BSplinePath< T, N > Class Template Reference

An extendable path defined by a sequence of guide knots. More...

#include <geomc/shape/CubicPath.h>

Inheritance diagram for BSplinePath< T, N >:

Public Types
using	elem_t
	The coordinate type of this object.
using	Knot = VecType<T,N>
using	point_t
	The type of a point in this object's space.
using	Spline

Public Member Functions
	BSplinePath ()=default
	Construct an empty path.
	BSplinePath (const BSpline< T, N > &segment)
	Construct a path having a single segment.
	BSplinePath (const std::initializer_list< VecType< T, N > > knots)
	Construct a path from a sequence of guide knots.
VecType< T, N >	acceleration (T s) const
	Evaluate the second derivative of the path at s, with respect to s.
Rect< T, N >	bounds () const
	Compute the axis-aligned bounding box of the path.
size_t	n_segments () const
	Return the number of complete segments in the path.
VecType< T, N >	operator() (T s) const
	Evaluate the path at s.
std::optional< BSpline< T, N > >	operator[] (size_t i) const
	Return the ith segment in the path.
std::optional< size_t >	segment (T s) const
	Return the index of the segment containing s.
VecType< T, N >	velocity (T s) const
	Evaluate the derivative of the path at s, with respect to s.

Public Attributes
std::vector< VecType< T, N > >	knots
	The sequence of guide knots.

Static Public Attributes
static constexpr index_t	N
	The dimension of this object.

Detailed Description

template<typename T, index_t N>
class geom::BSplinePath< T, N >

An extendable path defined by a sequence of guide knots.

B-spline paths are concatenated cubic B-splines, where each segment shares its first three control points with the previous segment.

B-spline curves are C2 continuous, and do not necessarily pass through the guide knots.

Member Typedef Documentation

point_t

using point_t

inherited

The type of a point in this object's space.

An N-vector of T if N > 1, otherwise a T.

Member Function Documentation

acceleration()

VecType< T, N > acceleration ( T s ) const

inlineinherited

Evaluate the second derivative of the path at s, with respect to s.

The range of s is the same as for operator().

bounds()

Rect< T, N > bounds ( ) const

inlineinherited

Compute the axis-aligned bounding box of the path.

O(n) on the number of segments.

n_segments()

template<typename T, index_t N>

size_t n_segments ( ) const

inline

Return the number of complete segments in the path.

A single segment is defined by four consecutive control points.

operator()()

VecType< T, N > operator() ( T s ) const

inlineinherited

Evaluate the path at s.

Segment i is evaluated for s in the range [i, i + 1]. If s is outside the range [0, n_segments()], the path is extrapolated using the first or last segment.

operator[]()

template<typename T, index_t N>

std::optional< BSpline< T, N > > operator[] ( size_t i ) const

inline

Return the ith segment in the path.

If there are no complete segments in the path, return std::nullopt.

segment()

std::optional< size_t > segment ( T s ) const

inlineinherited

Return the index of the segment containing s.

If there are no complete segments in the path, return std::nullopt.

velocity()

VecType< T, N > velocity ( T s ) const

inlineinherited

Evaluate the derivative of the path at s, with respect to s.

The range of s is the same as for operator().

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

• geomc/shape/CubicPath.h