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dis.h
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/*============================================================================
WCSLIB 8.2 - an implementation of the FITS WCS standard.
Copyright (C) 1995-2023, Mark Calabretta
This file is part of WCSLIB.
WCSLIB is free software: you can redistribute it and/or modify it under the
terms of the GNU Lesser General Public License as published by the Free
Software Foundation, either version 3 of the License, or (at your option)
any later version.
WCSLIB is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
more details.
You should have received a copy of the GNU Lesser General Public License
along with WCSLIB. If not, see http://www.gnu.org/licenses.
Author: Mark Calabretta, Australia Telescope National Facility, CSIRO.
http://www.atnf.csiro.au/people/Mark.Calabretta
$Id: dis.h,v 8.2.1.1 2023/11/16 10:05:57 mcalabre Exp mcalabre $
*=============================================================================
*
* WCSLIB 8.2 - C routines that implement the FITS World Coordinate System
* (WCS) standard. Refer to the README file provided with WCSLIB for an
* overview of the library.
*
*
* Summary of the dis routines
* ---------------------------
* Routines in this suite implement extensions to the FITS World Coordinate
* System (WCS) standard proposed by
*
= "Representations of distortions in FITS world coordinate systems",
= Calabretta, M.R. et al. (WCS Paper IV, draft dated 2004/04/22),
= available from http://www.atnf.csiro.au/people/Mark.Calabretta
*
* In brief, a distortion function may occupy one of two positions in the WCS
* algorithm chain. Prior distortions precede the linear transformation
* matrix, whether it be PCi_ja or CDi_ja, and sequent distortions follow it.
* WCS Paper IV defines FITS keywords used to specify parameters for predefined
* distortion functions. The following are used for prior distortions:
*
= CPDISja ...(string-valued, identifies the distortion function)
= DPja ...(record-valued, parameters)
= CPERRja ...(floating-valued, maximum value)
*
* Their counterparts for sequent distortions are CQDISia, DQia, and CQERRia.
* An additional floating-valued keyword, DVERRa, records the maximum value of
* the combined distortions.
*
* DPja and DQia are "record-valued". Syntactically, the keyvalues are
* standard FITS strings, but they are to be interpreted in a special way.
* The general form is
*
= DPja = '<field-specifier>: <float>'
*
* where the field-specifier consists of a sequence of fields separated by
* periods, and the ': ' between the field-specifier and the floating-point
* value is part of the record syntax. For example:
*
= DP1 = 'AXIS.1: 1'
*
* Certain field-specifiers are defined for all distortion functions, while
* others are defined only for particular distortions. Refer to WCS Paper IV
* for further details. wcspih() parses all distortion keywords and loads them
* into a disprm struct for analysis by disset() which knows (or possibly does
* not know) how to interpret them. Of the Paper IV distortion functions, only
* the general Polynomial distortion is currently implemented here.
*
* TPV - the TPV "projection":
* ---------------------------
* The distortion function component of the TPV celestial "projection" is also
* supported. The TPV projection, originally proposed in a draft of WCS Paper
* II, consists of a TAN projection with sequent polynomial distortion, the
* coefficients of which are encoded in PVi_ma keyrecords. Full details may be
* found at the registry of FITS conventions:
*
= http://fits.gsfc.nasa.gov/registry/tpvwcs/tpv.html
*
* Internally, wcsset() changes TPV to a TAN projection, translates the PVi_ma
* keywords to DQia and loads them into a disprm struct. These DQia keyrecords
* have the form
*
= DQia = 'TPV.m: <value>'
*
* where i, a, m, and the value for each DQia match each PVi_ma. Consequently,
* WCSLIB would handle a FITS header containing these keywords, along with
* CQDISia = 'TPV' and the required DQia.NAXES and DQia.AXIS.ihat keywords.
*
* Note that, as defined, TPV assumes that CDi_ja is used to define the linear
* transformation. The section on historical idiosyncrasies (below) cautions
* about translating CDi_ja to PCi_ja plus CDELTia in this case.
*
* SIP - Simple Imaging Polynomial:
* --------------------------------
* These routines also support the Simple Imaging Polynomial (SIP), whose
* design was influenced by early drafts of WCS Paper IV. It is described in
* detail in
*
= http://fits.gsfc.nasa.gov/registry/sip.html
*
* SIP, which is defined only as a prior distortion for 2-D celestial images,
* has the interesting feature that it records an approximation to the inverse
* polynomial distortion function. This is used by disx2p() to provide an
* initial estimate for its more precise iterative inversion. The
* special-purpose keywords used by SIP are parsed and translated by wcspih()
* as follows:
*
= A_p_q = <value> -> DP1 = 'SIP.FWD.p_q: <value>'
= AP_p_q = <value> -> DP1 = 'SIP.REV.p_q: <value>'
= B_p_q = <value> -> DP2 = 'SIP.FWD.p_q: <value>'
= BP_p_q = <value> -> DP2 = 'SIP.REV.p_q: <value>'
= A_DMAX = <value> -> DPERR1 = <value>
= B_DMAX = <value> -> DPERR2 = <value>
*
* SIP's A_ORDER and B_ORDER keywords are not used. WCSLIB would recognise a
* FITS header containing the above keywords, along with CPDISja = 'SIP' and
* the required DPja.NAXES keywords.
*
* DSS - Digitized Sky Survey:
* ---------------------------
* The Digitized Sky Survey resulted from the production of the Guide Star
* Catalogue for the Hubble Space Telescope. Plate solutions based on a
* polynomial distortion function were encoded in FITS using non-standard
* keywords. Sect. 5.2 of WCS Paper IV describes how DSS coordinates may be
* translated to a sequent Polynomial distortion using two auxiliary variables.
* That translation is based on optimising the non-distortion component of the
* plate solution.
