BezierPath< T, N > Class Template Reference

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

#include <geomc/shape/CubicPath.h>

Inheritance diagram for BezierPath< T, N >:

Classes
struct	Knot
	A knot in a Bezier path, along with its tangents. More...
struct	Tangent
	A pair of tangents for a knot or segment in a Bezier path. 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
	BezierPath ()=default
	Construct an empty path.
	BezierPath (const BezierSpline< T, N > &segment)
	Construct a path from a sequence of knots and tangents.
VecType< T, N >	acceleration (T s) const
	Evaluate the second derivative of the path at s, with respect to s.
void	add_knot (const Knot &k)
	Add a knot to the path, with tangents for the new segment.
void	add_knot (VecType< T, N > knot, VecType< T, N > tangent)
	Add a knot to the path, with a symmetrical tangent for the previous knot.
Rect< T, N >	bounds () const
	Compute the axis-aligned bounding box of the path.
void	clear ()
	Remove all knots and their tangents from the path.
VecType< T, N > &	knot (size_t i)
	Return a reference to the ith knot in the path.
VecType< T, N >	knot (size_t i) const
	Return the ith knot in 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< BezierSpline< T, N > >	operator[] (size_t i) const
	Return the ith segment in the path.
std::optional< Knot >	remove_knot (size_t i)
	Remove the ith knot from the path.
std::optional< size_t >	segment (T s) const
	Return the index of the segment containing s.
void	set_tangents_for_knot (size_t i, const Tangent &t)
	Set the tangents on either side of the ith knot in the path.
void	set_tangents_for_segment (size_t i, const Tangent &t)
	Set the tangents for the ith segment in the path.
void	set_velocity_for_knot (size_t i, VecType< T, N > v)
	Set the velocity for the ith knot in the path.
Tangent	tangents_for_knot (size_t i) const
	Return the tangents for the ith knot in the path.
Tangent	tangents_for_segment (size_t i) const
	Return the tangents for the ith segment in the path.
VecType< T, N >	velocity (T s) const
	Evaluate the derivative of the path at s, with respect to s.

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

Detailed Description

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

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

Bezier paths are concatenated cubic Bezier splines, where the first knot of each segment is the last knot of the previous segment.

Bezier curves are C0 continuous, and pass through the guide knots. It is allowed to have "broken tangents" at each knot, though the curve can be made C1 continuous by setting a tangent velocity for each knot.

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.

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< BezierSpline< 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.

remove_knot()

template<typename T, index_t N>

std::optional< Knot > remove_knot ( size_t i )

inline

Remove the ith knot from the path.

If i is not in the range of existing knots, 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.

set_tangents_for_knot()

template<typename T, index_t N>

void set_tangents_for_knot ( size_t i, const Tangent & t )

inline

Set the tangents on either side of the ith knot in the path.

If i is the first or last knot, then only the inward tangent is set.

set_velocity_for_knot()

template<typename T, index_t N>

void set_velocity_for_knot ( size_t i, VecType< T, N > v )

inline

Set the velocity for the ith knot in the path.

The segments to the left and right of the knot will be made C1 continuous.

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