Namespaces
namespace	helpers
namespace	optimization
namespace	serialization

Classes
struct	bezier_curve
class	constant_curve
	Represents a constant_curve curve, always returning the same value and a null derivative. More...
struct	cubic_hermite_spline
struct	curve_abc
	Represents a curve of dimension Dim. If value of parameter Safe is false, no verification is made on the evaluation of the curve. More...
struct	curve_constraints
struct	exact_cubic
struct	piecewise_curve
class	polynomial
	Represents a polynomial of an arbitrary order defined on the interval $[t_{min}, t_{max}]$ . It follows the equation : $x(t) = a + b(t - t_{min}) + ... + d(t - t_{min})^N$ where N is the order and $t \in [t_{min}, t_{max}]$ . More...
class	SE3Curve
	Composition of a curve of any type of dimension 3 and a curve representing an rotation (in current implementation, only SO3Linear can be used for the rotation part) The output is a vector of size 7 (pos_x,pos_y,pos_z,quat_x,quat_y,quat_z,quat_w) The output of the derivative of any order is a vector of size 6 (linear_x,linear_y,linear_z,angular_x,angular_y,angular_z). More...
class	sinusoidal
	Represents a sinusoidal curve, evaluating the following equation: p0 + amplitude * (sin(2pi/T + phi). More...
class	SO3Linear
	Represents a linear interpolation in SO3, using the slerp method provided by Eigen::Quaternion. More...
struct	SO3Smooth
struct	Bern
struct	linear_variable
struct	quadratic_variable

Typedefs
typedef Eigen::Matrix< double, 1, 1 >	point1_t
typedef Eigen::Vector3d	point3_t
typedef Eigen::Matrix< double, 6, 1 >	point6_t
typedef Eigen::VectorXd	pointX_t
typedef Eigen::Matrix< double, 3, 3 >	matrix3_t
typedef Eigen::Matrix< double, 4, 4 >	matrix4_t
typedef Eigen::Quaternion< double >	quaternion_t
typedef Eigen::Transform< double, 3, Eigen::Affine >	transform_t
typedef std::vector< point1_t, Eigen::aligned_allocator< point1_t > >	t_point1_t
typedef std::vector< point3_t, Eigen::aligned_allocator< point3_t > >	t_point3_t
typedef std::vector< pointX_t, Eigen::aligned_allocator< pointX_t > >	t_pointX_t
typedef Eigen::Ref< const matrix3_t >	matrix3_t_cst_ref
typedef curve_abc< double, double, true, pointX_t, pointX_t >	curve_abc_t
typedef curve_abc< double, double, true, point3_t, point3_t >	curve_3_t
typedef curve_3_t	curve_translation_t
typedef curve_abc< double, double, true, matrix3_t, point3_t >	curve_rotation_t
typedef curve_abc< double, double, true, transform_t, point6_t >	curve_SE3_t
typedef std::shared_ptr< curve_abc_t >	curve_ptr_t
typedef std::shared_ptr< curve_3_t >	curve3_ptr_t
typedef std::shared_ptr< curve_rotation_t >	curve_rotation_ptr_t
typedef std::shared_ptr< curve_translation_t >	curve_translation_ptr_t
typedef std::shared_ptr< curve_SE3_t >	curve_SE3_ptr_t
typedef polynomial< double, double, true, pointX_t, t_pointX_t >	polynomial_t
typedef exact_cubic< double, double, true, pointX_t, t_pointX_t, polynomial_t >	exact_cubic_t
typedef bezier_curve< double, double, true, pointX_t >	bezier_t
typedef linear_variable< double, true >	linear_variable_t
typedef bezier_curve< double, double, true, linear_variable_t >	bezier_linear_variable_t
typedef constant_curve< double, double, true, pointX_t, pointX_t >	constant_t
typedef cubic_hermite_spline< double, double, true, pointX_t >	cubic_hermite_spline_t
typedef piecewise_curve< double, double, true, pointX_t, pointX_t, curve_abc_t >	piecewise_t
typedef sinusoidal< double, double, true, pointX_t >	sinusoidal_t
typedef polynomial< double, double, true, point3_t, t_point3_t >	polynomial3_t
typedef polynomial< double, double, true, point1_t, t_point1_t >	polynomial1_t
typedef exact_cubic< double, double, true, point3_t, t_point3_t, polynomial_t >	exact_cubic3_t
typedef bezier_curve< double, double, true, point3_t >	bezier3_t
typedef constant_curve< double, double, true, point3_t, point3_t >	constant3_t
typedef cubic_hermite_spline< double, double, true, point3_t >	cubic_hermite_spline3_t
typedef piecewise_curve< double, double, true, point3_t, point3_t, curve_3_t >	piecewise3_t
typedef SO3Smooth< double, double, true >	SO3Smooth_t
typedef SO3Linear< double, double, true >	SO3Linear_t
typedef SE3Curve< double, double, true >	SE3Curve_t
typedef piecewise_curve< double, double, true, transform_t, point6_t, curve_SE3_t >	piecewise_SE3_t
typedef double	real
typedef std::vector< real >	t_time_t
typedef Eigen::VectorXd	time_waypoints_t
typedef Eigen::Matrix< double, Eigen::Dynamic, 1, 0, Eigen::Dynamic, 1 >	ret_pointX_t
typedef std::pair< pointX_t, pointX_t >	pair_pointX_tangent_t
typedef Eigen::MatrixXd	pointX_list_t
typedef std::vector< pair_pointX_tangent_t, Eigen::aligned_allocator< pair_pointX_tangent_t > >	t_pair_pointX_tangent_t
typedef ndcurves::curve_constraints< pointX_t >	curve_constraints_t
typedef ndcurves::curve_constraints< point3_t >	curve_constraints3_t
typedef std::pair< real, pointX_t >	waypoint_t
typedef std::vector< waypoint_t >	t_waypoint_t
typedef Eigen::Matrix< real, Eigen::Dynamic, Eigen::Dynamic >	point_listX_t
typedef Eigen::Matrix< real, 3, Eigen::Dynamic >	point_list3_t
typedef Eigen::Matrix< real, 6, Eigen::Dynamic >	point_list6_t
typedef polynomial_t::coeff_t	coeff_t
typedef ndcurves::Bern< double >	bernstein_t

