A Bezier polycurve class. More...

#include <polycurve.h>

Public Member Functions
	PolyCurve (std::deque< Curve > curves)
	Create the Bezier polycurve from deque of curves.

	PolyCurve (const PolyCurve &)=default

	PolyCurve (PolyCurve &&)=default

PolyCurve &	operator= (const PolyCurve &)=default

PolyCurve &	operator= (PolyCurve &&)=default

void	insertAt (unsigned idx, Curve curve)
	Insert new curve into polycurve.

void	insertFront (Curve curve)
	Insert new curve at the beginning of the polycurve.

void	insertBack (Curve curve)
	Insert new curve at the end of the polycurve.

void	removeAt (unsigned idx)
	Remove a subcurve from the polycurve.

void	removeFirst ()
	Remove a subcurve from the beginning of the polycurve.

void	removeBack ()
	Remove a subcurve from the end of the polycurve.

unsigned	size () const
	Get number of subcurves.

unsigned	curveIdx (double t) const
	Resolve polycurve parameter to subcurve index.

PointVector	polyline () const
	Get a polyline representation of the polycurve as a vector of points on curve.

PointVector	polyline (double flatness) const
	Get a polyline representation of the polycurve as a vector of points on curve.

ParamVector	polylineParams () const
	Get curve parameters corresponding to polyline points.

ParamVector	polylineParams (double flatness) const
	Get curve parameters corresponding to polyline points.

double	length () const
	Compute exact arc length using Chebyshev polynomials.

double	length (double t) const
	Compute exact arc length using Chebyshev polynomials.

double	length (double t1, double t2) const
	Compute exact arc length using Chebyshev polynomials.

double	step (double t, double ds) const
	Compute parameter t which is ds distance from given t.

std::pair< Point, Point >	endPoints () const
	Get first and last control points.

PointVector	controlPoints () const
	Get the control points of all subcurves.

void	setControlPoint (unsigned idx, const Point &point)
	Set the new coordinates to a control point.

Point	valueAt (double t) const
	Get the point on polycurve for a given t.

PointVector	valueAt (const ParamVector &t_vector) const
	Get the point vector on polycurve for given parameters.

double	curvatureAt (double t) const
	Get curvature of the polycurve for a given t.

double	curvatureDerivativeAt (double t) const
	Get curvature derivative of the polycurve for a given t.

Vector	tangentAt (double t) const
	Get the unit tangent of the polycurve for a given t.

Vector	normalAt (double t) const
	Get the unit normal of the polycurve for a given t.

Vector	derivativeAt (double t) const
	Get value of a derivative for a given t.

Vector	derivativeAt (unsigned n, double t) const
	Get value of an nth derivative for a given t.

BoundingBox	boundingBox () const
	Get the bounding box of the polycurve.

double	projectPoint (const Point &point) const
	Get the parameter t where polycurve is closest to given point.

ParamVector	projectPoint (const PointVector &point_vector) const
	Get the parameter t vector where polycurve is closest to given points.

double	distance (const Point &point) const
	Get distance of the point to the polycurve.

std::vector< double >	distance (const PointVector &point_vector) const
	Get the distance vector of points to the polycurve.


Curve &	curve (unsigned idx)
	Get a subcurve.

const Curve &	curve (unsigned idx) const
	Get a subcurve.


std::deque< Curve > &	curves ()
	Get list of all subcurves.

const std::deque< Curve > &	curves () const
	Get list of all subcurves.


PointVector	intersections (const Curve &curve) const
	Get the points of intersection with another curve or polycurve.

PointVector	intersections (const PolyCurve &curve) const
	Get the points of intersection with another curve or polycurve.

Protected Attributes
std::deque< Curve >	curves_
	Structure for holding underlying Bezier curves.

Detailed Description

A Bezier polycurve class.

A class for linking multiple Bezier curves with at least C0 continuity. It allows subcurve manipulation.

Warning: Range of parameter 't' depends on number of subcurves. To access n-th subcurve, t has to be in range [n-1, n)

Note: Parameter-taking accessors throw std::logic_error on an empty polycurve.

Constructor & Destructor Documentation

◆ PolyCurve()

PolyCurve ( std::deque< Curve > curves )

Create the Bezier polycurve from deque of curves.

Parameters

curves A list of curves

Member Function Documentation

◆ boundingBox()

BoundingBox boundingBox ( ) const

Get the bounding box of the polycurve.

