Class BSpline

Class defining a B-Spline polynomial.

Inheritance

Object

Polynomial

BSpline

Implements

IGroupAction<Polynomial, Double>

Inherited Members

Polynomial.Degree

Polynomial.Item[Int32]

Polynomial.Zero

Polynomial.One

Polynomial.Derive(Polynomial, Int32)

Polynomial.Add(Polynomial, Polynomial)

Polynomial.Subtract(Polynomial, Polynomial)

Polynomial.Opposite(Polynomial)

Polynomial.Multiply(Polynomial, Polynomial)

Polynomial.Multiply(Polynomial, Double)

Polynomial.Multiply(Double, Polynomial)

Polynomial.Divide(Polynomial, Double)

Polynomial.Coefficient(Int32)

Polynomial.IGroupAction<Polynomial, Double>.Multiply(Double)

Polynomial.IGroupAction<Polynomial, Double>.Divide(Double)

Namespace: BRIDGES.Arithmetic.Polynomials.Univariate.Specials

Assembly: BRIDGES.dll

Syntax

public class BSpline : Polynomial, IGroupAction<Polynomial, double>

Constructors

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BSpline(Int32, Int32, Int32, IList<Double>)

Initialises a new instance of BSpline class by defining its index, degree and knot vector.

Declaration

public BSpline(int spanIndex, int index, int degree, IList<double> knotVector)

Parameters

Type	Name	Description
Int32	spanIndex	Index of knot span on which the current BSpline is defined.
Int32	index	Index of the B-Spline polynomial.
Int32	degree	Degree of the B-Spline polynomial.
IList<Double>	knotVector	Knot vector of the B-Spline polynomial.

Fields

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_knotVector

Knot vector associated with the current BSpline.

Declaration

protected List<double> _knotVector

Field Value

Type	Description
List<Double>

Properties

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Index

Gets the index of the current BSpline.

Declaration

public int Index { get; }

Property Value

Type	Description
Int32

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KnotVector

Gets the knot vector associated with the current BSpline.

Declaration

public double[] KnotVector { get; }

Property Value

Type	Description
Double[]

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SpanIndex

Gets the index of knot span on which the current BSpline is defined.

Declaration

public int SpanIndex { get; }

Property Value

Type	Description
Int32

Methods

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ComputeCoefficients(Int32, Int32, Int32, IList<Double>)

Sets the coefficients of the current BSpline polynomial.

Declaration

protected static double[] ComputeCoefficients(int spanIndex, int index, int degree, IList<double> knotVector)

Parameters

Type	Name	Description
Int32	spanIndex	Index of knot span on which the current BSpline is defined.
Int32	index	Index of the BSpline polynomial.
Int32	degree	Degree of the BSpline polynomial.
IList<Double>	knotVector	Knot vector of the BSpline polynomial.

Returns

Type	Description
Double[]	The coefficients of the BSpline polynomial.

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EvaluateAt(Double, Int32, Int32, IList<Double>)

Evaluates the BSpline at a given value.

Declaration

public static double EvaluateAt(double val, int index, int degree, IList<double> knotVector)

Parameters

Type	Name	Description
Double	val	Value to evaluate at.
Int32	index	Index of the BSpline to evaluate.
Int32	degree	Degree of the BSpline to evaluate.
IList<Double>	knotVector	Knot Vector associated with the BSpline to evaluate.

Returns

Type	Description
Double	The value of the BSpline the given value.

Remarks

The code is adapted from algorithm 2.4 described in the NURBS Book, by L. Piegl and W. Tiller.

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EvaluateAt(Double)

Computes the current BSpline at a given value.

Declaration

public override double EvaluateAt(double val)

Parameters

Type	Name	Description
Double	val	Value to evaluate at.

Returns

Type	Description
Double	The computed value of the current BSpline.

Overrides

Polynomial.EvaluateAt(Double)

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EvaluateBasisAt(Double, Int32, Int32, IList<Double>)

Evaluates a BSpline basis at a given value.