Functions
template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>
ndcurves::bezier_curve curve_abc	waypoints () const
const point_t	waypointAtIndex (const std::size_t index) const
point_t	evalDeCasteljau (const Numeric t) const
	Evaluate the curve value at time t using deCasteljau algorithm. The algorithm will compute the centroids of parameters of consecutive control points of bezier curve, and perform it iteratively until getting one point in the list which will be the evaluation of bezier curve at time .
t_point_t	deCasteljauReduction (const Numeric t) const
t_point_t	deCasteljauReduction (const t_point_t &pts, const Numeric u) const
	Compute de Casteljau's reduction of the given list of points at time t. For the list of N points, compute a new list of points of size N-1 : with t the time when to evaluate bezier curve. \ The new list contains centroid of parameters of consecutive points in the list.
std::pair< bezier_curve_t, bezier_curve_t >	split (const Numeric t) const
	Split the bezier curve in 2 at time t.
piecewise_curve_t	split (const vector_x_t &times) const
	Split the bezier curve in several curves, all accessible within a piecewise_curve_t.
bezier_curve_t	extract (const Numeric t1, const Numeric t2)
	Extract a bezier curve defined between from the actual bezier curve defined between $[T_{min},T_{max}]$ with $T_{min} \leq t_1 \leq t_2 \leq T_{max}$ .
bezier_curve_t	cross (const bezier_curve_t &g) const
	Compute the cross product of the current bezier curve by another bezier curve. The cross product p1Xp2 of 2 bezier curves p1 and p2 is defined such that forall t, p1Xp2(t) = p1(t) X p2(t), with X designing the cross product. This method of course only makes sense for dimension 3 curves. It assumes that a method point_t cross(const point_t&, const point_t&) has been defined.
bezier_curve_t	cross (const bezier_curve_t::point_t &point) const
	Compute the cross product of the current bezier b by a point point. The cross product pXpoint of is defined such that forall t, bXpoint(t) = b(t) X point, with X designing the cross product. This method of course only makes sense for dimension 3 polynomials.
bezier_curve_t &	operator+= (const bezier_curve_t &other)
bezier_curve_t &	operator-= (const bezier_curve_t &other)
bezier_curve_t &	operator+= (const bezier_curve_t::point_t &point)
bezier_curve_t &	operator-= (const bezier_curve_t::point_t &point)
bezier_curve_t &	operator/= (const double d)
bezier_curve_t &	operator*= (const double d)
virtual std::size_t	dim () const
	Get dimension of curve.
virtual time_t	min () const
	Get the minimum time for which the curve is defined.
virtual time_t	max () const
	Get the maximum time for which the curve is defined.
virtual std::size_t	degree () const
	Get the degree of the curve.
template<class Archive>
void	serialize (Archive &ar, const unsigned int version)
Eigen::Vector3d	cross (const Eigen::VectorXd &a, const Eigen::VectorXd &b)
Eigen::Vector3d	cross (const Eigen::Vector3d &a, const Eigen::Vector3d &b)
Eigen::Vector3f	cross (const Eigen::Vector3f &a, const Eigen::Vector3f &b)
template<typename N, bool S>
linear_variable< N, S >	cross (const linear_variable< N, S > &a, const linear_variable< N, S > &b)
template<typename T>
bool	isApprox (const T a, const T b, const T eps=1e-6)
template<typename Polynomial>
Polynomial	polynomial_from_curve (const typename Polynomial::curve_abc_t &curve)
	Converts a cubic hermite spline or a bezier curve to a polynomial.
template<typename Bezier>
Bezier	bezier_from_curve (const typename Bezier::curve_abc_t &curve)
	Converts a cubic hermite spline or polynomial of order 3 or less to a cubic bezier curve.
template<typename Hermite>
Hermite	hermite_from_curve (const typename Hermite::curve_abc_t &curve)
	Converts a polynomial of order 3 or less/cubic bezier curve to a cubic hermite spline.
