Represents the knot vector for a B-Spline/NURBS Curve/Surface. More...

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

Classes
class	DerivativeBasisView

struct	DerivativeBasisWorkspace
	Scratch storage for derivativeBasisFunctionsBySpan(...) More...

Public Member Functions
	AXOM_STATIC_ASSERT_MSG (std::is_arithmetic< T >::value, "A knot vector must be defined using an arithmetic type")

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

Constructors for KnotVector
The KnotVector class provides constructors that allow initialization from a user-supplied array of knots and a specified degree and enforces several conditions to ensure validity: the degree must be at least -1 the knot array must contain at least (degree + 1) elements, if the knot array is not empty, its data pointer must not be nullptr. These checks guarantee that the constructed KnotVector adheres to the requirements for B-Spline/NURBS curves, such as monotonicity, clamped ends, and appropriate internal knot multiplicity. The isValid() method is used to verify that the resulting instance meets all necessary criteria for a valid knot span.
	KnotVector (axom::ArrayView< const T > knots, int degree)
	Constructor from a user-supplied knot vector (axom::ArrayView<const T>) More...

	KnotVector (axom::ArrayView< T > knots, int degree)

	KnotVector ()
	Default constructor for an empty (invalid) knot vector. More...

	KnotVector (axom::IndexType npts, int degree)
	Constructor for a normalized, uniform knot vector. More...

	KnotVector (const T *knots, axom::IndexType nkts, int degree)
	Constructor from a user-supplied knot vector (C-style array) More...

	KnotVector (const axom::Array< T > &knots, int degree)
	Constructor from a user-supplied knot vector (axom::Array) More...

Query/modify knot vector properties and sizes
void	makeUniform (axom::IndexType npts, int deg)
	Give the knot vector uniformly spaced internal knots. More...

int	getDegree () const
	Return the degree of the knot vector. More...

void	setDegree (int degree)
	Reset the knot vector for the given degree. More...

axom::IndexType	getNumKnots () const
	Return the number of knots in the knot vector. More...

axom::IndexType	getNumControlPoints () const
	Return the number of control points implied by the knot vector. More...

T	getMinKnot () const
	Return the value of the smallest knot, or 0 if there are no knots. More...

T	getMaxKnot () const
	Return the value of the largest knot, or 0 if there are no knots. More...

void	clear ()
	Clear the list of knots. More...

bool	isValid () const
	Return if the knot vector is valid. More...

bool	isValidSpan (axom::IndexType span) const
	Check if a knot span is valid. More...

bool	isValidSpan (axom::IndexType span, T t) const
	Check if a knot span is valid and contains the parameter value t. More...

Query/modify/access knots
axom::Array< T > &	getArray ()
	Accessor for the array of knots. More...

const axom::Array< T > &	getArray () const
	Const accessor for the array of knots. More...

const T &	operator[] (axom::IndexType i) const
	Getter for the knot vector. More...

T &	operator[] (axom::IndexType i)
	Setter for the knot vector. More...

axom::Array< T >	getUniqueKnots () const
	Return an array of the unique knot values. More...

axom::IndexType	getNumKnotSpans () const
	Return the number of valid knot spans. More...

Query/modify KnotVector parametrization
void	normalize ()
	Normalize the knot vector to the span of [0, 1]. More...

void	rescale (T a, T b)
	Rescale the knot vector to the span of [a, b]. More...

void	reverse ()
	Reverse the knot vector. More...

void	insertKnotBySpan (axom::IndexType span, T t, int r)
	Insert a knot into the vector r times. More...

void	insertKnot (T t, int target_multiplicity)
	Insert a knot into the vector to have the given multiplicity. More...

bool	isValidParameter (T t, T EPS=1e-5) const
	Checks if given parameter is in knot span (to a tolerance) More...

bool	isValidInteriorParameter (T t) const
	Checks if given parameter is interior to knot span (to a tolerance) More...

Functions for evaluating knot vector
axom::IndexType	findSpan (T t) const
	Returns the index of the knot span containing parameter t. More...

axom::IndexType	findSpan (T t, int &multiplicity) const
	Returns the index of the knot span containing parameter t and its multiplicity. More...

axom::Array< T >	calculateBasisFunctionsBySpan (axom::IndexType span, T t) const
	Evaluates the NURBS basis functions for span at parameter value t. More...

axom::Array< T >	calculateBasisFunctions (T t) const
	Evaluates the NURBS basis functions for parameter value t. More...

axom::Array< axom::Array< T > >	derivativeBasisFunctionsBySpan (axom::IndexType span, T t, int n) const
	Evaluates the NURBS basis functions and derivatives for span at parameter value t. More...

