new test case: setting an excision mask under Carpet

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@1457 f88db872-0e4f-0410-b76b-b9085cfa78c5
author: jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5> 2006-06-09 11:00:47 +0000
committer: jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5> 2006-06-09 11:00:47 +0000
commit: 49e55a961198c44b9930d3f04a46684d9daf1f8f (patch)
tree: 33a6176231fd8a46d99f762453ceac0ce8db3bbb /test
parent: fe4e962d3e30527e164e194af8f360c701134e04 (diff)
8 files changed, 7437 insertions, 0 deletions
diff --git a/test/Kerr-carpet-mask.par b/test/Kerr-carpet-mask.par
new file mode 100644
index 0000000..00646d2
--- /dev/null
+++ b/test/Kerr-carpet-mask.par
@@ -0,0 +1,153 @@
+# This parameter file sets up Kerr/Kerr-Schild initial data, then
+# finds the apparent horizon in it.  The local coordinate system origin
+# and the initial guess are both deliberately de-centered with respect
+# to the black hole, to make this a non-trivial test for the apparent
+# horizon finder.
+
+# flesh
+cactus::cctk_itlast = 0
+
+########################################
+
+#
+# ***** output setup (also see below for more output stuff) *****
+#
+ActiveThorns = "IOUtil"
+IOUtil::parfile_write = "no"
+IO::out_dir = $parfile
+
+########################################
+
+#
+# basic grid setup
+#
+
+ActiveThorns = "Carpet CarpetLib CarpetInterp CarpetReduce"
+Carpet::domain_from_coordbase    = true
+
+ActiveThorns = "SymBase Boundary"
+ActiveThorns = "CoordBase"
+CoordBase::domainsize = "minmax"	# specify continuum domain
+CoordBase::xmin = -3.0
+CoordBase::xmax = +3.0
+CoordBase::ymin = -3.0
+CoordBase::ymax = +3.0
+CoordBase::zmin =  0.0
+CoordBase::zmax = +3.0
+CoordBase::dx   = 0.2
+CoordBase::dy   = 0.2
+CoordBase::dz   = 0.2
+
+Grid::domain = "bitant"
+
+#
+# ghost zones
+#
+
+driver::ghost_size_x = 2
+driver::ghost_size_y = 2
+driver::ghost_size_z = 2
+
+# ghost zones are outside the nominal grid
+CoordBase::boundary_internal_x_lower = false
+CoordBase::boundary_internal_x_upper = false
+CoordBase::boundary_internal_y_lower = false
+CoordBase::boundary_internal_y_upper = false
+CoordBase::boundary_internal_z_lower = false
+CoordBase::boundary_internal_z_upper = false
+
+# ghost zone widths
+CoordBase::boundary_size_x_lower     = 2
+CoordBase::boundary_size_x_upper     = 2
+CoordBase::boundary_size_y_lower     = 2
+CoordBase::boundary_size_y_upper     = 2
+CoordBase::boundary_size_z_lower     = 2
+CoordBase::boundary_size_z_upper     = 2
+
+# ghost zones start 0.5 point outside nominal grid boundary
+CoordBase::boundary_shiftout_x_lower = 0
+CoordBase::boundary_shiftout_x_upper = 0
+CoordBase::boundary_shiftout_y_lower = 0
+CoordBase::boundary_shiftout_y_upper = 0
+CoordBase::boundary_shiftout_z_lower = 0
+CoordBase::boundary_shiftout_z_upper = 0
+
+# staggered grids everywhere
+CoordBase::boundary_staggered_x_lower = true
+CoordBase::boundary_staggered_x_upper = true
+CoordBase::boundary_staggered_y_lower = true
+CoordBase::boundary_staggered_y_upper = true
+CoordBase::boundary_staggered_z_lower = true
+CoordBase::boundary_staggered_z_upper = true
+
+# octant symmetry
+ActiveThorns = "ReflectionSymmetry"
+ReflectionSymmetry::avoid_origin_x = true
+ReflectionSymmetry::avoid_origin_y = true
+ReflectionSymmetry::avoid_origin_z = true
+ReflectionSymmetry::reflection_x = true
+ReflectionSymmetry::reflection_y = true
+ReflectionSymmetry::reflection_z = true
+
+ActiveThorns = "CartGrid3D"
+CartGrid3D::type = "CoordBase"
+
+########################################
+
+#
+# Kerr initial data
+#
+ActiveThorns = "ADMBase ADMCoupling StaticConformal CoordGauge SpaceMask Exact"
+ADMBase::initial_lapse = "exact"
+ADMBase::initial_shift = "exact"
+ADMBase::initial_data = "exact"
+ADMBase::lapse_evolution_method = "static"
+ADMBase::shift_evolution_method = "static"
+ADMBase::metric_type = "physical"
+
+Exact::exact_model = "Kerr/Kerr-Schild"
+Exact::Kerr_KerrSchild__mass = 1.0
+Exact::Kerr_KerrSchild__spin = 0.6
+
+SpaceMask::use_mask = true
+
+########################################
+
+ActiveThorns = "IOUtil"
+IOUtil::parfile_write = "no"
+
+########################################
+
+ActiveThorns = "SphericalSurface"
+ActiveThorns = "AEILocalInterp AHFinderDirect"
+
+AHFinderDirect::print_timing_stats = "true"
+AHFinderDirect::verbose_level = "algorithm highlights"
+
+AHFinderDirect::output_Theta_every = 1
+AHFinderDirect::h_base_file_name     = "Kerr.h"
+AHFinderDirect::Theta_base_file_name = "Kerr.Theta"
+
+AHFinderDirect::N_horizons = 1
+AHFinderDirect::origin_x[1] = 0.5
+AHFinderDirect::origin_y[1] = 0.7
+AHFinderDirect::origin_z[1] = 0.0
+
+AHFinderDirect::initial_guess_method[1] = "coordinate sphere"
+AHFinderDirect::initial_guess__coord_sphere__x_center[1] = -0.2
+AHFinderDirect::initial_guess__coord_sphere__y_center[1] =  0.3
+AHFinderDirect::initial_guess__coord_sphere__z_center[1] =  0.0
+AHFinderDirect::initial_guess__coord_sphere__radius[1] = 2.0
+
+AHFinderDirect::set_mask_for_all_horizons = true
+
+########################################
+
+ActiveThorns = "CarpetIOASCII"
+CarpetIOASCII::out3D_ghosts = true
+CarpetIOASCII::out3D_outer_ghosts = true
+
+IOASCII::out2d_every = 1
+IOASCII::out2d_vars = "SpaceMask::emask"
+
+########################################
diff --git a/test/Kerr-carpet-mask/BH_diagnostics.ah1.gp b/test/Kerr-carpet-mask/BH_diagnostics.ah1.gp
new file mode 100644
index 0000000..4a4f4bf
--- /dev/null
+++ b/test/Kerr-carpet-mask/BH_diagnostics.ah1.gp
@@ -0,0 +1,40 @@
+# apparent horizon 1/1
+#
+# column  1 = cctk_iteration
+# column  2 = cctk_time
+# column  3 = centroid_x
+# column  4 = centroid_y
+# column  5 = centroid_z
+# column  6 = min radius
+# column  7 = max radius
+# column  8 = mean radius
+# column  9 = quadrupole_xx
+# column 10 = quadrupole_xy
+# column 11 = quadrupole_xz
+# column 12 = quadrupole_yy
+# column 13 = quadrupole_yz
+# column 14 = quadrupole_zz
+# column 15 = min x
+# column 16 = max x
+# column 17 = min y
+# column 18 = max y
+# column 19 = min z
+# column 20 = max z
+# column 21 = xy-plane circumference
+# column 22 = xz-plane circumference
+# column 23 = yz-plane circumference
+# column 24 = ratio of xz/xy-plane circumferences
+# column 25 = ratio of yz/xy-plane circumferences
+# column 26 = area
+# column 27 = irreducible mass
+# column 28 = areal radius
+# column 29 = [not implemented yet] (outer) expansion Theta_(l)
+# column 30 = [not implemented yet] inner expansion Theta_(n)
+# column 31 = [not implemented yet] product of inner and outer expansions
+# column 32 = [not implemented yet] mean curvature
+# column 33 = [not implemented yet] d/d(coordinate radius) of area
+# column 34 = [not implemented yet] d/d(coordinate radius) of (outer) expansion Theta_(l)
+# column 35 = [not implemented yet] d/d(coordinate radius) of inner expansion Theta_(n)
+# column 36 = [not implemented yet] d/d(coordinate radius) of product of inner and outer expansions
+# column 37 = [not implemented yet] d/d(coordinate radius) of mean curvature
+0	0.000000	-0.000130	-0.001013	0.000000	1.037138385	2.759577678	1.997479253	1.200832969	7.966977104e-05	-9.709800141e-16	1.201178224	-6.457943300e-16	1.080466108	-1.897377061	1.897155124	-1.899186417	1.896297585	-1.799760903	1.799760903	12.57084448	10.83804138	11.23201094	0.8621569854	0.8934969288	45.26880825	0.9489964832	1.897992966	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000
diff --git a/test/Kerr-carpet-mask/Kerr.Theta.t0.ah1.gp b/test/Kerr-carpet-mask/Kerr.Theta.t0.ah1.gp
new file mode 100644
index 0000000..566553d
--- /dev/null
+++ b/test/Kerr-carpet-mask/Kerr.Theta.t0.ah1.gp
@@ -0,0 +1,2337 @@
+# N_patches = 6
+# origin = 0.5 0.7 0
+
+### +z patch
+# N_rho = 19
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = dsigma = dnu
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn
+-45	-45	3.48610029732299e-14
+-40	-45	-8.81517081552374e-14
+-35	-45	-5.88973314563646e-14
+-30	-45	-1.03195230138908e-13
+-25	-45	4.72955008490317e-14
+-20	-45	1.23290266884624e-13
+-15	-45	2.19269047363468e-14
+-10	-45	3.00315328161105e-14
+-5	-45	-7.07767178198537e-14
+0	-45	-3.66373598126302e-15
+5	-45	-1.35391697853038e-13
+10	-45	-6.66133814775094e-15
+15	-45	9.24260668000443e-14
+20	-45	8.82627304576999e-14
+25	-45	-8.95949980872501e-14
+30	-45	6.37268016134840e-14
+35	-45	-7.17204073907851e-14
+40	-45	-5.61772850460329e-14
+45	-45	7.01660951563099e-14
+
+-45	-40	-2.30371277609720e-14
+-40	-40	4.52415882534751e-14
+-35	-40	5.05706587716759e-14
+-30	-40	4.60742555219440e-15
+-25	-40	2.78665979180914e-14
+-20	-40	-1.05693231944315e-13
+-15	-40	-2.08721928629529e-14
+-10	-40	4.95159468982820e-14
+-5	-40	2.48689957516035e-14
+0	-40	-9.05941988094128e-14
+5	-40	5.85642645489770e-14
+10	-40	1.59872115546023e-14
+15	-40	5.31796828795450e-14
+20	-40	3.93574062229618e-14
+25	-40	-6.12843109593086e-14
+30	-40	-6.88338275267597e-15
+35	-40	-5.48450174164827e-14
+40	-40	-7.77156117237610e-15
+45	-40	2.88657986402541e-14
+
+-45	-35	8.79851747015437e-14
+-40	-35	1.62092561595273e-14
+-35	-35	8.88178419700125e-15
+-30	-35	9.60898027813073e-14
+-25	-35	-1.16573417585641e-14
+-20	-35	-9.14823772291129e-14
+-15	-35	4.91828799908944e-14
+-10	-35	4.77395900588817e-14
+-5	-35	1.15962794922098e-13
+0	-35	3.55271367880050e-15
+5	-35	-8.84847750626250e-14
+10	-35	7.69384556065233e-14
+15	-35	4.91828799908944e-14
+20	-35	-5.21804821573824e-14
+25	-35	5.67879077095768e-14
+30	-35	-1.51545442861334e-14
+35	-35	-1.03583808197527e-13
+40	-35	-1.03250741290140e-13
+45	-35	1.52988732793347e-13
+
+-45	-30	-1.03750341651221e-13
+-40	-30	3.69704267200177e-14
+-35	-30	-6.00630656322210e-14
+-30	-30	-1.45439216225896e-14
+-25	-30	1.31505917266850e-13
+-20	-30	-6.63358257213531e-14
+-15	-30	6.10622663543836e-15
+-10	-30	1.40998324127395e-14
+-5	-30	-1.14741549595010e-13
+0	-30	7.49955653134293e-14
+5	-30	-1.99840144432528e-15
+10	-30	-2.25930385511219e-14
+15	-30	3.41948691584548e-14