template<typename N, bool S>
linear_variable< N, S >	operator+ (const linear_variable< N, S > &w1, const linear_variable< N, S > &w2)
template<typename N, bool S>
linear_variable< N, S >	operator- (const linear_variable< N, S > &w1, const linear_variable< N, S > &w2)
template<typename N, bool S>
linear_variable< N, S >	operator- (const linear_variable< N, S > &w1)
template<typename N, bool S>
linear_variable< N, S >	operator* (const double k, const linear_variable< N, S > &w)
template<typename N, bool S>
linear_variable< N, S >	operator* (const linear_variable< N, S > &w, const double k)
template<typename N, bool S>
linear_variable< N, S >	operator/ (const linear_variable< N, S > &w, const double k)
template<typename BezierFixed, typename BezierLinear, typename X>
BezierFixed	evaluateLinear (const BezierLinear &bIn, const X x)
template<typename N, bool S>
std::ostream &	operator<< (std::ostream &os, const linear_variable< N, S > &l)
template<typename _Matrix_Type_>
void	PseudoInverse (_Matrix_Type_ &pinvmat)
	An inverse kinematics architecture enforcing an arbitrary number of strict priority levels (Reference : Boulic et Al. 2003).
template<typename Matrix3, typename Point>
Matrix3	skew (const Point &x)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator+ (const polynomial< T, N, S, P, TP > &p1, const polynomial< T, N, S, P, TP > &p2)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator+ (const polynomial< T, N, S, P, TP > &p1, const typename polynomial< T, N, S, P, TP >::point_t &point)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator+ (const typename polynomial< T, N, S, P, TP >::point_t &point, const polynomial< T, N, S, P, TP > &p1)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator- (const polynomial< T, N, S, P, TP > &p1, const typename polynomial< T, N, S, P, TP >::point_t &point)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator- (const typename polynomial< T, N, S, P, TP >::point_t &point, const polynomial< T, N, S, P, TP > &p1)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator- (const polynomial< T, N, S, P, TP > &p1)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator- (const polynomial< T, N, S, P, TP > &p1, const polynomial< T, N, S, P, TP > &p2)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator/ (const polynomial< T, N, S, P, TP > &p1, const double k)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator* (const polynomial< T, N, S, P, TP > &p1, const double k)
template<typename T, typename N, bool S, typename P, typename TP>
polynomial< T, N, S, P, TP >	operator* (const double k, const polynomial< T, N, S, P, TP > &p1)
template<typename PointList, typename T_Point>
T_Point	vectorFromEigenArray (const PointList &array)
template<typename PointList, typename T_Point>
T_Point	vectorFromEigenVector (const PointList &vector)
template<typename T_point, typename PointList>
PointList	vectorToEigenArray (const T_point &vect)
template<typename N>
Eigen::Matrix< N, Eigen::Dynamic, Eigen::Dynamic >	to_diagonal (const Eigen::Ref< const Eigen::Matrix< N, Eigen::Dynamic, 1 > > vec)
	Transforms a vector into a diagonal matrix.
template<typename N>
quadratic_variable< N >	operator* (const linear_variable< N > &w1, const linear_variable< N > &w2)
template<typename N>
quadratic_variable< N >	operator+ (const quadratic_variable< N > &w1, const quadratic_variable< N > &w2)
template<typename N>
quadratic_variable< N >	operator- (const quadratic_variable< N > &w1, const quadratic_variable< N > &w2)
template<typename N>
quadratic_variable< N >	operator* (const double k, const quadratic_variable< N > &w)
template<typename N>
quadratic_variable< N >	operator* (const quadratic_variable< N > &w, const double k)
template<typename N>
quadratic_variable< N >	operator/ (const quadratic_variable< N > &w, const double k)

