A Bezier curve class. More...

#include <bezier.h>

Public Member Functions
	Curve (Eigen::MatrixX2d points)
	Create the Bezier curve. More...

	Curve (const PointVector &points)
	Create the Bezier curve. More...

	Curve (const Curve &curve)

	Curve (Curve &&)=default

Curve &	operator= (const Curve &)

Curve &	operator= (Curve &&)=default

unsigned	order () const
	Get order of the curve (Nth order curve is described with N+1 points);. More...

PointVector	controlPoints () const
	Get a vector of control points. More...

Point	controlPoint (unsigned idx) const
	Get the control point at index idx. More...

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

PointVector	polyline (double flatness=0.5) const
	Get a polyline representation of the curve 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...

void	reverse ()
	Reverse order of control points.

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

void	manipulateCurvature (double t, const Point &point)
	Manipulate the curve so that it passes through wanted point for given 't'. More...

void	elevateOrder ()
	Raise the curve order by 1. More...

void	lowerOrder ()
	Lower the curve order by 1. More...

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

Eigen::MatrixX2d	valueAt (const std::vector< double > &t_vector) const
	Get the point vector on curve for given parameters. More...

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

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

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

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

const Curve &	derivative () const
	Get the derivative of a curve. More...

const Curve &	derivative (unsigned n) const
	Get the nth derivative of a curve. 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...

std::vector< double >	roots () const
	Get roots of the curve on both axes. More...

std::vector< double >	extrema () const
	Get all extrema of the curve. More...

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

std::pair< Curve, Curve >	splitCurve (double z=0.5) const
	Split the curve into two subcurves. More...

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

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

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

void	applyContinuity (const Curve &source_curve, const std::vector< double > &beta_coeffs)
	applyContinuity Apply geometric continuity based on the another curve. More...

Protected Member Functions
void	resetCache ()
	Reset all privately cached data.

Protected Attributes
Eigen::MatrixX2d	control_points_
	N x 2 matrix where each row corresponds to control Point. More...

Detailed Description

A Bezier curve class.

A class for storing and using any-order Bezier curve. It uses private and static caching for storing often accessed data. Private caching is used for data concerning individual curve, while static caching is used for common data (coefficient matrices)

Constructor & Destructor Documentation

◆ Curve() [1/2]

Curve ( Eigen::MatrixX2d points )

Create the Bezier curve.

Parameters

points Nx2 matrix where each row is one of N control points that define the curve

◆ Curve() [2/2]

Curve ( const PointVector & points )

Create the Bezier curve.

Parameters

points A vector of control points that define the curve

Member Function Documentation

◆ applyContinuity()

void applyContinuity	(	const Curve &	source_curve,
		const std::vector< double > &	beta_coeffs
	)

applyContinuity Apply geometric continuity based on the another curve.

Parameters

locked_curve	Curve on which calculation are based.
beta_coeffs	Beta-constraints used to calculate continuity. Size defines continuity order.

◆ boundingBox()

BoundingBox boundingBox ( ) const

Get the bounding box of curve.

Returns: Bounding box (if use_roots is false, returns the bounding box of control points)

◆ controlPoint()

Point controlPoint ( unsigned idx ) const

Get the control point at index idx.

Parameters

idx	Index of chosen control point

Returns: A vector of control points

◆ controlPoints()

PointVector controlPoints ( ) const

Get a vector of control points.

Returns: A vector of control points

◆ curvatureAt()

double curvatureAt ( double t ) const

Get curvature of the curve for a given t.

Parameters

t	Curve parameter

Returns: Curvature of a curve for a given t

◆ curvatureDerivativeAt()

double curvatureDerivativeAt ( double t ) const

Get curvature derivative of the curve for a given t.

Parameters

t	Curve parameter

Returns: Curvature derivative of a curve for a given t

◆ derivative() [1/2]

const Curve& derivative ( ) const

Get the derivative of a curve.

Returns: Derivative curve

◆ derivative() [2/2]

const Curve& derivative ( unsigned n ) const

Get the nth derivative of a curve.

Parameters

n	Desired number of derivative

Returns: Derivative curve

Warning: double n cannot be zero

◆ 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()

double distance ( const Point & point ) const

Get distance of the point to the curve.

