Lagrange Namespace Reference

Lagrange interpolation functions for obtaining smooth curves from discrete points. More...

Functions
template<typename T >
T	interpolate (const juce::Array< Point< T > > &points, T x)
	Interpolates a value at coordinate x using Lagrange polynomial interpolation.
template<typename T >
T	interpolate (T xArr[], T yArr[], int num, T x)
	Interpolates a value at coordinate x using Lagrange polynomial interpolation.

Detailed Description

Lagrange interpolation functions for obtaining smooth curves from discrete points.

Lagrange interpolation creates a polynomial that passes through all given points. Unlike splines, it uses a single polynomial rather than piecewise functions. Note that for large numbers of points, the resulting polynomial can oscillate significantly (Runge's phenomenon).

See also

interpolate

Function Documentation

interpolate() [1/2]

template<typename T >

T Lagrange::interpolate	(	const juce::Array< Point< T > > &	points,
		T	x
	)

Interpolates a value at coordinate x using Lagrange polynomial interpolation.

Creates a polynomial that passes through all the given points and evaluates it at the specified x coordinate. The resulting polynomial has degree n-1 where n is the number of points.

Parameters

points	An array of Point<T> defining the interpolation curve
x	The x coordinate at which to evaluate the interpolated value

Returns

The interpolated y value at coordinate x

Referenced by DelayLine::readLagrange(), and DelayLine::readSampleLagrange().

interpolate() [2/2]

template<typename T >

T Lagrange::interpolate	(	T	xArr[],
		T	yArr[],
		int	num,
		T	x
	)

Interpolates a value at coordinate x using Lagrange polynomial interpolation.

This overload accepts separate arrays for x and y coordinates rather than an array of points. Creates a polynomial that passes through all the given points and evaluates it at the specified x coordinate.

Parameters

xArr	Array of x coordinates
yArr	Array of y coordinates (must be same length as xArr)
num	Number of points in the arrays
x	The x coordinate at which to evaluate the interpolated value

Returns

The interpolated y value at coordinate x