*
* Following Paper IV, wcspih() translates the non-distortion component of DSS
* coordinates to standard WCS keywords (CRPIXja, PCi_ja, CRVALia, etc), and
* fills a wcsprm struct with their values. It encodes the DSS polynomial
* coefficients as
*
= AMDXm = <value> -> DQ1 = 'AMD.m: <value>'
= AMDYm = <value> -> DQ2 = 'AMD.m: <value>'
*
* WCSLIB would recognise a FITS header containing the above keywords, along
* with CQDISia = 'DSS' and the required DQia.NAXES keywords.
*
* WAT - the TNX and ZPX "projections":
* ------------------------------------
* The TNX and ZPX "projections" add a polynomial distortion function to the
* standard TAN and ZPN projections respectively. Unusually, the polynomial
* may be expressed as the sum of Chebyshev or Legendre polynomials, or as a
* simple sum of monomials, as described in
*
= http://fits.gsfc.nasa.gov/registry/tnx/tnx-doc.html
= http://fits.gsfc.nasa.gov/registry/zpxwcs/zpx.html
*
* The polynomial coefficients are encoded in special-purpose WATi_n keywords
* as a set of continued strings, thus providing the name for this distortion
* type. WATi_n are parsed and translated by wcspih() into the following set:
*
= DQi = 'WAT.POLY: <value>'
= DQi = 'WAT.XMIN: <value>'
= DQi = 'WAT.XMAX: <value>'
= DQi = 'WAT.YMIN: <value>'
= DQi = 'WAT.YMAX: <value>'
= DQi = 'WAT.CHBY.m_n: <value>' or
= DQi = 'WAT.LEGR.m_n: <value>' or
= DQi = 'WAT.MONO.m_n: <value>'
*
* along with CQDISia = 'WAT' and the required DPja.NAXES keywords. For ZPX,
* the ZPN projection parameters are also encoded in WATi_n, and wcspih()
* translates these to standard PVi_ma.
*
* Note that, as defined, TNX and ZPX assume that CDi_ja is used to define the
* linear transformation. The section on historical idiosyncrasies (below)
* cautions about translating CDi_ja to PCi_ja plus CDELTia in this case.
*
* TPD - Template Polynomial Distortion:
* -------------------------------------
* The "Template Polynomial Distortion" (TPD) is a superset of the TPV, SIP,
* DSS, and WAT (TNX & ZPX) polynomial distortions that also supports 1-D usage
* and inversions. Like TPV, SIP, and DSS, the form of the polynomial is fixed
* (the "template") and only the coefficients for the required terms are set
* non-zero. TPD generalizes TPV in going to 9th degree, SIP by accomodating
* TPV's linear and radial terms, and DSS in both respects. While in theory
* the degree of the WAT polynomial distortion in unconstrained, in practice it
* is limited to values that can be handled by TPD.
*
* Within WCSLIB, TPV, SIP, DSS, and WAT are all implemented as special cases
* of TPD. Indeed, TPD was developed precisely for that purpose. WAT
* distortions expressed as the sum of Chebyshev or Legendre polynomials are
* expanded for TPD as a simple sum of monomials. Moreover, the general
* Polynomial distortion is translated and implemented internally as TPD
* whenever possible.
*
* However, WCSLIB also recognizes 'TPD' as a distortion function in its own
* right (i.e. a recognized value of CPDISja or CQDISia), for use as both prior
* and sequent distortions. Its DPja and DQia keyrecords have the form
*
= DPja = 'TPD.FWD.m: <value>'
= DPja = 'TPD.REV.m: <value>'
*
* for the forward and reverse distortion functions. Moreover, like the
* general Polynomial distortion, TPD supports auxiliary variables, though only
* as a linear transformation of pixel coordinates (p1,p2):
*
= x = a0 + a1*p1 + a2*p2
= y = b0 + b1*p1 + b2*p2
*
* where the coefficients of the auxiliary variables (x,y) are recorded as
*
= DPja = 'AUX.1.COEFF.0: a0' ...default 0.0
= DPja = 'AUX.1.COEFF.1: a1' ...default 1.0
= DPja = 'AUX.1.COEFF.2: a2' ...default 0.0
= DPja = 'AUX.2.COEFF.0: b0' ...default 0.0
= DPja = 'AUX.2.COEFF.1: b1' ...default 0.0
= DPja = 'AUX.2.COEFF.2: b2' ...default 1.0
*
* Though nowhere near as powerful, in typical applications TPD is considerably
* faster than the general Polynomial distortion. As TPD has a finite and not
* too large number of possible terms (60), the coefficients for each can be
* stored (by disset()) in a fixed location in the disprm::dparm[] array. A
* large part of the speedup then arises from evaluating the polynomial using
* Horner's scheme.
*
* Separate implementations for polynomials of each degree, and conditionals
* for 1-D polynomials and 2-D polynomials with and without the radial
* variable, ensure that unused terms mostly do not impose a significant
* computational overhead.
*
* The TPD terms are as follows
*
= 0: 1 4: xx 12: xxxx 24: xxxxxx 40: xxxxxxxx
= 5: xy 13: xxxy 25: xxxxxy 41: xxxxxxxy
= 1: x 6: yy 14: xxyy 26: xxxxyy 42: xxxxxxyy
= 2: y 15: xyyy 27: xxxyyy 43: xxxxxyyy
= 3: r 7: xxx 16: yyyy 28: xxyyyy 44: xxxxyyyy
= 8: xxy 29: xyyyyy 45: xxxyyyyy
= 9: xyy 17: xxxxx 30: yyyyyy 46: xxyyyyyy
= 10: yyy 18: xxxxy 47: xyyyyyyy
= 11: rrr 19: xxxyy 31: xxxxxxx 48: yyyyyyyy
= 20: xxyyy 32: xxxxxxy
= 21: xyyyy 33: xxxxxyy 49: xxxxxxxxx
= 22: yyyyy 34: xxxxyyy 50: xxxxxxxxy
= 23: rrrrr 35: xxxyyyy 51: xxxxxxxyy
= 36: xxyyyyy 52: xxxxxxyyy
= 37: xyyyyyy 53: xxxxxyyyy
= 38: yyyyyyy 54: xxxxyyyyy
= 39: rrrrrrr 55: xxxyyyyyy
= 56: xxyyyyyyy
= 57: xyyyyyyyy
= 58: yyyyyyyyy
= 59: rrrrrrrrr
*
* where r = sqrt(xx + yy). Note that even powers of r are excluded since they
* can be accomodated by powers of (xx + yy).
