Represents a Bezier curve defined by an array of control points. More...

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/primal/geometry/BezierCurve.hpp>

Public Types
using	PointType = Point< T, NDIMS >

using	VectorType = Vector< T, NDIMS >

using	SegmentType = Segment< T, NDIMS >

using	WeightsVec = axom::Array< T >

using	CoordsVec = axom::Array< PointType >

using	BoundingBoxType = BoundingBox< T, NDIMS >

using	OrientedBoundingBoxType = OrientedBoundingBox< T, NDIMS >

Public Member Functions
	AXOM_STATIC_ASSERT_MSG ((NDIMS==1)\|\|(NDIMS==2)\|\|(NDIMS==3), "A Bezier Curve object may be defined in 1-, 2-, or 3-D")

	AXOM_STATIC_ASSERT_MSG (std::is_arithmetic< T >::value, "A Bezier Curve must be defined using an arithmetic type")

	BezierCurve (int ord=-1)
	Constructor for a Bezier Curve that reserves space for the given order of the curve. More...

	BezierCurve (PointType *pts, int ord)
	Constructor for a Bezier Curve from an array of coordinates. More...

	BezierCurve (PointType pts, T weights, int ord)
	Constructor for a Bezier Curve from an array of coordinates. More...

	BezierCurve (const axom::Array< PointType > &pts, int ord)
	Constructor for a Bezier Curve from an vector of coordinates. More...

	BezierCurve (const axom::Array< PointType > &pts, const axom::Array< T > &weights, int ord)
	Constructor for a Rational Bezier Curve from an vector of coordinates and weights. More...

void	setOrder (int ord)
	Sets the order of the Bezier Curve. More...

int	getOrder () const
	Returns the order of the Bezier Curve. More...

void	makeRational ()
	Make trivially rational. If already rational, do nothing. More...

void	makeNonrational ()
	Make nonrational by shrinking array of weights. More...

bool	isRational () const
	Use array size as flag for rationality. More...

void	clear ()
	Clears the list of control points, make nonrational. More...

PointType &	operator[] (int idx)
	Retrieves the control point at index idx. More...

const PointType &	operator[] (int idx) const
	Retrieves the control point at index idx. More...

const T &	getWeight (int idx) const
	Get a specific weight. More...

void	setWeight (int idx, T weight)
	Set the weight at a specific index. More...

CoordsVec	getControlPoints () const
	Returns a copy of the Bezier curve's control points. More...

WeightsVec	getWeights () const
	Returns a copy of the Bezier curve's weights. More...

void	reverseOrientation ()
	Reverses the order of the Bezier curve's control points and weights. More...

BoundingBoxType	boundingBox () const
	Returns an axis-aligned bounding box containing the Bezier curve. More...

OrientedBoundingBoxType	orientedBoundingBox () const
	Returns an oriented bounding box containing the Bezier curve. More...

PointType	evaluate (T t) const
	Evaluates a Bezier curve at a particular parameter value t. More...

void	evaluate_first_derivative (T t, PointType &eval, VectorType &Dt) const
	Computes the 0th and 1st derivative of a Bezier curve. More...

VectorType	dt (T t) const
	Computes the tangent of a Bezier curve at a particular parameter value t. More...

void	evaluate_second_derivative (T t, PointType &eval, VectorType &Dt, VectorType &DtDt) const
	Computes the 0th, 1st, and 2nd derivatives of a Bezier curve. More...

VectorType	dtdt (T t) const
	Computes the second derivative of a Bezier curve at a particular parameter value t. More...

void	split (T t, BezierCurve &c1, BezierCurve &c2) const
	Splits a Bezier curve into two Bezier curves at a given parameter value. More...

bool	isLinear (double tol=1E-8) const
	Predicate to check if the Bezier curve is approximately linear. More...

std::ostream &	print (std::ostream &os) const
	Simple formatted print of a Bezier Curve instance. More...

