fr.cnes.sirius.patrius.math.analysis.polynomials

Class ZernikePolynomial

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.polynomials.ZernikePolynomial

All Implemented Interfaces:

IParameterizable, Serializable

public class ZernikePolynomial
extends Object
implements IParameterizable

Class representing a Zernike polynomial.

Since:

4.13

Author:

veuillh

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
ZernikePolynomial(int radialDegree) Simple constructor.
ZernikePolynomial(int radialDegree, Parameter[][] coefficients) Constructor.

Method Summary

Modifier and Type	Method and Description
static int	arrayIndexToAzimuthalDegree(int radialDegree, int arrayIndex) Utility function to convert an array index of the computeZernikeMonomials(int, double, double) to an azimuthal degree.
static int	azimuthalDegreeToArrayIndex(int radialDegree, int azimuthalDegree) Utility function to convert an azimuthal degree to the array index of the computeZernikeMonomials(int, double, double).
double[]	computeDerivatives(double rho, double azimuth, Collection<Parameter> params) Compute the derivatives of this zernike polynomial with respect to the provided parameters.
static double[][]	computeRadialZernikeMonomials(int radialDegree, double rho) Compute the radial zernike monomials.
double	computeValue(double rho, double azimuth) Compute the value of this zernike polynomial.
Pair<Double,double[]>	computeValueAndDerivatives(double rho, double azimuth, Collection<Parameter> params) Compute the value and partial derivatives.
static double[][]	computeZernikeMonomials(int radialDegree, double rho, double azimuth) Compute the zernike monomials.
Parameter	getCoefficient(int radialDegreeIn, int azimuthalDegree) Getter for the required coefficient of the zernike polynomial.
ArrayList<Parameter>	getParameters() Get the supported parameters.
boolean	supportsParameter(Parameter param) Check if a parameter is supported.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ZernikePolynomial

public ZernikePolynomial(int radialDegree)

Simple constructor.

Note: the parameters are initialized with values of 0.
If their values isn't changed, the computeValue(double, double) method will return 0.

Parameters:

radialDegree - The radial degree of the polynomial (azimuthal degree is considered equal to the radial degree)

Throws:

NotPositiveException - if radialDegree < 0

ZernikePolynomial

public ZernikePolynomial(int radialDegree,
                         Parameter[][] coefficients)

Constructor.

Parameters:

radialDegree - The radial degree of the polynomial (azimuthal degree is considered equal to the radial degree)

coefficients - The coefficients of the polynomial. The 2D array must have the correct size: radialDegree+1 rows and for the column use azimuthalDegreeToArrayIndex(int, int) to get the correct indexes.

Throws:

NotPositiveException - if radialDegree < 0

DimensionMismatchException - if the coefficients.length != radialDegree + 1
if the coefficientsN.length != n + 1

NullArgumentException - if the coefficients array contains a null element

Method Detail

getCoefficient

public Parameter getCoefficient(int radialDegreeIn,
                                int azimuthalDegree)

Getter for the required coefficient of the zernike polynomial.

Parameters:

radialDegreeIn - The coefficient radial degree

azimuthalDegree - the coefficient azimuthal degree

Returns:

the coefficient parameter

computeValueAndDerivatives

public Pair<Double,double[]> computeValueAndDerivatives(double rho,
                                                        double azimuth,
                                                        Collection<Parameter> params)

Compute the value and partial derivatives. Equivalent to call computeValue(double, double) and computeDerivatives(double, double, java.util.Collection<fr.cnes.sirius.patrius.math.parameter.Parameter>) but performs the heavy computation only once.

Parameters:

rho - The distance variable

azimuth - The angular variable [rad]

params - The collection of parameters for the partial derivatives computation

Returns:

A pair where first element represents the value and second element represents the partial derivatives with respect to the provided parameters

Throws:

OutOfRangeException - if rho is outside [0, 1]

computeValue

public double computeValue(double rho,
                           double azimuth)

Compute the value of this zernike polynomial.

Parameters:

rho - The distance variable

azimuth - The angular variable [rad]

Returns:

The polynomial value

Throws:

OutOfRangeException - if rho is outside [0, 1]

computeDerivatives

public double[] computeDerivatives(double rho,
                                   double azimuth,
                                   Collection<Parameter> params)

Compute the derivatives of this zernike polynomial with respect to the provided parameters.

Parameters:

rho - The distance variable

azimuth - The angular variable [rad]

params - The collection of parameters

Returns:

the partial derivatives with respect to the provided parameters

Throws:

OutOfRangeException - if rho is outside [0, 1]

supportsParameter

public boolean supportsParameter(Parameter param)

Check if a parameter is supported.

Specified by:

supportsParameter in interface IParameterizable

Parameters:

param - parameter to check

Returns:

true if the parameter is supported

getParameters

public ArrayList<Parameter> getParameters()

Get the supported parameters.

Specified by:

getParameters in interface IParameterizable

Returns:

list of supported parameters

arrayIndexToAzimuthalDegree

public static int arrayIndexToAzimuthalDegree(int radialDegree,
                                              int arrayIndex)

Utility function to convert an array index of the computeZernikeMonomials(int, double, double) to an azimuthal degree.

Parameters:

radialDegree - The radial degree

arrayIndex - The array index

Returns:

the azimuthal degree

Throws:

NotPositiveException - if radialDegree < 0
if arrayIndex < 0

DimensionMismatchException - if arrayIndex > radialDegree + 1

azimuthalDegreeToArrayIndex

public static int azimuthalDegreeToArrayIndex(int radialDegree,
                                              int azimuthalDegree)

Utility function to convert an azimuthal degree to the array index of the computeZernikeMonomials(int, double, double).

Parameters:

radialDegree - The radial degree

azimuthalDegree - The azimuthal degree

Returns:

the array index of zernikeMonomials[radialDegree] corresponding to the azimuthalDegree

Throws:

NotPositiveException - if radialDegree < 0

IllegalArgumentException - if the azimuthal degree is greater in absolute value to the radial degree if the difference of the two degrees is not an even number

computeZernikeMonomials

public static double[][] computeZernikeMonomials(int radialDegree,
                                                 double rho,
                                                 double azimuth)

Compute the zernike monomials.

The monomials are stored in a 2D array. The row i corresponds to the radial degree i and contains an array of size i+1, containing the different azimuthal degrees. Use azimuthalDegreeToArrayIndex(int, int) and arrayIndexToAzimuthalDegree(int, int) to switch between azimuthal degrees and array index.

Parameters:

radialDegree - The radial degree

rho - The distance variable

azimuth - The angular variable [rad]

Returns:

the zernike monomials

Throws:

NotPositiveException - if radialDegree < 0

OutOfRangeException - if rho is outside [0, 1]

computeRadialZernikeMonomials

public static double[][] computeRadialZernikeMonomials(int radialDegree,
                                                       double rho)

Compute the radial zernike monomials.

The radial zernike monomials are 0 when radialDegree-azimuthalDegree is odd. The returned array does not contain these values.
The row n corresponds to the radial degree n, while each column j corresponds to the azimuthal degree n%2+2j:

• For even radial degrees 2n: R_(2n)^0, R_(2n)^2, R_(2n)^4, etc...
• For odd radial degrees 2n+1: R_(2n+1)^1, R_(2n+1)^3, R_(2n+1)^5, etc...

Parameters:

radialDegree - The radial degree

rho - The distance variable

Returns:

the radial zernike monomials

Throws:

NotPositiveException - if radialDegree < 0

OutOfRangeException - if rho is outside [0, 1]