*
* Note here that "x" refers to the axis to which the distortion function is
* attached, with "y" being the complementary axis. So, for example, with
* longitude on axis 1 and latitude on axis 2, for TPD attached to axis 1, "x"
* refers to axis 1 and "y" to axis 2. For TPD attached to axis 2, "x" refers
* to axis 2, and "y" to axis 1.
*
* TPV uses all terms up to 39. The m in its PVi_ma keywords translates
* directly to the TPD coefficient number.
*
* SIP uses all terms except for 0, 3, 11, 23, 39, and 59, with terms 1 and 2
* only used for the inverse. Its A_p_q, etc. keywords must be translated
* using a map.
*
* DSS uses terms 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 17, 19, and 21. The presence
* of a non-zero constant term arises through the use of auxiliary variables
* with origin offset from the reference point of the TAN projection. However,
* in the translation given by WCS Paper IV, the distortion polynomial is zero,
* or very close to zero, at the reference pixel itself. The mapping between
* DSS's AMDXm (or AMDYm) keyvalues and TPD coefficients, while still simple,
* is not quite as straightforward as for TPV and SIP.
*
* WAT uses all but the radial terms, namely 3, 11, 23, 39, and 59. While the
* mapping between WAT's monomial coefficients and TPD is fairly simple, for
* its expression in terms of a sum of Chebyshev or Legendre polynomials it is
* much less so.
*
* Historical idiosyncrasies:
* --------------------------
* In addition to the above, some historical distortion functions have further
* idiosyncrasies that must be taken into account when translating them to TPD.
*
* WCS Paper IV specifies that a distortion function returns a correction to be
* added to pixel coordinates (prior distortion) or intermediate pixel
* coordinates (sequent distortion). The correction is meant to be small so
* that ignoring the distortion function, i.e. setting the correction to zero,
* produces a commensurately small error.
*
* However, rather than an additive correction, some historical distortion
* functions (TPV, DSS) define a polynomial that returns the corrected
* coordinates directly.
*
* The difference between the two approaches is readily accounted for simply by
* adding or subtracting 1 from the coefficient of the first degree term of the
* polynomial. However, it opens the way for considerable confusion.
*
* Additional to the formalism of WCS Paper IV, both the Polynomial and TPD
* distortion functions recognise a keyword
*
= DPja = 'DOCORR: 0'
*
* which is meant to apply generally to indicate that the distortion function
* returns the corrected coordinates directly. Any other value for DOCORR (or
* its absence) indicates that the distortion function returns an additive
* correction.
*
* WCS Paper IV also specifies that the independent variables of a distortion
* function are pixel coordinates (prior distortion) or intermediate pixel
* coordinates (sequent distortion).
*
* On the contrary, the independent variables of the SIP polynomial are pixel
* coordinate offsets from the reference pixel. This is readily handled via
* the renormalisation parameters
*
= DPja = 'OFFSET.jhat: <value>'
*
* where the value corresponds to CRPIXja.
*
* Likewise, because TPV, TNX, and ZPX are defined in terms of CDi_ja, the
* independent variables of the polynomial are intermediate world coordinates
* rather than intermediate pixel coordinates. Because sequent distortions
* are always applied before CDELTia, if CDi_ja is translated to PCi_ja plus
* CDELTia, then either CDELTia must be unity, or the distortion polynomial
* coefficients must be adjusted to account for the change of scale.
*
* Summary of the dis routines:
* ----------------------------
* These routines apply the distortion functions defined by the extension to
* the FITS WCS standard proposed in Paper IV. They are based on the disprm
* struct which contains all information needed for the computations. The
* struct contains some members that must be set by the user, and others that
* are maintained by these routines, somewhat like a C++ class but with no
* encapsulation.
*
* dpfill(), dpkeyi(), and dpkeyd() are provided to manage the dpkey struct.
*
* disndp(), disini(), disinit(), discpy(), and disfree() are provided to
* manage the disprm struct, dissize() computes its total size including
* allocated memory, and disprt() prints its contents.
*
* disperr() prints the error message(s) (if any) stored in a disprm struct.
*
* wcshdo() normally writes SIP and TPV headers in their native form if at all
* possible. However, dishdo() may be used to set a flag that tells it to
* write the header in the form of the TPD translation used internally.
*
* A setup routine, disset(), computes intermediate values in the disprm struct
* from parameters in it that were supplied by the user. The struct always
* needs to be set up by disset(), though disset() need not be called
* explicitly - refer to the explanation of disprm::flag.
*
* disp2x() and disx2p() implement the WCS distortion functions, disp2x() using
* separate functions, such as dispoly() and tpd7(), to do the computation.
*
* An auxiliary routine, diswarp(), computes various measures of the distortion
* over a specified range of coordinates.
*
* PLEASE NOTE: Distortions are not yet handled by wcsbth(), or wcscompare().
*
*
* disndp() - Memory allocation for DPja and DQia
* ----------------------------------------------
* disndp() sets or gets the value of NDPMAX (default 256). This global
* variable controls the maximum number of dpkey structs, for holding DPja or
* DQia keyvalues, that disini() should allocate space for. It is also used by
* disinit() as the default value of ndpmax.
*
* PLEASE NOTE: This function is not thread-safe.
*
* Given:
* n int Value of NDPMAX; ignored if < 0. Use a value less
* than zero to get the current value.
*
* Function return value:
* int Current value of NDPMAX.