Friends
bool	operator== (const BezierCurve< T, NDIMS > &lhs, const BezierCurve< T, NDIMS > &rhs)
	Checks equality of two Bezier Curve. More...

bool	operator!= (const BezierCurve< T, NDIMS > &lhs, const BezierCurve< T, NDIMS > &rhs)

Detailed Description

template<typename T, int NDIMS>
class axom::primal::BezierCurve< T, NDIMS >

Represents a Bezier curve defined by an array of control points.

Template Parameters

T	the coordinate type, e.g., double, float, etc.
NDIMS	the number of dimensions

The order of a Bezier curve with N+1 control points is N. The curve is approximated by the control points, parametrized from t=0 to t=1.

Contains an array of positive weights to represent a rational Bezier curve. Nonrational Bezier curves are identified by an empty weights array. Algorithms for Rational Bezier curves derived from Gerald Farin, "Algorithms for rational Bezier curves" Computer-Aided Design, Volume 15, Number 2, 1983,

Member Typedef Documentation

◆ PointType

template<typename T , int NDIMS>

using axom::primal::BezierCurve< T, NDIMS >::PointType = Point<T, NDIMS>

◆ VectorType

template<typename T , int NDIMS>

using axom::primal::BezierCurve< T, NDIMS >::VectorType = Vector<T, NDIMS>

◆ SegmentType

template<typename T , int NDIMS>

using axom::primal::BezierCurve< T, NDIMS >::SegmentType = Segment<T, NDIMS>

◆ WeightsVec

template<typename T , int NDIMS>

using axom::primal::BezierCurve< T, NDIMS >::WeightsVec = axom::Array<T>

◆ CoordsVec

template<typename T , int NDIMS>

using axom::primal::BezierCurve< T, NDIMS >::CoordsVec = axom::Array<PointType>

◆ BoundingBoxType

template<typename T , int NDIMS>

using axom::primal::BezierCurve< T, NDIMS >::BoundingBoxType = BoundingBox<T, NDIMS>

◆ OrientedBoundingBoxType

template<typename T , int NDIMS>

using axom::primal::BezierCurve< T, NDIMS >::OrientedBoundingBoxType = OrientedBoundingBox<T, NDIMS>

Constructor & Destructor Documentation

◆ BezierCurve() [1/5]

template<typename T , int NDIMS>

axom::primal::BezierCurve< T, NDIMS >::BezierCurve ( int ord = -1 )

inlineexplicit

Constructor for a Bezier Curve that reserves space for the given order of the curve.

Parameters

[in] order the order of the resulting Bezier curve

Precondition: order is greater than or equal to -1.

References axom::primal::BezierCurve< T, NDIMS >::makeNonrational(), axom::utilities::max(), axom::Array< T, DIM, SPACE >::resize(), and SLIC_ASSERT.

◆ BezierCurve() [2/5]

template<typename T , int NDIMS>

axom::primal::BezierCurve< T, NDIMS >::BezierCurve	(	PointType *	pts,
		int	ord
	)

inline

Constructor for a Bezier Curve from an array of coordinates.

Parameters

[in]	pts	a vector with ord+1 control points
[in]	ord	The Curve's polynomial order

Precondition: order is greater than or equal to zero

References axom::primal::BezierCurve< T, NDIMS >::makeNonrational(), axom::utilities::max(), axom::Array< T, DIM, SPACE >::resize(), and SLIC_ASSERT.

◆ BezierCurve() [3/5]

template<typename T , int NDIMS>

axom::primal::BezierCurve< T, NDIMS >::BezierCurve	(	PointType *	pts,
		T *	weights,
		int	ord
	)

inline

Constructor for a Bezier Curve from an array of coordinates.

Parameters

[in]	pts	a vector with ord+1 control points
[in]	weights	a vector with ord+1 positive weights
[in]	ord	The Curve's polynomial order

Precondition: order is greater than or equal to zero

References axom::primal::BezierCurve< T, NDIMS >::makeNonrational(), axom::utilities::max(), axom::Array< T, DIM, SPACE >::resize(), and SLIC_ASSERT.

◆ BezierCurve() [4/5]

template<typename T , int NDIMS>

axom::primal::BezierCurve< T, NDIMS >::BezierCurve	(	const axom::Array< PointType > &	pts,
		int	ord
	)

inline

Constructor for a Bezier Curve from an vector of coordinates.