Variables
std::size_t	dim_
	Dim of curve.
time_t	T_min_
time_t	T_max_
time_t	mult_T_
std::size_t	size_
std::size_t	degree_
std::vector< Bern< Numeric > >	bernstein_
t_point_t	control_points_

Detailed Description

This file define a method register_types that register all the curves class of this package for a boost::Archive This is used to serialize pointer of the abstract class curve_abc

Typedef Documentation

◆ bernstein_t

typedef ndcurves::Bern<double> ndcurves::bernstein_t

◆ bezier3_t

typedef bezier_curve<double, double, true, point3_t> ndcurves::bezier3_t

◆ bezier_linear_variable_t

typedef bezier_curve<double, double, true, linear_variable_t> ndcurves::bezier_linear_variable_t

◆ bezier_t

typedef bezier_curve<double, double, true, pointX_t> ndcurves::bezier_t

◆ coeff_t

typedef polynomial_t::coeff_t ndcurves::coeff_t

◆ constant3_t

typedef constant_curve<double, double, true, point3_t, point3_t> ndcurves::constant3_t

◆ constant_t

typedef constant_curve<double, double, true, pointX_t, pointX_t> ndcurves::constant_t

◆ cubic_hermite_spline3_t

typedef cubic_hermite_spline<double, double, true, point3_t> ndcurves::cubic_hermite_spline3_t

◆ cubic_hermite_spline_t

typedef cubic_hermite_spline<double, double, true, pointX_t> ndcurves::cubic_hermite_spline_t

◆ curve3_ptr_t

typedef std::shared_ptr<curve_3_t> ndcurves::curve3_ptr_t

◆ curve_3_t

typedef curve_abc<double, double, true, point3_t, point3_t> ndcurves::curve_3_t

◆ curve_abc_t

typedef curve_abc<double, double, true, pointX_t, pointX_t> ndcurves::curve_abc_t

◆ curve_constraints3_t

typedef ndcurves::curve_constraints<point3_t> ndcurves::curve_constraints3_t

◆ curve_constraints_t

typedef ndcurves::curve_constraints<pointX_t> ndcurves::curve_constraints_t

◆ curve_ptr_t

typedef std::shared_ptr<curve_abc_t> ndcurves::curve_ptr_t

◆ curve_rotation_ptr_t

typedef std::shared_ptr<curve_rotation_t> ndcurves::curve_rotation_ptr_t

◆ curve_rotation_t

typedef curve_abc<double, double, true, matrix3_t, point3_t> ndcurves::curve_rotation_t

◆ curve_SE3_ptr_t

typedef std::shared_ptr<curve_SE3_t> ndcurves::curve_SE3_ptr_t

◆ curve_SE3_t

typedef curve_abc<double, double, true, transform_t, point6_t> ndcurves::curve_SE3_t

◆ curve_translation_ptr_t

typedef std::shared_ptr<curve_translation_t> ndcurves::curve_translation_ptr_t

◆ curve_translation_t

typedef curve_3_t ndcurves::curve_translation_t

◆ exact_cubic3_t

typedef exact_cubic<double, double, true, point3_t, t_point3_t, polynomial_t> ndcurves::exact_cubic3_t

◆ exact_cubic_t

typedef exact_cubic<double, double, true, pointX_t, t_pointX_t, polynomial_t> ndcurves::exact_cubic_t

◆ linear_variable_t

typedef linear_variable<double, true> ndcurves::linear_variable_t

◆ matrix3_t

typedef Eigen::Matrix<double, 3, 3> ndcurves::matrix3_t

◆ matrix3_t_cst_ref

typedef Eigen::Ref<const matrix3_t> ndcurves::matrix3_t_cst_ref

◆ matrix4_t

typedef Eigen::Matrix<double, 4, 4> ndcurves::matrix4_t

◆ pair_pointX_tangent_t

typedef std::pair<pointX_t, pointX_t> ndcurves::pair_pointX_tangent_t

◆ piecewise3_t

typedef piecewise_curve<double, double, true, point3_t, point3_t, curve_3_t> ndcurves::piecewise3_t

◆ piecewise_SE3_t

typedef piecewise_curve<double, double, true, transform_t, point6_t, curve_SE3_t> ndcurves::piecewise_SE3_t

◆ piecewise_t

typedef piecewise_curve<double, double, true, pointX_t, pointX_t, curve_abc_t> ndcurves::piecewise_t