*
*
* dpfill() - Fill the contents of a dpkey struct
* ----------------------------------------------
* dpfill() is a utility routine to aid in filling the contents of the dpkey
* struct. No checks are done on the validity of the inputs.
*
* WCS Paper IV specifies the syntax of a record-valued keyword as
*
= keyword = '<field-specifier>: <float>'
*
* However, some DPja and DQia record values, such as those of DPja.NAXES and
* DPja.AXIS.j, are intrinsically integer-valued. While FITS header parsers
* are not expected to know in advance which of DPja and DQia are integral and
* which are floating point, if the record's value parses as an integer (i.e.
* without decimal point or exponent), then preferably enter it into the dpkey
* struct as an integer. Either way, it doesn't matter as disset() accepts
* either data type for all record values.
*
* Given and returned:
* dp struct dpkey*
* Store for DPja and DQia keyvalues.
*
* Given:
* keyword const char *
* field const char *
* These arguments are concatenated with an intervening
* "." to construct the full record field name, i.e.
* including the keyword name, DPja or DQia (but
* excluding the colon delimiter which is NOT part of the
* name). Either may be given as a NULL pointer. Set
* both NULL to omit setting this component of the
* struct.
*
* j int Axis number (1-relative), i.e. the j in DPja or
* i in DQia. Can be given as 0, in which case the axis
* number will be obtained from the keyword component of
* the field name which must either have been given or
* preset.
*
* If j is non-zero, and keyword was given, then the
* value of j will be used to fill in the axis number.
*
* type int Data type of the record's value
* 0: Integer,
* 1: Floating point.
*
* i int For type == 0, the integer value of the record.
*
* f double For type == 1, the floating point value of the record.
*
* Function return value:
* int Status return value:
* 0: Success.
*
*
* dpkeyi() - Get the data value in a dpkey struct as int
* ------------------------------------------------------
* dpkeyi() returns the data value in a dpkey struct as an integer value.
*
* Given and returned:
* dp const struct dpkey *
* Parsed contents of a DPja or DQia keyrecord.
*
* Function return value:
* int The record's value as int.
*
*
* dpkeyd() - Get the data value in a dpkey struct as double
* ---------------------------------------------------------
* dpkeyd() returns the data value in a dpkey struct as a floating point
* value.
*
* Given and returned:
* dp const struct dpkey *
* Parsed contents of a DPja or DQia keyrecord.
*
* Function return value:
* double The record's value as double.
*
*
* disini() - Default constructor for the disprm struct
* ----------------------------------------------------
* disini() is a thin wrapper on disinit(). It invokes it with ndpmax set
* to -1 which causes it to use the value of the global variable NDPMAX. It
* is thereby potentially thread-unsafe if NDPMAX is altered dynamically via
* disndp(). Use disinit() for a thread-safe alternative in this case.
*
*
* disinit() - Default constructor for the disprm struct
* ----------------------------------------------------
* disinit() allocates memory for arrays in a disprm struct and sets all
* members of the struct to default values.
*
* PLEASE NOTE: every disprm struct must be initialized by disinit(), possibly
* repeatedly. On the first invokation, and only the first invokation,
* disprm::flag must be set to -1 to initialize memory management, regardless
* of whether disinit() will actually be used to allocate memory.
*
* Given:
* alloc int If true, allocate memory unconditionally for arrays in
* the disprm struct.
*
* If false, it is assumed that pointers to these arrays
* have been set by the user except if they are null
* pointers in which case memory will be allocated for
* them regardless. (In other words, setting alloc true
* saves having to initalize these pointers to zero.)
*
* naxis int The number of world coordinate axes, used to determine
* array sizes.
*
* Given and returned:
* dis struct disprm*
* Distortion function parameters. Note that, in order
* to initialize memory management disprm::flag must be
* set to -1 when dis is initialized for the first time
* (memory leaks may result if it had already been
* initialized).
*
* Given:
* ndpmax int The number of DPja or DQia keywords to allocate space
* for. If set to -1, the value of the global variable
* NDPMAX will be used. This is potentially
* thread-unsafe if disndp() is being used dynamically to
* alter its value.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
* 2: Memory allocation failed.
*
* For returns > 1, a detailed error message is set in
* disprm::err if enabled, see wcserr_enable().
*
*
* discpy() - Copy routine for the disprm struct
* ---------------------------------------------
* discpy() does a deep copy of one disprm struct to another, using disinit()
* to allocate memory unconditionally for its arrays if required. Only the
* "information to be provided" part of the struct is copied; a call to
* disset() is required to initialize the remainder.
*
* Given:
* alloc int If true, allocate memory unconditionally for arrays in
* the destination. Otherwise, it is assumed that
* pointers to these arrays have been set by the user
* except if they are null pointers in which case memory
* will be allocated for them regardless.
*
* dissrc const struct disprm*
* Struct to copy from.
*
* Given and returned:
* disdst struct disprm*
* Struct to copy to. disprm::flag should be set to -1
* if disdst was not previously initialized (memory leaks
* may result if it was previously initialized).
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
* 2: Memory allocation failed.
*
* For returns > 1, a detailed error message is set in
* disprm::err if enabled, see wcserr_enable().
*
*
* disfree() - Destructor for the disprm struct
* --------------------------------------------
* disfree() frees memory allocated for the disprm arrays by disinit().
* disinit() keeps a record of the memory it allocates and disfree() will only
* attempt to free this.
*
* PLEASE NOTE: disfree() must not be invoked on a disprm struct that was not
* initialized by disinit().
*
* Given:
* dis struct disprm*
* Distortion function parameters.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
*
*
* dissize() - Compute the size of a disprm struct
* -----------------------------------------------
* dissize() computes the full size of a disprm struct, including allocated
* memory.
*
* Given:
* dis const struct disprm*
* Distortion function parameters.
*
* If NULL, the base size of the struct and the allocated
* size are both set to zero.