Parameters

[in]	pts	a vector with ord+1 control points
[in]	ord	The Curve's polynomial order

Precondition: order is greater than or equal to zero

References axom::primal::BezierCurve< T, NDIMS >::makeNonrational(), axom::utilities::max(), axom::Array< T, DIM, SPACE >::resize(), and SLIC_ASSERT.

◆ BezierCurve() [5/5]

template<typename T , int NDIMS>

axom::primal::BezierCurve< T, NDIMS >::BezierCurve	(	const axom::Array< PointType > &	pts,
		const axom::Array< T > &	weights,
		int	ord
	)

inline

Constructor for a Rational Bezier Curve from an vector of coordinates and weights.

Parameters

[in]	pts	a vector with ord+1 control points
[in]	weights	a vector with ord+1 positive weights
[in]	ord	The Curve's polynomial order

Precondition: order is greater than or equal to zero

References axom::utilities::max(), axom::Array< T, DIM, SPACE >::resize(), axom::Array< T, DIM, SPACE >::size(), and SLIC_ASSERT.

Member Function Documentation

◆ AXOM_STATIC_ASSERT_MSG() [1/2]

template<typename T , int NDIMS>

axom::primal::BezierCurve< T, NDIMS >::AXOM_STATIC_ASSERT_MSG	(	(NDIMS==1)\|\|(NDIMS==2)\|\|(NDIMS==3)	,
		"A Bezier Curve object may be defined in 1-	,
		2-	,
		or 3-D"
	)

◆ AXOM_STATIC_ASSERT_MSG() [2/2]

template<typename T , int NDIMS>

axom::primal::BezierCurve< T, NDIMS >::AXOM_STATIC_ASSERT_MSG	(	std::is_arithmetic< T >::value	,
		"A Bezier Curve must be defined using an arithmetic type"
	)

◆ setOrder()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::setOrder ( int ord )

inline

Sets the order of the Bezier Curve.

References axom::primal::BezierCurve< T, NDIMS >::isRational(), and axom::Array< T, DIM, SPACE >::resize().

◆ getOrder()

template<typename T , int NDIMS>

int axom::primal::BezierCurve< T, NDIMS >::getOrder ( ) const

inline

Returns the order of the Bezier Curve.

References axom::Array< T, DIM, SPACE >::size().

◆ makeRational()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::makeRational ( )

inline

Make trivially rational. If already rational, do nothing.

References axom::Array< T, DIM, SPACE >::fill(), axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and axom::Array< T, DIM, SPACE >::resize().

◆ makeNonrational()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::makeNonrational ( )

inline

Make nonrational by shrinking array of weights.

References axom::Array< T, DIM, SPACE >::resize().

◆ isRational()

template<typename T , int NDIMS>

bool axom::primal::BezierCurve< T, NDIMS >::isRational ( ) const

inline

Use array size as flag for rationality.

References axom::Array< T, DIM, SPACE >::empty().

◆ clear()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::clear ( )

inline

Clears the list of control points, make nonrational.

References axom::Array< T, DIM, SPACE >::clear(), and axom::primal::BezierCurve< T, NDIMS >::makeNonrational().

◆ operator[]() [1/2]

template<typename T , int NDIMS>

PointType& axom::primal::BezierCurve< T, NDIMS >::operator[] ( int idx )

inline

Retrieves the control point at index idx.

◆ operator[]() [2/2]

template<typename T , int NDIMS>

const PointType& axom::primal::BezierCurve< T, NDIMS >::operator[] ( int idx ) const

inline

Retrieves the control point at index idx.

◆ getWeight()

template<typename T , int NDIMS>

const T& axom::primal::BezierCurve< T, NDIMS >::getWeight ( int idx ) const

inline

Get a specific weight.

Parameters

[in] idx The index of the weight

Precondition: Requires that the curve be rational

References axom::primal::BezierCurve< T, NDIMS >::isRational(), and SLIC_ASSERT.

◆ setWeight()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::setWeight	(	int	idx,
		T	weight
	)

inline

Set the weight at a specific index.

