belfem::Bezier Class Reference

#include <cl_Bezier.hpp>

Public Member Functions
	Bezier (const real aX0=0.0, const real aY0=0.0, const real adYdx0=0.0, const real aX1=1.0, const real aY1=1.0, const real adYdx1=0.0, const BezierType aType=BezierType::Horizontal)
	Bezier (const Vector< real > &aX, const Vector< real > &aY, const BezierType aType=BezierType::Horizontal)
	~Bezier ()=default
Vector< real > &	basis_x ()
	expose the x-coordinates of the basis
const Vector< real > &	basis_x () const
Vector< real > &	basis_y ()
	expose the y-coordinates of the basis
const Vector< real > &	basis_y () const
real	x_by_xi (const real aXi) const
	The parameter coordinate goes from -1 <= xi <= 1.
real	y_by_xi (const real aXi) const
	The parameter coordinate goes from -1 <= xi <= 1.
real	xi_by_x (const real aX) const
	Inverts the function x_by_xi.
real	xi_by_y (const real aY) const
	Inverts the function y_by_xi.
real	x (const real aY) const
	x-coordinate as funciton of the y-coordinate
real	y (const real aX) const
	y-coordinate as funciton of the x-coordinate
void	point (const real aXi, real &aX, real &aY) const
	point as function of parameter coordinate
void	dpoint (const real aXi, real &adXdXi, real &adYdXi) const
	tangent vector as function of parameter coordinate
void	ddpoint (const real aXi, real &ad2XdXi2, real &ad2YdXi2) const
	curvature vector as function of parameter coordinate
void	dddpoint (real &ad3XdXi3, real &ad3YdXi3) const
	aberrancy vector as function of parameter coordinate
real	dydx (const real aX) const
	derivative of Y with respect to X
real	dxdy (const real aY) const
	derivative of X with respect to Y
real	d2ydx2 (const real aX) const
	second derivative of Y with respect to X
real	d2xdy2 (const real aY) const
	second derivative of X with respect to Y
real	d3ydx3 (const real aX) const
	third derivative of Y with respect to X
real	d3xdy3 (const real aY) const
	third derivative of X with respect to Y
real	compute_length (const uint aNumIntegrationPoints=21) const
	computes the length of the curve
real	compute_length (const Vector< double > &aW, const Vector< double > &aXi) const
	computes the length of the curve, but provide points and weights note that we need the doubles here, not the reals
void	compute_basis_xwise (const real aX0, const real aY0, const real adYdx0, const real aX1, const real aY1, const real adYdx1)
void	compute_basis_ywise (const real aX0, const real aY0, const real adYdx0, const real aX1, const real aY1, const real adYdx1)

Constructor & Destructor Documentation

Bezier() [1/2]

belfem::Bezier::Bezier	(	const real	aX0 = 0.0,
		const real	aY0 = 0.0,
		const real	adYdx0 = 0.0,
		const real	aX1 = 1.0,
		const real	aY1 = 1.0,
		const real	adYdx1 = 0.0,
		const BezierType	aType = BezierType::Horizontal )

Bezier() [2/2]

belfem::Bezier::Bezier	(	const Vector< real > &	aX,
		const Vector< real > &	aY,
		const BezierType	aType = BezierType::Horizontal )

~Bezier()

belfem::Bezier::~Bezier ( )

default

Member Function Documentation

basis_x() [1/2]

Vector< real > & belfem::Bezier::basis_x ( )

inline

expose the x-coordinates of the basis

basis_x() [2/2]

const Vector< real > & belfem::Bezier::basis_x ( ) const

inline

basis_y() [1/2]