◆ point1_t

typedef Eigen::Matrix<double, 1, 1> ndcurves::point1_t

◆ point3_t

typedef Eigen::Vector3d ndcurves::point3_t

◆ point6_t

typedef Eigen::Matrix<double, 6, 1> ndcurves::point6_t

◆ point_list3_t

typedef Eigen::Matrix<real, 3, Eigen::Dynamic> ndcurves::point_list3_t

◆ point_list6_t

typedef Eigen::Matrix<real, 6, Eigen::Dynamic> ndcurves::point_list6_t

◆ point_listX_t

typedef Eigen::Matrix<real, Eigen::Dynamic, Eigen::Dynamic> ndcurves::point_listX_t

◆ pointX_list_t

typedef Eigen::MatrixXd ndcurves::pointX_list_t

◆ pointX_t

typedef Eigen::VectorXd ndcurves::pointX_t

◆ polynomial1_t

typedef polynomial<double, double, true, point1_t, t_point1_t> ndcurves::polynomial1_t

◆ polynomial3_t

typedef polynomial<double, double, true, point3_t, t_point3_t> ndcurves::polynomial3_t

◆ polynomial_t

typedef polynomial<double, double, true, pointX_t, t_pointX_t> ndcurves::polynomial_t

◆ quaternion_t

typedef Eigen::Quaternion<double> ndcurves::quaternion_t

◆ real

typedef double ndcurves::real

◆ ret_pointX_t

typedef Eigen::Matrix<double, Eigen::Dynamic, 1, 0, Eigen::Dynamic, 1> ndcurves::ret_pointX_t

◆ SE3Curve_t

typedef SE3Curve<double, double, true> ndcurves::SE3Curve_t

◆ sinusoidal_t

typedef sinusoidal<double, double, true, pointX_t> ndcurves::sinusoidal_t

◆ SO3Linear_t

typedef SO3Linear<double, double, true> ndcurves::SO3Linear_t

◆ SO3Smooth_t

typedef SO3Smooth<double, double, true> ndcurves::SO3Smooth_t

◆ t_pair_pointX_tangent_t

typedef std::vector<pair_pointX_tangent_t, Eigen::aligned_allocator<pair_pointX_tangent_t> > ndcurves::t_pair_pointX_tangent_t

◆ t_point1_t

typedef std::vector<point1_t, Eigen::aligned_allocator<point1_t> > ndcurves::t_point1_t

◆ t_point3_t

typedef std::vector<point3_t, Eigen::aligned_allocator<point3_t> > ndcurves::t_point3_t

◆ t_pointX_t

typedef std::vector<pointX_t, Eigen::aligned_allocator<pointX_t> > ndcurves::t_pointX_t

◆ t_time_t

typedef std::vector<real> ndcurves::t_time_t

◆ t_waypoint_t

typedef std::vector<waypoint_t> ndcurves::t_waypoint_t

◆ time_waypoints_t

typedef Eigen::VectorXd ndcurves::time_waypoints_t

◆ transform_t

typedef Eigen::Transform<double, 3, Eigen::Affine> ndcurves::transform_t

◆ waypoint_t

typedef std::pair<real, pointX_t> ndcurves::waypoint_t

Function Documentation

◆ bezier_from_curve()

template<typename Bezier>

Bezier ndcurves::bezier_from_curve ( const typename Bezier::curve_abc_t & curve )

Converts a cubic hermite spline or polynomial of order 3 or less to a cubic bezier curve.

Parameters

curve : the polynomial of order 3 or less/cubic hermite spline defined between [Tmin,Tmax] to convert.

Returns: the equivalent cubic bezier curve.

◆ cross() [1/6]

bezier_curve_t ndcurves::cross ( const bezier_curve_t & g ) const

Compute the cross product of the current bezier curve by another bezier curve. The cross product p1Xp2 of 2 bezier curves p1 and p2 is defined such that forall t, p1Xp2(t) = p1(t) X p2(t), with X designing the cross product. This method of course only makes sense for dimension 3 curves. It assumes that a method point_t cross(const point_t&, const point_t&) has been defined.

Parameters

pOther other polynomial to compute the cross product with.

Returns: a new polynomial defining the cross product between this and pother

◆ cross() [2/6]

bezier_curve_t ndcurves::cross ( const bezier_curve_t::point_t & point ) const

Compute the cross product of the current bezier b by a point point. The cross product pXpoint of is defined such that forall t, bXpoint(t) = b(t) X point, with X designing the cross product. This method of course only makes sense for dimension 3 polynomials.

Parameters

point point to compute the cross product with.