DerivativeBasisView	derivativeBasisFunctionsBySpan (axom::IndexType span, T t, int n, DerivativeBasisWorkspace &workspace) const
	Evaluates the NURBS basis functions and derivatives using a caller-supplied workspace. More...

axom::Array< axom::Array< T > >	derivativeBasisFunctions (T t, int n) const
	Evaluates the NURBS basis functions and derivatives for parameter value t. More...

Functions dealing with knot vector subdivision
void	splitBySpan (axom::IndexType span, KnotVector &k1, KnotVector &k2, bool normalize=false) const
	Split a knot vector at the value at index `span` More...

void	split (T t, KnotVector &k1, KnotVector &k2, bool normalize=false) const
	Split a knot vector at the value t. More...

Friends
bool	operator== (const KnotVector< T > &lhs, const KnotVector< T > &rhs)
	Check equality of two knot vectors. More...

bool	operator!= (const KnotVector< T > &lhs, const KnotVector< T > &rhs)
	Check inequality of two knot vectors. More...

Detailed Description

template<typename T>
class axom::primal::KnotVector< T >

Represents the knot vector for a B-Spline/NURBS Curve/Surface.

Template Parameters

T	the coordinate type, e.g., double, float, etc.

Contains methods for knot vector manipulation shared between NURBS curves and surfaces. This class maintains the degree and requirements on a knot vector, namely

Monotonicity (u_i <= u_i+1) Open/Clamped-ness (degree + 1 knots at beginning and end) Continuity (maximum internal knot multiplicity = degree)

Constructor & Destructor Documentation

◆ KnotVector() [1/6]

template<typename T >

axom::primal::KnotVector< T >::KnotVector	(	axom::ArrayView< const T >	knots,
		int	degree
	)

inline

Constructor from a user-supplied knot vector (axom::ArrayView<const T>)

Parameters

[in]	knots	the knot vector
[in]	degree	the degree of the curve

Precondition: degree >= 1. When degree is less than 0, the KnotVector is invalid; The knots can be empty when the degree is -1, otherwise knots.data() is not nullptr

See also: isValid() tests conditions for a valid knot span instance

References axom::ArrayView< T, DIM, SPACE >::data(), axom::ArrayView< T, DIM, SPACE >::empty(), axom::primal::KnotVector< T >::isValid(), axom::ArrayView< T, DIM, SPACE >::size(), and SLIC_ASSERT.

◆ KnotVector() [2/6]

template<typename T >

axom::primal::KnotVector< T >::KnotVector	(	axom::ArrayView< T >	knots,
		int	degree
	)

inline

◆ KnotVector() [3/6]

template<typename T >

axom::primal::KnotVector< T >::KnotVector ( )

inline

Default constructor for an empty (invalid) knot vector.

◆ KnotVector() [4/6]

template<typename T >

axom::primal::KnotVector< T >::KnotVector	(	axom::IndexType	npts,
		int	degree
	)

inline

Constructor for a normalized, uniform knot vector.

Parameters

[in]	npts	the number of control points
[in]	degree	the degree

Precondition: degree is greater than or equal to 0, and deg < npts.

References axom::primal::KnotVector< T >::makeUniform().

◆ KnotVector() [5/6]

template<typename T >

axom::primal::KnotVector< T >::KnotVector	(	const T *	knots,
		axom::IndexType	nkts,
		int	degree
	)

inline

Constructor from a user-supplied knot vector (C-style array)

Parameters

[in]	knots	the knot vector
[in]	nkts	the length of the knot vector
[in]	degree	the degree of the curve

See also: KnotVector(axom::ArrayView<const T> knots, int degree)

◆ KnotVector() [6/6]

template<typename T >

axom::primal::KnotVector< T >::KnotVector	(	const axom::Array< T > &	knots,
		int	degree
	)

inline

Constructor from a user-supplied knot vector (axom::Array)

Parameters

[in]	knots	the knot vector
[in]	degree	the degree of the curve

See also: KnotVector(axom::ArrayView<const T> knots, int degree)

Member Function Documentation

◆ AXOM_STATIC_ASSERT_MSG()

template<typename T >

axom::primal::KnotVector< T >::AXOM_STATIC_ASSERT_MSG	(	std::is_arithmetic< T >::value	,
		"A knot vector must be defined using an arithmetic type"
	)

◆ makeUniform()

template<typename T >

void axom::primal::KnotVector< T >::makeUniform	(	axom::IndexType	npts,
		int	deg
	)

inline

Give the knot vector uniformly spaced internal knots.