*
* Returned:
* sizes int[2] The first element is the base size of the struct as
* returned by sizeof(struct disprm). The second element
* is the total allocated size, in bytes, assuming that
* the allocation was done by disini(). This figure
* includes memory allocated for members of constituent
* structs, such as disprm::dp.
*
* It is not an error for the struct not to have been set
* up via tabset(), which normally results in additional
* memory allocation.
*
* Function return value:
* int Status return value:
* 0: Success.
*
*
* disprt() - Print routine for the disprm struct
* ----------------------------------------------
* disprt() prints the contents of a disprm struct using wcsprintf(). Mainly
* intended for diagnostic purposes.
*
* Given:
* dis const struct disprm*
* Distortion function parameters.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
*
*
* disperr() - Print error messages from a disprm struct
* -----------------------------------------------------
* disperr() prints the error message(s) (if any) stored in a disprm struct.
* If there are no errors then nothing is printed. It uses wcserr_prt(), q.v.
*
* Given:
* dis const struct disprm*
* Distortion function parameters.
*
* prefix const char *
* If non-NULL, each output line will be prefixed with
* this string.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
*
*
* dishdo() - write FITS headers using TPD
* ---------------------------------------
* dishdo() sets a flag that tells wcshdo() to write FITS headers in the form
* of the TPD translation used internally. Normally SIP and TPV would be
* written in their native form if at all possible.
*
* Given and returned:
* dis struct disprm*
* Distortion function parameters.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
* 3: No TPD translation.
*
*
* disset() - Setup routine for the disprm struct
* ----------------------------------------------
* disset(), sets up the disprm struct according to information supplied within
* it - refer to the explanation of disprm::flag.
*
* Note that this routine need not be called directly; it will be invoked by
* disp2x() and disx2p() if the disprm::flag is anything other than a
* predefined magic value.
*
* Given and returned:
* dis struct disprm*
* Distortion function parameters.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
* 2: Memory allocation failed.
* 3: Invalid parameter.
*
* For returns > 1, a detailed error message is set in
* disprm::err if enabled, see wcserr_enable().
*
*
* disp2x() - Apply distortion function
* ------------------------------------
* disp2x() applies the distortion functions. By definition, the distortion
* is in the pixel-to-world direction.
*
* Depending on the point in the algorithm chain at which it is invoked,
* disp2x() may transform pixel coordinates to corrected pixel coordinates, or
* intermediate pixel coordinates to corrected intermediate pixel coordinates,
* or image coordinates to corrected image coordinates.
*
*
* Given and returned:
* dis struct disprm*
* Distortion function parameters.
*
* Given:
* rawcrd const double[naxis]
* Array of coordinates.
*
* Returned:
* discrd double[naxis]
* Array of coordinates to which the distortion functions
* have been applied.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
* 2: Memory allocation failed.
* 3: Invalid parameter.
* 4: Distort error.
*
* For returns > 1, a detailed error message is set in
* disprm::err if enabled, see wcserr_enable().
*
*
* disx2p() - Apply de-distortion function
* ---------------------------------------
* disx2p() applies the inverse of the distortion functions. By definition,
* the de-distortion is in the world-to-pixel direction.
*
* Depending on the point in the algorithm chain at which it is invoked,
* disx2p() may transform corrected pixel coordinates to pixel coordinates, or
* corrected intermediate pixel coordinates to intermediate pixel coordinates,
* or corrected image coordinates to image coordinates.
*
* disx2p() iteratively solves for the inverse using disp2x(). It assumes
* that the distortion is small and the functions are well-behaved, being
* continuous and with continuous derivatives. Also that, to first order
* in the neighbourhood of the solution, discrd[j] ~= a + b*rawcrd[j], i.e.
* independent of rawcrd[i], where i != j. This is effectively equivalent to
* assuming that the distortion functions are separable to first order.
* Furthermore, a is assumed to be small, and b close to unity.
*
* If disprm::disx2p() is defined, then disx2p() uses it to provide an initial
* estimate for its more precise iterative inversion.
*
* Given and returned:
* dis struct disprm*
* Distortion function parameters.
*
* Given:
* discrd const double[naxis]
* Array of coordinates.
*
* Returned:
* rawcrd double[naxis]
* Array of coordinates to which the inverse distortion
* functions have been applied.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
* 2: Memory allocation failed.
* 3: Invalid parameter.
* 5: De-distort error.
*
* For returns > 1, a detailed error message is set in
* disprm::err if enabled, see wcserr_enable().
*
*
* diswarp() - Compute measures of distortion
* ------------------------------------------
* diswarp() computes various measures of the distortion over a specified range
* of coordinates.
*
* For prior distortions, the measures may be interpreted simply as an offset
* in pixel coordinates. For sequent distortions, the interpretation depends
* on the nature of the linear transformation matrix (PCi_ja or CDi_ja). If
* the latter introduces a scaling, then the measures will also be scaled.
* Note also that the image domain, which is rectangular in pixel coordinates,
* may be rotated, skewed, and/or stretched in intermediate pixel coordinates,
* and in general cannot be defined using pixblc[] and pixtrc[].
*
* PLEASE NOTE: the measures of total distortion may be essentially meaningless
* if there are multiple sequent distortions with different scaling.
*
* See also linwarp().
*
* Given and returned:
* dis struct disprm*
* Distortion function parameters.
*
* Given:
* pixblc const double[naxis]
* Start of the range of pixel coordinates (for prior
* distortions), or intermediate pixel coordinates (for
* sequent distortions). May be specified as a NULL
* pointer which is interpreted as (1,1,...).
*
* pixtrc const double[naxis]
* End of the range of pixel coordinates (prior) or
* intermediate pixel coordinates (sequent).
*
* pixsamp const double[naxis]
* If positive or zero, the increment on the particular
* axis, starting at pixblc[]. Zero is interpreted as a
* unit increment. pixsamp may also be specified as a
* NULL pointer which is interpreted as all zeroes, i.e.
