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#======================================================================
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# L I B V E C . P L
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# doc: Sat Mar 20 12:50:32 1999
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# dlm: Wed Nov 27 23:46:31 2013
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# (c) 1999 A.M. Thurnherr
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# uE-Info: 36 53 NIL 0 0 70 2 2 4 NIL ofnI
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#======================================================================
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# HISTORY:
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# Mar 20, 1999: - created for ANTS_2.1 (no more c-code)
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# May 27, 1999: - added polar/cartesian conversions
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# Sep 18, 1999: - argument typechecking
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# Dec 10, 1999: - vel_u(), vel_v(), vel_dir(), vel_mag()
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# Mar 07, 2000: - proj(), deg(), rad()
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# Apr 18, 2002: - area()
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# Jan 6, 2003: - changed dist() output to meters
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# Jan 16, 2003: - renamed vel_vel() to vel_speed()
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# Sep 3, 2003: - dir_bias()
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# May 13, 2004: - BUG: had fogotten to adapt area() to new dist()
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# May 21, 2004: - forced zero distance on &dist() if lat/lon does
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# not change (avoid roundoff error)
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# Jun 22, 2004: - added GMTdeg(), dir()
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# Nov 11, 2004: - BUG: roundoff test in dist() was done before
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# conversion to numbers
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# Jul 1, 2006: - Version 3.3 [HISTORY]
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# Jul 24, 2006: - modified to use equal()
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# Nov 16, 2006: - added degmin()
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# Dec 19, 2007: - addapted vel_speed(), vel_dir() to new &antsFunUsage()
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# - same routines now return nan on nan input
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# Jan 15, 2007: - BUG: vel_dir() was broken
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# Jun 14, 2009: - added p_vel()
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# Nov 5, 2009: - added angle(); vel_bias() => angle_diff()
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# Apr 22, 2010: - added angle_ts()
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# Jun 5, 2012: - added &closestPointOnStraightLine()
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# Jun 11, 2012: - addeed $t output to &closestPointOnStraightLine()
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# Nov 27, 2013: - added &angle_pos(), mag_heading()
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require "$ANTS/libPOSIX.pl"; # acos()
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#----------------------------------------------------------------------
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# &rad() calc radians
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# °() calc degrees
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#----------------------------------------------------------------------
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$PI = 3.14159265358979;
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sub rad(@)
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{
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my($d) = &antsFunUsage(1,"f","<deg>",@_);
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return $d/180 * $PI;
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}
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sub deg(@)
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{
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my($r) = &antsFunUsage(1,"f","<rad>",@_);
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return $r/$PI * 180;
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}
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#----------------------------------------------------------------------
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# &proj(from_x,from_y,onto_unit_x,onto_unit_y)
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# project vector onto another
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#----------------------------------------------------------------------
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# to transform CM velocity components u/v to along/across mean l/c:
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# - mean dir d = &vel_dir(<u>,<v>); with <.> indicating ensemble avg
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# - l = proj(u,v,sin(rad(d)),cos(rad(d))); NEW: l = p_vel(d[,u,v])
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# - c = -proj(u,v,-cos(rad(d)),sin(rad(d)));
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sub proj(@)
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{
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my($fx,$fy,$oux,$ouy) =
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&antsFunUsage(4,"ffff","<from_x> <from_y> " .
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"<onto_unit_x> <onto_unit_y>",@_);
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return $fx*$oux + $fy*$ouy;
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}
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{ my(@fc);
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sub p_vel(@)
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{
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my($u,$v,$d) = &antsFunUsage(3,'..f','[u, v,] dir',\@fc,'u','v',undef,@_);
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return nan unless numbersp($d,$u,$v);
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return proj($u,$v,sin(rad($d)),cos(rad($d)));
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}
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}
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#----------------------------------------------------------------------
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# &polar_r(x,y),&vel_vel(u,v) calc polar radius, velocity
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# &polar_phi(x,y),&vel_dir(u,v) calc polar degrees cclockwise from
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# horiz (phi) OR clockwise from N (dir)
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# &cartesian_x(r,phi),&vel_u(m,dir) calc x and u from polar coords
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# &cartesian_y(r,phi),&vel_v(m,dir) calc y and v from polar coords
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#----------------------------------------------------------------------
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sub polar_r(@)
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{
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my($x,$y) = &antsFunUsage(2,"ff","<x> <y>",@_);
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return sqrt($x*$x+$y*$y);
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}
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{ my(@fc);
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sub vel_speed(@)
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{
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my($u,$v) = &antsFunUsage(2,'..','[u, v]',\@fc,'u','v',@_); # . allows for nans
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return nan unless numbersp($u,$v);
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return sqrt($u*$u+$v*$v);
