The spline curve's scalar type.

Creates a spline from a knot vector and control points.

Parameters

knots	The spline's knot vector.
ctrls	The spline's control point vector.

Copy constructor for splines.

Parameters

spline

The input spline.

Computes the non-zero spline basis function derivatives up to given order.

The function computes

\begin{align*} \frac{d^i}{du^i} N_{i,p}(u), \hdots, \frac{d^i}{du^i} N_{i+p+1,p}(u) \end{align*}

with i ranging from 0 up to the specified order.

Parameters

u	Parameter \(u \in [0;1]\) at which the non-zero basis function derivatives are computed.
order	The order up to which the basis function derivatives are computes.
degree	The degree of the underlying spline
knots	The underlying spline's knot vector.

Computes the non-zero spline basis function derivatives up to given order.

The function computes

\begin{align*} \frac{d^i}{du^i} N_{i,p}(u), \hdots, \frac{d^i}{du^i} N_{i+p+1,p}(u) \end{align*}

with i ranging from 0 up to the specified order.

Parameters

u	Parameter \(u \in [0;1]\) at which the non-zero basis function derivatives are computed.
order	The order up to which the basis function derivatives are computes.

Computes the non-zero spline basis function derivatives up to given order.

The function computes

\begin{align*} \frac{d^i}{du^i} N_{i,p}(u), \hdots, \frac{d^i}{du^i} N_{i+p+1,p}(u) \end{align*}

with i ranging from 0 up to the specified order.

Parameters

u	Parameter \(u \in [0;1]\) at which the non-zero basis function derivatives are computed.
order	The order up to which the basis function derivatives are computes. Using the template version of this function is more efficieent since temporary objects are allocated on the stack whenever this is possible.

Computes the non-zero basis functions at the given site.

Splines have local support and a point from their image is defined by exactly \(p+1\) control points \(P_i\) where \(p\) is the spline degree.

This function computes the \(p+1\) non-zero basis function values for a given parameter value \(u\). It returns

\begin{align*} N_{i,p}(u), \hdots, N_{i+p+1,p}(u) \end{align*}

Parameters

u	Parameter \(u \in [0;1]\) at which the non-zero basis functions are computed.

Returns the spline's non-zero basis functions.

The function computes and returns

\begin{align*} N_{i,p}(u), \hdots, N_{i+p+1,p}(u) \end{align*}

Parameters

u	The site at which the basis functions are computed.
degree	The degree of the underlying spline.
knots	The underlying spline's knot vector.

Evaluation of spline derivatives of up-to given order.

The function returns

\begin{align*} \frac{d^i}{du^i}C(u) & = \sum_{i=0}^{n} \frac{d^i}{du^i} N_{i,p}(u)P_i \end{align*}

for i ranging between 0 and order.

Parameters

u	Parameter \(u \in [0;1]\) at which the spline derivative is evaluated.
order	The order up to which the derivatives are computed.

Evaluation of spline derivatives of up-to given order.

The function returns

\begin{align*} \frac{d^i}{du^i}C(u) & = \sum_{i=0}^{n} \frac{d^i}{du^i} N_{i,p}(u)P_i \end{align*}

for i ranging between 0 and order.

Parameters

u	Parameter \(u \in [0;1]\) at which the spline derivative is evaluated.
order	The order up to which the derivatives are computed. Using the template version of this function is more efficieent since temporary objects are allocated on the stack whenever this is possible.

Returns the spline value at a given site \(u\).

The function returns

\begin{align*} C(u) & = \sum_{i=0}^{n}N_{i,p}P_i \end{align*}

Parameters

u	Parameter \(u \in [0;1]\) at which the spline is evaluated.

Returns

The spline value at the given location \(u\).

Returns the span within the knot vector in which u is falling.

Parameters

u	The site for which the span is determined.