* unit increments on all axes.
*
* If negative, the grid size on the particular axis (the
* absolute value being rounded to the nearest integer).
* For example, if pixsamp is (-128.0,-128.0,...) then
* each axis will be sampled at 128 points between
* pixblc[] and pixtrc[] inclusive. Use caution when
* using this option on non-square images.
*
* Returned:
* nsamp int* The number of pixel coordinates sampled.
*
* Can be specified as a NULL pointer if not required.
*
* maxdis double[naxis]
* For each individual distortion function, the
* maximum absolute value of the distortion.
*
* Can be specified as a NULL pointer if not required.
*
* maxtot double* For the combination of all distortion functions, the
* maximum absolute value of the distortion.
*
* Can be specified as a NULL pointer if not required.
*
* avgdis double[naxis]
* For each individual distortion function, the
* mean value of the distortion.
*
* Can be specified as a NULL pointer if not required.
*
* avgtot double* For the combination of all distortion functions, the
* mean value of the distortion.
*
* Can be specified as a NULL pointer if not required.
*
* rmsdis double[naxis]
* For each individual distortion function, the
* root mean square deviation of the distortion.
*
* Can be specified as a NULL pointer if not required.
*
* rmstot double* For the combination of all distortion functions, the
* root mean square deviation of the distortion.
*
* Can be specified as a NULL pointer if not required.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null disprm pointer passed.
* 2: Memory allocation failed.
* 3: Invalid parameter.
* 4: Distort error.
*
*
* disprm struct - Distortion parameters
* -------------------------------------
* The disprm struct contains all of the information required to apply a set of
* distortion functions. It consists of certain members that must be set by
* the user ("given") and others that are set by the WCSLIB routines
* ("returned"). While the addresses of the arrays themselves may be set by
* disinit() if it (optionally) allocates memory, their contents must be set by
* the user.
*
* int flag
* (Given and returned) This flag must be set to zero whenever any of the
* following members of the disprm struct are set or modified:
*
* - disprm::naxis,
* - disprm::dtype,
* - disprm::ndp,
* - disprm::dp.
*
* This signals the initialization routine, disset(), to recompute the
* returned members of the disprm struct. disset() will reset flag to
* indicate that this has been done.
*
* PLEASE NOTE: flag must be set to -1 when disinit() is called for the
* first time for a particular disprm struct in order to initialize memory
* management. It must ONLY be used on the first initialization otherwise
* memory leaks may result.
*
* int naxis
* (Given or returned) Number of pixel and world coordinate elements.
*
* If disinit() is used to initialize the disprm struct (as would normally
* be the case) then it will set naxis from the value passed to it as a
* function argument. The user should not subsequently modify it.
*
* char (*dtype)[72]
* (Given) Pointer to the first element of an array of char[72] containing
* the name of the distortion function for each axis.
*
* int ndp
* (Given) The number of entries in the disprm::dp[] array.
*
* int ndpmax
* (Given) The length of the disprm::dp[] array.
*
* ndpmax will be set by disinit() if it allocates memory for disprm::dp[],
* otherwise it must be set by the user. See also disndp().
*
* struct dpkey dp
* (Given) Address of the first element of an array of length ndpmax of
* dpkey structs.
*
* As a FITS header parser encounters each DPja or DQia keyword it should
* load it into a dpkey struct in the array and increment ndp. However,
* note that a single disprm struct must hold only DPja or DQia keyvalues,
* not both. disset() interprets them as required by the particular
* distortion function.
*
* double *maxdis
* (Given) Pointer to the first element of an array of double specifying
* the maximum absolute value of the distortion for each axis computed over
* the whole image.
*
* It is not necessary to reset the disprm struct (via disset()) when
* disprm::maxdis is changed.
*
* double totdis
* (Given) The maximum absolute value of the combination of all distortion
* functions specified as an offset in pixel coordinates computed over the
* whole image.
*
* It is not necessary to reset the disprm struct (via disset()) when
* disprm::totdis is changed.
*
* int *docorr
* (Returned) Pointer to the first element of an array of int containing
* flags that indicate the mode of correction for each axis.
*
* If docorr is zero, the distortion function returns the corrected
* coordinates directly. Any other value indicates that the distortion
* function computes a correction to be added to pixel coordinates (prior
* distortion) or intermediate pixel coordinates (sequent distortion).
*
* int *Nhat
* (Returned) Pointer to the first element of an array of int containing
* the number of coordinate axes that form the independent variables of the
* distortion function for each axis.
*
* int **axmap
* (Returned) Pointer to the first element of an array of int* containing
* pointers to the first elements of the axis mapping arrays for each axis.
*
* An axis mapping associates the independent variables of a distortion
* function with the 0-relative image axis number. For example, consider
* an image with a spectrum on the first axis (axis 0), followed by RA
* (axis 1), Dec (axis2), and time (axis 3) axes. For a distortion in
* (RA,Dec) and no distortion on the spectral or time axes, the axis
* mapping arrays, axmap[j][], would be
*
= j=0: [-1, -1, -1, -1] ...no distortion on spectral axis,
= 1: [ 1, 2, -1, -1] ...RA distortion depends on RA and Dec,
= 2: [ 2, 1, -1, -1] ...Dec distortion depends on Dec and RA,
= 3: [-1, -1, -1, -1] ...no distortion on time axis,
*
* where -1 indicates that there is no corresponding independent
* variable.
*
* double **offset
* (Returned) Pointer to the first element of an array of double*
* containing pointers to the first elements of arrays of offsets used to
* renormalize the independent variables of the distortion function for
* each axis.
*
* The offsets are subtracted from the independent variables before
* scaling.
*
* double **scale
* (Returned) Pointer to the first element of an array of double*
* containing pointers to the first elements of arrays of scales used to
* renormalize the independent variables of the distortion function for
* each axis.