Parameters

[in]	npts	The number of (implied) control points
[in]	deg	The degree of the curve

Precondition: Requires that npts + deg + 1 > 0 and deg < npts

References SLIC_ASSERT.

◆ getDegree()

template<typename T >

int axom::primal::KnotVector< T >::getDegree ( ) const

inline

Return the degree of the knot vector.

◆ setDegree()

template<typename T >

void axom::primal::KnotVector< T >::setDegree ( int degree )

inline

Reset the knot vector for the given degree.

Parameters

[in] degree The target degree

If the target degree is greater than the current degree, the knot vector must be expanded to remain valid (clamped)

Warning: This method will always replace existing knot values

References axom::primal::KnotVector< T >::getNumControlPoints(), axom::primal::KnotVector< T >::makeUniform(), and SLIC_ASSERT.

◆ getNumKnots()

template<typename T >

axom::IndexType axom::primal::KnotVector< T >::getNumKnots ( ) const

inline

Return the number of knots in the knot vector.

◆ getNumControlPoints()

template<typename T >

axom::IndexType axom::primal::KnotVector< T >::getNumControlPoints ( ) const

inline

Return the number of control points implied by the knot vector.

◆ getMinKnot()

template<typename T >

T axom::primal::KnotVector< T >::getMinKnot ( ) const

inline

Return the value of the smallest knot, or 0 if there are no knots.

◆ getMaxKnot()

template<typename T >

T axom::primal::KnotVector< T >::getMaxKnot ( ) const

inline

Return the value of the largest knot, or 0 if there are no knots.

◆ clear()

template<typename T >

void axom::primal::KnotVector< T >::clear ( )

inline

Clear the list of knots.

◆ isValid()

template<typename T >

bool axom::primal::KnotVector< T >::isValid ( ) const

inline

Return if the knot vector is valid.

References axom::primal::KnotVector< T >::getMaxKnot(), and axom::primal::KnotVector< T >::getMinKnot().

◆ isValidSpan() [1/2]

template<typename T >

bool axom::primal::KnotVector< T >::isValidSpan ( axom::IndexType span ) const

inline

Check if a knot span is valid.

Parameters

[in] span The span to check

A valid span is one that is within the knot vector and has a non-zero length

Returns: True if the span is valid, false otherwise

◆ isValidSpan() [2/2]

template<typename T >

bool axom::primal::KnotVector< T >::isValidSpan	(	axom::IndexType	span,
		T	t
	)		const

inline

Check if a knot span is valid and contains the parameter value t.

Parameters

[in]	span	The span to check
[in]	t	The parameter value

A valid span is one that is within the knot vector, has a non-zero length, and contains the parameter value t

Returns: True if the span is valid, false otherwise

References axom::primal::KnotVector< T >::isValidSpan().

◆ getArray() [1/2]

template<typename T >

axom::Array<T>& axom::primal::KnotVector< T >::getArray ( )

inline

Accessor for the array of knots.

◆ getArray() [2/2]

template<typename T >

const axom::Array<T>& axom::primal::KnotVector< T >::getArray ( ) const

inline

Const accessor for the array of knots.

◆ operator[]() [1/2]

template<typename T >

const T& axom::primal::KnotVector< T >::operator[] ( axom::IndexType i ) const

inline

Getter for the knot vector.

Parameters

[in] i The vector index

Returns: A const reference to the knot value at index i

◆ operator[]() [2/2]

template<typename T >

T& axom::primal::KnotVector< T >::operator[] ( axom::IndexType i )

inline

Setter for the knot vector.

Parameters

[in] i The vector index

Precondition: Assumes that the knot vector will remain valid after the change

Returns: A reference to the knot value at index i

References axom::primal::KnotVector< T >::isValid(), and SLIC_ASSERT.

◆ getUniqueKnots()

template<typename T >

axom::Array<T> axom::primal::KnotVector< T >::getUniqueKnots ( ) const

inline

Return an array of the unique knot values.

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

◆ getNumKnotSpans()

template<typename T >

axom::IndexType axom::primal::KnotVector< T >::getNumKnotSpans ( ) const

inline

Return the number of valid knot spans.

