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#======================================================================
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# R D I _ C O O R D S . P L
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# doc: Sun Jan 19 17:57:53 2003
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# dlm: Mon Nov 27 07:13:25 2017
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# (c) 2003 A.M. Thurnherr
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# uE-Info: 58 62 NIL 0 0 72 10 2 4 NIL ofnI
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#======================================================================
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# RDI Workhorse Coordinate Transformations
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# HISTORY:
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# Jan 19, 2003: - written
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# Jan 21, 2003: - made it obey HEADING_BIAS (magnetic declination)
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# Jan 22, 3003: - corrected magnetic declination
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# Feb 16, 2003: - use pitch correction from RDI manual
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# Oct 11, 2003: - BUG: return value of atan() had been interpreted
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# as degrees instead of radians
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# Feb 27, 2004: - added velApplyHdgBias()
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# - changed non-zero HEADING_ALIGNMENT from error to warning
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# Sep 16, 2005: - added deg() for [mkprofile]
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# Aug 26, 2006: - BUG: incorrect transformation for uplookers
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# Nov 30, 2007: - optimized &velInstrumentToEarth(), velBeamToInstrument()
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# - added support for 3-beam solutions
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# Feb 12, 2008: - added threeBeamFlag
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# Mar 18, 2009: - added &gimbal_pitch(), &angle_from_vertical()
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# May 19, 2009: - added &velBeamToVertical()
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# May 23, 2009: - debugged & renamed to &velBeamToBPEarth
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# May 23, 2010: - changed prototypes of rad() & deg() to conform to ANTS
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# Dec 20, 2010: - cosmetics
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# Dec 23, 2010: - added &velBeamToBPInstrument
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# Jan 22, 2011: - made velApplyHdgBias calculate sin/cos every time to allow
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# per-ensemble corrections
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# Jan 15, 2012: - replaced defined(@...) by (@...) to get rid of warning
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# Aug 7, 2013: - BUG: &velBeamToBPInstrument did not return any val unless
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# all beam velocities are defined
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# Nov 27, 2013: - added &RDI_pitch(), &tilt_azimuth()
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# Mar 4, 2014: - added support for ensembles with missing PITCH/ROLL/HEADING
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# May 29, 2014: - BUG: vertical velocity can be calculated even without
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# heading
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# - removed some old debug statements
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# - removed unused code from &velBeamToBPInstrument
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# Jan 5, 2016: - added &velEarthToInstrument(@), &velInstrumentToBeam(@)
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# Jan 9, 2016: - added &velEarthToBeam(), &velBeamToEarth()
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# Feb 29, 2016: - debugged & verified velEarthToInstrument(), velInstrumentToBeam()
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# - added velBeamToEarth()
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# May 19, 2016: - begin implemeting bin interpolation
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# May 25, 2016: - continued
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# May 26, 2016: - made it work
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# May 30, 2016: - begin implementing 2nd order attitude transformations
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# Jun 6, 2016: - toEarth transformation in beamToBPEarth was but crude approximation;
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# updated with transformation taken from Lohrman et al. (JAOT 1990)
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# - BUG: v34 sign was inconsistent with RDI coord manual
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# Jun 8, 2016: - added $ens as arg to velInstrumentToBeam() for consistency
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# Jul 7, 2016: - added velEarthToBPw() with algorithm debugged and verified
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# by Paul Wanis from TRDI
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# Oct 12, 2017: - documentation
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# Nov 26, 2017: - BUG: velBeamtoBPEarth() did not respect missing values
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# Nov 27, 2017: - BUG: numbersp() from [antslib.pl] was used
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use strict;
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use POSIX;
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my($PI) = 3.14159265358979;
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sub rad(@) { return $_[0]/180 * $PI; }
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sub deg(@) { return $_[0]/$PI * 180; }
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#----------------------------------------------------------------------
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# Tweakables
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#----------------------------------------------------------------------
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$RDI_Coords::minValidVels = 3; # 3-beam solutions ok (velBeamToInstrument)
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$RDI_Coords::binMapping = 'linterp'; # 'linterp' or 'none' (earthVels, BPearthVels)