Returns: Bounding box

◆ controlPoints()

PointVector controlPoints ( ) const

Get the control points of all subcurves.

Returns: A vector of control points

◆ curvatureAt()

double curvatureAt ( double t ) const

Get curvature of the polycurve for a given t.

Parameters

t	A Polycurve parameter

Returns: Curvature of a polycurve for a given t

◆ curvatureDerivativeAt()

double curvatureDerivativeAt ( double t ) const

Get curvature derivative of the polycurve for a given t.

Parameters

t	A Polycurve parameter

Returns: Curvature derivative of a polycurve for a given t

◆ curve() [1/2]

Curve & curve ( unsigned idx )

Get a subcurve.

Parameters

idx	Subcurve index

Returns: A reference to the subcurve at idx

Note: idx must be in range [0, size())

◆ curve() [2/2]

const Curve & curve ( unsigned idx ) const

Get a subcurve.

Parameters

idx	Subcurve index

Returns: A reference to the subcurve at idx

Note: idx must be in range [0, size())

◆ curveIdx()

unsigned curveIdx ( double t ) const

Resolve polycurve parameter to subcurve index.

Parameters

t	A polycurve parameter

Returns: An index of the subcurve where parameter t is

Note: t is clamped into [0, size()]

Exceptions

std::logic_error if the polycurve is empty

◆ curves() [1/2]

std::deque< Curve > & curves ( )

Get list of all subcurves.

Returns: A reference to the deque of subcurves

◆ curves() [2/2]

const std::deque< Curve > & curves ( ) const

Get list of all subcurves.

Returns: A reference to the deque of subcurves

◆ derivativeAt() [1/2]

Vector derivativeAt ( double t ) const

Get value of a derivative for a given t.

Parameters

t	Curve parameter

Returns: Curve derivative at t

◆ derivativeAt() [2/2]

Vector derivativeAt	(	unsigned	n,
		double	t
	)		const

Get value of an nth derivative for a given t.

Parameters

n	Desired number of derivative
t	Curve parameter

Returns: nth curve derivative at t

◆ distance() [1/2]

double distance ( const Point & point ) const

Get distance of the point to the polycurve.

Parameters

point Point to project on the polycurve

Returns: Distance to the curve

◆ distance() [2/2]

std::vector< double > distance ( const PointVector & point_vector ) const

Get the distance vector of points to the polycurve.

Parameters

point_vector Points to project on the polycurve

Returns: Vector of distances

◆ endPoints()

std::pair< Point, Point > endPoints ( ) const

Get first and last control points.

Returns: A pair of end points

Exceptions

std::logic_error if the polycurve is empty

◆ insertAt()

void insertAt	(	unsigned	idx,
		Curve	curve
	)

Insert new curve into polycurve.

Parameters

idx	Index where to insert new curve
curve	A curve to insert

Note: idx must be in range [0, size()]

◆ insertBack()

void insertBack ( Curve curve )

Insert new curve at the end of the polycurve.

Parameters

curve A curve to insert

◆ insertFront()

void insertFront ( Curve curve )

Insert new curve at the beginning of the polycurve.

Parameters

curve A curve to insert

◆ intersections() [1/2]

PointVector intersections ( const Curve & curve ) const

Get the points of intersection with another curve or polycurve.

Parameters

curve Curve or polycurve to intersect with

Returns: A vector of points of intersection between curves

◆ intersections() [2/2]

PointVector intersections ( const PolyCurve & curve ) const

Get the points of intersection with another curve or polycurve.

Parameters

curve Curve or polycurve to intersect with

Returns: A vector of points of intersection between curves

◆ length() [1/3]

double length ( ) const

Compute exact arc length using Chebyshev polynomials.

Returns: Arc length

◆ length() [2/3]

double length ( double t ) const

Compute exact arc length using Chebyshev polynomials.

Parameters

t	A Polycurve parameter to which length is computed

Returns: Arc length from start to parameter t

◆ length() [3/3]

double length	(	double	t1,
		double	t2
	)		const

Compute exact arc length using Chebyshev polynomials.

Parameters

t1	A Polycurve parameter from which length is computed
t2	A Polycurve parameter to which length is computed

Returns: Arc length between parameters t1 and t2

◆ normalAt()

Vector normalAt ( double t ) const

Get the unit normal of the polycurve for a given t.