◆ normalize()

template<typename T >

void axom::primal::KnotVector< T >::normalize ( )

inline

Normalize the knot vector to the span of [0, 1].

References axom::primal::KnotVector< T >::getMaxKnot(), and axom::primal::KnotVector< T >::getMinKnot().

◆ rescale()

template<typename T >

void axom::primal::KnotVector< T >::rescale	(	T	a,
		T	b
	)

inline

Rescale the knot vector to the span of [a, b].

Parameters

[in]	a	The lower bound of the new knot vector
[in]	b	The upper bound of the new knot vector

Precondition: Requires a < b

References axom::primal::KnotVector< T >::getMaxKnot(), axom::primal::KnotVector< T >::getMinKnot(), axom::utilities::lerp(), and SLIC_ASSERT.

◆ reverse()

template<typename T >

void axom::primal::KnotVector< T >::reverse ( )

inline

Reverse the knot vector.

References axom::primal::KnotVector< T >::getMaxKnot(), axom::primal::KnotVector< T >::getMinKnot(), and axom::utilities::swap().

◆ insertKnotBySpan()

template<typename T >

void axom::primal::KnotVector< T >::insertKnotBySpan	(	axom::IndexType	span,
		T	t,
		int	r
	)

inline

Insert a knot into the vector r times.

Parameters

[in]	span	The span into which the knot will be inserted
[in]	t	The value of the knot to insert
[in]	r	The number of times to insert the knot

Precondition: Assumes that the input span is correct for input t, and that the knot is not present enough times to exceed the degree

References axom::primal::KnotVector< T >::isValid(), axom::primal::KnotVector< T >::isValidSpan(), and SLIC_ASSERT.

◆ insertKnot()

template<typename T >

void axom::primal::KnotVector< T >::insertKnot	(	T	t,
		int	target_multiplicity
	)

inline

Insert a knot into the vector to have the given multiplicity.

Parameters

[in]	t	The value of the knot to insert
[in]	target_mutliplicity	The number of times the knot will be present

Precondition: Assumes that the input t is within the knot vector (up to some tolerance)

Note: If the knot is already present, it will be inserted up to the given multiplicity, or the maximum permitted by the degree

References axom::utilities::clampVal(), axom::primal::KnotVector< T >::findSpan(), axom::primal::KnotVector< T >::insertKnotBySpan(), axom::primal::KnotVector< T >::isValidParameter(), and SLIC_ASSERT.

◆ isValidParameter()

template<typename T >

bool axom::primal::KnotVector< T >::isValidParameter	(	T	t,
		T	EPS = `1e-5`
	)		const

inline

Checks if given parameter is in knot span (to a tolerance)

References axom::primal::KnotVector< T >::getMaxKnot(), and axom::primal::KnotVector< T >::getMinKnot().

◆ isValidInteriorParameter()

template<typename T >

bool axom::primal::KnotVector< T >::isValidInteriorParameter ( T t ) const

inline

Checks if given parameter is interior to knot span (to a tolerance)

References axom::primal::KnotVector< T >::getMaxKnot(), and axom::primal::KnotVector< T >::getMinKnot().

◆ findSpan() [1/2]

template<typename T >

axom::IndexType axom::primal::KnotVector< T >::findSpan ( T t ) const

inline

Returns the index of the knot span containing parameter t.

Parameters

[in] t The parameter value

For knot vector {u_0, ..., u_n}, returns i such that u_i <= t < u_i+1 if t == u_n, returns i such that u_i < t <= u_i+1 (i.e. i = n - degree - 1)

Implementation adapted from Algorithm A2.1 on page 68 of "The NURBS Book"

Precondition: Assumes that the input t is in the span [u_0, u_n] (up to some tolerance)

Note: If t is outside the knot span up to this tolerance, it is clamped to the span

Returns: The index of the knot span containing t

References axom::primal::KnotVector< T >::getMaxKnot(), axom::primal::KnotVector< T >::getMinKnot(), axom::primal::KnotVector< T >::isValidParameter(), and SLIC_ASSERT.

◆ findSpan() [2/2]

template<typename T >

axom::IndexType axom::primal::KnotVector< T >::findSpan	(	T	t,
		int &	multiplicity
	)		const

inline

Returns the index of the knot span containing parameter t and its multiplicity.

