HermitePath< T, N > Class Template Reference

An extendable path defined by a sequence of knots and tangent velocities. More...

#include <geomc/shape/CubicPath.h>

Inheritance diagram for HermitePath< T, N >:

Classes
struct	Knot
	A knot in a Hermite path, along with its tangent velocity. More...

Public Types
using	elem_t
	The coordinate type of this object.
using	point_t
	The type of a point in this object's space.
using	Spline

Public Member Functions
	HermitePath ()=default
	Construct an empty path.
	HermitePath (const HermiteSpline< T, N > &segment)
	Construct a path having a single segment.
	HermitePath (const std::initializer_list< Knot > knots)
	Construct a path from a sequence of 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< HermiteSpline< 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< Knot >	knots
	The sequence of knots which the path passes through.

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

Detailed Description

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

An extendable path defined by a sequence of knots and tangent velocities.

Hermite paths are concatenated cubic Hermite splines, where the first knot of each segment is the last knot of the previous segment. Each knot has an associated tangent velocity.

Hermite curves are C1 continuous, and pass through their 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.

Each 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< HermiteSpline< 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