Class Bernstein

Class defining a Bernstein polynomial.

Inheritance

Object

Polynomial

Bernstein

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.EvaluateAt(Double)

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

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

Namespace: BRIDGES.Arithmetic.Polynomials.Univariate.Specials

Assembly: BRIDGES.dll

Syntax

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

Constructors

Bernstein(Int32, Int32)

Initialises a new instance of Bernstein class by defining its index and degree.

Declaration

public Bernstein(int index, int degree)

Parameters

Type	Name	Description
Int32	index	Index of the Bernstein polynomial.
Int32	degree	Degree of the Bernstein polynomial.

Properties

Index

Gets the index of the current Bernstein.

Declaration

public int Index { get; }

Property Value

Type	Description
Int32

Methods

EvaluateAt(Double, Int32, Int32)

Evaluates a Bernstein of a given index and degree, at a given value.

Declaration

public static double EvaluateAt(double val, int index, int degree)

Parameters

Type	Name	Description
Double	val	Value to evaluate at.
Int32	index	Index of the Bernstein to evaluate.
Int32	degree	Degree of the Bernstein to evaluate.

Returns

Type	Description
Double	The value of the Bernstein polynomial at the given value.

Remarks

The code is adapted from algorithm 1.2 described in the NURBS Book, by L. Piegl and W. Tiller.

EvaluateBasisAt(Double, Int32)

Evaluates a Bernstein polynomial basis of a given degree, at a given value.

Declaration

public static double[] EvaluateBasisAt(double val, int degree)

Parameters

Type	Name	Description
Double	val	Value to evaluate at.
Int32	degree	Degree of the Bernstein polynomial basis.

Returns

Type	Description
Double[]	The values of the Bernstein polynomials at the given value.

Remarks

The code is adapted from algorithm 1.3 described in the NURBS Book, by L. Piegl and W. Tiller.

ToBSpline()

Creates a BSpline polynomial from the current Bernstein polynomial.

Declaration

public BSpline ToBSpline()

Returns

Type	Description
BSpline	The new BSpline polynomial.

Implements

IGroupAction<TSelf, TValue>