+20	-30	4.06341627012807e-14
+25	-30	1.13242748511766e-14
+30	-30	-4.10782519111308e-14
+35	-30	6.63913368725844e-14
+40	-30	-8.77076189453874e-15
+45	-30	8.71525074330748e-14
+
+-45	-25	-3.01425551185730e-14
+-40	-25	9.34807786734382e-14
+-35	-25	-8.89288642724750e-14
+-30	-25	1.90958360235527e-14
+-25	-25	-8.82627304576999e-15
+-20	-25	3.09752223870419e-14
+-15	-25	1.55431223447522e-15
+-10	-25	-5.02375918642883e-14
+-5	-25	-5.30131494258512e-14
+0	-25	2.54241072639161e-14
+5	-25	5.99520433297585e-14
+10	-25	-1.22124532708767e-14
+15	-25	1.10189635194047e-13
+20	-25	-6.43929354282591e-14
+25	-25	5.05151476204446e-14
+30	-25	-7.74935671188359e-14
+35	-25	-3.33066907387547e-14
+40	-25	1.05027098129540e-13
+45	-25	3.05311331771918e-14
+
+-45	-20	4.97379915032070e-14
+-40	-20	1.83186799063151e-15
+-35	-20	-5.39013278455514e-14
+-30	-20	7.13318293321663e-14
+-25	-20	-3.25295346215171e-14
+-20	-20	4.87387907810444e-14
+-15	-20	4.38538094726937e-14
+-10	-20	-7.36077865326479e-14
+-5	-20	-2.05946371067967e-14
+0	-20	-4.41868763800812e-14
+5	-20	1.82631687550838e-14
+10	-20	-7.16093850883226e-15
+15	-20	8.32667268468867e-14
+20	-20	7.18314296932476e-14
+25	-20	1.23567822640780e-13
+30	-20	-1.34781075189494e-13
+35	-20	4.88498130835069e-14
+40	-20	-7.30526750203353e-14
+45	-20	5.62883073484954e-14
+
+-45	-15	-1.23900889548167e-13
+-40	-15	1.23234755733392e-14
+-35	-15	-5.88418203051333e-15
+-30	-15	-3.70814490224802e-14
+-25	-15	-3.95239396766556e-14
+-20	-15	-5.00710584105946e-14
+-15	-15	-1.78745906964650e-14
+-10	-15	4.37427871702312e-14
+-5	-15	2.55351295663786e-15
+0	-15	4.68514116391816e-14
+5	-15	-7.23865412055602e-14
+10	-15	4.74620343027254e-14
+15	-15	5.45674616603264e-14
+20	-15	-7.82152120848423e-14
+25	-15	4.62407889756378e-14
+30	-15	7.93809462606987e-14
+35	-15	-8.70414851306123e-14
+40	-15	4.69624339416441e-14
+45	-15	-1.23234755733392e-13
+
+-45	-10	4.92383911421257e-14
+-40	-10	-3.81916720471054e-14
+-35	-10	-1.80411241501588e-14
+-30	-10	-2.75890421619351e-14
+-25	-10	1.28785870856518e-14
+-20	-10	4.18554080283684e-14
+-15	-10	6.77791156533658e-14
+-10	-10	-2.16493489801906e-15
+-5	-10	-5.68989300120393e-14
+0	-10	1.40998324127395e-14
+5	-10	5.09037256790634e-14
+10	-10	-5.68989300120393e-14
+15	-10	5.39568389967826e-14
+20	-10	-8.32667268468867e-14
+25	-10	-8.21565038222616e-15
+30	-10	-1.37667655053519e-14
+35	-10	2.93098878501041e-14
+40	-10	-2.53130849614536e-14
+45	-10	-6.53921361504217e-14
+
+-45	-5	-3.05866443284231e-14
+-40	-5	-4.14668299697496e-14
+-35	-5	-8.97060203897126e-14
+-30	-5	6.90558721316847e-14
+-25	-5	-1.85407245112401e-14
+-20	-5	2.25375273998907e-14
+-15	-5	4.44644321362375e-14
+-10	-5	1.85407245112401e-14
+-5	-5	-5.99520433297585e-14
+0	-5	3.48054918219987e-14
+5	-5	-5.80091530366644e-14
+10	-5	5.59552404411079e-14
+15	-5	-3.29736238313671e-14
+20	-5	7.10542735760100e-14
+25	-5	-9.16489106828067e-14
+30	-5	-1.29896093881143e-14
+35	-5	-1.22013510406305e-13
+40	-5	4.79616346638068e-14
+45	-5	-2.11164419283705e-13
+
+-45	0	-2.27595720048157e-14
+-40	0	3.16968673530482e-14
+-35	0	4.68514116391816e-14
+-30	0	2.43138842392909e-14
+-25	0	-8.88178419700125e-15
+-20	0	1.91513471747840e-14
+-15	0	-4.99600361081320e-14
+-10	0	7.38298311375729e-15
+-5	0	-7.27196081129478e-15
+0	0	2.94209101525666e-15
+5	0	1.11022302462516e-16
+10	0	7.03881397612349e-14
+15	0	-1.43218770176645e-14
+20	0	3.49720252756924e-15
+25	0	7.73825448163734e-14
+30	0	1.88737914186277e-14
+35	0	1.05471187339390e-14
+40	0	1.01030295240889e-14
+45	0	-6.43929354282591e-15
+
+-45	5	7.90478793533111e-14
+-40	5	-6.70019595361282e-14
+-35	5	-3.09197112358106e-14
+-30	5	-6.16173778666962e-15
+-25	5	-2.86992651865603e-14
+-20	5	7.88258347483861e-14
+-15	5	3.96349619791181e-14
+-10	5	1.14019904629004e-13
+-5	5	-1.97619698383278e-14
+0	5	-2.80331313717852e-14
+5	5	1.26010313294955e-14
+10	5	-1.14908083048704e-14
+15	5	2.99760216648792e-15
+20	5	-6.16728890179274e-14
+25	5	-7.04991620636974e-14
+30	5	6.12843109593086e-14
+35	5	-5.09592368302947e-14
+40	5	6.98330282489223e-14
+45	5	-2.10942374678780e-14
+
+-45	10	-1.93733917797090e-14
+-40	10	5.48450174164827e-14
+-35	10	-1.27675647831893e-14
+-30	10	1.72528658026749e-13
+-25	10	-4.44089209850063e-15
+-20	10	-1.33226762955019e-15
+-15	10	2.25375273998907e-14
+-10	10	2.74225087082414e-14
+-5	10	-9.06497099606440e-14
+0	10	-1.95399252334028e-14
+5	10	-3.44724249146111e-14
+10	10	3.92463839204993e-14
+15	10	-1.21791465801380e-13
+20	10	-3.68594044175552e-14
+25	10	8.78186412478499e-14
+30	10	-1.35114142096882e-13
+35	10	-5.79536418854332e-14
+40	10	-1.05138120432002e-13
+45	10	4.21884749357559e-14
+
+-45	15	-5.79536418854332e-14
+-40	15	-1.50990331349021e-13
+-35	15	7.21644966006352e-14
+-30	15	-3.33066907387547e-15
+-25	15	-6.93334278878410e-14
+-20	15	5.33462163332388e-14
+-15	15	8.31557045444242e-14
+-10	15	-2.63122856836162e-14
+-5	15	4.19109191795997e-14
+0	15	8.84292639113937e-14
+5	15	-1.37112543541207e-14
+10	15	2.17048601314218e-14
+15	15	1.01363362148277e-13
+20	15	9.86988268891764e-14
+25	15	-7.39408534400354e-14
+30	15	2.55351295663786e-15
+35	15	1.65423230669148e-14
+40	15	1.69420033557799e-13
+45	15	-9.12603326241879e-14
+
+-45	20	-5.15143483426073e-14
+-40	20	4.41868763800812e-14
+-35	20	-1.21236354289067e-13
+-30	20	6.85007606193722e-14
+-25	20	-1.07580611086178e-13
+-20	20	-1.49880108324396e-14
+-15	20	1.13520304267922e-13
+-10	20	-4.90718576884319e-14
+-5	20	6.32272012524027e-14
+0	20	-7.26640969617165e-14
+5	20	-8.77076189453874e-14
+10	20	7.71605002114484e-14
+15	20	1.10134124042816e-13
+20	20	-1.44328993201270e-14
+25	20	-5.11812814352197e-14
+30	20	6.73905375947470e-14
+35	20	-1.81410442223751e-13
+40	20	6.36157793110215e-14
+45	20	-1.67532654415936e-13
+
+-45	25	1.03028696685215e-13
+-40	25	-7.89368570508486e-14
+-35	25	2.86437540353290e-14
+-30	25	-1.11466391672366e-13
+-25	25	-1.00142116821189e-13
+-20	25	1.11022302462516e-15
+-15	25	-9.70334923522387e-14
+-10	25	-2.09832151654155e-14
+-5	25	2.68673971959288e-14
+0	25	-1.46549439250521e-14
+5	25	1.06581410364015e-14
+10	25	8.41549052665869e-14
+15	25	1.14352971536391e-13
+20	25	-1.62980740014973e-13
+25	25	2.12385664610792e-13
+30	25	-8.41549052665869e-14
+35	25	6.59472476627343e-14
+40	25	1.33892896769794e-13
+45	25	-8.01581023779363e-14
+
+-45	30	-5.15143483426073e-14
+-40	30	1.01585406753202e-13
+-35	30	-6.56141807553468e-14
+-30	30	2.88657986402541e-15
+-25	30	-1.44328993201270e-14
+-20	30	-6.05071548420710e-14
+-15	30	1.08246744900953e-13
+-10	30	-5.14033260401447e-14
+-5	30	6.13953332617712e-14
+0	30	-1.49880108324396e-13
+5	30	1.25899290992493e-13
+10	30	-1.44884104713583e-13
+15	30	-1.58206781009085e-13
+20	30	-4.07451850037432e-14
+25	30	-1.48547840694846e-13
+30	30	1.08357767203415e-13
+35	30	-1.34781075189494e-13
+40	30	5.24025267623074e-14
+45	30	6.11732886568461e-14
+
+-45	35	-9.47020240005259e-14
+-40	35	4.99600361081320e-15
+-35	35	6.88338275267597e-15
+-30	35	-3.54161144855425e-14
+-25	35	-2.23154827949656e-14
+-20	35	-3.19744231092045e-14
+-15	35	4.27435864480685e-14
+-10	35	-3.99680288865056e-14
+-5	35	7.72715225139109e-14
+0	35	3.29736238313671e-14
+5	35	-5.54001289287953e-14
+10	35	2.08055794814754e-13
+15	35	6.22835116814713e-14
+20	35	-1.52100554373646e-14
+25	35	1.34892097491957e-13
+30	35	-8.89288642724750e-14
+35	35	-4.27435864480685e-14
+40	35	9.88098491916389e-14
+45	35	-1.55875312657372e-13
+
+-45	40	1.33226762955019e-14
+-40	40	4.55191440096314e-15
+-35	40	6.21724893790088e-14
+-30	40	4.55191440096314e-14
+-25	40	-2.77555756156289e-15
+-20	40	1.89626092605977e-13
+-15	40	5.67323965583455e-14
+-10	40	-1.37445610448594e-13
+-5	40	6.05071548420710e-14
+0	40	-2.77555756156289e-14
+5	40	1.43218770176645e-13
+10	40	-8.99280649946377e-15
+15	40	-6.75015598972095e-14
+20	40	-2.27817764653082e-13
+25	40	-9.28146448586631e-14
+30	40	1.93178806284777e-14
+35	40	2.58792987040124e-13
+40	40	2.68673971959288e-14
+45	40	-9.52571355128384e-14
+
+-45	45	-1.05138120432002e-13
+-40	45	-3.40838468559923e-14
+-35	45	1.52766688188422e-13
+-30	45	2.35367281220533e-14
+-25	45	2.66453525910038e-14
+-20	45	-7.19424519957101e-14
+-15	45	-1.65423230669148e-14
+-10	45	-4.50750547997814e-14
+-5	45	-6.75015598972095e-14
+0	45	1.09912079437890e-14
+5	45	-5.55111512312578e-14
+10	45	9.17044218340379e-14
+15	45	9.58122470251510e-14
+20	45	5.99520433297585e-15
+25	45	3.27515792264421e-14
+30	45	-4.32986979603811e-15
+35	45	1.82076576038526e-14
+40	45	-7.08322289710850e-14
+45	45	-1.59872115546023e-14
+
+
+### +x patch
+# N_rho = 19
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn
+45	-45	1.31006316905768e-14
+45	-40	-9.11493103217254e-14
+45	-35	-3.16413562018170e-14
+45	-30	5.22915044598449e-14
+45	-25	3.47499806707674e-14
+45	-20	3.75255382323303e-14
+45	-15	-2.93098878501041e-14
+45	-10	7.54951656745106e-15
+45	-5	-1.07580611086178e-13
+45	0	-2.53130849614536e-14
+45	5	-4.66293670342566e-14
+45	10	7.18314296932476e-14
+45	15	-1.21347376591530e-13
+45	20	1.33004718350094e-13
+45	25	7.50510764646606e-14
+45	30	2.43138842392909e-14
+45	35	-6.75015598972095e-14
+45	40	2.82107670557252e-13
+45	45	-2.15827355987130e-13
+
+50	-45	1.77635683940025e-15
+50	-40	5.55111512312578e-14
+50	-35	-1.22124532708767e-15
+50	-30	-2.58681964737661e-14
+50	-25	4.46309655899313e-14
+50	-20	-1.27675647831893e-14
+50	-15	2.78665979180914e-14
+50	-10	-2.81996648254790e-14
+50	-5	-4.44089209850063e-16
+50	0	7.16093850883226e-14
+50	5	2.63122856836162e-14
+50	10	1.99840144432528e-14
+50	15	-6.01740879346835e-14
+50	20	-1.40332190312620e-13
+50	25	-5.49560397189452e-14
+50	30	3.90798504668055e-14
+50	35	-1.31117339208231e-13
+50	40	2.24265050974282e-14
+50	45	-7.14983627858601e-14
+
+55	-45	-2.08721928629529e-14
+55	-40	-6.83897383169096e-14
+55	-35	-5.21804821573824e-14
+55	-30	-4.58522109170190e-14
+55	-25	3.19744231092045e-14
+55	-20	-5.24025267623074e-14
+55	-15	-1.56763491077072e-13
+55	-10	4.27435864480685e-14
+55	-5	3.74145159298678e-14
