astro
Class WcsProjection.PolynomialPixelProjection

java.lang.Object
  util.PropertyContainer
      util.PropertyResources
          util.PropertyBundles
              astro.WcsProjection
                  astro.WcsProjection.LinearPixelProjection
                      astro.WcsProjection.PolynomialPixelProjection

All Implemented Interfaces:

Cloneable, Initializable, LocalizedSupplying, PropertySupplying, ResourceSupplying, VectorFunction

Enclosing class:

WcsProjection

public static class WcsProjection.PolynomialPixelProjection
extends WcsProjection.LinearPixelProjection

This now fits intermediate world coordinates from pixel coordinates with Legendre polynomials such that the pixel coordinates are slightly distorted before calculating the intermediate coordinates. Note that this is a bivariant fit, i.e. we fit to the tensor product of to univariant Legendre polynomials, which means that we have ten parameters to fit for a cubic correction: xi=Σ_nΣ_m P_nm*x^n*y^m, where the outer produrct P_nm reads as P_nm(x,y)=P_n(x)*P_m(y). E.g. P_21=(x^2-1)*y

This projection demands rij to be in the center of the projection, from the default head values the starting values for the polynomial are derived.

Nested Class Summary

Nested classes/interfaces inherited from class astro.WcsProjection.LinearPixelProjection

WcsProjection.LinearPixelProjection.Type

Nested classes/interfaces inherited from class astro.WcsProjection

WcsProjection.EulerRotation, WcsProjection.Gnomonic, WcsProjection.LinearGnomonicRaDe, WcsProjection.LinearPixelProjection, WcsProjection.PolynomialGnomonicRaDe, WcsProjection.PolynomialPixelProjection, WcsProjection.ReadWcs, WcsProjection.ThreeStepWcs, WcsProjection.VariableGnomonicRaDe, WcsProjection.VariablePixelProjection

Nested classes/interfaces inherited from class util.PropertyResources

PropertyResources.URLResource

Field Summary

private static boolean	DEBUG
private static int	DEFETAORDER
private static String	DEFETASTART
private static double	DEFHIGHSCALE
private static int	DEFXIORDER
private static String	DEFXISTART
private Vector2D	doff The constant offset we fit.
private VectorG	eta In eta_ij*L_m(x)*L_n(y) series, these are the non-linear eta_ij.
static String	KEY_ETAORDER
static String	KEY_ETASTART
static String	KEY_HIGHSCALE
static String	KEY_XIORDER
static String	KEY_XISTART
static String	LEGPOLYETA How we code the Legendre polynomials>2 in η (e.g.
static String	LEGPOLYXI How we code the Legendre polynomials>2 in ξ (e.g.
private boolean	offset If true, we also fit for the constant (not recommended).
private VectorG	xi In a xi_ij*L_m(x)*L_n(y) series, these are the non-linear xi_ij.

Fields inherited from class astro.WcsProjection.LinearPixelProjection

IMROT, KEY_CRPIX1, KEY_CRPIX2, KEY_IMROTUNIT, KEY_PSCALEUNIT, PSCALE

Fields inherited from class astro.WcsProjection

KEY_PARAMETERSCALE

Fields inherited from class util.PropertyBundles

KEY_LOCALECOUNTRY, KEY_LOCALELANGUAGE, KEY_RESOURCEBUNDLES

Fields inherited from class util.PropertyResources

KEY_NOINITONCREATE, localurl, locate, POSTFIX_DIR, POSTFIX_EXT, POSTFIX_FILE, POSTFIX_LIST, POSTFIX_URL, urlset

Fields inherited from class util.PropertyContainer

KEY_LISTSEPARATOR, KEY_MAPKEYVALUECHAR, KEY_MAPSEPARATOR

Fields inherited from interface util.ResourceSupplying

KEY_URLRESOURCES, KEY_URLUSECONFIG, KEY_URLUSECURRENT, KEY_URLUSEHOME

Fields inherited from interface util.PropertySupplying

CONFIG, KEY_CLASS

Constructor Summary

WcsProjection.PolynomialPixelProjection()
We only allow full variations in the transformation matrix.

WcsProjection.PolynomialPixelProjection(Map<String,String> u2f)
We only allow full variations in the transformation matrix.