Parameters

t	A Polycurve parameter

Returns: Unit normal of a polycurve for given t

◆ polyline() [1/2]

PointVector polyline ( ) const

Get a polyline representation of the polycurve as a vector of points on curve.

Returns: A vector of polyline vertices

Note: Each subcurve uses its own auto-calculated flatness (0.1% of bounding box diagonal)

◆ polyline() [2/2]

PointVector polyline ( double flatness ) const

Get a polyline representation of the polycurve as a vector of points on curve.

Parameters

flatness Error tolerance of approximation

Returns: A vector of polyline vertices

◆ polylineParams() [1/2]

ParamVector polylineParams ( ) const

Get curve parameters corresponding to polyline points.

Returns: A vector of curve parameters for each polyline vertex

Note: Each subcurve uses its own auto-calculated flatness (0.1% of bounding box diagonal)

◆ polylineParams() [2/2]

ParamVector polylineParams ( double flatness ) const

Get curve parameters corresponding to polyline points.

Parameters

flatness Error tolerance of approximation

Returns: A vector of curve parameters for each polyline vertex

◆ projectPoint() [1/2]

double projectPoint ( const Point & point ) const

Get the parameter t where polycurve is closest to given point.

Parameters

point Point to project on polycurve

Returns: double t

◆ projectPoint() [2/2]

ParamVector projectPoint ( const PointVector & point_vector ) const

Get the parameter t vector where polycurve is closest to given points.

Parameters

point_vector Points to project on polycurve

Returns: Vector of parameters t

◆ removeAt()

void removeAt ( unsigned idx )

Remove a subcurve from the polycurve.

Parameters

idx	Index of subcurve to remove

Note: idx must be in range [0, size())

◆ removeBack()

void removeBack ( )

Remove a subcurve from the end of the polycurve.

Note: Requires a non-empty polycurve

◆ removeFirst()

void removeFirst ( )

Remove a subcurve from the beginning of the polycurve.

Note: Requires a non-empty polycurve

◆ setControlPoint()

void setControlPoint	(	unsigned	idx,
		const Point &	point
	)

Set the new coordinates to a control point.

Parameters

idx	Global control-point index across all subcurves
point	New control point

Note: No-op if idx is out of range

◆ size()

unsigned size ( ) const

Get number of subcurves.

Returns: Number of subcurves

◆ step()

double step	(	double	t,
		double	ds
	)		const

Compute parameter t which is ds distance from given t.

Parameters

t	Curve parameter
ds	Distance to iterate

Returns: New parameter t

◆ tangentAt()

Vector tangentAt ( double t ) const

Get the unit tangent of the polycurve for a given t.

Parameters

t	A Polycurve parameter

Returns: Unit tangent of a polycurve for a given t

◆ valueAt() [1/2]

PointVector valueAt ( const ParamVector & t_vector ) const

Get the point vector on polycurve for given parameters.

Parameters

t_vector Curve parameters

Returns: Vector of points on a polycurve for given parameters

◆ valueAt() [2/2]

Point valueAt ( double t ) const

Get the point on polycurve for a given t.

Parameters

t	Curve parameter

Returns: Point on a polycurve for a given t

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

include/Bezier/polycurve.h

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PolyCurve()

Member Function Documentation

◆ boundingBox()

◆ controlPoints()

◆ curvatureAt()

◆ curvatureDerivativeAt()

◆ curve() [1/2]

◆ curve() [2/2]

◆ curveIdx()

◆ curves() [1/2]

◆ curves() [2/2]

◆ derivativeAt() [1/2]

◆ derivativeAt() [2/2]

◆ distance() [1/2]

◆ distance() [2/2]

◆ endPoints()

◆ insertAt()

◆ insertBack()

◆ insertFront()

◆ intersections() [1/2]

◆ intersections() [2/2]

◆ length() [1/3]

◆ length() [2/3]

◆ length() [3/3]

◆ normalAt()

◆ polyline() [1/2]

◆ polyline() [2/2]

◆ polylineParams() [1/2]

◆ polylineParams() [2/2]

◆ projectPoint() [1/2]

◆ projectPoint() [2/2]

◆ removeAt()

◆ removeBack()

◆ removeFirst()

◆ setControlPoint()

◆ size()

◆ step()

◆ tangentAt()

◆ valueAt() [1/2]

◆ valueAt() [2/2]