+55	0	9.81437153768638e-14
+55	5	-1.77635683940025e-15
+55	10	3.78586051397178e-14
+55	15	-6.37268016134840e-14
+55	20	2.63122856836162e-14
+55	25	-9.23705556488130e-14
+55	30	7.82707232360735e-14
+55	35	-3.11972669919669e-14
+55	40	1.88626891883814e-13
+55	45	8.84847750626250e-14
+
+60	-45	8.84847750626250e-14
+60	-40	-2.28705943072782e-14
+60	-35	-6.71684929898220e-14
+60	-30	2.89768209427166e-14
+60	-25	-8.68194405256872e-14
+60	-20	-1.12132525487141e-14
+60	-15	1.42108547152020e-14
+60	-10	-2.33146835171283e-15
+60	-5	9.10382880192628e-15
+60	0	5.16253706450698e-14
+60	5	-4.44089209850063e-16
+60	10	-1.46549439250521e-14
+60	15	-2.60125254669674e-13
+60	20	7.20534742981727e-14
+60	25	-7.01660951563099e-14
+60	30	-1.71640479607049e-13
+60	35	-4.67403893367191e-14
+60	40	-8.04911692853238e-14
+60	45	-2.03614902716254e-13
+
+65	-45	-1.04360964314765e-14
+65	-40	-2.04281036531029e-14
+65	-35	8.71525074330748e-14
+65	-30	3.10862446895044e-14
+65	-25	-9.63673585374636e-14
+65	-20	-4.44089209850063e-16
+65	-15	-5.10702591327572e-14
+65	-10	-2.35367281220533e-14
+65	-5	-1.21458398893992e-13
+65	0	-1.19459997449667e-13
+65	5	1.08468789505878e-13
+65	10	-4.32986979603811e-15
+65	15	1.38000721960907e-13
+65	20	-2.51909604287448e-13
+65	25	6.99440505513849e-15
+65	30	-1.55431223447522e-15
+65	35	2.23598917159507e-13
+65	40	-2.10831352376317e-13
+65	45	2.72670774847938e-13
+
+70	-45	-8.54871728961371e-15
+70	-40	-1.02140518265514e-13
+70	-35	6.88338275267597e-15
+70	-30	-6.10622663543836e-14
+70	-25	2.72004641033163e-14
+70	-20	-1.63202784619898e-14
+70	-15	-1.41664457942170e-13
+70	-10	6.70574706873595e-14
+70	-5	1.43218770176645e-14
+70	0	-6.13953332617712e-14
+70	5	3.69704267200177e-14
+70	10	-3.55271367880050e-15
+70	15	1.06026298851702e-13
+70	20	4.09672296086683e-14
+70	25	-1.35336186701807e-13
+70	30	1.40332190312620e-13
+70	35	1.66755498298699e-13
+70	40	4.65183447317941e-14
+70	45	-1.13353770814228e-13
+
+75	-45	-3.75255382323303e-14
+75	-40	-2.62012633811537e-14
+75	-35	1.09912079437890e-14
+75	-30	1.45994327738208e-13
+75	-25	-2.34257058195908e-14
+75	-20	3.33066907387547e-15
+75	-15	1.01585406753202e-13
+75	-10	-5.35127497869325e-14
+75	-5	-1.87627691161651e-14
+75	0	8.54871728961371e-14
+75	5	-1.42552636361870e-13
+75	10	1.40443212615082e-13
+75	15	-4.05231403988182e-14
+75	20	1.08801856413265e-14
+75	25	-1.48103751484996e-13
+75	30	-4.27435864480685e-14
+75	35	-2.78554956878452e-13
+75	40	3.66706665033689e-13
+75	45	-9.76996261670138e-15
+
+80	-45	-6.23945339839338e-14
+80	-40	-5.55111512312578e-15
+80	-35	-6.21724893790088e-15
+80	-30	-1.41220368732320e-13
+80	-25	1.83297821365613e-13
+80	-20	-2.33146835171283e-14
+80	-15	3.44169137633799e-15
+80	-10	-1.21347376591530e-13
+80	-5	2.73114864057789e-14
+80	0	-1.11022302462516e-14
+80	5	1.30562227695918e-13
+80	10	-2.84217094304040e-14
+80	15	-4.87387907810444e-14
+80	20	-1.07580611086178e-13
+80	25	4.95159468982820e-14
+80	30	1.09690034832965e-13
+80	35	5.56221735337203e-14
+80	40	-5.44009282066327e-15
+80	45	-2.83884027396653e-13
+
+85	-45	-1.46549439250521e-14
+85	-40	-2.37587727269783e-14
+85	-35	6.43929354282591e-15
+85	-30	-3.17523785042795e-14
+85	-25	-4.66293670342566e-15
+85	-20	-4.26325641456060e-14
+85	-15	4.49640324973188e-14
+85	-10	-4.32986979603811e-15
+85	-5	-1.65201186064223e-13
+85	0	1.65423230669148e-14
+85	5	-8.39328606616618e-14
+85	10	1.13131726209303e-13
+85	15	1.06581410364015e-14
+85	20	2.66453525910038e-14
+85	25	2.86992651865603e-13
+85	30	-2.14273043752655e-14
+85	35	-9.02611319020252e-14
+85	40	7.77156117237610e-16
+85	45	1.58095758706622e-13
+
+90	-45	1.15463194561016e-14
+90	-40	7.17204073907851e-14
+90	-35	2.95319324550292e-14
+90	-30	3.95239396766556e-14
+90	-25	-5.29576382746200e-14
+90	-20	-1.14352971536391e-14
+90	-15	-4.16333634234434e-14
+90	-10	-1.85407245112401e-14
+90	-5	3.19744231092045e-14
+90	0	5.04041253179821e-14
+90	5	2.04281036531029e-14
+90	10	-2.70894418008538e-14
+90	15	1.11133324764978e-13
+90	20	-7.21644966006352e-15
+90	25	7.06101843661600e-14
+90	30	-1.87738713464114e-13
+90	35	-1.16573417585641e-14
+90	40	2.12052597703405e-14
+90	45	-4.10449452203920e-13
+
+95	-45	-1.12576614696991e-13
+95	-40	-2.58681964737661e-14
+95	-35	-1.64313007644523e-14
+95	-30	4.98490138056695e-14
+95	-25	5.55111512312578e-16
+95	-20	3.64153152077051e-14
+95	-15	6.69464483848969e-14
+95	-10	-2.59792187762287e-14
+95	-5	-7.16093850883226e-14
+95	0	-8.18234369148740e-14
+95	5	1.46549439250521e-14
+95	10	-6.29496454962464e-14
+95	15	4.62963001268690e-14
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+95	25	1.58428825614010e-13
+95	30	7.54951656745106e-15
+95	35	-1.62869717712510e-13
+95	40	2.75779399316889e-13
+95	45	3.80917519748891e-13
+
+100	-45	3.86357612569554e-14
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+100	-35	7.77156117237610e-16
+100	-30	-7.79376563286860e-14
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+100	-20	6.92779167366098e-14
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+100	-10	6.20614670765463e-14
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+100	40	9.04831765069503e-14
+100	45	-1.60871316268185e-13
+
+105	-45	4.47419878923938e-14
+105	-40	-9.99200722162641e-15
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+105	40	-2.49911202843123e-13
+105	45	7.12763181809350e-14
+
+110	-45	3.58602036953926e-14
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+110	-35	3.10862446895044e-15
+110	-30	4.66293670342566e-14
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+110	40	-5.52891066263328e-14
+110	45	-2.20934381900406e-14
+
+115	-45	3.66373598126302e-14
+115	-40	-5.06261699229071e-14
+115	-35	2.22044604925031e-14
+115	-30	-3.31956684362922e-14
+115	-25	-4.88498130835069e-14
+115	-20	1.05471187339390e-14
+115	-15	5.99520433297585e-15
+115	-10	7.33857419277228e-14
+115	-5	2.22044604925031e-14
+115	0	2.37587727269783e-14
+115	5	7.77156117237610e-14
+115	10	1.42996725571720e-13
+115	15	-2.31703545239270e-13
+115	20	1.32116539930394e-14
+115	25	-1.84741111297626e-13
+115	30	-2.95319324550292e-14
+115	35	-2.32036612146658e-14
+115	40	1.93511873192165e-13
+115	45	2.44249065417534e-15
+
+120	-45	3.21964677141295e-15
+120	-40	4.71844785465692e-14
+120	-35	-5.81756864903582e-14
+120	-30	7.42739203474230e-14
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+120	0	-2.83106871279415e-14
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+120	40	7.16093850883226e-14
+120	45	-1.65756297576536e-13
+
+125	-45	-9.69224700497762e-14
+125	-40	9.21485110438880e-15
+125	-35	-5.92859095149834e-14
+125	-30	7.88258347483861e-14
+125	-25	1.66533453693773e-14
+125	-20	-2.77555756156289e-15
+125	-15	1.09245945623115e-13
+125	-10	3.28626015289046e-14
+125	-5	-6.26165785888588e-14
+125	0	1.50990331349021e-14
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+125	10	-4.04121180963557e-14
+125	15	1.01696429055664e-13
+125	20	8.73745520379998e-14
+125	25	-8.40438829641244e-14
+125	30	-6.99440505513849e-15
+125	35	-2.14273043752655e-14
+125	40	-1.30229160788531e-13
+125	45	-2.83217893581877e-13
+
+130	-45	3.43058914609173e-14
+130	-40	1.59205981731247e-13
+130	-35	1.99840144432528e-14
+130	-30	-3.64153152077051e-14
+130	-25	-4.28546087505310e-14
+130	-20	-4.67403893367191e-14
+130	-15	-9.99200722162641e-16
+130	-10	-7.30526750203353e-14
+130	-5	8.64863736182997e-14
+130	0	-9.12603326241879e-14
+130	5	1.10578213252666e-13
+130	10	1.08801856413265e-14
+130	15	-5.55111512312578e-15
+130	20	5.24025267623074e-14
+130	25	-6.03961325396085e-14
+130	30	9.79216707719388e-14
+130	35	1.49880108324396e-13
+130	40	-9.49240686054509e-14
+130	45	-3.69371200292790e-13
+
+135	-45	1.52655665885959e-13
+135	-40	9.71445146547012e-14
+135	-35	-4.47419878923938e-14
+135	-30	1.03472785895065e-13
+135	-25	3.19744231092045e-14
+135	-20	-1.09690034832965e-13
+135	-15	1.88737914186277e-15
+135	-10	1.64313007644523e-14
+135	-5	5.70654634657330e-14
+135	0	-4.47419878923938e-14
+135	5	-1.63202784619898e-14
+135	10	-6.99440505513849e-15
+135	15	1.63424829224823e-13
+135	20	-3.86357612569554e-14
+135	25	2.64455124465712e-13
+135	30	2.36477504245158e-14
+135	35	1.16129328375791e-13
+135	40	6.88338275267597e-14
+135	45	-4.50750547997814e-14
+
+
+### +y patch
+# N_rho = 19
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = 90 - dsigma = 90 - dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn
+45	45	6.76125821996720e-14
+40	45	1.95621296938953e-13
+35	45	2.54574139546548e-13
+30	45	1.98729921407903e-14
+25	45	2.39475106411646e-13
+20	45	2.10387263166467e-13
+15	45	1.32782673745169e-13
+10	45	1.04249942012302e-13
+5	45	-1.68975944347949e-13
+0	45	1.10134124042816e-13
+-5	45	-2.33701946683595e-13
+-10	45	-1.31006316905768e-14
+-15	45	3.41948691584548e-14
+-20	45	5.42899059041702e-14
+-25	45	1.01363362148277e-13
+-30	45	1.07913677993565e-13
+-35	45	-5.07371922253697e-14
+-40	45	2.23154827949656e-14
+-45	45	-3.99680288865056e-14
+
+45	50	-2.25930385511219e-13
+40	50	-9.38138455808257e-14
+35	50	3.95239396766556e-14
+30	50	2.36699548850083e-13
+25	50	1.22568621918617e-13
+20	50	-6.57252030578093e-14
+15	50	2.46913600676635e-13
+10	50	-1.03028696685215e-13
+5	50	-1.80966353013901e-14
+0	50	7.28306304154103e-14
+-5	50	1.12576614696991e-13
+-10	50	-1.22013510406305e-13
+-15	50	3.03090885722668e-14
+-20	50	-1.82298620643451e-13
+-25	50	5.88418203051333e-14
+-30	50	2.33146835171283e-14
+-35	50	-6.27276008913213e-14
+-40	50	7.26085858104852e-14
+-45	50	1.37445610448594e-13
+
+45	55	-2.40696351738734e-13
+40	55	1.35225164399344e-13
+35	55	7.13873404833976e-14
+30	55	-9.32587340685131e-14
+25	55	-2.18713935851156e-14
+20	55	-1.62092561595273e-14
+15	55	1.62314606200198e-13
+10	55	-9.58122470251510e-14
+5	55	6.35047570085590e-14
+0	55	3.35287353436797e-14
+-5	55	-2.44249065417534e-15
+-10	55	-3.49720252756924e-14
+-15	55	2.85327317328665e-14
+-20	55	-1.24678045665405e-13
+-25	55	-5.10702591327572e-15
+-30	55	2.08721928629529e-14