Method Summary

private static void	addLegendreCards(Collection<nom.tam.fits.HeaderCard> ret, int order, VectorG l, String card)
VectorG	estimateParameters(nom.tam.fits.Header h) We refer to the parental parsing methods, but sneak in on the returned parameters, adding zero for all higher-order terms.
VectorG	estimateParameterScales(VectorG start) We refer to the parental parsing methods, but sneak in on the returned parameters, adding different length scales for all higher-order terms.
VectorG	evaluate(VectorG pxpy) We evaluate the target pixel position at the first two indices and return intermediate world coordinates.
VectorG	evaluate(VectorG pxpy, VectorG print) We evaluate the target pixel position at the first two indices and return intermediate world coordinates.
Collection<nom.tam.fits.HeaderCard>	getCards() We always return a collcetion in LPU and LPV.
VectorG	getParameters() We query the cij from the parent and add the projection center at the end
double	getPixelArea(VectorG pxpy) The pixel area is the determinant of the c_ij plus non-linear terms.
private static int	order(VectorG l)
boolean	parseHeader(nom.tam.fits.Header h) We parse a header first reading in the linear matrix with the parental method, then continuing to read the Legendre polynomial coefficients named LEGPOLYXI and LEGPOLYETA.
private static VectorG	readLegendre(String prae, nom.tam.fits.Header h) We read header cards of syntax prae_ similar to LPV2_3.
void	setConstantFit(boolean nuoff) Set the flag, whether a constant offset should be fitted along with the polynomial.
void	setParameters(VectorG vv) The first four parameters are the cij, then we have the coefficients to the Legendre bivariant in x, followed by the Legender in y.

Methods inherited from class astro.WcsProjection.LinearPixelProjection

evaluateMatrix, getCij, getRj, setRj

Methods inherited from class astro.WcsProjection

argumentDimension, functionDimension, getStandardKeys

Methods inherited from class util.PropertyBundles

clone, getLocalized, getLocalized, getLocalizedString, getLocalizedString, loadResource

Methods inherited from class util.PropertyResources

createFrom, createFrom, createFrom, getApplet, getAsResources, getLocalClassLoader, getPropertiesToKey, getPropertiesToKey, getResource, getResourceAsStream, getResourceFromKey, getResources, init, keyCreate, keyCreate, reload, setApplet

Methods inherited from class util.PropertyContainer

augment, augment, augment, defaultBoolean, defaultChar, defaultDouble, defaultFloat, defaultInt, defaultLong, defaultObject, defaultObject, defaultProperties, defaultProperty, getAsBoolean, getAsChar, getAsDouble, getAsEnums, getAsFloat, getAsInt, getAsList, getAsLong, getAsMap, getAsMap, getAsObject, getAsObject, getProperties, getProperty, has, isNew, parseObject, reload, removeProperty, rescanned, setObject, setProperties, setProperty, stringProperties, toString

Methods inherited from class java.lang.Object

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

Methods inherited from interface util.ResourceSupplying

getResource, getResourceAsStream, getResources

Methods inherited from interface util.PropertySupplying

defaultBoolean, defaultChar, defaultDouble, defaultFloat, defaultInt, defaultLong, defaultObject, defaultObject, defaultProperties, defaultProperty, getAsBoolean, getAsChar, getAsDouble, getAsFloat, getAsInt, getAsList, getAsLong, getAsMap, getAsObject, getAsObject, getProperties, getProperty, has, parseObject, removeProperty, setObject, setProperty, stringProperties

Methods inherited from interface util.Initializable

init

Field Detail

LEGPOLYXI

public static final String LEGPOLYXI

How we code the Legendre polynomials>2 in ξ (e.g. LPU3_0).

See Also:

Constant Field Values

LEGPOLYETA

public static final String LEGPOLYETA

How we code the Legendre polynomials>2 in η (e.g. LPU3_0).

See Also:

Constant Field Values

KEY_HIGHSCALE

public static final String KEY_HIGHSCALE

See Also:

Constant Field Values

KEY_XIORDER

public static final String KEY_XIORDER

See Also:

Constant Field Values

KEY_ETAORDER

public static final String KEY_ETAORDER

See Also:

Constant Field Values

KEY_XISTART

public static final String KEY_XISTART

See Also:

Constant Field Values

KEY_ETASTART

public static final String KEY_ETASTART

See Also:

Constant Field Values

DEBUG

private static final boolean DEBUG

See Also:

Constant Field Values

DEFXIORDER

private static final int DEFXIORDER

See Also:

Constant Field Values

DEFETAORDER

private static final int DEFETAORDER

See Also:

Constant Field Values

DEFHIGHSCALE

private static final double DEFHIGHSCALE

See Also:

Constant Field Values

DEFXISTART

private static final String DEFXISTART

See Also:

Constant Field Values

DEFETASTART

private static final String DEFETASTART

See Also:

Constant Field Values

xi

private VectorG xi

In a xi_ij*L_m(x)*L_n(y) series, these are the non-linear xi_ij.

eta

private VectorG eta

In eta_ij*L_m(x)*L_n(y) series, these are the non-linear eta_ij.

offset

private boolean offset

If true, we also fit for the constant (not recommended).

doff

private Vector2D doff

The constant offset we fit.