Declaration

public static double[] EvaluateBasisAt(double val, int knotSpanIndex, int degree, IList<double> knotVector)

Parameters

Type	Name	Description
Double	val	Value to evaluate at.
Int32	knotSpanIndex	Index of knot span containing the value.
Int32	degree	Degree of the BSpline basis.
IList<Double>	knotVector	Knot vector of the BSpline basis.

Returns

Type	Description
Double[]	The values of the non-zero BSpline polynomials of the basis, i.e. those ranging from N_{`knotSpanIndex` - `degree`, `degree`} to N_{`knotSpanIndex`, `degree`}.

Remarks

The code is adapted from algorithm 2.2 described in the NURBS Book, by L. Piegl and W. Tiller.

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EvaluateBasisDerivativesAt(Double, Int32, Int32, IList<Double>, Int32)

Evaluates the BSpline basis' derivatives of a given order, at a given value.

Declaration

public static double[][] EvaluateBasisDerivativesAt(double val, int knotSpanIndex, int degree, IList<double> knotVector, int order)

Parameters

Type	Name	Description
Double	val	Value to evaluate at.
Int32	knotSpanIndex	Index of knot span containing the value.
Int32	degree	Initial degree of the BSpline basis.
IList<Double>	knotVector	Initial knot vector of the BSpline basis.
Int32	order	Order of the derivatives.

Returns

Type	Description
Double[][]	The values of successive derivatives of the non-zero BSpline polynomial of the basis, i.e. those ranging from N_{`knotSpanIndex` - `degree`, `degree`} to N_{`knotSpanIndex`, `degree`}. The first index corresponds to the order of derivation, the second to the index of the BSpline polynomial shifted to start from zero.

Remarks

The code is adapted from algorithm 2.3 described in the NURBS Book, by L. Piegl and W. Tiller.

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EvaluateDerivativesAt(Double, Int32, Int32, IList<Double>, Int32)

Evaluates the BSpline derivative of a given order; at a given value.

Declaration

public static double[] EvaluateDerivativesAt(double val, int index, int degree, IList<double> knotVector, int order)

Parameters

Type	Name	Description
Double	val	Value to evaluate at.
Int32	index	Index of the BSpline to evaluate.
Int32	degree	Initial degree of the BSpline to evaluate.
IList<Double>	knotVector	Initial knot Vector associated with the BSpline to evaluate.
Int32	order	Order of the derivative.

Returns

Type	Description
Double[]	The value of the successive BSpline derivatives at the given value. The index corresponds to the order of derivation.

Remarks

The code is adapted from algorithm 2.5 described in the NURBS Book, by L. Piegl and W. Tiller.

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FindKnotSpanIndex(Double, Int32, IList<Double>)

Identifies the index of the knot span containing a given value, using a binary search.

Declaration

public static int FindKnotSpanIndex(double val, int degree, IList<double> knotVector)

Parameters

Type	Name	Description
Double	val	Value to locate in the knot vector.
Int32	degree	Degree of the BSpline basis.
IList<Double>	knotVector	Knot vector of the BSpline basis.

Returns

Type	Description
Int32	The (zero-based) index of the knot span containing the value.

Remarks

The code is adapted from algorithm 2.1 described in the NURBS Book, by L. Piegl and W. Tiller.

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SetKnotVector(IList<Double>, Int32, out List<Double>)

Sets the knot vector of the current BSpline polynomial while ensuring its validity.

Declaration

protected static bool SetKnotVector(IList<double> knotVector, int degree, out List<double> knotList)

Parameters

Type	Name	Description
IList<Double>	knotVector	Knot vector to evaluate.
Int32	degree	Degree of the B-Spline polynomial.
List<Double>	knotList	Knot vector to set.

Returns

Type	Description
Boolean

Implements

IGroupAction<TSelf, TValue>