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$RDI_Coords::beamTransformation = 'LHR90'; # set to 'RDI' to use 1st order transformations from RDI manual
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#----------------------------------------------------------------------
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# beam to earth transformation
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#----------------------------------------------------------------------
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$RDI_Coords::threeBeam_1 = 0; # stats from velBeamToInstrument
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$RDI_Coords::threeBeam_2 = 0;
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$RDI_Coords::threeBeam_3 = 0;
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$RDI_Coords::threeBeam_4 = 0;
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$RDI_Coords::fourBeam = 0;
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$RDI_Coords::threeBeamFlag = 0; # flag last transformation
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{ # STATIC SCOPE
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my(@B2I);
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sub velBeamToInstrument(@)
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{
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my($ADCP,$ens,$v1,$v2,$v3,$v4) = @_;
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return undef unless (defined($v1) + defined($v2) +
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defined($v3) + defined($v4)
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>= $RDI_Coords::minValidVels);
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unless (@B2I) {
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my($a) = 1 / (2 * sin(rad($ADCP->{BEAM_ANGLE})));
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my($b) = 1 / (4 * cos(rad($ADCP->{BEAM_ANGLE})));
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my($c) = $ADCP->{CONVEX_BEAM_PATTERN} ? 1 : -1;
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my($d) = $a / sqrt(2);
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@B2I = ([$c*$a, -$c*$a, 0, 0 ],
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[0, 0, -$c*$a, $c*$a],
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[$b, $b, $b, $b ],
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[$d, $d, -$d, -$d ]);
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}
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if (!defined($v1)) { # 3-beam solutions
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$RDI_Coords::threeBeamFlag = 1;
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$RDI_Coords::threeBeam_1++;
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$v1 = -($v2*$B2I[3][1]+$v3*$B2I[3][2]+$v4*$B2I[3][3])/$B2I[3][0];
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} elsif (!defined($v2)) {
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$RDI_Coords::threeBeamFlag = 1;
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$RDI_Coords::threeBeam_2++;
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$v2 = -($v1*$B2I[3][0]+$v3*$B2I[3][2]+$v4*$B2I[3][3])/$B2I[3][1];
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} elsif (!defined($v3)) {
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$RDI_Coords::threeBeamFlag = 1;
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$RDI_Coords::threeBeam_3++;
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$v3 = -($v1*$B2I[3][0]+$v2*$B2I[3][1]+$v4*$B2I[3][3])/$B2I[3][2];
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} elsif (!defined($v4)) {
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$RDI_Coords::threeBeamFlag = 1;
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$RDI_Coords::threeBeam_4++;
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$v4 = -($v1*$B2I[3][0]+$v2*$B2I[3][1]+$v3*$B2I[3][2])/$B2I[3][3];
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} else {
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$RDI_Coords::threeBeamFlag = 0;
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$RDI_Coords::fourBeam++;
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}
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return ($v1*$B2I[0][0]+$v2*$B2I[0][1],
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$v3*$B2I[1][2]+$v4*$B2I[1][3],
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$v1*$B2I[2][0]+$v2*$B2I[2][1]+$v3*$B2I[2][2]+$v4*$B2I[2][3],
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$v1*$B2I[3][0]+$v2*$B2I[3][1]+$v3*$B2I[3][2]+$v4*$B2I[3][3]);
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}
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} # STATIC SCOPE
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#----------------------------------------------------------------------
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# velInstrumentToEarth(\%ADCP,ens,v1,v2,v3,v4) => (u,v,w,e)
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# - $RDI_Coords::beamTransformation = 'LHR90'
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# - from Lohrmann, Hackett & Roet (J. Tech., 1990)
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# - eq A1 maps to RDI matrix M (sec 5.6) with
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# alpha = roll
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# beta = gimball_pitch
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# psi = calculation_pitch
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# psi = asin{sin(beta) cos(alpha) / sqrt[1- sin(alpha)^2 sin(beta)^2]}
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# - (I only checked for 0 heading, but this is sufficient)
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# - $RDI_Coords::beamTransformation = 'RDI'
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# - default prior to LADCP_w V1.3
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# - from RDI manual
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# - 99% accurate for p/r<8deg
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# => 1cm/s error for 1m/s winch speed!
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#----------------------------------------------------------------------
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{ # STATIC SCOPE
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my($hdg,$pitch,$roll,@I2E);
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sub velInstrumentToEarth(@)
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{
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my($ADCP,$ens,$v1,$v2,$v3,$v4) = @_;
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return undef unless (defined($v1) && defined($v2) &&