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}
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}
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sub polar_phi(@)
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{
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my($x,$y) = &antsFunUsage(2,"ff","<x> <y>",@_);
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return 180 / $PI * atan2($y,$x);
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}
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{ my(@fc);
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sub vel_dir(@)
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{
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my($u,$v) = &antsFunUsage(2,'..','[u, v]',\@fc,'u','v',@_); # . allows for nans
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return nan unless numbersp($u,$v);
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my($dir) = 180 / $PI * atan2($u,$v);
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return ($dir >= 0) ? $dir : $dir+360;
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}
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}
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sub cartesian_x(@)
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{
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my($r,$phi) = &antsFunUsage(2,"ff","<r> <phi>",@_);
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return $r * cos($PI*$phi/180);
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}
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sub vel_u(@) { return &cartesian_x($_[0],90-$_[1]); }
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sub cartesian_y(@)
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{
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my($r,$phi) = &antsFunUsage(2,"ff","<r> <phi>",@_);
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return $r * sin($PI*$phi/180);
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}
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sub vel_v(@) { return &cartesian_y($_[0],90-$_[1]); }
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#----------------------------------------------------------------------
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# magnetic heading from magnetometer; losely based on info found on-line;
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# note that mag_x = mag_y = 0 is singularity
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#----------------------------------------------------------------------
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sub mag_heading($$)
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{
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if ($_[1] != 0) { return 270 - deg(atan2($_[0],$_[1])); }
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elsif ($_[0] < 0) { return 180; }
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else { return 0; }
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}
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#----------------------------------------------------------------------
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# &angle(val)
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# return angle in range [-180,180]
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# &angle_pos(val)
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# return angle in range [0,360]
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# &angle_diff(ref_dir,dir)
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# return rotation between two angles in range [-180,180]
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# &rotation_ts(dir)
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# return time series of rotation
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# &angle_ts(dir)
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# return time series of angle without "wrap-around jumps"
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#----------------------------------------------------------------------
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sub angle(@)
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{
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my($val) = &antsFunUsage(1,"f","<val>",@_);
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$val += 360 while ($val < -180);
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$val -= 360 while ($val > 180);
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return $val;
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}
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sub angle_pos(@)
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{
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my($val) = angle(@_);
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return ($val < 0) ? 360+$val : $val;
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}
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sub angle_diff(@)
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{
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my($m,$s) = &antsFunUsage(2,"ff","<minuend> <subtrahend>",@_);
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return angle($m-$s);
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}
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{ my($last_in);
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sub rotation_ts(@)
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{
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my($a) = &antsFunUsage(1,"f","<angle>",@_);
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my($rot) = defined($last_in) ? angle_diff($a,$last_in) : nan;
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$last_in = $a;
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return $rot;
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}
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}
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{ my($last_in,$last_out);
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sub angle_ts(@)
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{
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my($a) = &antsFunUsage(1,"f","<angle>",@_);
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$last_out = $last_in = $a
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unless (defined($last_in));
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$last_out += angle_diff($a,$last_in);
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$last_in = $a;
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return $last_out;
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}
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}
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#----------------------------------------------------------------------
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# &ddeg(deg),&GMTdeg(deg) convert degree formats
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#----------------------------------------------------------------------
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sub ddeg(@)
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{
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my($deg) = &antsFunUsage(1,"","<degrees in GMT format>",@_);
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my($d,$m,$s) = split(':',$deg);
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return ($d>=0) ? $d+$m/60+$s/3600
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: $d-$m/60-$s/3600;
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}
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# NB: without roundoff code, results are as follows:
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# abc -Lvec 'GMTdeg(ddeg("10:11"))' -> 10:11:8.52651e-13
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# abc -Lvec 'GMTdeg(ddeg("10:10"))' -> 10:9:60
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sub GMTdeg(@)
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{
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my($deg) = &antsFunUsage(1,"f","<degrees>",@_);
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my($sgn); if ($deg < 0) { $sgn = '-'; $deg *= -1; }
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my($min) = 60*($deg-int($deg));
