Detailed Description

template<size_t Order, size_t Pieces>
class gtsam::PiecewisePolynomial< Order, Pieces >

A one-dimensional piecewise polynomial kernel.

On interval \([b_j,b_{j+1}]\), the value is \(p_j(t)=\sum_{k=0}^{Order} a_{j,k}t^k\). Coefficients for each piece are therefore stored in ascending power order. The \(r\)-th derivative uses the exact power rule, \(p_j^{(r)}(t)=\sum_{k=r}^{Order}\frac{k!}{(k-r)!}a_{j,k}t^{k-r}\). Values outside the declared interval range are evaluated at the nearest endpoint, which lets cumulative kernels remain constant outside support.

Template Parameters

Order	Polynomial order of every piece.
Pieces	Number of polynomial pieces.

Inheritance diagram for gtsam::PiecewisePolynomial< Order, Pieces >:

Public Member Functions
	PiecewisePolynomial (const Parameters &parameters)
	Construct a kernel from fixed-size coefficient data.
double	getCenter () const override
	Return the representative center of the kernel support.
double	getBeginning () const override
	Return the first boundary of the kernel support.
double	getEnd () const override
	Return the last boundary of the kernel support.
size_t	getValidDerivatives () const override
	Return the largest derivative order available analytically.
const std::array< double, pieces+1 > &	getIntervals () const
	Return interval boundaries, primarily for validation and visualization.
double	evaluate (double t, OptionalJacobian< 1, 1 > H={}) const override
	Evaluate the selected polynomial piece and optionally its slope.
double	evaluateDerivative (size_t derivative, double t, OptionalJacobian< 1, 1 > H={}) const override
	Evaluate an analytic derivative and optionally the next derivative.
Public Member Functions inherited from gtsam::KernelBase
double	getLength () const
	Width of the kernel support.
virtual	~KernelBase ()=default
	Destroy the polymorphic kernel interface.

Static Public Attributes
static constexpr size_t	order = Order
static constexpr size_t	pieces = Pieces

Classes
struct	Parameters
	Coefficients, interval boundaries, and center defining the kernel. More...