A Bezier polycurve class. More...

#include <polycurve.h>

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

	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. More...

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

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

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

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. More...

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

PointVector	polyline (double flatness=0.5) const
	Get a polyline representation of the polycurve as a vector of points on curve. More...

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

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

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

double	iterateByLength (double t, double s) const
	Compute parameter t which is S distance from given t. More...

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

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

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

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

PointVector	valueAt (const std::vector< double > &t_vector) const
	Get the point vector on polycurve for given parameters. More...

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

double	curvatureDerivativeAt (double t) const
	Get curvature derivative of curve for a given t. More...

Vector	tangentAt (double t, bool normalize=true) const
	Get the tangent of the polycurve for a given t. More...

Vector	normalAt (double t, bool normalize=true) const
	Get the normal of the polycurve for a given t. More...

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

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

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

template<typename Curve_PolyCurve >
PointVector	intersections (const Curve_PolyCurve &curve) const
	Get the points of intersection with another curve or polycurve. More...

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

std::vector< double >	projectPoint (const PointVector &point_vector) const
	Get the parameter t vector where polycurve is closest to given points. More...

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

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


Curve &	curve (unsigned idx)
	Get pointer of a subcurve. More...

const Curve &	curve (unsigned idx) const


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

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

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>

Constructor & Destructor Documentation

◆ PolyCurve()

PolyCurve ( std::deque< Curve > curves )

Create the Bezier polycurve from deque of curves.

Parameters

curve_list 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 Polyurve parameter

Returns: Curvature of a polycurve for a given t

◆ curvatureDerivativeAt()

double curvatureDerivativeAt ( double t ) const

Get curvature derivative of curve for a given t.

Parameters

t	Curve parameter

Returns: Curvature derivative of a curve for a given t

◆ curve()

Curve& curve ( unsigned idx )

Get pointer of a subcurve.

Parameters

idx	Subcurve index

Returns: A reference to curve

◆ curveIdx()

unsigned curveIdx ( double t ) const

Resolve polycurve parameter to subcurve index.

Parameters

t	A polycurve parameter

Returns: An index of of subcurve where parameter t is

◆ curves()

std::deque<Curve>& curves ( )

Get list of all subcurves.

Returns: A vector of curve references

◆ 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

◆ 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

◆ 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()

PointVector intersections ( const Curve_PolyCurve & curve ) const

Get the points of intersection with another curve or polycurve.

Parameters

curve Curve to intersect with

Returns: A vector af points of intersection between curves

◆ iterateByLength()

double iterateByLength	(	double	t,
		double	s
	)		const

Compute parameter t which is S distance from given t.

Parameters

t	Curve parameter
s	Distance to iterate

Returns: New parameter t

◆ 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 paramaters t1 and t2

◆ normalAt()

Vector normalAt	(	double	t,
		bool	normalize = `true`
	)		const

Get the normal of the polycurve for a given t.

Parameters

t	A Polyurve parameter
normalize	If the resulting normal should be normalized

Returns: Normal of a polycurve for given t

◆ polyline()

PointVector polyline ( double flatness = 0.5 ) 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

◆ 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]

std::vector<double> 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

◆ setControlPoint()

void setControlPoint	(	unsigned	idx,
		const Point &	point
	)

Set the new coordinates to a control point.

Parameters

index	Index of chosen control point
point	New control point

◆ size()

unsigned size ( ) const

Get number of subcurves.

Returns: Number of subcurves

◆ tangentAt()

Vector tangentAt	(	double	t,
		bool	normalize = `true`
	)		const

Get the tangent of the polycurve for a given t.

Parameters

t	A Polyurve parameter
normalize	If the resulting tangent should be normalized

Returns: Tangent of a polycurve for a given t

◆ valueAt() [1/2]

PointVector valueAt ( const std::vector< double > & 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()

◆ curveIdx()

◆ curves()

◆ derivativeAt() [1/2]

◆ derivativeAt() [2/2]

◆ distance() [1/2]

◆ distance() [2/2]

◆ endPoints()

◆ insertAt()

◆ insertBack()

◆ insertFront()

◆ intersections()

◆ iterateByLength()

◆ length() [1/3]

◆ length() [2/3]

◆ length() [3/3]

◆ normalAt()

◆ polyline()

◆ projectPoint() [1/2]

◆ projectPoint() [2/2]

◆ removeAt()

◆ setControlPoint()

◆ size()

◆ tangentAt()

◆ valueAt() [1/2]

◆ valueAt() [2/2]