+-35	55	0.00000000000000
+-40	55	1.11022302462516e-16
+-45	55	1.11688436277291e-13
+
+45	60	-4.98490138056695e-14
+40	60	-9.76996261670138e-15
+35	60	3.15303338993544e-14
+30	60	5.25135490647699e-14
+25	60	1.38333788868295e-13
+20	60	1.86184401229639e-13
+15	60	-3.16413562018170e-14
+10	60	4.06341627012807e-14
+5	60	9.10382880192628e-15
+0	60	1.90958360235527e-14
+-5	60	-9.11493103217254e-14
+-10	60	-9.43689570931383e-14
+-15	60	4.25215418431435e-14
+-20	60	7.57172102794357e-14
+-25	60	3.35287353436797e-14
+-30	60	5.72875080706581e-14
+-35	60	-2.77555756156289e-14
+-40	60	8.32667268468867e-15
+-45	60	1.04694031222152e-13
+
+45	65	5.01820807130571e-14
+40	65	-5.60662627435704e-14
+35	65	1.85296222809939e-13
+30	65	-5.19584375524573e-14
+25	65	-1.07802655691103e-13
+20	65	-7.27196081129478e-14
+15	65	-2.80886425230165e-13
+10	65	-2.33146835171283e-15
+5	65	5.39568389967826e-14
+0	65	-1.89848137210902e-14
+-5	65	6.10622663543836e-15
+-10	65	1.40110145707695e-13
+-15	65	-4.79616346638068e-14
+-20	65	1.36557432028894e-14
+-25	65	7.89368570508486e-14
+-30	65	-6.33937347060964e-14
+-35	65	1.77635683940025e-15
+-40	65	-1.33226762955019e-15
+-45	65	-4.18554080283684e-14
+
+45	70	1.63868918434673e-13
+40	70	-9.80326930744013e-14
+35	70	4.96269692007445e-14
+30	70	7.12763181809350e-14
+25	70	-2.28705943072782e-14
+20	70	-1.11022302462516e-13
+15	70	-8.10462807976364e-15
+10	70	-4.08562073062058e-14
+5	70	-9.85878045867139e-14
+0	70	-5.71764857681956e-14
+-5	70	6.15063555642337e-14
+-10	70	1.97619698383278e-14
+-15	70	7.19424519957101e-14
+-20	70	-7.81597009336110e-14
+-25	70	5.28466159721575e-14
+-30	70	8.24895707296491e-14
+-35	70	-7.08322289710850e-14
+-40	70	8.64863736182997e-14
+-45	70	6.01740879346835e-14
+
+45	75	2.96429547574917e-14
+40	75	5.68434188608080e-14
+35	75	-1.70530256582424e-13
+30	75	-3.49720252756924e-14
+25	75	-2.48578935213573e-13
+20	75	-3.68594044175552e-14
+15	75	-6.39488462184090e-14
+10	75	-5.70654634657330e-14
+5	75	-5.97299987248334e-14
+0	75	-1.05915276549240e-13
+-5	75	9.09272657168003e-14
+-10	75	9.61453139325386e-14
+-15	75	-5.90638649100583e-14
+-20	75	-7.46069872548105e-14
+-25	75	8.26005930321116e-14
+-30	75	-4.03010957938932e-14
+-35	75	8.58202398035246e-14
+-40	75	1.21458398893992e-13
+-45	75	-5.01820807130571e-14
+
+45	80	-5.90638649100583e-14
+40	80	4.24105195406810e-14
+35	80	1.43218770176645e-14
+30	80	-2.00728322852228e-13
+25	80	6.98330282489223e-14
+20	80	-4.97379915032070e-14
+15	80	-1.25344179480180e-13
+10	80	1.14352971536391e-14
+5	80	1.48991929904696e-13
+0	80	1.94178007006940e-13
+-5	80	3.33066907387547e-15
+-10	80	1.82076576038526e-14
+-15	80	-1.32227562232856e-13
+-20	80	2.57571741713036e-14
+-25	80	-2.90878432451791e-14
+-30	80	7.30526750203353e-14
+-35	80	4.66293670342566e-15
+-40	80	1.72084568816899e-14
+-45	80	-1.00919272938427e-13
+
+45	85	-3.09974268475344e-13
+40	85	1.68309810533174e-13
+35	85	-1.10356168647741e-13
+30	85	-1.23678844943242e-13
+25	85	8.58202398035246e-14
+20	85	2.15161222172355e-13
+15	85	-8.88178419700125e-16
+10	85	-7.22755189030977e-14
+5	85	6.77236045021345e-15
+0	85	4.75175454539567e-14
+-5	85	6.89448498292222e-14
+-10	85	-1.04027897407377e-13
+-15	85	-3.09752223870419e-14
+-20	85	6.72795152922845e-14
+-25	85	2.88657986402541e-15
+-30	85	7.47180095572730e-14
+-35	85	-1.26565424807268e-13
+-40	85	2.07611705604904e-14
+-45	85	-7.92699239582362e-14
+
+45	90	1.54098955817972e-13
+40	90	-1.30673249998381e-13
+35	90	4.59632332194815e-14
+30	90	-1.91513471747840e-13
+25	90	1.03472785895065e-13
+20	90	-1.85851334322251e-13
+15	90	1.60760293965723e-13
+10	90	-1.85407245112401e-14
+5	90	7.21644966006352e-14
+0	90	1.49991130626859e-13
+-5	90	-1.69086966650411e-13
+-10	90	-4.68514116391816e-14
+-15	90	-2.68673971959288e-14
+-20	90	9.19264664389630e-14
+-25	90	-5.72875080706581e-14
+-30	90	-1.17683640610267e-14
+-35	90	1.12021503184678e-13
+-40	90	1.02362562870439e-13
+-45	90	1.56097357262297e-13
+
+45	95	-1.92179605562615e-13
+40	95	-2.65343302885412e-13
+35	95	-1.13020703906841e-13
+30	95	-1.19126930542279e-13
+25	95	-4.10782519111308e-14
+20	95	2.72781797150401e-13
+15	95	6.02851102371460e-14
+10	95	-8.54871728961371e-14
+5	95	-1.02695629777827e-13
+0	95	1.63535851527286e-13
+-5	95	4.34097202628436e-14
+-10	95	4.72955008490317e-14
+-15	95	8.28226376370367e-14
+-20	95	6.99440505513849e-14
+-25	95	-7.84927678409986e-14
+-30	95	6.86117829218347e-14
+-35	95	2.07611705604904e-14
+-40	95	-2.46469511466785e-14
+-45	95	-3.33066907387547e-15
+
+45	100	-1.82076576038526e-14
+40	100	1.57429624891847e-13
+35	100	-1.65423230669148e-13
+30	100	-3.43058914609173e-14
+25	100	1.52655665885959e-13
+20	100	-3.77475828372553e-14
+15	100	1.54654067330284e-13
+10	100	-2.17159623616681e-13
+5	100	-7.53841433720481e-14
+0	100	9.10382880192628e-14
+-5	100	1.17572618307804e-13
+-10	100	1.06692432666478e-13
+-15	100	9.76996261670138e-15
+-20	100	1.03916875104915e-13
+-25	100	1.51101353651484e-13
+-30	100	-3.24185123190546e-14
+-35	100	-7.54951656745106e-15
+-40	100	-1.02917674382752e-13
+-45	100	7.16093850883226e-14
+
+45	105	-1.11022302462516e-14
+40	105	-2.30926389122033e-14
+35	105	-3.17523785042795e-14
+30	105	-1.55431223447522e-13
+25	105	2.08610906327067e-13
+20	105	-2.43138842392909e-14
+15	105	1.69975145070111e-13
+10	105	8.39328606616618e-14
+5	105	4.25215418431435e-14
+0	105	-2.49800180540660e-14
+-5	105	6.20614670765463e-14
+-10	105	7.03881397612349e-14
+-15	105	3.89688281643430e-14
+-20	105	1.94400051611865e-13
+-25	105	-1.67643676718399e-13
+-30	105	-2.55351295663786e-14
+-35	105	8.33777491493493e-14
+-40	105	5.30686605770825e-14
+-45	105	-8.71525074330748e-14
+
+45	110	1.88737914186277e-15
+40	110	-2.33146835171283e-14
+35	110	2.01616501271928e-13
+30	110	1.02806652080289e-13
+25	110	-2.73669975570101e-13
+20	110	-9.90318937965640e-14
+15	110	-1.42663658664333e-13
+10	110	-2.30038210702332e-13
+5	110	-8.18234369148740e-14
+0	110	1.59539048638635e-13
+-5	110	-1.92068583260152e-14
+-10	110	-5.44009282066327e-15
+-15	110	4.38538094726937e-14
+-20	110	-4.38538094726937e-14
+-25	110	7.14983627858601e-14
+-30	110	8.43769498715119e-15
+-35	110	-4.77395900588817e-15
+-40	110	-5.17363929475323e-14
+-45	110	2.45359288442160e-14
+
+45	115	-2.47579734491410e-14
+40	115	1.62758695410048e-13
+35	115	3.96349619791181e-14
+30	115	-3.49720252756924e-14
+25	115	-5.29576382746200e-14
+20	115	6.69464483848969e-14
+15	115	1.51878509768721e-13
+10	115	-5.02931030155196e-14
+5	115	7.79376563286860e-14
+0	115	-9.83657599817889e-14
+-5	115	1.45661260830821e-13
+-10	115	-1.43440814781570e-13
+-15	115	1.06581410364015e-14
+-20	115	9.47020240005259e-14
+-25	115	7.04991620636974e-14
+-30	115	-5.54001289287953e-14
+-35	115	-3.48610029732299e-14
+-40	115	-8.43769498715119e-14
+-45	115	-1.60760293965723e-13
+
+45	120	-2.22044604925031e-15
+40	120	-4.07229805432507e-13
+35	120	4.13336032067946e-13
+30	120	4.41868763800812e-14
+25	120	-1.04360964314765e-14
+20	120	-1.88959958791202e-13
+15	120	-1.09245945623115e-13
+10	120	-5.49560397189452e-14
+5	120	-1.43662859386495e-13
+0	120	3.98570065840431e-14
+-5	120	4.46309655899313e-14
+-10	120	3.48610029732299e-14
+-15	120	1.15463194561016e-14
+-20	120	7.33857419277228e-14
+-25	120	-1.30118138486068e-13
+-30	120	-1.50990331349021e-14
+-35	120	-8.59312621059871e-14
+-40	120	1.57651669496772e-14
+-45	120	-3.66373598126302e-15
+
+45	125	-1.95954363846340e-13
+40	125	1.11022302462516e-15
+35	125	1.44328993201270e-15
+30	125	6.88338275267597e-14
+25	125	-2.29816166097407e-14
+20	125	1.94178007006940e-13
+15	125	1.18793863634892e-14
+10	125	-9.17044218340379e-14
+5	125	3.38618022510673e-14
+0	125	-1.85407245112401e-13
+-5	125	-7.18314296932476e-14
+-10	125	8.84847750626250e-14
+-15	125	3.17523785042795e-14
+-20	125	-7.34967642301854e-14
+-25	125	6.43929354282591e-14
+-30	125	6.06181771445335e-14
+-35	125	5.32907051820075e-14
+-40	125	4.03010957938932e-14
+-45	125	7.87148124459236e-14
+
+45	130	-4.32986979603811e-14
+40	130	-8.26005930321116e-14
+35	130	2.03281835808866e-13
+30	130	-1.22235555011230e-13
+25	130	7.42739203474230e-14
+20	130	2.44915199232310e-13
+15	130	2.44249065417534e-15
+10	130	4.35207425653061e-14
+5	130	2.08721928629529e-13
+0	130	-7.57172102794357e-14
+-5	130	-8.45989944764369e-14
+-10	130	-1.35447209004269e-14
+-15	130	4.98490138056695e-14
+-20	130	-8.13793477050240e-14
+-25	130	-8.85957973650875e-14
+-30	130	-5.71764857681956e-14
+-35	130	2.12052597703405e-14
+-40	130	7.27196081129478e-14
+-45	130	1.01585406753202e-13
+
+45	135	-1.51989532071184e-13
+40	135	4.10782519111308e-14
+35	135	2.40918396343659e-14
+30	135	1.32116539930394e-14
+25	135	3.33066907387547e-16
+20	135	3.24962279307783e-13
+15	135	-6.69464483848969e-14
+10	135	-7.73825448163734e-14
+5	135	7.57172102794357e-14
+0	135	-6.00630656322210e-14
+-5	135	5.32907051820075e-15
+-10	135	-7.56061879769732e-14
+-15	135	1.71085368094737e-13
+-20	135	4.07451850037432e-14
+-25	135	-1.15352172258554e-13
+-30	135	1.05138120432002e-13
+-35	135	2.02060590481778e-14
+-40	135	-5.96189764223709e-14
+-45	135	-1.47659662275146e-14
+
+
+### -x patch
+# N_rho = 19
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = drho = dnu
+# dpy = 180 - dsigma = 180 - dphi
+#
+# dpx	dpy	gridfn
+-135	45	-6.51700915454967e-14
+-135	40	-8.55981951985996e-14
+-135	35	-7.34967642301854e-14
+-135	30	2.10942374678780e-14
+-135	25	5.57331958361829e-14
+-135	20	1.18793863634892e-14
+-135	15	-1.00364161426114e-13
+-135	10	-1.02029495963052e-13
+-135	5	-2.46469511466785e-14
+-135	-2.84217e-14	1.01141317543352e-13
+-135	-5	1.48048240333765e-13
+-135	-10	-1.46382905796827e-13
+-135	-15	1.01196828694583e-13
+-135	-20	-6.16173778666962e-14
+-135	-25	-1.44328993201270e-15
+-135	-30	-3.66373598126302e-15
+-135	-35	-4.93494134445882e-14
+-135	-40	-9.22595333463505e-14
+-135	-45	4.27435864480685e-15
+
+-130	45	-6.97220059464598e-14
+-130	40	-4.68514116391816e-14
+-130	35	5.36237720893951e-14
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+-130	15	-3.60822483003176e-14