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defined($v3) && defined($v4) &&
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defined($ADCP->{ENSEMBLE}[$ens]->{PITCH}) &&
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defined($ADCP->{ENSEMBLE}[$ens]->{ROLL}));
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unless (@I2E &&
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$pitch == $ADCP->{ENSEMBLE}[$ens]->{PITCH} &&
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$roll == $ADCP->{ENSEMBLE}[$ens]->{ROLL}) {
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printf(STDERR "$0: warning HEADING_ALIGNMENT == %g ignored\n",
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$ADCP->{HEADING_ALIGNMENT})
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if ($ADCP->{HEADING_ALIGNMENT});
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$hdg = $ADCP->{ENSEMBLE}[$ens]->{HEADING} - $ADCP->{HEADING_BIAS}
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if defined($ADCP->{ENSEMBLE}[$ens]->{HEADING});
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$pitch = $ADCP->{ENSEMBLE}[$ens]->{PITCH};
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$roll = $ADCP->{ENSEMBLE}[$ens]->{ROLL};
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my($rad_gimbal_pitch) = atan(tan(rad($pitch)) * cos(rad($roll)));
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my($rad_calc_pitch) = ($RDI_Coords::beamTransformation eq 'RDI') ? $rad_gimbal_pitch :
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asin(sin($rad_gimbal_pitch)*cos(rad($roll)) /
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sqrt(1-sin(rad($roll))**2*sin($rad_gimbal_pitch)**2));
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my($sh,$ch) = (sin(rad($hdg)),cos(rad($hdg)))
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if defined($hdg);
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my($sp,$cp) = (sin($rad_calc_pitch),cos($rad_calc_pitch));
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my($sr,$cr) = (sin(rad($roll)), cos(rad($roll)));
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@I2E = $ADCP->{ENSEMBLE}[$ens]->{XDUCER_FACING_UP}
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? (
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[-$ch*$cr-$sh*$sp*$sr, $sh*$cp,-$ch*$sr+$sh*$sp*$cr],
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[-$ch*$sp*$sr+$sh*$cr, $ch*$cp, $sh*$sr+$ch*$sp*$cr],
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[+$cp*$sr, $sp, -$cp*$cr, ],
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) : (
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[$ch*$cr+$sh*$sp*$sr, $sh*$cp, $ch*$sr-$sh*$sp*$cr],
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[$ch*$sp*$sr-$sh*$cr, $ch*$cp,-$sh*$sr-$ch*$sp*$cr],
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[-$cp*$sr, $sp, $cp*$cr, ],
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);
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}
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return defined($ADCP->{ENSEMBLE}[$ens]->{HEADING})
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? ($v1*$I2E[0][0]+$v2*$I2E[0][1]+$v3*$I2E[0][2],
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$v1*$I2E[1][0]+$v2*$I2E[1][1]+$v3*$I2E[1][2],
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$v1*$I2E[2][0]+$v2*$I2E[2][1]+$v3*$I2E[2][2],
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$v4)
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: (undef,undef,
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$v1*$I2E[2][0]+$v2*$I2E[2][1]+$v3*$I2E[2][2],
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$v4);
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}
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} # STATIC SCOPE
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sub velBeamToEarth(@)
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{
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my($ADCP,$e,@v) = @_;
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return velInstrumentToEarth($ADCP,$e,velBeamToInstrument($ADCP,$e,@v));
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}
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#----------------------------------------------------------------------
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# velEarthToInstrument() transforms earth to instrument coordinates
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# - based on manually inverted rotation matrix M (Sec 5.6 in coord-trans manual)
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# - Paul Wanis from TRDI pointed out that M is orthonormal, which
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# implies that M^-1 = M' (where M' is the transpose), confirming
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# the (unnecessary) derivation
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# - code was verified for both down- and uplookers
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# - missing heading data (IMP) causes undef beam velocities
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#----------------------------------------------------------------------
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{ # STATIC SCOPE
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my($hdg,$pitch,$roll,@E2I);
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sub velEarthToInstrument(@)
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{
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my($ADCP,$ens,$u,$v,$w,$ev) = @_;
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unless (@E2I &&
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$pitch == $ADCP->{ENSEMBLE}[$ens]->{PITCH} &&
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$roll == $ADCP->{ENSEMBLE}[$ens]->{ROLL}) {
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$hdg = $ADCP->{ENSEMBLE}[$ens]->{HEADING} - $ADCP->{HEADING_BIAS}
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if defined($ADCP->{ENSEMBLE}[$ens]->{HEADING});
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$pitch = $ADCP->{ENSEMBLE}[$ens]->{PITCH};
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$roll = $ADCP->{ENSEMBLE}[$ens]->{ROLL};
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my($rad_gimbal_pitch) = atan(tan(rad($pitch)) * cos(rad($roll)));
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my($useRoll) = ($ADCP->{ENSEMBLE}[$ens]->{XDUCER_FACING_UP}) ? $roll+180 : $roll;
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my($sh,$ch) = (sin(rad($hdg)),cos(rad($hdg)))
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if defined($hdg);
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my($sp,$cp) = (sin($rad_gimbal_pitch),cos($rad_gimbal_pitch));
