math::CVectorFixedDouble< DOFs >
 
using type = double
 
using tang2mat_jacob = mrpt::math::CMatrixFixed< double, 1, 1 >
 Type for Jacobian: tangent space to SO(n) matrix. More...
 
using mat2tang_jacob = mrpt::math::CMatrixFixed< double, 1, 1 >
 Type for Jacobian: SO(n) matrix to tangent space. More...
 

Static Public Member Functions

static type exp (const tangent_vector &x)
 SO(2) exponential map $ x \rightarrow \exp(x^\wedge) $. More...
 
static tangent_vector log (const type &R)
 SO(2) logarithm map $ \mathbf{R} \rightarrow \log(\mathbf{R}^\vee)$. More...
 
static tang2mat_jacob jacob_dexpe_de (const tangent_vector &x)
 Jacobian for exp(), the identity matrix [ 1 ] More...
 
static mat2tang_jacob jacob_dlogv_dv (const type &R)
 Jacobian for log(), the identity matrix [ 1 ] More...
 

Static Public Attributes

static constexpr size_t DOFs = 1
 

Member Typedef Documentation

◆ mat2tang_jacob

Type for Jacobian: SO(n) matrix to tangent space.

Definition at line 97 of file SO.h.

◆ tang2mat_jacob

Type for Jacobian: tangent space to SO(n) matrix.

Definition at line 95 of file SO.h.

◆ tangent_vector

Definition at line 91 of file SO.h.

◆ type

using mrpt::poses::Lie::SO< 2 >::type = double

Definition at line 92 of file SO.h.

Member Function Documentation

◆ exp()

static type mrpt::poses::Lie::SO< 2 >::exp ( const tangent_vector x)
static

SO(2) exponential map $ x \rightarrow \exp(x^\wedge) $.

  • Input: 1-len vector in Lie algebra so(3)
  • Output: angle for the rotation (radians)

◆ jacob_dexpe_de()

static tang2mat_jacob mrpt::poses::Lie::SO< 2 >::jacob_dexpe_de ( const tangent_vector x)
static

Jacobian for exp(), the identity matrix [ 1 ]

◆ jacob_dlogv_dv()

static mat2tang_jacob mrpt::poses::Lie::SO< 2 >::jacob_dlogv_dv ( const type R)
static

Jacobian for log(), the identity matrix [ 1 ]

◆ log()

static tangent_vector mrpt::poses::Lie::SO< 2 >::log ( const type R)
static

SO(2) logarithm map $ \mathbf{R} \rightarrow \log(\mathbf{R}^\vee)$.

  • Input: rotation angle [radians]
  • Output: 1-len vector in Lie algebra so(2) (with the same value)

Member Data Documentation

◆ DOFs

constexpr size_t mrpt::poses::Lie::SO< 2 >::DOFs = 1
static

Definition at line 90 of file SO.h.




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