Parameters

[in]	t	The parameter value
[out]	multiplicity	The multiplicity of the knot at t

For knot vector {u_0, ..., u_n}, returns i such that u_i <= t < u_i+1 if t == u_n, returns i such that u_i < t <= u_i+1 (i.e. i = n - degree - 1)

Precondition: Assumes that the input t is within the knot vector (up to some tolerance)

Note: If t is outside the knot span up to this tolerance, the returned multiplicity will be equal to the degree + 1 (required for clamped curves)

Returns: The index of the knot span containing t

References axom::primal::KnotVector< T >::findSpan(), axom::primal::KnotVector< T >::getMaxKnot(), axom::primal::KnotVector< T >::getMinKnot(), axom::primal::KnotVector< T >::isValidParameter(), and SLIC_ASSERT.

◆ calculateBasisFunctionsBySpan()

template<typename T >

axom::Array<T> axom::primal::KnotVector< T >::calculateBasisFunctionsBySpan	(	axom::IndexType	span,
		T	t
	)		const

inline

Evaluates the NURBS basis functions for span at parameter value t.

Parameters

[in]	span	The span in which to evaluate the basis functions
[in]	t	The parameter value

Precondition: Assumes that the input t is within the correct span Implementation adapted from Algorithm A2.2 on page 70 of "The NURBS Book".

Returns: An array of the m_deg + 1 non-zero basis functions evaluated at t

References axom::primal::KnotVector< T >::isValidSpan(), and SLIC_ASSERT.

◆ calculateBasisFunctions()

template<typename T >

axom::Array<T> axom::primal::KnotVector< T >::calculateBasisFunctions ( T t ) const

inline

Evaluates the NURBS basis functions for parameter value t.

Parameters

[in] t The parameter value

Precondition: Assumes that the input t is within the knot vector (up to a tolerance)

Returns: An array of the m_deg + 1 non-zero basis functions evaluated at t

References axom::primal::KnotVector< T >::calculateBasisFunctionsBySpan(), axom::primal::KnotVector< T >::findSpan(), axom::primal::KnotVector< T >::isValidParameter(), and SLIC_ASSERT.

◆ derivativeBasisFunctionsBySpan() [1/2]

template<typename T >

axom::Array<axom::Array<T> > axom::primal::KnotVector< T >::derivativeBasisFunctionsBySpan	(	axom::IndexType	span,
		T	t,
		int	n
	)		const

inline

Evaluates the NURBS basis functions and derivatives for span at parameter value t.

Parameters

[in]	span	The span in which to evaluate the basis functions
[in]	t	The parameter value
[in]	n	The number of derivatives to compute

Implementation adapted from Algorithm A2.2 on page 70 of "The NURBS Book".

Precondition: Assumes that the input t is within the provided knot span

Returns: An array of the n + 1 derivatives evaluated at t

References axom::primal::KnotVector< T >::isValidSpan(), axom::Array< T, DIM, SPACE, StoragePolicy >::resize(), SLIC_ASSERT, and axom::utilities::swap().

◆ derivativeBasisFunctionsBySpan() [2/2]

template<typename T >

DerivativeBasisView axom::primal::KnotVector< T >::derivativeBasisFunctionsBySpan	(	axom::IndexType	span,
		T	t,
		int	n,
		DerivativeBasisWorkspace &	workspace
	)		const

inline

Evaluates the NURBS basis functions and derivatives using a caller-supplied workspace.

Note: This overload avoids per-call dynamic allocations by reusing memory in workspace.

Warning: The returned views are only valid until workspace is reused.

References axom::primal::KnotVector< T >::DerivativeBasisWorkspace::a, axom::primal::KnotVector< T >::DerivativeBasisWorkspace::ders, axom::primal::KnotVector< T >::DerivativeBasisWorkspace::ensure(), axom::primal::KnotVector< T >::isValidSpan(), axom::primal::KnotVector< T >::DerivativeBasisWorkspace::left, axom::primal::KnotVector< T >::DerivativeBasisWorkspace::ndu, axom::primal::KnotVector< T >::DerivativeBasisWorkspace::right, SLIC_ASSERT, and axom::utilities::swap().

◆ derivativeBasisFunctions()

template<typename T >

axom::Array<axom::Array<T> > axom::primal::KnotVector< T >::derivativeBasisFunctions	(	T	t,
		int	n
	)		const

inline

Evaluates the NURBS basis functions and derivatives for parameter value t.