+-130	10	-3.91908727692680e-14
+-130	5	-9.98090499138016e-14
+-130	-2.84217e-14	6.63913368725844e-14
+-130	-5	-1.16240350678254e-13
+-130	-10	1.19348975147204e-14
+-130	-15	-1.10633724403897e-13
+-130	-20	-2.04281036531029e-14
+-130	-25	-4.41868763800812e-14
+-130	-30	-7.03326286100037e-14
+-130	-35	2.52020626589911e-14
+-130	-40	-9.47575351517571e-14
+-130	-45	2.27595720048157e-14
+
+-125	45	7.10542735760100e-14
+-125	40	5.15143483426073e-14
+-125	35	6.13953332617712e-14
+-125	30	1.73194791841524e-14
+-125	25	7.10542735760100e-14
+-125	20	9.31477117660506e-14
+-125	15	1.77635683940025e-15
+-125	10	7.43849426498855e-15
+-125	5	1.28674848554056e-13
+-125	-2.84217e-14	-1.51767487466259e-13
+-125	-5	5.11812814352197e-14
+-125	-10	2.47579734491410e-14
+-125	-15	-6.17284001691587e-14
+-125	-20	3.99680288865056e-14
+-125	-25	-2.95319324550292e-14
+-125	-30	-4.79616346638068e-14
+-125	-35	-5.83977310952832e-14
+-125	-40	9.07052211118753e-14
+-125	-45	5.77315972805081e-15
+
+-120	45	-2.17603712826531e-14
+-120	40	-1.15130127653629e-13
+-120	35	1.72639680329212e-13
+-120	30	-4.20774526332934e-14
+-120	25	4.55191440096314e-14
+-120	20	-1.84297022087776e-14
+-120	15	1.48769885299771e-14
+-120	10	-2.12052597703405e-14
+-120	5	1.36557432028894e-14
+-120	-2.84217e-14	8.84847750626250e-14
+-120	-5	6.25055562863963e-14
+-120	-10	-1.08357767203415e-13
+-120	-15	1.13131726209303e-13
+-120	-20	1.78745906964650e-14
+-120	-25	2.09832151654155e-14
+-120	-30	3.76365605347928e-14
+-120	-35	-7.22755189030977e-14
+-120	-40	9.10382880192628e-15
+-120	-45	3.79696274421804e-14
+
+-115	45	-5.28466159721575e-14
+-115	40	-6.03961325396085e-14
+-115	35	7.54951656745106e-15
+-115	30	-6.59472476627343e-14
+-115	25	-1.33226762955019e-15
+-115	20	-6.78346268045971e-14
+-115	15	3.39728245535298e-14
+-115	10	-7.77156117237610e-15
+-115	5	3.75255382323303e-14
+-115	-2.84217e-14	-2.48689957516035e-14
+-115	-5	-7.92699239582362e-14
+-115	-10	1.86517468137026e-14
+-115	-15	-5.92859095149834e-14
+-115	-20	1.37667655053519e-14
+-115	-25	1.03361763592602e-13
+-115	-30	-1.63202784619898e-14
+-115	-35	-5.05151476204446e-14
+-115	-40	-4.45199432874688e-14
+-115	-45	-6.67244037799719e-14
+
+-110	45	3.49720252756924e-14
+-110	40	-1.44328993201270e-14
+-110	35	-1.33559829862406e-13
+-110	30	6.63913368725844e-14
+-110	25	6.07291994469961e-14
+-110	20	1.47659662275146e-14
+-110	15	5.55111512312578e-16
+-110	10	3.83026943495679e-14
+-110	5	3.59712259978551e-14
+-110	-2.84217e-14	4.06341627012807e-14
+-110	-5	5.31796828795450e-14
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+-110	-20	2.24265050974282e-14
+-110	-25	-8.90398865749376e-14
+-110	-30	6.99440505513849e-14
+-110	-35	2.44249065417534e-15
+-110	-40	-7.74935671188359e-14
+-110	-45	-2.12052597703405e-14
+
+-105	45	1.45439216225896e-14
+-105	40	-8.43769498715119e-15
+-105	35	1.36557432028894e-14
+-105	30	1.57651669496772e-14
+-105	25	-8.41549052665869e-14
+-105	20	4.70734562441066e-14
+-105	15	3.86357612569554e-14
+-105	10	8.00470800754738e-14
+-105	5	3.21964677141295e-14
+-105	-2.84217e-14	-3.28626015289046e-14
+-105	-5	2.26485497023532e-14
+-105	-10	-6.96109836439973e-14
+-105	-15	-9.32587340685131e-15
+-105	-20	-9.60342916300760e-14
+-105	-25	8.43769498715119e-15
+-105	-30	7.64943663966733e-14
+-105	-35	4.32986979603811e-14
+-105	-40	-3.05311331771918e-14
+-105	-45	-8.99280649946377e-14
+
+-100	45	4.44089209850063e-15
+-100	40	-6.77236045021345e-15
+-100	35	1.07247544178790e-13
+-100	30	-1.02140518265514e-14
+-100	25	3.99680288865056e-14
+-100	20	4.86277684785819e-14
+-100	15	1.45439216225896e-14
+-100	10	4.81836792687318e-14
+-100	5	-4.55191440096314e-15
+-100	-2.84217e-14	3.21964677141295e-14
+-100	-5	-2.34257058195908e-14
+-100	-10	-1.17572618307804e-13
+-100	-15	3.46389583683049e-14
+-100	-20	4.01900734914307e-14
+-100	-25	4.22994972382185e-14
+-100	-30	-2.53130849614536e-14
+-100	-35	4.56301663120939e-14
+-100	-40	-4.46309655899313e-14
+-100	-45	6.43929354282591e-15
+
+-95	45	4.97379915032070e-14
+-95	40	5.49560397189452e-14
+-95	35	1.41775480244632e-13
+-95	30	-7.48290318597356e-14
+-95	25	5.32907051820075e-15
+-95	20	3.50830475781549e-14
+-95	15	4.22994972382185e-14
+-95	10	-8.30446822419617e-14
+-95	5	-2.65343302885412e-14
+-95	-2.84217e-14	6.10622663543836e-15
+-95	-5	-3.38618022510673e-14
+-95	-10	-9.76996261670138e-15
+-95	-15	-8.20454815197991e-14
+-95	-20	1.64313007644523e-14
+-95	-25	-5.52891066263328e-14
+-95	-30	7.32747196252603e-15
+-95	-35	-6.55031584528842e-15
+-95	-40	2.58681964737661e-14
+-95	-45	-1.24900090270330e-13
+
+-90	45	-8.09352584951739e-14
+-90	40	7.78266340262235e-14
+-90	35	-3.84137166520304e-14
+-90	30	1.21347376591530e-13
+-90	25	8.54871728961371e-15
+-90	20	-4.21884749357559e-14
+-90	15	-2.73114864057789e-14
+-90	10	-3.99680288865056e-15
+-90	5	4.21884749357559e-14
+-90	-2.84217e-14	1.15463194561016e-14
+-90	-5	3.57491813929300e-14
+-90	-10	-5.50670620214078e-14
+-90	-15	5.19584375524573e-14
+-90	-20	2.66453525910038e-14
+-90	-25	3.33066907387547e-15
+-90	-30	1.07691633388640e-14
+-90	-35	8.49320613838245e-14
+-90	-40	-6.62803145701218e-14
+-90	-45	-1.36557432028894e-14
+
+-85	45	1.99840144432528e-14
+-85	40	2.78665979180914e-14
+-85	35	8.54871728961371e-14
+-85	30	2.43138842392909e-14
+-85	25	-1.66533453693773e-14
+-85	20	-3.23074900165921e-14
+-85	15	5.77315972805081e-15
+-85	10	1.68753899743024e-14
+-85	5	2.26485497023532e-14
+-85	-2.84217e-14	2.49800180540660e-14
+-85	-5	-3.18634008067420e-14
+-85	-10	4.64073224293315e-14
+-85	-15	-8.84847750626250e-14
+-85	-20	3.74145159298678e-14
+-85	-25	7.38298311375729e-14
+-85	-30	-1.05471187339390e-14
+-85	-35	-2.17603712826531e-14
+-85	-40	4.11892742135933e-14
+-85	-45	3.90798504668055e-14
+
+-80	45	9.94759830064140e-14
+-80	40	8.43769498715119e-15
+-80	35	5.16253706450698e-14
+-80	30	9.59232693276135e-14
+-80	25	-9.43689570931383e-15
+-80	20	8.10462807976364e-14
+-80	15	-4.32986979603811e-15
+-80	10	5.93969318174459e-14
+-80	5	-9.99200722162641e-15
+-80	-2.84217e-14	-6.17284001691587e-14
+-80	-5	1.87627691161651e-14
+-80	-10	2.30926389122033e-14
+-80	-15	2.87547763377916e-14
+-80	-20	-4.49640324973188e-14
+-80	-25	-1.02473585172902e-13
+-80	-30	-7.54951656745106e-15
+-80	-35	3.45279360658424e-14
+-80	-40	2.63122856836162e-14
+-80	-45	1.21569421196455e-13
+
+-75	45	7.52731210695856e-14
+-75	40	1.68753899743024e-14
+-75	35	3.17523785042795e-14
+-75	30	-1.17128529097954e-13
+-75	25	2.26485497023532e-14
+-75	20	-5.24025267623074e-14
+-75	15	5.07371922253697e-14
+-75	10	4.45199432874688e-14
+-75	5	6.99440505513849e-15
+-75	-2.84217e-14	-3.09752223870419e-14
+-75	-5	7.40518757424979e-14
+-75	-10	-4.94049245958195e-14
+-75	-15	7.09432512735475e-14
+-75	-20	5.17363929475323e-14
+-75	-25	2.06501482580279e-14
+-75	-30	-5.92859095149834e-14
+-75	-35	1.46549439250521e-14
+-75	-40	1.38777878078145e-14
+-75	-45	-5.82867087928207e-14
+
+-70	45	1.31894495325469e-13
+-70	40	2.15383266777280e-14
+-70	35	-3.99680288865056e-15
+-70	30	9.11493103217254e-14
+-70	25	-2.23154827949656e-14
+-70	20	-4.92939022933570e-14
+-70	15	2.32036612146658e-14
+-70	10	-1.87627691161651e-14
+-70	5	-4.66293670342566e-15
+-70	-2.84217e-14	-1.14352971536391e-14
+-70	-5	-3.43058914609173e-14
+-70	-10	-5.86197757002083e-14
+-70	-15	-7.47180095572730e-14
+-70	-20	3.50830475781549e-14
+-70	-25	-1.43218770176645e-14
+-70	-30	3.97459842815806e-14
+-70	-35	-2.39808173319034e-14
+-70	-40	-3.95239396766556e-14
+-70	-45	6.66133814775094e-16
+
+-65	45	3.68594044175552e-14
+-65	40	8.43769498715119e-14
+-65	35	2.55351295663786e-15
+-65	30	2.99760216648792e-15
+-65	25	4.72955008490317e-14
+-65	20	7.10542735760100e-14
+-65	15	-4.44089209850063e-16
+-65	10	2.90878432451791e-14
+-65	5	5.22915044598449e-14
+-65	-2.84217e-14	-9.96980276113391e-14
+-65	-5	1.26565424807268e-14
+-65	-10	-5.99520433297585e-15
+-65	-15	3.90798504668055e-14
+-65	-20	-2.95319324550292e-14
+-65	-25	-2.89768209427166e-14
+-65	-30	1.00364161426114e-13
+-65	-35	-2.00950367457153e-14
+-65	-40	5.10702591327572e-15
+-65	-45	9.65894031423886e-15
+
+-60	45	-4.84057238736568e-14
+-60	40	-5.51780843238703e-14
+-60	35	9.62563362350011e-14
+-60	30	-1.97619698383278e-14
+-60	25	-1.57651669496772e-14
+-60	20	6.09512440519211e-14
+-60	15	5.35127497869325e-14
+-60	10	-5.54001289287953e-14
+-60	5	6.32827124036339e-14
+-60	-2.84217e-14	2.14273043752655e-14
+-60	-5	3.33066907387547e-15
+-60	-10	1.78745906964650e-14
+-60	-15	6.20614670765463e-14
+-60	-20	3.55271367880050e-14
+-60	-25	-5.59552404411079e-14
+-60	-30	7.49400541621981e-14
+-60	-35	8.77076189453874e-14
+-60	-40	-4.64073224293315e-14
+-60	-45	9.28146448586631e-14
+
+-55	45	1.15574216863479e-13
+-55	40	-1.02806652080289e-13
+-55	35	8.75965966429249e-14
+-55	30	3.46389583683049e-14
+-55	25	-9.53681578153009e-14
+-55	20	9.88098491916389e-15
+-55	15	-4.05231403988182e-14
+-55	10	6.22835116814713e-14
+-55	5	3.99680288865056e-15
+-55	-2.84217e-14	8.08242361927114e-14
+-55	-5	-1.37667655053519e-14
+-55	-10	-1.05471187339390e-13
+-55	-15	5.19584375524573e-14
+-55	-20	5.48450174164827e-14
+-55	-25	5.97299987248334e-14
+-55	-30	-5.90638649100583e-14
+-55	-35	-1.59872115546023e-14
+-55	-40	4.29656310529936e-14
+-55	-45	6.32827124036339e-15
+
+-50	45	-1.73194791841524e-14
+-50	40	-4.55191440096314e-15
+-50	35	7.21644966006352e-15
+-50	30	3.71924713249427e-14
+-50	25	-2.01283434364541e-13
+-50	20	2.98649993624167e-14
+-50	15	-4.90718576884319e-14
+-50	10	3.55271367880050e-15
+-50	5	-4.54081217071689e-14
+-50	-2.84217e-14	3.85247389544929e-14
+-50	-5	-5.16808817963010e-14
+-50	-10	-2.19269047363468e-14
+-50	-15	-3.11417558407356e-14
+-50	-20	-8.07687250414801e-14
+-50	-25	5.39013278455514e-14
+-50	-30	1.11799458579753e-13
+-50	-35	1.31006316905768e-14
+-50	-40	3.35287353436797e-14
+-50	-45	7.19424519957101e-14
+
+-45	45	-3.93018950717305e-14
+-45	40	-1.22346577313692e-13
+-45	35	-6.38378239159465e-14
+-45	30	4.99600361081320e-14
+-45	25	-6.27276008913213e-14