Returns: a new polynomial defining the cross product between this and point

◆ cross() [3/6]

Eigen::Vector3d ndcurves::cross	(	const Eigen::Vector3d &	a,
		const Eigen::Vector3d &	b )

inline

◆ cross() [4/6]

Eigen::Vector3f ndcurves::cross	(	const Eigen::Vector3f &	a,
		const Eigen::Vector3f &	b )

inline

◆ cross() [5/6]

Eigen::Vector3d ndcurves::cross	(	const Eigen::VectorXd &	a,
		const Eigen::VectorXd &	b )

inline

◆ cross() [6/6]

template<typename N, bool S>

linear_variable< N, S > ndcurves::cross	(	const linear_variable< N, S > &	a,
		const linear_variable< N, S > &	b )

◆ deCasteljauReduction() [1/2]

t_point_t ndcurves::deCasteljauReduction ( const Numeric t ) const

◆ deCasteljauReduction() [2/2]

t_point_t ndcurves::deCasteljauReduction	(	const t_point_t &	pts,
		const Numeric	u ) const

Compute de Casteljau's reduction of the given list of points at time t. For the list $pts$ of N points, compute a new list of points of size N-1 :
$<br>( pts[0]*(1-t)+pts[1], pts[1]*(1-t)+pts[2], ...,
pts[0]*(N-2)+pts[N-1] )$
with t the time when to evaluate bezier curve.
\ The new list contains centroid of parameters ${t,1-t}$ of consecutive points in the list.

Parameters

pts	: list of points.
u	: NORMALIZED time when to evaluate the curve.

Returns: reduced list of point (size of pts - 1).

◆ degree()

virtual std::size_t ndcurves::degree ( ) const

virtual

Get the degree of the curve.

Returns: , the degree of the curve.

◆ dim()

virtual std::size_t ndcurves::dim ( ) const

virtual

Get dimension of curve.

Returns: dimension of curve.

◆ evalDeCasteljau()

point_t ndcurves::evalDeCasteljau ( const Numeric t ) const

Evaluate the curve value at time t using deCasteljau algorithm. The algorithm will compute the $N-1$ centroids of parameters ${t,1-t}$ of consecutive $N$ control points of bezier curve, and perform it iteratively until getting one point in the list which will be the evaluation of bezier curve at time $t$ .

Parameters

t	: time when to evaluate the curve.

Returns: point corresponding on curve at time t.

◆ evaluateLinear()

template<typename BezierFixed, typename BezierLinear, typename X>

BezierFixed ndcurves::evaluateLinear	(	const BezierLinear &	bIn,
		const X	x )

◆ extract()

bezier_curve_t ndcurves::extract	(	const Numeric	t1,
		const Numeric	t2 )

Extract a bezier curve defined between $[t_1,t_2]$ from the actual bezier curve defined between $[T_{min},T_{max}]$ with $T_{min} \leq t_1 \leq t_2 \leq T_{max}$ .

Parameters

t1	: start time of bezier curve extracted.
t2	: end time of bezier curve extracted.

Returns: bezier curve extract defined between .

◆ hermite_from_curve()

template<typename Hermite>

Hermite ndcurves::hermite_from_curve ( const typename Hermite::curve_abc_t & curve )

Converts a polynomial of order 3 or less/cubic bezier curve to a cubic hermite spline.

Parameters

curve : the polynomial of order 3 or less/cubic bezier curve defined between [Tmin,Tmax] to convert.

Returns: the equivalent cubic hermite spline.

◆ isApprox()

template<typename T>

bool ndcurves::isApprox	(	const T	a,
		const T	b,
		const T	eps = 1e-6 )

◆ max()

virtual time_t ndcurves::max ( ) const

virtual

Get the maximum time for which the curve is defined.

Returns: $t_{max}$ , upper bound of time range.

◆ min()

virtual time_t ndcurves::min ( ) const

virtual

Get the minimum time for which the curve is defined.

Returns: $t_{min}$ , lower bound of time range.

◆ operator*() [1/7]

template<typename N, bool S>

linear_variable< N, S > ndcurves::operator*	(	const double	k,
		const linear_variable< N, S > &	w )

◆ operator*() [2/7]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator*	(	const double	k,
		const polynomial< T, N, S, P, TP > &	p1 )

◆ operator*() [3/7]

template<typename N>

quadratic_variable< N > ndcurves::operator*	(	const double	k,
		const quadratic_variable< N > &	w )

◆ operator*() [4/7]

template<typename N>

quadratic_variable< N > ndcurves::operator*	(	const linear_variable< N > &	w1,
		const linear_variable< N > &	w2 )

inline

◆ operator*() [5/7]

template<typename N, bool S>

linear_variable< N, S > ndcurves::operator*	(	const linear_variable< N, S > &	w,
		const double	k )