*
* The scale is applied to the independent variables after the offsets are
* subtracted.
*
* int **iparm
* (Returned) Pointer to the first element of an array of int*
* containing pointers to the first elements of the arrays of integer
* distortion parameters for each axis.
*
* double **dparm
* (Returned) Pointer to the first element of an array of double*
* containing pointers to the first elements of the arrays of floating
* point distortion parameters for each axis.
*
* int i_naxis
* (Returned) Dimension of the internal arrays (normally equal to naxis).
*
* int ndis
* (Returned) The number of distortion functions.
*
* struct wcserr *err
* (Returned) If enabled, when an error status is returned, this struct
* contains detailed information about the error, see wcserr_enable().
*
* int (**disp2x)(DISP2X_ARGS)
* (For internal use only.)
* int (**disx2p)(DISX2P_ARGS)
* (For internal use only.)
* double *dummy
* (For internal use only.)
* int m_flag
* (For internal use only.)
* int m_naxis
* (For internal use only.)
* char (*m_dtype)[72]
* (For internal use only.)
* double **m_dp
* (For internal use only.)
* double *m_maxdis
* (For internal use only.)
*
*
* dpkey struct - Store for DPja and DQia keyvalues
* ------------------------------------------------
* The dpkey struct is used to pass the parsed contents of DPja or DQia
* keyrecords to disset() via the disprm struct. A disprm struct must hold
* only DPja or DQia keyvalues, not both.
*
* All members of this struct are to be set by the user.
*
* char field[72]
* (Given) The full field name of the record, including the keyword name.
* Note that the colon delimiter separating the field name and the value in
* record-valued keyvalues is not part of the field name. For example, in
* the following:
*
= DP3A = 'AXIS.1: 2'
*
* the full record field name is "DP3A.AXIS.1", and the record's value
* is 2.
*
* int j
* (Given) Axis number (1-relative), i.e. the j in DPja or i in DQia.
*
* int type
* (Given) The data type of the record's value
* - 0: Integer (stored as an int),
* - 1: Floating point (stored as a double).
*
* union value
* (Given) A union comprised of
* - dpkey::i,
* - dpkey::f,
*
* the record's value.
*
*
* Global variable: const char *dis_errmsg[] - Status return messages
* ------------------------------------------------------------------
* Error messages to match the status value returned from each function.
*
*===========================================================================*/
#ifndef WCSLIB_DIS
#define WCSLIB_DIS
#ifdef __cplusplus
extern "C" {
#endif
extern const char *dis_errmsg[];
enum dis_errmsg_enum {
DISERR_SUCCESS = 0, // Success.
DISERR_NULL_POINTER = 1, // Null disprm pointer passed.
DISERR_MEMORY = 2, // Memory allocation failed.
DISERR_BAD_PARAM = 3, // Invalid parameter value.
DISERR_DISTORT = 4, // Distortion error.
DISERR_DEDISTORT = 5 // De-distortion error.
};
// For use in declaring distortion function prototypes (= DISX2P_ARGS).
#define DISP2X_ARGS int inverse, const int iparm[], const double dparm[], \
int ncrd, const double rawcrd[], double *discrd
// For use in declaring de-distortion function prototypes (= DISP2X_ARGS).
#define DISX2P_ARGS int inverse, const int iparm[], const double dparm[], \
int ncrd, const double discrd[], double *rawcrd
// Struct used for storing DPja and DQia keyvalues.
struct dpkey {
char field[72]; // Full record field name (no colon).
int j; // Axis number, as in DPja (1-relative).
int type; // Data type of value.
union {
int i; // Integer record value.
double f; // Floating point record value.
} value; // Record value.
};
// Size of the dpkey struct in int units, used by the Fortran wrappers.
#define DPLEN (sizeof(struct dpkey)/sizeof(int))
struct disprm {
// Initialization flag (see the prologue above).
//--------------------------------------------------------------------------
int flag; // Set to zero to force initialization.
// Parameters to be provided (see the prologue above).
//--------------------------------------------------------------------------
int naxis; // The number of pixel coordinate elements,
// given by NAXIS.
char (*dtype)[72]; // For each axis, the distortion type.
int ndp; // Number of DPja or DQia keywords, and the
int ndpmax; // number for which space was allocated.
struct dpkey *dp; // DPja or DQia keyvalues (not both).
double totdis; // The maximum combined distortion.
double *maxdis; // For each axis, the maximum distortion.
// Information derived from the parameters supplied.
//--------------------------------------------------------------------------
int *docorr; // For each axis, the mode of correction.
int *Nhat; // For each axis, the number of coordinate
// axes that form the independent variables
// of the distortion function.
int **axmap; // For each axis, the axis mapping array.
double **offset; // For each axis, renormalization offsets.
double **scale; // For each axis, renormalization scales.
int **iparm; // For each axis, the array of integer
// distortion parameters.
double **dparm; // For each axis, the array of floating
// point distortion parameters.
int i_naxis; // Dimension of the internal arrays.
int ndis; // The number of distortion functions.
// Error handling, if enabled.
//--------------------------------------------------------------------------
struct wcserr *err;
// Private - the remainder are for internal use.
//--------------------------------------------------------------------------
int (**disp2x)(DISP2X_ARGS); // For each axis, pointers to the
int (**disx2p)(DISX2P_ARGS); // distortion function and its inverse.
int m_flag, m_naxis; // The remainder are for memory management.
char (*m_dtype)[72];
struct dpkey *m_dp;
double *m_maxdis;
};
// Size of the disprm struct in int units, used by the Fortran wrappers.