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my($sr,$cr) = (sin(rad($useRoll)), cos(rad($useRoll)));
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@E2I = ([$ch*$cr+$sh*$sp*$sr, $ch*$sp*$sr-$sh*$cr, -$cp*$sr], # M^-1 = R^-1 * P^-1 * R^-1
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[$sh*$cp, $ch*$cp, $sp ],
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[$ch*$sr-$sh*$sp*$cr, -$sh*$sr-$ch*$sp*$cr, $cp*$cr]);
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}
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return defined($ADCP->{ENSEMBLE}[$ens]->{HEADING})
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? ($u*$E2I[0][0]+$v*$E2I[0][1]+$w*$E2I[0][2],
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$u*$E2I[1][0]+$v*$E2I[1][1]+$w*$E2I[1][2],
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$u*$E2I[2][0]+$v*$E2I[2][1]+$w*$E2I[2][2],
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$ev)
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: (undef,undef,undef,undef);
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} # velEarthToIntrument()
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} # STATIC SCOPE
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#----------------------------------------------------------------------
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# velInstrumentToBeam() transforms instrument to beam coordinates
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# - based on manually solved eq system in sec 5.3 of coord manual
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# - does not implement bin-remapping
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# - returns undef for 3-beam solutions, as it is not known which
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# beam was bad
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#----------------------------------------------------------------------
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{ # STATIC SCOPE
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my($a,$b,$c,$d);
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sub velInstrumentToBeam(@)
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{
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my($ADCP,$ens,$x,$y,$z,$ev) = @_;
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return undef unless (defined($x) + defined($y) +
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defined($z) + defined($ev) == 4);
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unless (defined($a)) {
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$a = 1 / (2 * sin(rad($ADCP->{BEAM_ANGLE})));
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$b = 1 / (4 * cos(rad($ADCP->{BEAM_ANGLE})));
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$c = $ADCP->{CONVEX_BEAM_PATTERN} ? 1 : -1;
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$d = $a / sqrt(2);
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}
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return ( $x/(2*$a*$c) + $z/(4*$b) + $ev/(4*$d),
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-$x/(2*$a*$c) + $z/(4*$b) + $ev/(4*$d),
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-$y/(2*$a*$c) + $z/(4*$b) - $ev/(4*$d),
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$y/(2*$a*$c) + $z/(4*$b) - $ev/(4*$d));
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}
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} # STATIC SCOPE
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#----------------------------------------------------------------------
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# velEarthToBeam() combines velEarthToInstrument and velInstrumentToBeam
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#----------------------------------------------------------------------
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sub velEarthToBeam(@)
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{
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my($ADCP,$ens,$u,$v,$w,$ev) = @_;
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return velInstrumentToBeam($ADCP,$ens,
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velEarthToInstrument($ADCP,$ens,$u,$v,$w,$ev));
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}
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#----------------------------------------------------------------------
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# velEarthToBPw() returns w12 and w34 for beam-coordinate data
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# - I am grateful for Paul Wanis from TRDI who corrected a
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# bug in my transformation (fixed in V1.3). [The bug did not
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# affect the final w profiles significantly, because w12 and w34
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# are used only as diagnostics.]
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# - algorithm:
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# 1) rotate into instrument coordinates
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# 2) w12 = w + e*tan(beam_angle)/sqrt(2)
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# w34 = w - e*tan(beam_angle)/sqrt(2)
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# 3) rotate into horizontal coords (earth coords w/o
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# considering heading, i.e. same as earth coords
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# in case of w
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# - the commented-out version above is a "brute-force"
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# implementation which should give the same result
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#----------------------------------------------------------------------
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#sub velEarthToBPw(@)
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#{
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# my(@bpv) = velBeamToBPEarth(&velEarthToBeam(@_));
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# return ($bpv[1],$bpv[3]);
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|
322 |
#}
|
|
323 |
|
|
324 |
sub velEarthToBPw(@)
|
|
325 |
{
|
|
326 |
my($ADCP,$ens,$u,$v,$w,$ev) = @_;
|
|
327 |
my(@iv) = velEarthToInstrument(@_);
|
|
328 |
my(@iv12) = my(@iv34) = @iv;
|
|
329 |
$iv12[2] += $iv[3] * tan(rad($ADCP->{BEAM_ANGLE}))/sqrt(2);
|
|
330 |
$iv34[2] -= $iv[3] * tan(rad($ADCP->{BEAM_ANGLE}))/sqrt(2);
|
|
331 |
my(@ev12) = velInstrumentToEarth($ADCP,$ens,@iv12);
|
|
332 |
my(@ev34) = velInstrumentToEarth($ADCP,$ens,@iv34);
|
|
333 |
return ($ev12[2],$ev34[2]);