Constructor Detail

WcsProjection.PolynomialPixelProjection

public WcsProjection.PolynomialPixelProjection()

We only allow full variations in the transformation matrix.

WcsProjection.PolynomialPixelProjection

public WcsProjection.PolynomialPixelProjection(Map<String,String> u2f)

We only allow full variations in the transformation matrix.

Method Detail

setConstantFit

public void setConstantFit(boolean nuoff)

Set the flag, whether a constant offset should be fitted along with the polynomial. Mostly intended for stand-alone and debug mode.

evaluate

public VectorG evaluate(VectorG pxpy)

We evaluate the target pixel position at the first two indices and return intermediate world coordinates. From the linear transformation we take the center of projection, which now is the center of the ccd plus the linear matrix cij. These values are then used in the coefficients to the direct Legendre product, stored in xi and eta.

Specified by:

evaluate in interface VectorFunction

Overrides:

evaluate in class WcsProjection.LinearPixelProjection

evaluate

public VectorG evaluate(VectorG pxpy,
                        VectorG print)

We evaluate the target pixel position at the first two indices and return intermediate world coordinates. From the linear transformation we take the center of projection, which now is the center of the ccd plus the linear matrix cij. These values are then used in the coefficients to the direct Legendre product, stored in xi and eta.

setParameters

public void setParameters(VectorG vv)

The first four parameters are the cij, then we have the coefficients to the Legendre bivariant in x, followed by the Legender in y. Due to the bivariant nature (L_x*L_y), the number of parameters in the Legendre is (n+1)*(n+2)/2, where n is the order (KEY_XIORDER and KEY_ETAORDER, respectively). There is no constant term, and the linear terms are already consumed in cij, thus for order of three, only 7 (10-3) parameter remain.

Overrides:

setParameters in class WcsProjection.LinearPixelProjection

getParameters

public VectorG getParameters()

We query the cij from the parent and add the projection center at the end

Overrides:

getParameters in class WcsProjection.LinearPixelProjection

estimateParameters

public VectorG estimateParameters(nom.tam.fits.Header h)
                           throws nom.tam.fits.HeaderCardException

We refer to the parental parsing methods, but sneak in on the returned parameters, adding zero for all higher-order terms. The center of projection is only allowed in the center of the CCD.

Overrides:

estimateParameters in class WcsProjection.LinearPixelProjection

Throws:

nom.tam.fits.HeaderCardException

estimateParameterScales

public VectorG estimateParameterScales(VectorG start)

We refer to the parental parsing methods, but sneak in on the returned parameters, adding different length scales for all higher-order terms. The center of projection is only allowed in the center of the CCD.

Overrides:

estimateParameterScales in class WcsProjection

parseHeader

public boolean parseHeader(nom.tam.fits.Header h)
                    throws nom.tam.fits.HeaderCardException

We parse a header first reading in the linear matrix with the parental method, then continuing to read the Legendre polynomial coefficients named LEGPOLYXI and LEGPOLYETA. A standard header key would read as LPU2_1=1.4e-4, denoting for the ξ-axis the coefficient for the direct Legendre product L_2(x)*L_1(y), where x and y are normalized CCD pixel stretching from -1 to 1. As all units in WCS-context are in degrees, this hold also for the LPU and LPVs.

Overrides:

parseHeader in class WcsProjection.LinearPixelProjection

Throws:

nom.tam.fits.HeaderCardException

getCards

public Collection<nom.tam.fits.HeaderCard> getCards()
                                             throws nom.tam.fits.HeaderCardException

We always return a collcetion in LPU and LPV.

Overrides:

getCards in class WcsProjection.LinearPixelProjection

Throws:

nom.tam.fits.HeaderCardException

addLegendreCards

private static void addLegendreCards(Collection<nom.tam.fits.HeaderCard> ret,
                                     int order,
                                     VectorG l,
                                     String card)
                              throws nom.tam.fits.HeaderCardException

Throws:

nom.tam.fits.HeaderCardException

order

private static final int order(VectorG l)

readLegendre

private static VectorG readLegendre(String prae,
                                    nom.tam.fits.Header h)
                             throws nom.tam.fits.HeaderCardException

We read header cards of syntax prae_ similar to LPV2_3. These are interpreted as direct legendre product coefficients. There is always order+1 coefficients, for order three these would be LPV3_0, LPV2_1, LPV1_2, and LPV0_3. All must be present, even if zero. The smalles order is two, linear and constant terms are already described in standard linear WCS.

Throws:

nom.tam.fits.HeaderCardException

getPixelArea

public double getPixelArea(VectorG pxpy)

The pixel area is the determinant of the c_ij plus non-linear terms.

Overrides:

getPixelArea in class WcsProjection.LinearPixelProjection