Parameters

[in]	idx	The index of the weight
[in]	weight	The updated value of the weight

Precondition: Requires that the curve be rational; Requires that the weight be positive

References axom::primal::BezierCurve< T, NDIMS >::isRational(), and SLIC_ASSERT.

◆ getControlPoints()

template<typename T , int NDIMS>

CoordsVec axom::primal::BezierCurve< T, NDIMS >::getControlPoints ( ) const

inline

Returns a copy of the Bezier curve's control points.

◆ getWeights()

template<typename T , int NDIMS>

WeightsVec axom::primal::BezierCurve< T, NDIMS >::getWeights ( ) const

inline

Returns a copy of the Bezier curve's weights.

◆ reverseOrientation()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::reverseOrientation ( )

inline

Reverses the order of the Bezier curve's control points and weights.

References axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and axom::utilities::swap().

◆ boundingBox()

template<typename T , int NDIMS>

BoundingBoxType axom::primal::BezierCurve< T, NDIMS >::boundingBox ( ) const

inline

Returns an axis-aligned bounding box containing the Bezier curve.

References axom::Array< T, DIM, SPACE >::data(), and axom::Array< T, DIM, SPACE >::size().

◆ orientedBoundingBox()

template<typename T , int NDIMS>

OrientedBoundingBoxType axom::primal::BezierCurve< T, NDIMS >::orientedBoundingBox ( ) const

inline

Returns an oriented bounding box containing the Bezier curve.

References axom::Array< T, DIM, SPACE >::data(), and axom::Array< T, DIM, SPACE >::size().

◆ evaluate()

template<typename T , int NDIMS>

PointType axom::primal::BezierCurve< T, NDIMS >::evaluate ( T t ) const

inline

Evaluates a Bezier curve at a particular parameter value t.

Parameters

[in] t parameter value at which to evaluate

Returns: p the value of the Bezier curve at t

Note: We typically evaluate the curve at t between 0 and 1

References axom::utilities::annotations::end(), axom::primal::BezierCurve< T, NDIMS >::evaluate(), axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and axom::utilities::lerp().

◆ evaluate_first_derivative()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::evaluate_first_derivative	(	T	t,
		PointType &	eval,
		VectorType &	Dt
	)		const

inline

Computes the 0th and 1st derivative of a Bezier curve.

Parameters

[in]	t	Parameter value at which to compute tangent
[out]	eval	The value of the curve at t
[out]	Dt	The tangent vector of the curve at t

References axom::utilities::annotations::end(), axom::primal::BezierCurve< T, NDIMS >::evaluate_first_derivative(), axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and axom::utilities::lerp().

◆ dt()

template<typename T , int NDIMS>

VectorType axom::primal::BezierCurve< T, NDIMS >::dt ( T t ) const

inline

Computes the tangent of a Bezier curve at a particular parameter value t.

Parameters

[in] t parameter value at which to compute tangent

Returns: p the tangent vector of the Bezier curve at t

Note: We typically find the tangent of the curve at t between 0 and 1

References axom::utilities::annotations::end(), axom::primal::BezierCurve< T, NDIMS >::evaluate_first_derivative(), axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and axom::utilities::lerp().

◆ evaluate_second_derivative()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::evaluate_second_derivative	(	T	t,
		PointType &	eval,
		VectorType &	Dt,
		VectorType &	DtDt
	)		const

inline

Computes the 0th, 1st, and 2nd derivatives of a Bezier curve.

Parameters

[in]	t	Parameter value at which to compute tangent
[out]	eval	The value of the curve at t
[out]	Dt	The tangent vector of the curve at t

References axom::utilities::annotations::end(), axom::primal::BezierCurve< T, NDIMS >::evaluate_second_derivative(), axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and axom::utilities::lerp().

◆ dtdt()

template<typename T , int NDIMS>

VectorType axom::primal::BezierCurve< T, NDIMS >::dtdt ( T t ) const

inline

Computes the second derivative of a Bezier curve at a particular parameter value t.