|
|
334 |
}
|
|
335 |
|
|
336 |
#======================================================================
|
|
337 |
# velBeamToBPEarth(@) calculates the vertical- and horizontal vels
|
|
338 |
# from the two beam pairs separately. Note that (w1+w2)/2 is
|
|
339 |
# identical to the w estimated according to RDI (ignoring 3-beam
|
|
340 |
# solutions).
|
|
341 |
#======================================================================
|
|
342 |
|
|
343 |
{ # STATIC SCOPE
|
|
344 |
my($TwoCosBAngle,$TwoSinBAngle);
|
|
345 |
|
|
346 |
sub velBeamToBPEarth(@)
|
|
347 |
{
|
|
348 |
my($ADCP,$ens,$b1,$b2,$b3,$b4) = @_;
|
|
349 |
my($v12,$w12,$v34,$w34);
|
|
350 |
|
|
351 |
return (undef,undef,undef,undef)
|
|
352 |
unless (defined($ADCP->{ENSEMBLE}[$ens]->{PITCH}) &&
|
|
353 |
defined($ADCP->{ENSEMBLE}[$ens]->{ROLL}));
|
|
354 |
|
|
355 |
unless (defined($TwoCosBAngle)) {
|
|
356 |
$TwoCosBAngle = 2 * cos(rad($ADCP->{BEAM_ANGLE}));
|
|
357 |
$TwoSinBAngle = 2 * sin(rad($ADCP->{BEAM_ANGLE}));
|
|
358 |
}
|
|
359 |
my($rad_roll) = rad($ADCP->{ENSEMBLE}[$ens]->{ROLL});
|
|
360 |
my($sr) = sin($rad_roll); my($cr) = cos($rad_roll);
|
|
361 |
my($rad_gimbal_pitch) = atan(tan(rad($ADCP->{ENSEMBLE}[$ens]->{PITCH})) * $cr); # gimbal pitch
|
|
362 |
my($rad_calc_pitch) = ($RDI_Coords::beamTransformation eq 'RDI') ? $rad_gimbal_pitch :
|
|
363 |
asin(sin($rad_gimbal_pitch)*cos($rad_roll) /
|
|
364 |
sqrt(1-sin($rad_roll)**2*sin($rad_gimbal_pitch)**2));
|
|
365 |
my($sp) = sin($rad_calc_pitch); my($cp) = cos($rad_calc_pitch);
|
|
366 |
|
|
367 |
# Sign convention:
|
|
368 |
# - refer to Coord manual Fig. 3
|
|
369 |
# - v12 is horizontal velocity from beam1 to beam2, i.e. westward for upward-looking ADCP
|
|
370 |
# with beam 3 pointing north (heading = 0)
|
|
371 |
|
|
372 |
my($v12_ic,$w12_ic,$v34_ic,$w34_ic,$w_ic);
|
|
373 |
|
|
374 |
if (numberp($b1) && numberp($b2)) {
|
|
375 |
$v12_ic = ($b1-$b2)/$TwoSinBAngle; # instrument coords...
|
|
376 |
$w12_ic = ($b1+$b2)/$TwoCosBAngle; # consistent with RDI convention
|
|
377 |
}
|
|
378 |
if (numberp($b3) && numberp($b4)) {
|
|
379 |
$v34_ic = ($b4-$b3)/$TwoSinBAngle;
|
|
380 |
$w34_ic = ($b3+$b4)/$TwoCosBAngle;
|
|
381 |
}
|
|
382 |
|
|
383 |
if ($ADCP->{ENSEMBLE}[$ens]->{XDUCER_FACING_DOWN}) { # beampair Earth coords
|
|
384 |
if (numberp($w12_ic) && numberp($w34_ic)) {
|
|
385 |
$w_ic = ($w12_ic+$w34_ic) / 2;
|
|
386 |
$v12 = $v12_ic*$cr + $v34_ic*0 + $w_ic*$sr; # Lohrman et al. (1990) A1
|
|
387 |
$v34 = $v12_ic*$sp*$sr + $v34_ic*$cp - $w_ic*$sp*$cr; # - defined for z upward => DL
|
|
388 |
$w12 =-$v12_ic*$cp*$sr + $v34_ic*$sp + $w12_ic*$cp*$cr;
|
|
389 |
$w34 =-$v12_ic*$cp*$sr + $v34_ic*$sp + $w34_ic*$cp*$cr;
|
|
390 |
} elsif (numberp($w12_ic)) {
|
|
391 |
$v12 = $v12_ic*$cr + $w12_ic*$sr;
|
|
392 |
$w12 =-$v12_ic*$cp*$sr + $w12_ic*$cp*$cr;
|
|
393 |
} elsif (numberp($w34_ic)) {
|
|
394 |
$v34 = $v34_ic*$cp - $w34_ic*$sp*$cr;
|
|
395 |
$w34 = $v34_ic*$sp + $w34_ic*$cp*$cr;
|
|
396 |
}
|
|
397 |
} else {
|
|
398 |
if (numberp($w12_ic) && numberp($w34_ic)) {
|
|
399 |
$w_ic = ($w12_ic+$w34_ic) / 2;
|
|
400 |
$v12 =-$v12_ic*$cr + $v34_ic*0 - $w_ic*$sr; # - as above with 1st & 3rd cols negated
|
|
401 |
$v34 =-$v12_ic*$sp*$sr + $v34_ic*$cp + $w_ic*$sp*$cr;
|
|
402 |
$w12 = $v12_ic*$cp*$sr + $v34_ic*$sp - $w12_ic*$cp*$cr;
|
|
403 |
$w34 = $v12_ic*$cp*$sr + $v34_ic*$sp - $w34_ic*$cp*$cr;
|
|
404 |
} elsif (numberp($w12_ic)) {
|
|
405 |
$v12 =-$v12_ic*$cr - $w12_ic*$sr;
|
|
406 |
$w12 = $v12_ic*$cp*$sr - $w12_ic*$cp*$cr;
|
|
407 |
} elsif (numberp($w34_ic)) {
|
|
408 |
$v34 = $v34_ic*$cp + $w34_ic*$sp*$cr;
|
|
409 |
$w34 = $v34_ic*$sp - $w34_ic*$cp*$cr;
|
|
410 |
}
|
|
411 |
}
|
|
412 |
|
|
413 |
return ($v12,$w12,$v34,$w34);