+-45	20	-6.31716901011714e-14
+-45	15	2.28705943072782e-14
+-45	10	-1.45994327738208e-14
+-45	5	-5.71764857681956e-14
+-45	-2.84217e-14	8.42659275690494e-14
+-45	-5	3.41948691584548e-14
+-45	-10	-6.28386231937839e-14
+-45	-15	2.62567745323850e-14
+-45	-20	-1.95399252334028e-14
+-45	-25	-1.23789867245705e-14
+-45	-30	1.79301018476963e-14
+-45	-35	-5.71209746169643e-14
+-45	-40	2.75335310107039e-14
+-45	-45	-3.44169137633799e-15
+
+
+### -y patch
+# N_rho = 19
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = 90 + dsigma = 90 + dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn
+-45	-135	3.20299342604358e-14
+-40	-135	5.72875080706581e-14
+-35	-135	-5.75650638268144e-14
+-30	-135	1.19571019752129e-13
+-25	-135	2.53685961126848e-14
+-20	-135	-1.09745545984197e-13
+-15	-135	1.44884104713583e-13
+-10	-135	-2.47024622979097e-14
+-5	-135	-1.07691633388640e-13
+-2.84217e-14	-135	-6.88893386779910e-14
+5	-135	-5.17363929475323e-14
+10	-135	-1.08801856413265e-14
+15	-135	1.17350573702879e-13
+20	-135	-2.64233079860787e-14
+25	-135	3.13638004456607e-14
+30	-135	-1.39888101102770e-14
+35	-135	8.44879721739744e-14
+40	-135	1.27675647831893e-14
+45	-135	-7.23865412055602e-14
+
+-45	-130	-1.65423230669148e-14
+-40	-130	-6.45594688819529e-14
+-35	-130	-5.44564393578639e-14
+-30	-130	3.78030939884866e-14
+-25	-130	-9.32587340685131e-15
+-20	-130	1.09967590589122e-13
+-15	-130	7.28306304154103e-14
+-10	-130	-3.05866443284231e-14
+-5	-130	2.76445533131664e-14
+-2.84217e-14	-130	8.43769498715119e-15
+5	-130	-7.83817455385361e-14
+10	-130	-1.02307051719208e-13
+15	-130	-7.94919685631612e-14
+20	-130	-7.08322289710850e-14
+25	-130	-1.00253139123652e-13
+30	-130	6.38378239159465e-14
+35	-130	-1.27675647831893e-14
+40	-130	-6.70574706873595e-14
+45	-130	4.40758540776187e-14
+
+-45	-125	-4.91828799908944e-14
+-40	-125	-2.42028619368284e-14
+-35	-125	-2.97539770599542e-14
+-30	-125	-3.23074900165921e-14
+-25	-125	8.47655279301307e-14
+-20	-125	6.55031584528842e-15
+-15	-125	1.52988732793347e-13
+-10	-125	-4.89608353859694e-14
+-5	-125	-5.51225731726390e-14
+-2.84217e-14	-125	-7.42739203474230e-14
+5	-125	4.29656310529936e-14
+10	-125	2.43138842392909e-14
+15	-125	5.29576382746200e-14
+20	-125	7.26085858104852e-14
+25	-125	-5.15143483426073e-14
+30	-125	-5.55111512312578e-14
+35	-125	4.88498130835069e-15
+40	-125	-4.99600361081320e-15
+45	-125	3.16413562018170e-14
+
+-45	-120	2.09832151654155e-14
+-40	-120	1.76525460915400e-14
+-35	-120	1.88737914186277e-14
+-30	-120	1.47659662275146e-14
+-25	-120	1.28785870856518e-14
+-20	-120	-1.94289029309402e-14
+-15	-120	-5.61772850460329e-14
+-10	-120	6.32827124036339e-14
+-5	-120	-1.02917674382752e-13
+-2.84217e-14	-120	-2.08721928629529e-14
+5	-120	-1.03250741290140e-14
+10	-120	-7.67164110015983e-14
+15	-120	5.88418203051333e-14
+20	-120	2.27595720048157e-14
+25	-120	-1.43884903991420e-13
+30	-120	3.99680288865056e-14
+35	-120	6.15063555642337e-14
+40	-120	8.99280649946377e-15
+45	-120	6.06181771445335e-14
+
+-45	-115	8.94839757847876e-14
+-40	-115	-4.72955008490317e-14
+-35	-115	7.98250354705488e-14
+-30	-115	6.43929354282591e-15
+-25	-115	3.07531777821168e-14
+-20	-115	-2.57571741713036e-14
+-15	-115	3.73034936274053e-14
+-10	-115	-9.52571355128384e-14
+-5	-115	-3.33066907387547e-15
+-2.84217e-14	-115	6.62803145701218e-14
+5	-115	2.13162820728030e-14
+10	-115	-3.41948691584548e-14
+15	-115	5.86197757002083e-14
+20	-115	6.39488462184090e-14
+25	-115	-1.14352971536391e-14
+30	-115	-8.80406858527749e-14
+35	-115	3.00870439673417e-14
+40	-115	5.09592368302947e-14
+45	-115	3.44169137633799e-15
+
+-45	-110	2.99760216648792e-15
+-40	-110	3.14193115968919e-14
+-35	-110	-5.99520433297585e-15
+-30	-110	2.44249065417534e-15
+-25	-110	-1.88737914186277e-14
+-20	-110	-3.08642000845794e-14
+-15	-110	-2.62012633811537e-14
+-10	-110	-7.57172102794357e-14
+-5	-110	-6.73905375947470e-14
+-2.84217e-14	-110	-8.53761505936745e-14
+5	-110	3.70814490224802e-14
+10	-110	-9.32587340685131e-15
+15	-110	-9.73665592596262e-14
+20	-110	-3.63042929052426e-14
+25	-110	3.33066907387547e-14
+30	-110	3.44169137633799e-14
+35	-110	-4.97379915032070e-14
+40	-110	1.95399252334028e-14
+45	-110	2.29816166097407e-14
+
+-45	-105	-2.46469511466785e-14
+-40	-105	-2.32036612146658e-14
+-35	-105	-3.90798504668055e-14
+-30	-105	2.44249065417534e-14
+-25	-105	2.10942374678780e-15
+-20	-105	-5.88418203051333e-15
+-15	-105	-1.06581410364015e-14
+-10	-105	-3.26405569239796e-14
+-5	-105	6.27276008913213e-14
+-2.84217e-14	-105	1.02140518265514e-14
+5	-105	3.09752223870419e-14
+10	-105	-2.44249065417534e-14
+15	-105	2.42028619368284e-14
+20	-105	6.94999613415348e-14
+25	-105	-4.91828799908944e-14
+30	-105	1.19015908239817e-13
+35	-105	-2.22044604925031e-15
+40	-105	-7.28306304154103e-14
+45	-105	-1.73194791841524e-14
+
+-45	-100	-1.39888101102770e-14
+-40	-100	-5.83977310952832e-14
+-35	-100	-1.54321000422897e-14
+-30	-100	4.59632332194815e-14
+-25	-100	4.55191440096314e-15
+-20	-100	1.31006316905768e-14
+-15	-100	-1.69864122767649e-14
+-10	-100	-2.64233079860787e-14
+-5	-100	-1.27675647831893e-14
+-2.84217e-14	-100	-6.66133814775094e-15
+5	-100	-3.10862446895044e-14
+10	-100	1.40998324127395e-14
+15	-100	5.52891066263328e-14
+20	-100	-6.49480469405717e-14
+25	-100	1.45439216225896e-13
+30	-100	-4.90718576884319e-14
+35	-100	-3.04201108747293e-14
+40	-100	-2.17603712826531e-14
+45	-100	6.73905375947470e-14
+
+-45	-95	8.98170426921752e-14
+-40	-95	-6.41708908233340e-14
+-35	-95	2.04281036531029e-14
+-30	-95	7.88258347483861e-15
+-25	-95	7.41628980449605e-14
+-20	-95	-2.22044604925031e-14
+-15	-95	1.68753899743024e-14
+-10	-95	5.44009282066327e-15
+-5	-95	-3.95239396766556e-14
+-2.84217e-14	-95	7.76045894212984e-14
+5	-95	-2.00950367457153e-14
+10	-95	3.11972669919669e-14
+15	-95	-3.97459842815806e-14
+20	-95	-3.28626015289046e-14
+25	-95	6.12843109593086e-14
+30	-95	-1.93178806284777e-14
+35	-95	4.44089209850063e-16
+40	-95	1.07469588783715e-13
+45	-95	-4.60742555219440e-14
+
+-45	-90	-1.88737914186277e-15
+-40	-90	7.99360577730113e-15
+-35	-90	3.04201108747293e-14
+-30	-90	3.46389583683049e-14
+-25	-90	4.10782519111308e-15
+-20	-90	-4.61852778244065e-14
+-15	-90	2.62012633811537e-14
+-10	-90	9.95870053088765e-14
+-5	-90	-9.29256671611256e-14
+-2.84217e-14	-90	-7.37188088351104e-14
+5	-90	-1.37667655053519e-14
+10	-90	-3.80806497446429e-14
+15	-90	-1.89848137210902e-14
+20	-90	-3.17523785042795e-14
+25	-90	6.90558721316847e-14
+30	-90	-2.87547763377916e-14
+35	-90	2.36477504245158e-14
+40	-90	-4.66293670342566e-15
+45	-90	-5.59552404411079e-14
+
+-45	-85	-6.32827124036339e-14
+-40	-85	5.88418203051333e-15
+-35	-85	-5.38458166943201e-14
+-30	-85	1.38777878078145e-14
+-25	-85	2.34257058195908e-14
+-20	-85	-5.96189764223709e-14
+-15	-85	2.72004641033163e-14
+-10	-85	2.60902410786912e-14
+-5	-85	7.52731210695856e-14
+-2.84217e-14	-85	4.30766533554561e-14
+5	-85	-2.77555756156289e-15
+10	-85	4.70734562441066e-14
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+20	-85	-5.95079541199084e-14
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+35	-85	-7.82707232360735e-14
+40	-85	9.99200722162641e-15
+45	-85	6.97220059464598e-14
+
+-45	-80	6.43929354282591e-14
+-40	-80	1.83186799063151e-14
+-35	-80	-9.54791801177635e-15
+-30	-80	-6.75015598972095e-14
+-25	-80	4.36317648677687e-14
+-20	-80	2.22044604925031e-16
+-15	-80	-1.98729921407903e-14
+-10	-80	1.03250741290140e-14
+-5	-80	4.11892742135933e-14
+-2.84217e-14	-80	4.92939022933570e-14
+5	-80	4.18554080283684e-14
+10	-80	4.04121180963557e-14
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+20	-80	3.77475828372553e-15
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+30	-80	6.32827124036339e-15
+35	-80	1.54321000422897e-14
+40	-80	4.51860771022439e-14
+45	-80	-2.32036612146658e-14
+
+-45	-75	-5.78426195829707e-14
+-40	-75	-1.24344978758018e-14
+-35	-75	1.27675647831893e-14
+-30	-75	5.57331958361829e-14
+-25	-75	-5.39568389967826e-14
+-20	-75	-2.94209101525666e-14
+-15	-75	1.26565424807268e-14
+-10	-75	-3.96349619791181e-14
+-5	-75	-7.10542735760100e-15
+-2.84217e-14	-75	-1.98729921407903e-14
+5	-75	3.27515792264421e-14
+10	-75	-1.45439216225896e-14
+15	-75	8.21565038222616e-15
+20	-75	-1.44328993201270e-15
+25	-75	-2.68673971959288e-14
+30	-75	-3.46389583683049e-14
+35	-75	-4.82947015711943e-14
+40	-75	-1.39221967287995e-13
+45	-75	4.30766533554561e-14
+
+-45	-70	-3.26405569239796e-14
+-40	-70	-4.78506123613442e-14
+-35	-70	5.66213742558830e-14
+-30	-70	8.43769498715119e-15
+-25	-70	5.42899059041702e-14
+-20	-70	-2.02060590481778e-14
+-15	-70	3.70814490224802e-14
+-10	-70	5.85087533977457e-14
+-5	-70	-5.17363929475323e-14
+-2.84217e-14	-70	-4.44089209850063e-16
+5	-70	1.08801856413265e-14
+10	-70	-3.57491813929300e-14
+15	-70	1.07469588783715e-13
+20	-70	2.91988655476416e-14
+25	-70	2.26485497023532e-14
+30	-70	2.22044604925031e-15
+35	-70	7.57172102794357e-14
+40	-70	-7.57172102794357e-14
+45	-70	3.55271367880050e-14
+
+-45	-65	2.28705943072782e-14
+-40	-65	-9.04831765069503e-14
+-35	-65	-8.58202398035246e-14
+-30	-65	-2.24265050974282e-14
+-25	-65	8.74855743404623e-14
+-20	-65	3.10862446895044e-14
+-15	-65	-2.86437540353290e-14
+-10	-65	5.90638649100583e-14
+-5	-65	-1.77635683940025e-15
+-2.84217e-14	-65	6.31716901011714e-14
+5	-65	3.66373598126302e-14
+10	-65	1.66533453693773e-15
+15	-65	-3.20854454116670e-14
+20	-65	-8.35997937542743e-14
+25	-65	1.90958360235527e-14
+30	-65	-3.47499806707674e-14
+35	-65	-2.88657986402541e-15
+40	-65	-1.38444811170757e-13
+45	-65	-4.66293670342566e-15
+
+-45	-60	1.12132525487141e-14
+-40	-60	-3.85247389544929e-14
+-35	-60	2.33146835171283e-14
+-30	-60	5.10702591327572e-15
+-25	-60	4.04121180963557e-14
+-20	-60	-6.90558721316847e-14
+-15	-60	5.02931030155196e-14
+-10	-60	4.37427871702312e-14
+-5	-60	1.83186799063151e-14
+-2.84217e-14	-60	-2.30926389122033e-14
+5	-60	4.09672296086683e-14
+10	-60	2.52020626589911e-14
+15	-60	-4.58522109170190e-14
+20	-60	3.80806497446429e-14