◆ operator*() [6/7]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator*	(	const polynomial< T, N, S, P, TP > &	p1,
		const double	k )

◆ operator*() [7/7]

template<typename N>

quadratic_variable< N > ndcurves::operator*	(	const quadratic_variable< N > &	w,
		const double	k )

◆ operator*=()

bezier_curve_t & ndcurves::operator*= ( const double d )

◆ operator+() [1/5]

template<typename N, bool S>

linear_variable< N, S > ndcurves::operator+	(	const linear_variable< N, S > &	w1,
		const linear_variable< N, S > &	w2 )

inline

◆ operator+() [2/5]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator+	(	const polynomial< T, N, S, P, TP > &	p1,
		const polynomial< T, N, S, P, TP > &	p2 )

◆ operator+() [3/5]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator+	(	const polynomial< T, N, S, P, TP > &	p1,
		const typename polynomial< T, N, S, P, TP >::point_t &	point )

◆ operator+() [4/5]

template<typename N>

quadratic_variable< N > ndcurves::operator+	(	const quadratic_variable< N > &	w1,
		const quadratic_variable< N > &	w2 )

inline

◆ operator+() [5/5]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator+	(	const typename polynomial< T, N, S, P, TP >::point_t &	point,
		const polynomial< T, N, S, P, TP > &	p1 )

◆ operator+=() [1/2]

bezier_curve_t & ndcurves::operator+= ( const bezier_curve_t & other )

◆ operator+=() [2/2]

bezier_curve_t & ndcurves::operator+= ( const bezier_curve_t::point_t & point )

◆ operator-() [1/7]

template<typename N, bool S>

linear_variable< N, S > ndcurves::operator- ( const linear_variable< N, S > & w1 )

◆ operator-() [2/7]

template<typename N, bool S>

linear_variable< N, S > ndcurves::operator-	(	const linear_variable< N, S > &	w1,
		const linear_variable< N, S > &	w2 )

◆ operator-() [3/7]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator- ( const polynomial< T, N, S, P, TP > & p1 )

◆ operator-() [4/7]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator-	(	const polynomial< T, N, S, P, TP > &	p1,
		const polynomial< T, N, S, P, TP > &	p2 )

◆ operator-() [5/7]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator-	(	const polynomial< T, N, S, P, TP > &	p1,
		const typename polynomial< T, N, S, P, TP >::point_t &	point )

◆ operator-() [6/7]

template<typename N>

quadratic_variable< N > ndcurves::operator-	(	const quadratic_variable< N > &	w1,
		const quadratic_variable< N > &	w2 )

◆ operator-() [7/7]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator-	(	const typename polynomial< T, N, S, P, TP >::point_t &	point,
		const polynomial< T, N, S, P, TP > &	p1 )

◆ operator-=() [1/2]

bezier_curve_t & ndcurves::operator-= ( const bezier_curve_t & other )

◆ operator-=() [2/2]

bezier_curve_t & ndcurves::operator-= ( const bezier_curve_t::point_t & point )

◆ operator/() [1/3]

template<typename N, bool S>

linear_variable< N, S > ndcurves::operator/	(	const linear_variable< N, S > &	w,
		const double	k )

◆ operator/() [2/3]

template<typename T, typename N, bool S, typename P, typename TP>

polynomial< T, N, S, P, TP > ndcurves::operator/	(	const polynomial< T, N, S, P, TP > &	p1,
		const double	k )

◆ operator/() [3/3]

template<typename N>

quadratic_variable< N > ndcurves::operator/	(	const quadratic_variable< N > &	w,
		const double	k )

◆ operator/=()

bezier_curve_t & ndcurves::operator/= ( const double d )

◆ operator<<()

template<typename N, bool S>

std::ostream & ndcurves::operator<<	(	std::ostream &	os,
		const linear_variable< N, S > &	l )

◆ polynomial_from_curve()

template<typename Polynomial>

Polynomial ndcurves::polynomial_from_curve ( const typename Polynomial::curve_abc_t & curve )

Converts a cubic hermite spline or a bezier curve to a polynomial.

Parameters

curve : the bezier curve/cubic hermite spline defined between [Tmin,Tmax] to convert.

Returns: the equivalent polynomial.

◆ PseudoInverse()

template<typename _Matrix_Type_>

void ndcurves::PseudoInverse ( _Matrix_Type_ & pinvmat )

An inverse kinematics architecture enforcing an arbitrary number of strict priority levels (Reference : Boulic et Al. 2003).

