BSpline< K, G > Class Template Reference

Cardinal Bspline on a Lie group. More...

#include <bspline.hpp>

Public Member Functions
	BSpline ()
	Construct a constant bspline defined on [0, 1) equal to identity.
	BSpline (double t0, double dt, std::vector< G > &&ctrl_pts)
	Create a BSpline.
template<std::ranges::range Rv> requires (std::is_same_v<std::ranges::range_value_t<Rv>, G>)
	BSpline (double t0, double dt, const Rv &ctrl_pts)
	Create a BSpline.
	BSpline (const BSpline &)=default
	Copy constructor.
	BSpline (BSpline &&)=default
	Move constructor.
BSpline &	operator= (const BSpline &)=default
	Copy assignment.
BSpline &	operator= (BSpline &&)=default
	Move assignment.
	~BSpline ()=default
	Descructor.
double	dt () const
	Distance between knots.
double	t_min () const
	Minimal time for which spline is defined.
double	t_max () const
	Maximal time for which spline is defined.
const std::vector< G > &	ctrl_pts () const
	Access spline control points.
template<typename S = double>
CastT< S, G >	operator() (const S &t, OptTangent< CastT< S, G > > vel={}, OptTangent< CastT< S, G > > acc={}) const
	Evaluate BSpline.

Detailed Description

template<int K, LieGroup G>
class BSpline< K, G >

Cardinal Bspline on a Lie group.

The curve is defined by

\[ g(t) = g_0 * \exp(\tilde B_1(t) v_1) * ... \exp(\tilde B_N(t) v_N) \]

where \(\tilde B_i(t)\) are cumulative Bspline basis functions and \(v_i = g_i \ominus g_{i-1}\) are the control point differences. The control points - knot time correspondence is as follows

KNOT  -K  -K+1   -K+2  ...    0    1   ...  N-K
CTRL   0     1      2  ...    K  K+1          N
                              ^               ^
                            t_min           t_max

The first K ctrl_pts are exterior points and are outside the support of the spline, which means that the spline is defined on \( [t_{min}, t_{max}] = [t0, (N-K)*dt] \).

For interpolation purposes use an odd spline degree and set

t0 = (timestamp of first control point) + dt*(K-1)/2

which aligns control points with the maximum of the corresponding basis function.

Definition at line 47 of file bspline.hpp.

Constructor & Destructor Documentation

BSpline() [1/2]

template<int K, LieGroup G>

BSpline< K, G >::BSpline	(	double	t0,
		double	dt,
		std::vector< G > &&	ctrl_pts
	)

Create a BSpline.

Parameters

t0	start of spline
dt	distance between spline knots
ctrl_pts	spline control points

BSpline() [2/2]

template<int K, LieGroup G>

template<std::ranges::range Rv>
requires (std::is_same_v<std::ranges::range_value_t<Rv>, G>)

BSpline< K, G >::BSpline	(	double	t0,
		double	dt,
		const Rv &	ctrl_pts
	)

Create a BSpline.

Template Parameters

R	range type

Parameters

t0	start of spline
dt	distance between spline knots
ctrl_pts	spline control points

Member Function Documentation

operator()()

template<int K, LieGroup G>

template<typename S = double>

CastT< S, G > BSpline< K, G >::operator()	(	const S &	t,
		OptTangent< CastT< S, G > >	vel = {},
		OptTangent< CastT< S, G > >	acc = {}
	)		const

Evaluate BSpline.

Template Parameters

S

time type

Parameters

[in]	t	time point to evaluate at
[out]	vel	output body velocity at evaluation time
[out]	acc	output body acceleration at evaluation time

Returns

spline value at time t

Note

Input t is clamped to spline interval of definition

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The documentation for this class was generated from the following file:

• include/smooth/spline/bspline.hpp