Parameters

point Point to project on curve

Returns: Distance to the curve

◆ elevateOrder()

void elevateOrder ( )

Raise the curve order by 1.

Curve will always retain its shape

Warning: Resets cached data

◆ endPoints()

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

Get first and last control points.

Returns: A pair of end points

◆ extrema()

std::vector<double> extrema ( ) const

Get all extrema of the curve.

Returns: A vector of parameters where extrema are

◆ intersections()

PointVector intersections ( const Curve & curve ) const

Get the points of intersection with another curve.

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	Curve 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	Curve parameter from which length is computed
t2	Curve parameter to which length is computed

Returns: Arc length between paramaters t1 and t2

◆ lowerOrder()

void lowerOrder ( )

Lower the curve order by 1.

If current shape cannot be described by lower order, it will be best aproximation

Warning: CAN THROW: Cannot be called for curves of 1st order; Resets cached data

◆ manipulateCurvature()

void manipulateCurvature	(	double	t,
		const Point &	point
	)

Manipulate the curve so that it passes through wanted point for given 't'.

Parameters

t	Curve parameter
point	Point where curve should pass for a given t

Warning: CAN THROW: Only works for quadratic and cubic curves; Resets cached data

◆ normalAt()

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

Get the normal of the curve for a given t.

Parameters

t	Curve parameter
normalize	If the resulting normal should be normalized

Returns: Normal of a curve for given t

◆ order()

unsigned order ( ) const

Get order of the curve (Nth order curve is described with N+1 points);.

Returns: Order of curve

◆ polyline()

PointVector polyline ( double flatness = 0.5 ) const

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

Parameters

flatness Error tolerance of approximation

Returns: A vector of polyline vertices

◆ projectPoint()

double projectPoint ( const Point & point ) const

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

Parameters

point Point to project on curve

Returns: double t

◆ roots()

std::vector<double> roots ( ) const

Get roots of the curve on both axes.

Returns: A vector of parameters where curve passes through axes

◆ setControlPoint()

void setControlPoint	(	unsigned	idx,
		const Point &	point
	)

Set the new coordinates to a control point.

Parameters

idx	Index of chosen control point
point	New control point

◆ splitCurve()

std::pair<Curve, Curve> splitCurve ( double z = 0.5 ) const

Split the curve into two subcurves.

Parameters

z	double t at which to split the curve

Returns: Pair of two subcurves

◆ tangentAt()

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

Get the tangent of the curve for a given t.

Parameters

t	Curve parameter
normalize	If the resulting tangent should be normalized

Returns: Tangent of a curve for a given t

◆ valueAt() [1/2]

Eigen::MatrixX2d valueAt ( const std::vector< double > & t_vector ) const

Get the point vector on curve for given parameters.

Parameters

t_vector Curve parameters

Returns: Matrix of points on a curve for given parameters

◆ valueAt() [2/2]

Point valueAt ( double t ) const

Get the point on curve for a given t.

Parameters

t	Curve parameter

Returns: Point on a curve for a given t

Field Documentation

◆ control_points_

Eigen::MatrixX2d control_points_

protected

N x 2 matrix where each row corresponds to control Point.

Warning: Any changes made to control_points_ require a call to resetCache() funtion!

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

include/Bezier/bezier.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Curve() [1/2]

◆ Curve() [2/2]

Member Function Documentation

◆ applyContinuity()

◆ boundingBox()

◆ controlPoint()

◆ controlPoints()

◆ curvatureAt()

◆ curvatureDerivativeAt()

◆ derivative() [1/2]

◆ derivative() [2/2]

◆ derivativeAt() [1/2]

◆ derivativeAt() [2/2]

◆ distance()

◆ elevateOrder()

◆ endPoints()

◆ extrema()

◆ intersections()

◆ iterateByLength()

◆ length() [1/3]

◆ length() [2/3]

◆ length() [3/3]

◆ lowerOrder()

◆ manipulateCurvature()

◆ normalAt()

◆ order()

◆ polyline()

◆ projectPoint()

◆ roots()

◆ setControlPoint()

◆ splitCurve()

◆ tangentAt()

◆ valueAt() [1/2]

◆ valueAt() [2/2]

Field Documentation

◆ control_points_