◆ serialize()

template<class Archive>

void ndcurves::serialize	(	Archive &	ar,
		const unsigned int	version )

◆ skew()

template<typename Matrix3, typename Point>

Matrix3 ndcurves::skew ( const Point & x )

◆ split() [1/2]

std::pair< bezier_curve_t, bezier_curve_t > ndcurves::split ( const Numeric t ) const

Split the bezier curve in 2 at time t.

Parameters

t	: list of points.

Returns: pair containing the first element of both bezier curve obtained.

◆ split() [2/2]

piecewise_curve_t ndcurves::split ( const vector_x_t & times ) const

Split the bezier curve in several curves, all accessible within a piecewise_curve_t.

Parameters

times : list of times of size n.

Returns: a piecewise_curve_t comprising n+1 curves

◆ to_diagonal()

template<typename N>

Eigen::Matrix< N, Eigen::Dynamic, Eigen::Dynamic > ndcurves::to_diagonal ( const Eigen::Ref< const Eigen::Matrix< N, Eigen::Dynamic, 1 > > vec )

Transforms a vector into a diagonal matrix.

◆ vectorFromEigenArray()

template<typename PointList, typename T_Point>

T_Point ndcurves::vectorFromEigenArray ( const PointList & array )

◆ vectorFromEigenVector()

template<typename PointList, typename T_Point>

T_Point ndcurves::vectorFromEigenVector ( const PointList & vector )

◆ vectorToEigenArray()

template<typename T_point, typename PointList>

PointList ndcurves::vectorToEigenArray ( const T_point & vect )

◆ waypointAtIndex()

const point_t ndcurves::waypointAtIndex ( const std::size_t index ) const

◆ waypoints()

template<typename Time = double, typename Numeric = Time, bool Safe = false, typename Point = Eigen::Matrix<Numeric, Eigen::Dynamic, 1>>

ndcurves::bezier_curve curve_abc ndcurves::waypoints ( ) const

Variable Documentation

◆ bernstein_

std::vector<Bern<Numeric> > ndcurves::bernstein_

◆ control_points_

t_point_t ndcurves::control_points_

◆ degree_

std::size_t ndcurves::degree_

◆ dim_

std::size_t ndcurves::dim_

Dim of curve.

◆ mult_T_

time_t ndcurves::mult_T_

◆ size_

std::size_t ndcurves::size_

◆ T_max_

time_t ndcurves::T_max_

Ending time of cubic hermite spline : T_max_ is equal to last time of control points.

◆ T_min_

time_t ndcurves::T_min_

Starting time of cubic hermite spline : T_min_ is equal to first time of control points.

Namespaces

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ bernstein_t

◆ bezier3_t

◆ bezier_linear_variable_t

◆ bezier_t

◆ coeff_t

◆ constant3_t

◆ constant_t

◆ cubic_hermite_spline3_t

◆ cubic_hermite_spline_t

◆ curve3_ptr_t

◆ curve_3_t

◆ curve_abc_t

◆ curve_constraints3_t

◆ curve_constraints_t

◆ curve_ptr_t

◆ curve_rotation_ptr_t

◆ curve_rotation_t

◆ curve_SE3_ptr_t

◆ curve_SE3_t

◆ curve_translation_ptr_t

◆ curve_translation_t

◆ exact_cubic3_t

◆ exact_cubic_t

◆ linear_variable_t

◆ matrix3_t

◆ matrix3_t_cst_ref

◆ matrix4_t

◆ pair_pointX_tangent_t

◆ piecewise3_t

◆ piecewise_SE3_t

◆ piecewise_t

◆ point1_t

◆ point3_t

◆ point6_t

◆ point_list3_t

◆ point_list6_t

◆ point_listX_t

◆ pointX_list_t

◆ pointX_t

◆ polynomial1_t

◆ polynomial3_t

◆ polynomial_t

◆ quaternion_t

◆ real

◆ ret_pointX_t

◆ SE3Curve_t

◆ sinusoidal_t

◆ SO3Linear_t

◆ SO3Smooth_t

◆ t_pair_pointX_tangent_t

◆ t_point1_t

◆ t_point3_t

◆ t_pointX_t

◆ t_time_t

◆ t_waypoint_t

◆ time_waypoints_t

◆ transform_t

◆ waypoint_t

Function Documentation

◆ bezier_from_curve()

◆ cross() [1/6]

◆ cross() [2/6]

◆ cross() [3/6]

◆ cross() [4/6]

◆ cross() [5/6]

◆ cross() [6/6]

◆ deCasteljauReduction() [1/2]

◆ deCasteljauReduction() [2/2]

◆ degree()

◆ dim()

◆ evalDeCasteljau()

◆ evaluateLinear()

◆ extract()