Parameters

[in]	t	The parameter value
[in]	n	The number of derivatives to compute

Precondition: Assumes that the input t is within the knot vector (up to a tolerance)

Returns: An array of the n + 1 derivatives evaluated at t

References axom::primal::KnotVector< T >::derivativeBasisFunctionsBySpan(), axom::primal::KnotVector< T >::findSpan(), axom::primal::KnotVector< T >::isValidParameter(), and SLIC_ASSERT.

◆ splitBySpan()

template<typename T >

void axom::primal::KnotVector< T >::splitBySpan	(	axom::IndexType	span,
		KnotVector< T > &	k1,
		KnotVector< T > &	k2,
		bool	normalize = `false`
	)		const

inline

Split a knot vector at the value at index span

Parameters

[in]	span	The span at which the knot will be split
[out]	k1	The first knot vector
[out]	k2	The second knot vector
[in]	normalize	Whether to normalize the output knot vectors

Warning: Assumes that the multiplicity of the knot at which the vector will be split is equal to the degree, or the returned knot vectors will be invalid

References axom::primal::KnotVector< T >::getNumKnots(), axom::primal::KnotVector< T >::isValid(), axom::primal::KnotVector< T >::isValidSpan(), axom::primal::KnotVector< T >::normalize(), and SLIC_ASSERT.

◆ split()

template<typename T >

void axom::primal::KnotVector< T >::split	(	T	t,
		KnotVector< T > &	k1,
		KnotVector< T > &	k2,
		bool	normalize = `false`
	)		const

inline

Split a knot vector at the value t.

Parameters

[in]	t	The value at which the knot will be split
[out]	k1	The first knot vector
[out]	k2	The second knot vector
[in]	normalize	Whether to normalize the output knot vectors

Precondition: Assumes that the input t is interior to the knot vector

References axom::primal::KnotVector< T >::findSpan(), axom::primal::KnotVector< T >::insertKnotBySpan(), axom::primal::KnotVector< T >::isValidInteriorParameter(), axom::primal::KnotVector< T >::normalize(), SLIC_ASSERT, and axom::primal::KnotVector< T >::splitBySpan().

◆ print()

template<typename T >

std::ostream& axom::primal::KnotVector< T >::print ( std::ostream & os ) const

inline

Simple formatted print of a knot vector instance.

Parameters

os	The output stream to write to

Returns: A reference to the modified ostream

Friends And Related Function Documentation

◆ operator==

template<typename T >

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

friend

Check equality of two knot vectors.

Parameters

[in]	lhs	The first knot vector
[in]	rhs	The second knot vector

Returns: True if the knot vectors are equal, false otherwise

◆ operator!=

template<typename T >

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

friend

Check inequality of two knot vectors.

Parameters

[in]	lhs	The first knot vector
[in]	rhs	The second knot vector

Returns: True if the knot vectors are not equal, false otherwise

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/main/src/axom/primal/geometry/KnotVector.hpp

Classes

Public Member Functions

Friends

Detailed Description

template<typename T> class axom::primal::KnotVector< T >

Constructor & Destructor Documentation

◆ KnotVector() [1/6]

◆ KnotVector() [2/6]

◆ KnotVector() [3/6]

◆ KnotVector() [4/6]

◆ KnotVector() [5/6]

◆ KnotVector() [6/6]

Member Function Documentation

◆ AXOM_STATIC_ASSERT_MSG()

◆ makeUniform()

◆ getDegree()

◆ setDegree()

◆ getNumKnots()

◆ getNumControlPoints()

◆ getMinKnot()

◆ getMaxKnot()

◆ clear()

◆ isValid()

◆ isValidSpan() [1/2]

◆ isValidSpan() [2/2]

◆ getArray() [1/2]

◆ getArray() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ getUniqueKnots()

◆ getNumKnotSpans()

◆ normalize()

◆ rescale()

◆ reverse()

◆ insertKnotBySpan()

◆ insertKnot()

◆ isValidParameter()

◆ isValidInteriorParameter()

◆ findSpan() [1/2]

◆ findSpan() [2/2]

◆ calculateBasisFunctionsBySpan()

◆ calculateBasisFunctions()

◆ derivativeBasisFunctionsBySpan() [1/2]

◆ derivativeBasisFunctionsBySpan() [2/2]

◆ derivativeBasisFunctions()

◆ splitBySpan()

◆ split()

◆ print()

Friends And Related Function Documentation

◆ operator==

◆ operator!=

template<typename T>
class axom::primal::KnotVector< T >