|
|
414 |
}
|
|
415 |
}
|
|
416 |
|
|
417 |
#===================================================================
|
|
418 |
# velBeamToBPInstrument(@) calculates the instrument-coordinate vels
|
|
419 |
# from the two beam pairs separately.
|
|
420 |
# - in spite of the function name, the output is in ship
|
|
421 |
# coordinates (instr coords with w up)
|
|
422 |
#===================================================================
|
|
423 |
|
|
424 |
{ # STATIC SCOPE
|
|
425 |
my($TwoCosBAngle,$TwoSinBAngle);
|
|
426 |
|
|
427 |
sub velBeamToBPInstrument(@)
|
|
428 |
{
|
|
429 |
my($ADCP,$ens,$b1,$b2,$b3,$b4) = @_;
|
|
430 |
my($v12,$w12,$v34,$w34);
|
|
431 |
|
|
432 |
return (undef,undef,undef,undef)
|
|
433 |
unless (defined($ADCP->{ENSEMBLE}[$ens]->{PITCH}) &&
|
|
434 |
defined($ADCP->{ENSEMBLE}[$ens]->{ROLL}));
|
|
435 |
|
|
436 |
unless (defined($TwoCosBAngle)) {
|
|
437 |
$TwoCosBAngle = 2 * cos(rad($ADCP->{BEAM_ANGLE}));
|
|
438 |
$TwoSinBAngle = 2 * sin(rad($ADCP->{BEAM_ANGLE}));
|
|
439 |
}
|
|
440 |
|
|
441 |
# Sign convention:
|
|
442 |
# - refer to Coord manual Fig. 3
|
|
443 |
# - v12 is horizontal velocity from beam1 to beam2
|
|
444 |
# - w is +ve upward, regardless of instrument orientation
|
|
445 |
|
|
446 |
if (defined($b1) && defined($b2)) {
|
|
447 |
$v12 = ($b1-$b2)/$TwoSinBAngle;
|
|
448 |
$w12 = ($b1+$b2)/$TwoCosBAngle;
|
|
449 |
$w12 *= -1 if ($ADCP->{ENSEMBLE}[$ens]->{XDUCER_FACING_UP});
|
|
450 |
}
|
|
451 |
if (defined($b3) && defined($b4)) {
|
|
452 |
$v34 = ($b4-$b3)/$TwoSinBAngle;
|
|
453 |
$w34 = ($b3+$b4)/$TwoCosBAngle;
|
|
454 |
$w34 *= -1 if ($ADCP->{ENSEMBLE}[$ens]->{XDUCER_FACING_UP});
|
|
455 |
}
|
|
456 |
|
|
457 |
return ($v12,$w12,$v34,$w34);
|
|
458 |
}
|
|
459 |
}
|
|
460 |
|
|
461 |
#======================================================================
|
|
462 |
# velApplyHdgBias() applies the heading bias, which is used to correct
|
|
463 |
# for magnetic declination for data recorded in Earth-coordinates ONLY.
|
|
464 |
# Bias correction for beam-coordinate data is done in velInstrumentToEarth()
|
|
465 |
#======================================================================
|
|
466 |
|
|
467 |
sub velApplyHdgBias(@)
|
|
468 |
{
|
|
469 |
my($ADCP,$ens,$v1,$v2,$v3,$v4) = @_;
|
|
470 |
return (undef,undef,undef,undef)
|
|
471 |
unless (defined($v1) && defined($v2) &&
|
|
472 |
defined($ADCP->{ENSEMBLE}[$ens]->{HEADING}));
|
|
473 |
|
|
474 |
my($sh) = sin(rad(-$ADCP->{HEADING_BIAS}));
|
|
475 |
my($ch) = cos(rad(-$ADCP->{HEADING_BIAS}));
|
|
476 |
|
|
477 |
return ( $v1*$ch + $v2*$sh,
|
|
478 |
-$v1*$sh + $v2*$ch,
|
|
479 |
$v3 ,
|
|
480 |
$v4 );
|
|
481 |
}
|
|
482 |
|
|
483 |
#----------------------------------------------------------------------
|
|
484 |
# Pitch/Roll Functions
|
|
485 |
#----------------------------------------------------------------------
|
|
486 |
|
|
487 |
sub gimbal_pitch($$) # RDI coord trans manual
|
|
488 |
{
|
|
489 |
my($RDI_pitch,$RDI_roll) = @_;
|
|
490 |
return 'nan' unless defined($RDI_pitch) && defined($RDI_roll);
|
|
491 |
return deg(atan(tan(rad($RDI_pitch)) * cos(rad($RDI_roll))));
|
|
492 |