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my($sec) = 60*($min-int($min));
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$sec=0,$min++ if equal($sec,60);
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$sec=0 if equal($sec,0);
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return sprintf("$sgn%d:%d:%g",int($deg),int($min),$sec);
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}
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sub degmin(@)
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{
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my($deg) = &antsFunUsage(1,"f","<degrees>",@_);
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my($sgn); if ($deg < 0) { $sgn = '-'; $deg *= -1; }
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my($min) = 60*($deg-int($deg));
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$min=0 if equal($min,0);
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return sprintf("$sgn%d:%04.1f",int($deg),$min);
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}
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#----------------------------------------------------------------------
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# &dist(lat1,lon1,lat2,lon2) distance on globe (in m)
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# &dist12(...) ditto but with deg/min/sec separate
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# &dir(lat1,lon1,lat2,lon2) direction btw two points
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# &area(gmt_region) approximate area
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#----------------------------------------------------------------------
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sub dist(@)
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{
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my($lat1,$lon1,$lat2,$lon2) =
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&antsFunUsage(4,"","lat1 lon1 lat2 lon2",@_);
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$lat1 = &ddeg($lat1);
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$lat2 = &ddeg($lat2);
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$lon1 = &ddeg($lon1);
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$lon2 = &ddeg($lon2);
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return 0 if ($lat1 == $lat2 && $lon1 == $lon2); # avoid roundoff
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$radius = 6378139; # const
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$pi = 3.14159265358979;
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$d2r = $pi/180.0;
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$ct1 = cos($d2r*$lat1);
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$st1 = sin($d2r*$lat1);
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$cp1 = cos($d2r*$lon1);
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$sp1 = sin($d2r*$lon1);
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$ct2 = cos($d2r*$lat2);
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$st2 = sin($d2r*$lat2);
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$cp2 = cos($d2r*$lon2);
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$sp2 = sin($d2r*$lon2);
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$cosine = $ct1*$cp1*$ct2*$cp2 + $ct1*$sp1*$ct2*$sp2 + $st1*$st2;
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if ($cosine > 1.0) { $cosine = 1.0; }
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if ($cosine < -1.0) { $cosine = -1.0; }
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return $radius * acos($cosine);
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}
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sub dist12(@)
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{
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my($la1d,$la1m,$la1s,$lo1d,$lo1m,$lo1s,
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$la2d,$la2m,$la2s,$lo2d,$lo2m,$lo2s) =
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&antsFunUsage(12,"ffffffffffff","lat1 m s lon1 m s lat2 m s lon2 m s",@_);
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return dist(
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($la1d>=0)?$la1d+$la1m/60+$la1s/3600 : $la1d-$la1m/60-$la1s/3600,
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($lo1d>=0)?$lo1d+$lo1m/60+$lo1s/3600 : $lo1d-$lo1m/60-$lo1s/3600,
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($la2d>=0)?$la2d+$la2m/60+$la2s/3600 : $la2d-$la2m/60-$la2s/3600,
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($lo2d>=0)?$lo2d+$lo2m/60+$lo2s/3600 : $lo2d-$lo2m/60-$lo2s/3600
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);
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}
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sub dir(@)
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{
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my($lat1,$lon1,$lat2,$lon2) =
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&antsFunUsage(4,"","lat1 lon1 lat2 lon2",@_);
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my($dx) = dist(($lat1+$lat2)/2,$lon1,($lat1+$lat2)/2,$lon2);
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$dx *= -1 if ($lon2 < $lon1);
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my($dy) = dist($lat1,($lon1+$lon2)/2,$lat2,($lon1+$lon2)/2);
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$dy *= -1 if ($lat2 < $lat1);
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return ($dx == 0 && $dy == 0) ? nan : vel_dir($dx,$dy);
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}
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sub area(@)
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{
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my($R) = &antsFunUsage(1,"",'<"W/E/S/N">',@_);
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my($W,$E,$S,$N) = split('/',$R);
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return (&dist($S,$W,$S,$E) + &dist($N,$W,$N,$E)) / 2 *
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(&dist($S,$W,$N,$W) + &dist($S,$E,$N,$E)) / 2;
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}
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#----------------------------------------------------------------------
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# ($lat,$lon,$t) = &closestPointOnStraightLine(lat,lon,lat1,lonA,lat2,lon2)
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# - determine point on line segment from <lat1,lonA> to <lat2,lon2> that
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# is closest to target point <lat,lon>
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# - $t [0-1] output indicates where along the line segment the closest
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# point lies
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# - http://stackoverflow.com/questions/3120357/get-closest-point-to-a-line
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# - NOT DONE IN PLANAR GEOMETRY => USE ONLY IN SMALL DOMAINS
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#----------------------------------------------------------------------
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sub closestPointOnStraightLine(@)
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{
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my($latP,$lonP,$latA,$lonA,$latB,$lonB) =
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&antsFunUsage(6,'ffffff','pnt_lat, pnt_lon, lne_latA, lne_lonA, lne_latB, lne_lonB',@_);
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my($ABlon) = $lonB - $lonA; my($ABlat) = $latB - $latA;
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my($APlon) = $lonP - $lonA; my($APlat) = $latP - $latA;
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my($t) = ($APlon*$ABlon + $APlat*$ABlat) / ($ABlon**2 + $ABlat**2);
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return (undef,undef) unless ($t>=0 && $t<=1);
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return ($latA + $t*$ABlat,$lonA + $t*$ABlon, $t);
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}
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1;
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