#define DISLEN (sizeof(struct disprm)/sizeof(int))
int disndp(int n);
int dpfill(struct dpkey *dp, const char *keyword, const char *field, int j,
int type, int i, double f);
int dpkeyi(const struct dpkey *dp);
double dpkeyd(const struct dpkey *dp);
int disini(int alloc, int naxis, struct disprm *dis);
int disinit(int alloc, int naxis, struct disprm *dis, int ndpmax);
int discpy(int alloc, const struct disprm *dissrc, struct disprm *disdst);
int disfree(struct disprm *dis);
int dissize(const struct disprm *dis, int sizes[2]);
int disprt(const struct disprm *dis);
int disperr(const struct disprm *dis, const char *prefix);
int dishdo(struct disprm *dis);
int disset(struct disprm *dis);
int disp2x(struct disprm *dis, const double rawcrd[], double discrd[]);
int disx2p(struct disprm *dis, const double discrd[], double rawcrd[]);
int diswarp(struct disprm *dis, const double pixblc[], const double pixtrc[],
const double pixsamp[], int *nsamp,
double maxdis[], double *maxtot,
double avgdis[], double *avgtot,
double rmsdis[], double *rmstot);
#ifdef __cplusplus
}
#endif
#endif // WCSLIB_DIS
disp2x
int disp2x(struct disprm *dis, const double rawcrd[], double discrd[])
Apply distortion function.
dpkeyd
double dpkeyd(const struct dpkey *dp)
Get the data value in a dpkey struct as double.
DISP2X_ARGS
#define DISP2X_ARGS
Definition dis.h:1070
dis_errmsg_enum
dis_errmsg_enum
Definition dis.h:1060
DISERR_MEMORY
@ DISERR_MEMORY
Definition dis.h:1063
DISERR_NULL_POINTER
@ DISERR_NULL_POINTER
Definition dis.h:1062
DISERR_DEDISTORT
@ DISERR_DEDISTORT
Definition dis.h:1066
DISERR_BAD_PARAM
@ DISERR_BAD_PARAM
Definition dis.h:1064
DISERR_DISTORT
@ DISERR_DISTORT
Definition dis.h:1065
DISERR_SUCCESS
@ DISERR_SUCCESS
Definition dis.h:1061
disinit
int disinit(int alloc, int naxis, struct disprm *dis, int ndpmax)
Default constructor for the disprm struct.
discpy
int discpy(int alloc, const struct disprm *dissrc, struct disprm *disdst)
Copy routine for the disprm struct.
dpfill
int dpfill(struct dpkey *dp, const char *keyword, const char *field, int j, int type, int i, double f)
Fill the contents of a dpkey struct.
dpkeyi
int dpkeyi(const struct dpkey *dp)
Get the data value in a dpkey struct as int.
dissize
int dissize(const struct disprm *dis, int sizes[2])
Compute the size of a disprm struct.
dis_errmsg
const char * dis_errmsg[]
Status return messages.
disfree
int disfree(struct disprm *dis)
Destructor for the disprm struct.
disini
int disini(int alloc, int naxis, struct disprm *dis)
Default constructor for the disprm struct.
diswarp
int diswarp(struct disprm *dis, const double pixblc[], const double pixtrc[], const double pixsamp[], int *nsamp, double maxdis[], double *maxtot, double avgdis[], double *avgtot, double rmsdis[], double *rmstot)
Compute measures of distortion.
disndp
int disndp(int n)
Memory allocation for DPja and DQia.
dishdo
int dishdo(struct disprm *dis)
write FITS headers using TPD.
disx2p
int disx2p(struct disprm *dis, const double discrd[], double rawcrd[])
Apply de-distortion function.
DISX2P_ARGS
#define DISX2P_ARGS
Definition dis.h:1074
disperr
int disperr(const struct disprm *dis, const char *prefix)
Print error messages from a disprm struct.
disset
int disset(struct disprm *dis)
Setup routine for the disprm struct.
disprt
int disprt(const struct disprm *dis)
Print routine for the disprm struct.
disprm
Distortion parameters.
Definition dis.h:1093
disprm::totdis
double totdis
Definition dis.h:1106
disprm::iparm
int ** iparm
Definition dis.h:1118
disprm::scale
double ** scale
Definition dis.h:1117
disprm::naxis
int naxis
Definition dis.h:1100
disprm::err
struct wcserr * err
Definition dis.h:1127
disprm::dtype
char(* dtype)[72]
Definition dis.h:1102
disprm::flag
int flag
Definition dis.h:1096
disprm::m_maxdis
double * m_maxdis
Definition dis.h:1137
disprm::i_naxis
int i_naxis
Definition dis.h:1122
disprm::disp2x
int(** disp2x)(DISP2X_ARGS)
Definition dis.h:1131
disprm::ndpmax
int ndpmax
Definition dis.h:1104
disprm::m_naxis
int m_naxis
Definition dis.h:1134
disprm::dp
struct dpkey * dp
Definition dis.h:1105
disprm::ndis
int ndis
Definition dis.h:1123
disprm::docorr
int * docorr
Definition dis.h:1111
disprm::offset
double ** offset
Definition dis.h:1116
disprm::m_dtype
char(* m_dtype)[72]
Definition dis.h:1135
disprm::dparm
double ** dparm
Definition dis.h:1120
disprm::axmap
int ** axmap
Definition dis.h:1115
disprm::m_dp
struct dpkey * m_dp
Definition dis.h:1136
disprm::maxdis
double * maxdis
Definition dis.h:1107
disprm::ndp
int ndp
Definition dis.h:1103
disprm::disx2p
int(** disx2p)(DISX2P_ARGS)
Definition dis.h:1132
disprm::Nhat
int * Nhat
Definition dis.h:1112
disprm::m_flag
int m_flag
Definition dis.h:1134
dpkey
Store for DPja and DQia keyvalues.
Definition dis.h:1079
dpkey::value
union dpkey::@0 value
dpkey::i
int i
Definition dis.h:1084
dpkey::field
char field[72]
Definition dis.h:1080
dpkey::type
int type
Definition dis.h:1082
dpkey::j
int j
Definition dis.h:1081
dpkey::f
double f
Definition dis.h:1085
wcserr
Error message handling.
Definition wcserr.h:243