}
|
|
493 |
|
|
494 |
sub RDI_pitch($$)
|
|
495 |
{
|
|
496 |
my($gimbal_pitch,$roll) = @_;
|
|
497 |
return 'nan' unless defined($gimbal_pitch) && defined($roll);
|
|
498 |
return deg(atan(tan(rad($gimbal_pitch))/cos(rad($roll))));
|
|
499 |
}
|
|
500 |
|
|
501 |
sub tilt_azimuth($$)
|
|
502 |
{
|
|
503 |
my($gimbal_pitch,$roll) = @_;
|
|
504 |
return 'nan' unless defined($gimbal_pitch) && defined($roll);
|
|
505 |
return angle(deg(atan2(sin(rad($gimbal_pitch)),sin(rad($roll)))));
|
|
506 |
}
|
|
507 |
|
|
508 |
# - angle from vertical is home grown
|
|
509 |
# - angle between two unit vectors given by acos(v1 dot v2)
|
|
510 |
# - vertical unit vector v1 = (0 0 1) => dot product = z-component of v2
|
|
511 |
# - when vertical unit vector is pitched in x direction, followed by
|
|
512 |
# roll in y direction:
|
|
513 |
# x = sin(pitch)
|
|
514 |
# y = cos(pitch) * sin(roll)
|
|
515 |
# z = cos(pitch) * cos(roll)
|
|
516 |
# has been checked with sqrt(x^2+y^2+z^2) == 1
|
|
517 |
# - for small angles, this is very similar to sqrt(pitch^2+roll^2)
|
|
518 |
|
|
519 |
sub angle_from_vertical($$)
|
|
520 |
{
|
|
521 |
my($RDI_pitch,$RDI_roll) = @_;
|
|
522 |
return 'nan' unless defined($RDI_pitch) && defined($RDI_roll);
|
|
523 |
my($rad_pitch) = atan(tan(rad($RDI_pitch)) * cos(rad($RDI_roll)));
|
|
524 |
return deg(acos(cos($rad_pitch) * cos(rad($RDI_roll))));
|
|
525 |
}
|
|
526 |
|
|
527 |
#----------------------------------------------------------------------
|
|
528 |
# alongBeamDZ(ADCP_dta,ens,beam) => (dz_to_bin1_center,bin_dz)
|
|
529 |
# - calculate vertical distances:
|
|
530 |
# - between transducer and bin1
|
|
531 |
# - between adjacent bins
|
|
532 |
# - no soundspeed correction
|
|
533 |
# - for UL (Fig. 3 Coord Manual):
|
|
534 |
# b1 = phi + roll b2 = phi - roll
|
|
535 |
# b3 = phi - pitch b4 = phi + pitch
|
|
536 |
# - for DL:
|
|
537 |
# b1 = phi + roll b2 = phi - roll
|
|
538 |
# b3 = phi + pitch b4 = phi - pitch
|
|
539 |
#----------------------------------------------------------------------
|
|
540 |
|
|
541 |
sub alongBeamDZ($$$)
|
|
542 |
{
|
|
543 |
my($ADCP,$ens,$beam) = @_;
|
|
544 |
|
|
545 |
my($tilt); # determine tilt of given beam
|
|
546 |
my($pitch) = $ADCP->{ENSEMBLE}[$ens]->{PITCH};
|
|
547 |
my($roll) = $ADCP->{ENSEMBLE}[$ens]->{ROLL};
|
|
548 |
if ($beam == 0) { # beam 1
|
|
549 |
$tilt = &angle_from_vertical($pitch,$ADCP->{BEAM_ANGLE}+$roll);
|
|
550 |
} elsif ($beam == 1) { # beam 2
|
|
551 |
$tilt = &angle_from_vertical($pitch,$ADCP->{BEAM_ANGLE}-$roll);
|
|
552 |
} elsif ($beam == 2) { # beam 3
|
|
553 |
$tilt = $ADCP->{ENSEMBLE}[$ens]->{XDUCER_FACING_UP}
|
|
554 |
? &angle_from_vertical($ADCP->{BEAM_ANGLE}-$pitch,$roll)
|
|
555 |
: &angle_from_vertical($ADCP->{BEAM_ANGLE}+$pitch,$roll);
|
|
556 |
} else { # beam 4
|
|
557 |
$tilt = $ADCP->{ENSEMBLE}[$ens]->{XDUCER_FACING_UP}
|
|
558 |
? &angle_from_vertical($ADCP->{BEAM_ANGLE}+$pitch,$roll)
|
|
559 |
: &angle_from_vertical($ADCP->{BEAM_ANGLE}-$pitch,$roll);
|
|
560 |
}
|
|
561 |
return ($ADCP->{DISTANCE_TO_BIN1_CENTER}*cos(rad($tilt)),
|
|
562 |
$ADCP->{BIN_LENGTH}*cos(rad($tilt)));