+25	-60	-7.19424519957101e-14
+30	-60	-1.43218770176645e-14
+35	-60	-4.32986979603811e-15
+40	-60	1.87627691161651e-14
+45	-60	-4.41868763800812e-14
+
+-45	-55	-3.69704267200177e-14
+-40	-55	4.99600361081320e-14
+-35	-55	-5.39568389967826e-14
+-30	-55	-5.44009282066327e-15
+-25	-55	4.77951012101130e-14
+-20	-55	-1.99285032920216e-14
+-15	-55	-1.17350573702879e-13
+-10	-55	5.21804821573824e-15
+-5	-55	9.93094495527203e-14
+-2.84217e-14	-55	7.43849426498855e-15
+5	-55	3.83026943495679e-14
+10	-55	-3.73034936274053e-14
+15	-55	-3.44169137633799e-15
+20	-55	-2.53130849614536e-14
+25	-55	2.08721928629529e-14
+30	-55	1.00475183728577e-13
+35	-55	5.24025267623074e-14
+40	-55	-3.77475828372553e-15
+45	-55	2.28705943072782e-14
+
+-45	-50	-7.78266340262235e-14
+-40	-50	-9.94759830064140e-14
+-35	-50	-2.30926389122033e-14
+-30	-50	1.06692432666478e-13
+-25	-50	-7.27751192641790e-14
+-20	-50	-6.23390228327025e-14
+-15	-50	1.00475183728577e-13
+-10	-50	7.67164110015983e-14
+-5	-50	5.64548408021892e-14
+-2.84217e-14	-50	-3.39173134022985e-14
+5	-50	4.44644321362375e-14
+10	-50	-1.04194430861071e-13
+15	-50	3.01980662698043e-14
+20	-50	-1.07802655691103e-13
+25	-50	1.21902488103842e-13
+30	-50	3.18634008067420e-14
+35	-50	4.31876756579186e-14
+40	-50	2.58681964737661e-14
+45	-50	-7.18314296932476e-14
+
+-45	-45	2.34257058195908e-14
+-40	-45	2.89213097914853e-14
+-35	-45	6.99440505513849e-15
+-30	-45	-3.84137166520304e-14
+-25	-45	7.23865412055602e-14
+-20	-45	-4.27435864480685e-14
+-15	-45	3.71924713249427e-15
+-10	-45	1.09190434471884e-13
+-5	-45	-5.81756864903582e-14
+-2.84217e-14	-45	-1.66089364483923e-13
+5	-45	-1.31006316905768e-14
+10	-45	-5.48450174164827e-14
+15	-45	5.93969318174459e-15
+20	-45	1.21014309684142e-14
+25	-45	-5.38458166943201e-14
+30	-45	-4.42978986825437e-14
+35	-45	7.54951656745106e-15
+40	-45	-1.55431223447522e-15
+45	-45	5.40678612992451e-14
+
+
+### -z patch
+# N_rho = 19
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = dsigma = dnu
+# dpy = 180 - drho = 180 - dmu
+#
+# dpx	dpy	gridfn
+135	45	-1.11799458579753e-13
+140	45	-9.25926002537381e-14
+145	45	1.61648472385423e-13
+150	45	-1.34336985979644e-14
+155	45	-2.83773005094190e-13
+160	45	6.08402217494586e-14
+165	45	-7.46069872548105e-14
+170	45	-8.67084182232247e-14
+175	45	-9.90318937965640e-14
+180	45	2.03170813506404e-14
+185	45	1.62758695410048e-13
+190	45	-5.27355936696949e-14
+195	45	7.21644966006352e-15
+200	45	-4.21884749357559e-15
+205	45	-9.01501095995627e-14
+210	45	3.84137166520304e-14
+215	45	1.68753899743024e-14
+220	45	1.16462395283179e-13
+225	45	-2.36144437337771e-13
+
+135	40	2.08277839419679e-13
+140	40	1.19348975147204e-13
+145	40	1.90514271025677e-13
+150	40	-9.47020240005259e-14
+155	40	6.11732886568461e-14
+160	40	-9.49240686054509e-14
+165	40	-5.41788836017076e-14
+170	40	-2.50022225145585e-13
+175	40	-7.29416527178728e-14
+180	40	-8.71525074330748e-14
+185	40	2.33146835171283e-14
+190	40	-7.32747196252603e-14
+195	40	6.22835116814713e-14
+200	40	1.80966353013901e-14
+205	40	7.99360577730113e-15
+210	40	1.30451205393456e-13
+215	40	2.47579734491410e-14
+220	40	-5.10702591327572e-15
+225	40	-6.21724893790088e-14
+
+135	35	3.70814490224802e-14
+140	35	1.89848137210902e-14
+145	35	1.72195591119362e-13
+150	35	7.20534742981727e-14
+155	35	3.53050921830800e-14
+160	35	9.71445146547012e-14
+165	35	1.34559030584569e-13
+170	35	3.43058914609173e-14
+175	35	-1.25455201782643e-14
+180	35	1.36113342819044e-13
+185	35	-8.83737527601625e-14
+190	35	1.05471187339390e-13
+195	35	-8.59312621059871e-14
+200	35	1.84297022087776e-14
+205	35	-6.49480469405717e-14
+210	35	-4.26325641456060e-14
+215	35	8.48210390813620e-14
+220	35	-1.53765888910584e-13
+225	35	5.17363929475323e-14
+
+135	30	-1.35336186701807e-13
+140	30	-1.05804254246777e-13
+145	30	2.04281036531029e-14
+150	30	6.11732886568461e-14
+155	30	4.13002965160558e-14
+160	30	9.98090499138016e-14
+165	30	1.28230759344206e-13
+170	30	-1.69864122767649e-14
+175	30	-1.18904885937354e-13
+180	30	1.28896893158981e-13
+185	30	4.40758540776187e-14
+190	30	-7.30526750203353e-14
+195	30	7.72715225139109e-14
+200	30	-9.35918009759007e-14
+205	30	1.45439216225896e-14
+210	30	3.67483821150927e-14
+215	30	-5.22915044598449e-14
+220	30	3.43058914609173e-14
+225	30	1.64757096854373e-13
+
+135	25	-7.27196081129478e-14
+140	25	1.01585406753202e-13
+145	25	9.75886038645513e-14
+150	25	-1.81632486828676e-13
+155	25	1.26676447109730e-13
+160	25	-1.49547041417009e-13
+165	25	-6.31716901011714e-14
+170	25	-1.50990331349021e-14
+175	25	1.89848137210902e-14
+180	25	4.77395900588817e-14
+185	25	5.81756864903582e-14
+190	25	9.67004254448511e-14
+195	25	-2.42028619368284e-14
+200	25	5.27355936696949e-14
+205	25	-5.58442181386454e-14
+210	25	-1.18460796727504e-13
+215	25	6.91668944341473e-14
+220	25	-2.73114864057789e-14
+225	25	3.94129173741931e-14
+
+135	20	8.90398865749376e-14
+140	20	1.72084568816899e-13
+145	20	1.21569421196455e-13
+150	20	-5.73985303731206e-14
+155	20	6.55031584528842e-15
+160	20	-1.95843341543878e-13
+165	20	-5.56221735337203e-14
+170	20	6.73905375947470e-14
+175	20	-7.74935671188359e-14
+180	20	-1.96509475358653e-14
+185	20	1.27287069773274e-13
+190	20	-4.50750547997814e-14
+195	20	1.05249142734465e-13
+200	20	-1.40998324127395e-14
+205	20	-1.80022663442969e-13
+210	20	-6.93334278878410e-14
+215	20	-3.84692278032617e-14
+220	20	1.54321000422897e-14
+225	20	-4.18554080283684e-14
+
+135	15	8.85957973650875e-14
+140	15	-5.60662627435704e-14
+145	15	-7.24975635080227e-14
+150	15	-1.28896893158981e-13
+155	15	-1.15019105351166e-13
+160	15	9.49240686054509e-14
+165	15	3.69704267200177e-14
+170	15	-5.74540415243519e-14
+175	15	4.94049245958195e-14
+180	15	-1.49880108324396e-14
+185	15	-1.88737914186277e-15
+190	15	2.81996648254790e-14
+195	15	-2.67563748934663e-14
+200	15	-6.71684929898220e-15
+205	15	6.89448498292222e-14
+210	15	-2.44249065417534e-15
+215	15	-7.41073868937292e-14
+220	15	7.21644966006352e-16
+225	15	1.12132525487141e-14
+
+135	10	-2.93098878501041e-14
+140	10	-1.75415237890775e-14
+145	10	-1.46105350040671e-13
+150	10	6.00630656322210e-14
+155	10	-1.59872115546023e-14
+160	10	-4.32986979603811e-15
+165	10	-2.30371277609720e-14
+170	10	8.53761505936745e-14
+175	10	4.92383911421257e-14
+180	10	-1.02695629777827e-14
+185	10	7.21644966006352e-15
+190	10	1.12132525487141e-14
+195	10	5.93969318174459e-15
+200	10	6.36157793110215e-14
+205	10	2.05391259555654e-14
+210	10	5.50670620214078e-14
+215	10	-4.20219414820622e-14
+220	10	-6.82787160144471e-15
+225	10	4.67403893367191e-14
+
+135	5	-1.95288230031565e-13
+140	5	-1.02029495963052e-13
+145	5	1.31006316905768e-14
+150	5	-4.64073224293315e-14
+155	5	6.05071548420710e-14
+160	5	8.32667268468867e-15
+165	5	3.10307335382731e-14
+170	5	4.54081217071689e-14
+175	5	5.17363929475323e-14
+180	5	-5.54001289287953e-14
+185	5	1.31561428418081e-14
+190	5	-1.56541446472147e-14
+195	5	4.10782519111308e-15
+200	5	1.48214773787458e-14
+205	5	-1.11577413974828e-14
+210	5	1.24844579119099e-13
+215	5	6.43929354282591e-15
+220	5	-2.22599716437344e-14
+225	5	3.26960680752109e-14
+
+135	-2.84217e-14	-4.54081217071689e-14
+140	-2.84217e-14	-3.21964677141295e-14
+145	-2.84217e-14	1.22124532708767e-13
+150	-2.84217e-14	-6.59472476627343e-14
+155	-2.84217e-14	-1.02251540567977e-13
+160	-2.84217e-14	2.26485497023532e-14
+165	-2.84217e-14	-9.73110481083950e-14
+170	-2.84217e-14	-1.14352971536391e-14
+175	-2.84217e-14	-6.11732886568461e-14
+180	-2.84217e-14	3.79696274421804e-14
+185	-2.84217e-14	-3.69149155687865e-14
+190	-2.84217e-14	6.76125821996720e-14
+195	-2.84217e-14	2.83106871279415e-14
+200	-2.84217e-14	-1.62647673107585e-14
+205	-2.84217e-14	-6.81676937119846e-14
+210	-2.84217e-14	-8.35442826030430e-14
+215	-2.84217e-14	9.42579347906758e-14
+220	-2.84217e-14	3.77475828372553e-14
+225	-2.84217e-14	-3.30291349825984e-14
+
+135	-5	-1.11466391672366e-13
+140	-5	1.72750702631674e-13
+145	-5	-3.06421554796543e-14
+150	-5	6.96109836439973e-14
+155	-5	-1.68753899743024e-14
+160	-5	-5.58442181386454e-14
+165	-5	-5.56776846849516e-14
+170	-5	-7.16648962395539e-14
+175	-5	-9.47575351517571e-14
+180	-5	-1.07691633388640e-14
+185	-5	4.18554080283684e-14
+190	-5	1.63202784619898e-14
+195	-5	-4.75175454539567e-14
+200	-5	9.85878045867139e-14
+205	-5	-6.81676937119846e-14
+210	-5	-2.06501482580279e-14
+215	-5	-2.06501482580279e-14
+220	-5	1.20792265079217e-13
+225	-5	-4.78506123613442e-14
+
+135	-10	-1.29896093881143e-14
+140	-10	2.93098878501041e-14
+145	-10	-2.77555756156289e-15
+150	-10	3.06421554796543e-14
+155	-10	-1.25399690631411e-13
+160	-10	-7.46624984060418e-14
+165	-10	-2.54241072639161e-14
+170	-10	6.81676937119846e-14
+175	-10	-6.94444501903035e-14
+180	-10	-8.02136135291676e-14
+185	-10	-7.88258347483861e-15
+190	-10	-5.99520433297585e-15
+195	-10	-6.13398221105399e-14
+200	-10	-1.26010313294955e-14
+205	-10	-3.94129173741931e-14
+210	-10	-9.02056207507940e-14
+215	-10	2.39253061806721e-14
+220	-10	1.11688436277291e-13
+225	-10	5.21249710061511e-14
+
+135	-15	-1.33337785257481e-13
+140	-15	1.77635683940025e-14
+145	-15	-5.29576382746200e-14
+150	-15	-2.13162820728030e-14
+155	-15	1.04805053524615e-13
+160	-15	2.42028619368284e-14
+165	-15	-1.89848137210902e-14
+170	-15	2.79776202205539e-14
+175	-15	9.30922006148194e-14
+180	-15	-8.37663272079681e-14
+185	-15	-3.60822483003176e-14
+190	-15	-1.16573417585641e-15
+195	-15	-2.44804176929847e-14
+200	-15	4.11892742135933e-14
+205	-15	-2.48689957516035e-14
+210	-15	-1.79301018476963e-14
+215	-15	3.68594044175552e-14
+220	-15	-8.63198401646059e-14
+225	-15	7.04991620636974e-15
+
+135	-20	-4.36317648677687e-14
+140	-20	6.45039577307216e-14
+145	-20	-1.93178806284777e-14
+150	-20	-5.61772850460329e-14
+155	-20	-1.11965992033447e-13
+160	-20	7.28306304154103e-14
+165	-20	-9.22040221951193e-14
+170	-20	-4.49640324973188e-14
+175	-20	5.73430192218893e-14
+180	-20	-3.74700270810990e-14
+185	-20	-2.88102874890228e-14