Vector< real > & belfem::Bezier::basis_y ( )

inline

expose the y-coordinates of the basis

basis_y() [2/2]

const Vector< real > & belfem::Bezier::basis_y ( ) const

inline

compute_basis_xwise()

void belfem::Bezier::compute_basis_xwise	(	const real	aX0,
		const real	aY0,
		const real	adYdx0,
		const real	aX1,
		const real	aY1,
		const real	adYdx1 )

compute_basis_ywise()

void belfem::Bezier::compute_basis_ywise	(	const real	aX0,
		const real	aY0,
		const real	adYdx0,
		const real	aX1,
		const real	aY1,
		const real	adYdx1 )

compute_length() [1/2]

real belfem::Bezier::compute_length

(

const uint

aNumIntegrationPoints = 21

)

const

computes the length of the curve

compute_length() [2/2]

real belfem::Bezier::compute_length	(	const Vector< double > &	aW,
		const Vector< double > &	aXi ) const

computes the length of the curve, but provide points and weights note that we need the doubles here, not the reals

computes the length of the curve, but provide points and weights

d2xdy2()

real belfem::Bezier::d2xdy2

(

const real

aY

)

const

second derivative of X with respect to Y

Parameters

aY

Returns

second derivative of X

d2ydx2()

real belfem::Bezier::d2ydx2

(

const real

aX

)

const

second derivative of Y with respect to X

Parameters

aX

Returns

aY

d3xdy3()

real belfem::Bezier::d3xdy3

(

const real

aY

)

const

third derivative of X with respect to Y

Parameters

aY

Returns

aX

d3ydx3()

real belfem::Bezier::d3ydx3

(

const real

aX

)

const

third derivative of Y with respect to X

Parameters

aX

Returns

aY

dddpoint()

void belfem::Bezier::dddpoint	(	real &	ad3XdXi3,
		real &	ad3YdXi3 ) const

aberrancy vector as function of parameter coordinate

Parameters

ad3XdXi3
ad3YdXi3

ddpoint()

void belfem::Bezier::ddpoint	(	const real	aXi,
		real &	ad2XdXi2,
		real &	ad2YdXi2 ) const

curvature vector as function of parameter coordinate

Parameters

aXi
ad2XdXi2
ad2YdXi2

dpoint()

void belfem::Bezier::dpoint	(	const real	aXi,
		real &	adXdXi,
		real &	adYdXi ) const

tangent vector as function of parameter coordinate

Parameters

aXi
adXdXi
adYdXi

dxdy()

real belfem::Bezier::dxdy

(

const real

aY

)

const

derivative of X with respect to Y

Parameters

aY

Returns

aX

dydx()

real belfem::Bezier::dydx

(

const real

aX

)

const

derivative of Y with respect to X

Parameters

aX

Returns

aY

point()

void belfem::Bezier::point	(	const real	aXi,
		real &	aX,
		real &	aY ) const

point as function of parameter coordinate

Parameters

aXi
aX
aY

x()

real belfem::Bezier::x

(

const real

aY

)

const

x-coordinate as funciton of the y-coordinate

Parameters

aY

Returns

x_by_xi()

real belfem::Bezier::x_by_xi

(

const real

aXi

)

const

The parameter coordinate goes from -1 <= xi <= 1.

This funciton computes the spatial x-coordinate

Parameters

aXi

Returns

aX

xi_by_x()

real belfem::Bezier::xi_by_x

(

const real

aX

)

const

Inverts the function x_by_xi.

Queries outside [ mX(0), mX(3) ] saturate to xi = -1 / xi = +1.

Parameters

aX

Returns

aXi

xi_by_y()

real belfem::Bezier::xi_by_y

(

const real

aY

)

const

Inverts the function y_by_xi.

Queries outside [ mY(0), mY(3) ] saturate to xi = -1 / xi = +1.

Parameters

aY

Returns

aXi

y()

real belfem::Bezier::y

(

const real

aX

)

const

y-coordinate as funciton of the x-coordinate

Parameters

aX

Returns

y_by_xi()

real belfem::Bezier::y_by_xi

(

const real

aXi

)

const

The parameter coordinate goes from -1 <= xi <= 1.

This funciton computes the spatial y-coordinate

Parameters

aXi

Returns

aY

---

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

• src/numerics/bezier/cl_Bezier.hpp
• src/numerics/bezier/cl_Bezier.cpp