|
|
563 |
}
|
|
564 |
|
|
565 |
#----------------------------------------------------------------------
|
|
566 |
# binterp(ADCP_dta,ens,bin,ADCP_field) => @interpolated_vals
|
|
567 |
# - interpolate beam velocities to nominal bin center
|
|
568 |
# - field can be VELOCITY, ECHO_AMPLITUDE, ...
|
|
569 |
#
|
|
570 |
# earthVels(ADCP_dta,ens,bin) => (u,v,w,err_vel)
|
|
571 |
# BPEarthVels(ADCP_dta,ens,bin) => (v12,w12,v34,w34)
|
|
572 |
# - new interface (V1.7)
|
|
573 |
#----------------------------------------------------------------------
|
|
574 |
|
|
575 |
sub binterp1($$$$$) # interpolate along a single beam
|
|
576 |
{
|
|
577 |
my($ADCP,$ens,$target_dz,$ADCP_field,$beam) = @_;
|
|
578 |
|
|
579 |
my($dz2bin1,$bin_dz) = &alongBeamDZ($ADCP,$ens,$beam);
|
|
580 |
my($floor_bin) = int(($target_dz-$dz2bin1) / $bin_dz);
|
|
581 |
$floor_bin-- if ($floor_bin == $ADCP->{N_BINS}-1);
|
|
582 |
|
|
583 |
my($y1) = $ADCP->{ENSEMBLE}[$ens]->{$ADCP_field}[$floor_bin][$beam];
|
|
584 |
my($y2) = $ADCP->{ENSEMBLE}[$ens]->{$ADCP_field}[$floor_bin+1][$beam];
|
|
585 |
$y2 = $y1 unless defined($y2);
|
|
586 |
$y1 = $y2 unless defined($y1);
|
|
587 |
return undef unless defined($y1);
|
|
588 |
|
|
589 |
my($dz1) = $dz2bin1 + $floor_bin * $bin_dz;
|
|
590 |
my($dz2) = $dz1 + $bin_dz;
|
|
591 |
my($ifac) = ($target_dz - $dz1) / ($dz2 - $dz1);
|
|
592 |
die("assertion failed\nifac = $ifac (target_dz = $target_dz, dz1 = $dz1, dz2 = $dz2)")
|
|
593 |
unless ($ifac>= -0.5 && $ifac<=2);
|
|
594 |
return $y1 + $ifac*($y2-$y1);
|
|
595 |
}
|
|
596 |
|
|
597 |
sub binterp($$$$)
|
|
598 |
{
|
|
599 |
my($ADCP,$ens,$target_bin,$ADCP_field) = @_;
|
|
600 |
|
|
601 |
my($crt) = cos(rad($ADCP->{ENSEMBLE}[$ens]->{TILT})); # calc center depth of target bin
|
|
602 |
my($target_dz) = ($ADCP->{DISTANCE_TO_BIN1_CENTER} + $target_bin*$ADCP->{BIN_LENGTH}) * $crt;
|
|
603 |
|
|
604 |
return (&binterp1($ADCP,$ens,$target_dz,$ADCP_field,0), # interpolate all four beams
|
|
605 |
&binterp1($ADCP,$ens,$target_dz,$ADCP_field,1),
|
|
606 |
&binterp1($ADCP,$ens,$target_dz,$ADCP_field,2),
|
|
607 |
&binterp1($ADCP,$ens,$target_dz,$ADCP_field,3));
|
|
608 |
}
|
|
609 |
|
|
610 |
sub earthVels($$$)
|
|
611 |
{
|
|
612 |
my($ADCP,$ens,$bin) = @_;
|
|
613 |
if ($RDI_Coords::binMapping eq 'linterp') {
|
|
614 |
return velInstrumentToEarth($ADCP,$ens,
|
|
615 |
velBeamToInstrument($ADCP,$ens,
|
|
616 |
binterp($ADCP,$ens,$bin,'VELOCITY')));
|
|
617 |
} elsif ($RDI_Coords::binMapping eq 'none') {
|
|
618 |
return velInstrumentToEarth($ADCP,$ens,
|
|
619 |
velBeamToInstrument($ADCP,$ens,
|
|
620 |
@{$ADCP->{ENSEMBLE}[$ens]->{VELOCITY}[$bin]}));
|
|
621 |
} else {
|
|
622 |
die("earthVels(): unknown bin mapping '$RDI_Coords::binMapping '\n");
|
|
623 |
}
|
|
624 |
}
|
|
625 |
|
|
626 |
sub BPEarthVels($$$)
|
|
627 |
{
|
|
628 |
my($ADCP,$ens,$bin) = @_;
|
|
629 |
if ($RDI_Coords::binMapping eq 'linterp') {
|
|
630 |
return velBeamToBPEarth($ADCP,$ens,binterp($ADCP,$ens,$bin,'VELOCITY'));
|
|
631 |
} elsif ($RDI_Coords::binMapping eq 'none') {
|
|
632 |
return velBeamToBPEarth($ADCP,$ens,@{$ADCP->{ENSEMBLE}[$ens]->{VELOCITY}[$bin]});
|
|
633 |
} else {
|
|
634 |
die("BPEarthVels(): unknown bin mapping '$RDI_Coords::binMapping '\n");
|
|
635 |
}
|
|
636 |
}
|
|
637 |
|
|
638 |
#----------------------------------------------------------------------
|
|
639 |
|
|
640 |
1;
|