Parameters

[in] t parameter value at which to compute tangent

Returns: p the 2nd derivative vector of the Bezier curve at t

Note: We typically find the second derivative of the curve at t between 0 and 1

References axom::utilities::annotations::end(), axom::primal::BezierCurve< T, NDIMS >::evaluate_second_derivative(), axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and axom::utilities::lerp().

◆ split()

template<typename T , int NDIMS>

void axom::primal::BezierCurve< T, NDIMS >::split	(	T	t,
		BezierCurve< T, NDIMS > &	c1,
		BezierCurve< T, NDIMS > &	c2
	)		const

inline

Splits a Bezier curve into two Bezier curves at a given parameter value.

Parameters

[in]	t	parameter value between 0 and 1 at which to evaluate
[out]	c1	First output Bezier curve
[out]	c2	Second output Bezier curve

Precondition: Parameter t must be between 0 and 1

References axom::utilities::annotations::end(), axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::getWeight(), axom::primal::BezierCurve< T, NDIMS >::isRational(), axom::primal::Point< T, NDIMS >::lerp(), axom::utilities::lerp(), axom::primal::BezierCurve< T, NDIMS >::makeRational(), axom::primal::BezierCurve< T, NDIMS >::setOrder(), axom::primal::BezierCurve< T, NDIMS >::setWeight(), and SLIC_ASSERT.

◆ isLinear()

template<typename T , int NDIMS>

bool axom::primal::BezierCurve< T, NDIMS >::isLinear ( double tol = 1E-8 ) const

inline

Predicate to check if the Bezier curve is approximately linear.

This function checks if the internal control points of the BezierCurve are approximately on the line defined by its two endpoints

Parameters

[in] tol Threshold for sum of squared distances

Returns: True if c1 is near-linear

References axom::primal::BezierCurve< T, NDIMS >::getOrder(), and axom::primal::squared_distance().

◆ print()

template<typename T , int NDIMS>

std::ostream& axom::primal::BezierCurve< T, NDIMS >::print ( std::ostream & os ) const

inline

Simple formatted print of a Bezier Curve instance.

Parameters

os	The output stream to write to

Returns: A reference to the modified ostream

References axom::primal::BezierCurve< T, NDIMS >::getOrder(), and axom::primal::BezierCurve< T, NDIMS >::isRational().

Friends And Related Function Documentation

◆ operator==

template<typename T , int NDIMS>

bool operator==	(	const BezierCurve< T, NDIMS > &	lhs,
		const BezierCurve< T, NDIMS > &	rhs
	)

friend

Checks equality of two Bezier Curve.

◆ operator!=

template<typename T , int NDIMS>

bool operator!=	(	const BezierCurve< T, NDIMS > &	lhs,
		const BezierCurve< T, NDIMS > &	rhs
	)

friend

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/primal/geometry/BezierCurve.hpp

Public Types

Public Member Functions

Friends

Detailed Description

template<typename T, int NDIMS> class axom::primal::BezierCurve< T, NDIMS >

Member Typedef Documentation

◆ PointType

◆ VectorType

◆ SegmentType

◆ WeightsVec

◆ CoordsVec

◆ BoundingBoxType

◆ OrientedBoundingBoxType

Constructor & Destructor Documentation

◆ BezierCurve() [1/5]

◆ BezierCurve() [2/5]

◆ BezierCurve() [3/5]

◆ BezierCurve() [4/5]

◆ BezierCurve() [5/5]

Member Function Documentation

◆ AXOM_STATIC_ASSERT_MSG() [1/2]

◆ AXOM_STATIC_ASSERT_MSG() [2/2]

◆ setOrder()

◆ getOrder()

◆ makeRational()

◆ makeNonrational()

◆ isRational()

◆ clear()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ getWeight()

◆ setWeight()

◆ getControlPoints()

◆ getWeights()

◆ reverseOrientation()

◆ boundingBox()

◆ orientedBoundingBox()

◆ evaluate()

◆ evaluate_first_derivative()

◆ dt()

◆ evaluate_second_derivative()

◆ dtdt()

◆ split()

◆ isLinear()

◆ print()

Friends And Related Function Documentation

◆ operator==

◆ operator!=

template<typename T, int NDIMS>
class axom::primal::BezierCurve< T, NDIMS >