se::math Namespace Reference

Functions
template<typename T >
constexpr bool	is_power_of_two (const T x)
constexpr int	log2_const (int n)
static unsigned	power_two_up (const float x)
template<typename T >
T	fracf (const T &v)
template<typename T >
T	floorf (const T &v)
template<typename T >
T	fabs (const T &v)
template<typename Scalar >
constexpr Scalar	sq (Scalar a)
template<typename Scalar >
constexpr Scalar	cu (Scalar a)
template<typename Scalar >
bool	in (const Scalar v, const Scalar a, const Scalar b)
static Eigen::Vector3f	plane_normal (const Eigen::Vector3f &p1, const Eigen::Vector3f &p2, const Eigen::Vector3f &p3)
	Compute the normal vector of a plane defined by 3 points.
static Eigen::Matrix3f	hat (const Eigen::Vector3f &omega)
	hat-operator
static Eigen::Matrix3f	exp_and_theta (const Eigen::Vector3f &omega, float &theta)
static Eigen::Matrix4f	exp (const Eigen::Matrix< float, 6, 1 > &a)
	Group exponential.

Variables
const Eigen::Vector3f	g_invalid_normal = Eigen::Vector3f::Zero()
	The value used for a normal vector that can't be computed.

Function Documentation

is_power_of_two()

template<typename T >

constexpr bool se::math::is_power_of_two ( const T  x )

constexpr

log2_const()

constexpr int se::math::log2_const ( int  n )

constexpr

power_two_up()

static unsigned se::math::power_two_up ( const float  x )

inlinestatic

fracf()

template<typename T >

T se::math::fracf

(

const T &

v

)

floorf()

template<typename T >

T se::math::floorf

(

const T &

v

)

fabs()

template<typename T >

T se::math::fabs

(

const T &

v

)

sq()

template<typename Scalar >

constexpr Scalar se::math::sq ( Scalar  a )

constexpr

cu()

template<typename Scalar >

constexpr Scalar se::math::cu ( Scalar  a )

constexpr

in()

template<typename Scalar >

bool se::math::in	(	const Scalar	v,
		const Scalar	a,
		const Scalar	b
	)

plane_normal()

static Eigen::Vector3f se::math::plane_normal ( const Eigen::Vector3f &  p1, const Eigen::Vector3f &  p2, const Eigen::Vector3f &  p3  )

inlinestatic

Compute the normal vector of a plane defined by 3 points.

The direction of the normal depends on the order of the points.

hat()

static Eigen::Matrix3f se::math::hat ( const Eigen::Vector3f &  omega )

inlinestatic

hat-operator

It takes in the 3-vector representation omega (= rotation vector) and returns the corresponding matrix representation of Lie algebra element.

Formally, the hat()-operator of SO(3) is defined as

hat(.): R^3 -> R^{3x3}, hat(omega) = sum_i omega_i * G_i (for i=0,1,2)

with G_i being the ith infinitesimal generator of SO(3).

The corresponding inverse is the vee()-operator, see below.

Parameters

[in]

omega

rotation vector

Returns

Corresponding matrix representation of Lie algebra element.

exp_and_theta()

static Eigen::Matrix3f se::math::exp_and_theta ( const Eigen::Vector3f &  omega, float &  theta  )

inlinestatic

exp()

static Eigen::Matrix4f se::math::exp ( const Eigen::Matrix< float, 6, 1 > &  a )

inlinestatic

Group exponential.

This functions takes in an element of tangent space (= twist a) and returns the corresponding element of the group SE(3).

The first three components of a represent the translational part upsilon in the tangent space of SE(3), while the last three components of a represents the rotation vector omega. To be more specific, this function computes expmat(hat(a)) with expmat(.) being the matrix exponential and hat(.) the hat-operator of SE(3), see below.

Variable Documentation

g_invalid_normal

const Eigen::Vector3f se::math::g_invalid_normal = Eigen::Vector3f::Zero()

inline

The value used for a normal vector that can't be computed.