+190	-20	-4.99045249569008e-14
+195	-20	-4.32986979603811e-15
+200	-20	5.78981307342019e-14
+205	-20	4.72955008490317e-14
+210	-20	8.35997937542743e-14
+215	-20	2.81996648254790e-14
+220	-20	-1.49380507963315e-13
+225	-20	-2.74225087082414e-14
+
+135	-25	9.34807786734382e-14
+140	-25	9.21485110438880e-15
+145	-25	6.77236045021345e-15
+150	-25	-1.01585406753202e-14
+155	-25	3.35287353436797e-14
+160	-25	2.00950367457153e-14
+165	-25	3.16413562018170e-14
+170	-25	2.99760216648792e-15
+175	-25	-3.91908727692680e-14
+180	-25	1.11022302462516e-13
+185	-25	-3.08086889333481e-14
+190	-25	2.27040608535845e-14
+195	-25	-4.95159468982820e-14
+200	-25	-4.72399896978004e-14
+205	-25	3.74700270810990e-14
+210	-25	-2.50910403565285e-14
+215	-25	3.10862446895044e-14
+220	-25	7.10542735760100e-15
+225	-25	-3.59712259978551e-14
+
+135	-30	-1.60982338570648e-14
+140	-30	3.69704267200177e-14
+145	-30	-4.44089209850063e-14
+150	-30	3.93574062229618e-14
+155	-30	2.83106871279415e-15
+160	-30	-7.53841433720481e-14
+165	-30	7.54951656745106e-15
+170	-30	3.25850457727483e-14
+175	-30	-5.12923037376822e-14
+180	-30	-9.60342916300760e-15
+185	-30	-1.52100554373646e-14
+190	-30	-2.65898414397725e-14
+195	-30	1.41220368732320e-13
+200	-30	-1.32116539930394e-14
+205	-30	-9.55902024202260e-14
+210	-30	9.49240686054509e-14
+215	-30	2.75890421619351e-14
+220	-30	4.62407889756378e-14
+225	-30	2.64233079860787e-14
+
+135	-35	-2.16493489801906e-14
+140	-35	-1.89848137210902e-14
+145	-35	1.68753899743024e-14
+150	-35	3.83026943495679e-14
+155	-35	3.61932706027801e-14
+160	-35	1.12132525487141e-14
+165	-35	-4.20774526332934e-14
+170	-35	3.40838468559923e-14
+175	-35	-2.32591723658970e-14
+180	-35	-3.04756220259605e-14
+185	-35	-5.54556400800266e-14
+190	-35	4.79616346638068e-14
+195	-35	-2.04836148043341e-14
+200	-35	-5.91748872125208e-14
+205	-35	-1.22679644221080e-13
+210	-35	4.47419878923938e-14
+215	-35	-1.01807451358127e-13
+220	-35	-2.33146835171283e-14
+225	-35	9.76996261670138e-14
+
+135	-40	-1.11355369369903e-13
+140	-40	-8.12683254025615e-14
+145	-40	5.83977310952832e-14
+150	-40	-6.49480469405717e-14
+155	-40	-3.06976666308856e-14
+160	-40	-1.88737914186277e-15
+165	-40	7.16093850883226e-15
+170	-40	-9.56457135714572e-14
+175	-40	-3.17523785042795e-14
+180	-40	-4.74065231514942e-14
+185	-40	-1.62647673107585e-14
+190	-40	8.64308624670684e-14
+195	-40	5.39013278455514e-14
+200	-40	5.33462163332388e-14
+205	-40	4.96824803519758e-14
+210	-40	8.09352584951739e-14
+215	-40	-1.17683640610267e-14
+220	-40	-3.40838468559923e-14
+225	-40	5.27355936696949e-15
+
+135	-45	-2.07611705604904e-14
+140	-45	-9.29256671611256e-14
+145	-45	-5.30686605770825e-14
+150	-45	-3.88578058618805e-15
+155	-45	4.97935026544383e-14
+160	-45	4.57966997657877e-14
+165	-45	1.32116539930394e-14
+170	-45	3.66373598126302e-15
+175	-45	6.87783163755284e-14
+180	-45	-6.10622663543836e-14
+185	-45	-1.52100554373646e-14
+190	-45	5.47339951140202e-14
+195	-45	-6.92779167366098e-14
+200	-45	-4.50750547997814e-14
+205	-45	6.67244037799719e-14
+210	-45	1.05915276549240e-13
+215	-45	-1.03250741290140e-14
+220	-45	6.66133814775094e-16
+225	-45	4.04121180963557e-14
+
+
diff --git a/test/Kerr-carpet-mask/Kerr.h.ah1.dx b/test/Kerr-carpet-mask/Kerr.h.ah1.dx
new file mode 100644
index 0000000..861b455
--- /dev/null
+++ b/test/Kerr-carpet-mask/Kerr.h.ah1.dx
@@ -0,0 +1,17 @@
+# list the size of each patch (N_rho x N_sigma)
+object "+z patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "+x patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "+y patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "-x patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "-y patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "-z patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+
+# collect all patch sizes into a single OpenDX group
+# for the ImportAHFinderDirectGnuplot macro to read
+object "patchsizes" class group
+member 0 value "+z patch"
+member 1 value "+x patch"
+member 2 value "+y patch"
+member 3 value "-x patch"
+member 4 value "-y patch"
+member 5 value "-z patch"
diff --git a/test/Kerr-carpet-mask/Kerr.h.t0.ah1.gp b/test/Kerr-carpet-mask/Kerr.h.t0.ah1.gp
new file mode 100644
index 0000000..c507ecc
--- /dev/null
+++ b/test/Kerr-carpet-mask/Kerr.h.t0.ah1.gp
@@ -0,0 +1,2337 @@
+# N_patches = 6
+# origin = 0.5 0.7 0
+
+### +z patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = dsigma = dnu
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-45	2.45901997027683	-0.9197158418	-0.7197158418	1.419715842
+-40	-45	2.43665405986180	-0.7433602522	-0.7817790474	1.481779047
+-35	-45	2.41092683044404	-0.5697586275	-0.8277736515	1.527773652
+-30	-45	2.38264967856070	-0.4005569301	-0.8598103581	1.559810358
+-25	-45	2.35242157803781	-0.2366504971	-0.8797520891	1.579752089
+-20	-45	2.32064127460952	-0.07840491450	-0.8891544419	1.589154442
+-15	-45	2.28757174077146	0.07415299265	-0.8892826677	1.589282668
+-10	-45	2.25332004130534	0.2212101631	-0.8810957333	1.581095733
+-5	-45	2.21789920164036	0.3630540718	-0.8652991218	1.565299122
+0	-45	2.18130168392700	0.5000000000	-0.8424132125	1.542413213
+5	-45	2.14346212566735	0.6323497525	-0.8127645929	1.512764593
+10	-45	2.10420493680401	0.7603407152	-0.7764655648	1.476465565
+15	-45	2.06340218848216	0.8841163235	-0.7335416355	1.433541635
+20	-45	2.02090101955123	1.003696583	-0.6838949893	1.383894989
+25	-45	1.97653548831930	1.118943417	-0.6273284415	1.327328441
+30	-45	1.93004595469674	1.229488802	-0.5635116689	1.263511669
+35	-45	1.88127539137421	1.334745607	-0.4921402748	1.192140275
+40	-45	1.83013046862235	1.433867273	-0.4129396770	1.112939677
+45	-45	1.77648956218502	1.525656727	-0.3256567269	1.025656727
+
+-45	-40	2.41096150770611	-0.9661548823	-0.5302500210	1.466154882
+-40	-40	2.38699927507664	-0.7906891847	-0.5906891847	1.538183473
+-35	-40	2.35951937144060	-0.6153072644	-0.6365379022	1.592823847
+-30	-40	2.32932876711495	-0.4421709682	-0.6693166075	1.631887986
+-25	-40	2.29704507353194	-0.2727132598	-0.6904627127	1.657088933
+-20	-40	2.26312723163996	-0.1078157923	-0.7012629582	1.669960165
+-15	-40	2.22788437902302	0.05204159855	-0.7028097119	1.671803514
+-10	-40	2.19143485050750	0.2066573952	-0.6959501291	1.663628581
+-5	-40	2.15386283220065	0.3559707786	-0.6813774455	1.646261533
+0	-40	2.11522372000491	0.5000000000	-0.6596395989	1.620355377
+5	-40	2.07552211621102	0.6387905626	-0.6311337176	1.586383390
+10	-40	2.03464756218978	0.7723552633	-0.5960761880	1.544603453
+15	-40	1.99252519488528	0.9006349744	-0.5546134444	1.495190080
+20	-40	1.94906203501760	1.023466232	-0.5068028676	1.438211653
+25	-40	1.90424462005588	1.140577359	-0.4526901107	1.373722581
+30	-40	1.85794934309674	1.251506595	-0.3922120258	1.301647606
+35	-40	1.81007852540820	1.355595319	-0.3253098934	1.221916749
+40	-40	1.76070901059745	1.452043891	-0.2520438909	1.134601727
+45	-40	1.70988424503137	1.539815495	-0.1725087985	1.039815495
+
+-45	-35	2.36168911444784	-0.9965723375	-0.3479112322	1.496572338
+-40	-35	2.33558765046648	-0.8229818990	-0.4039951207	1.576668431
+-35	-35	2.30597968243843	-0.6473236160	-0.4473236160	1.638547935
+-30	-35	2.27364430722705	-0.4720626477	-0.4789127499	1.683661894
+-25	-35	2.23921394768569	-0.2990208252	-0.4998096004	1.713505689
+-20	-35	2.20320527696391	-0.1294960725	-0.5110273142	1.729526245
+-15	-35	2.16590047976925	0.03565765534	-0.5134241088	1.732949222
+-10	-35	2.12747466853160	0.1958666397	-0.5077361652	1.724825997
+-5	-35	2.08807850400550	0.3507375070	-0.4946087473	1.706078101
+0	-35	2.04783500232742	0.5000000000	-0.4745899029	1.677488229
+5	-35	2.00681149495753	0.6434532687	-0.4481151506	1.639678364
+10	-35	1.96495602558967	0.7809004910	-0.4154767153	1.593065847
+15	-35	1.92226073094301	0.9121089880	-0.3769273733	1.538011682
+20	-35	1.87871159312381	1.036782288	-0.3326641273	1.474797215
+25	-35	1.83432361635222	1.154543426	-0.2828623511	1.403672908
+30	-35	1.78914401751919	1.264921789	-0.2276933454	1.324883402
+35	-35	1.74313612851786	1.367284851	-0.1672848514	1.238611132
+40	-35	1.69642779967215	1.460933010	-0.1018744289	1.145195367
+45	-35	1.64918473554252	1.545067380	-0.03176405724	1.045067380
+
+-45	-30	2.31186282025649	-1.013469481	-0.1738020125	1.513469481
+-40	-30	2.28320313242105	-0.8422012434	-0.2235139910	1.599573154
+-35	-30	2.25116018771624	-0.6672544553	-0.2624498984	1.667012124
+-30	-30	2.21649671488303	-0.4912474653	-0.2912474653	1.716890973
+-25	-30	2.17988453180882	-0.3162655709	-0.3106442363	1.750487166
+-20	-30	2.14180928175829	-0.1438847961	-0.3213666541	1.769058938
+-15	-30	2.10257533347098	0.02472414852	-0.3240771331	1.773753625
+-10	-30	2.06240904733647	0.1886715455	-0.3193877663	1.765631404
+-5	-30	2.02151519256840	0.3472727925	-0.3078688002	1.745679969
+0	-30	1.98008774221827	0.5000000000	-0.2900438711	1.714806286
+5	-30	1.93826030802299	0.6464372295	-0.2663603313	1.673785192
+10	-30	1.89602033674675	0.7862114486	-0.2371467500	1.623185785
+15	-30	1.85342243612943	0.9189561784	-0.2027251031	1.563565744
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+-25	30	1.51062943411956	-0.06566060240	1.400362294	1.213063077
+-20	30	1.46891521690785	0.05840504426	1.400483014	1.213272169
+-15	30	1.43053312987362	0.1766356760	1.396753283	1.206812087
+-10	30	1.39530237422146	0.2893738237	1.389656677	1.194520405
+-5	30	1.36305693515197	0.3970198789	1.379580625	1.177068170
+0	30	1.33362120269366	0.5000000000	1.366810601	1.154949841
+5	30	1.30685765453972	0.5987342172	1.351561295	1.128537267
+10	30	1.28264333758706	0.6936198682	1.333972649	1.098072838
+15	30	1.26087753181753	0.7850145881	1.314121086	1.063688924
+20	30	1.24152257207831	0.8732346830	1.292046064	1.025453864
+25	30	1.22454636393857	0.9585357721	1.267727651	0.9833331365
+30	30	1.20997015916060	1.041115105	1.241115105	0.9372388552
+35	30	1.19784295902803	1.121096419	1.212119857	0.8870176125
+40	30	1.18823389254863	1.198513849	1.180618920	0.8324563890
+45	30	1.18127538058853	1.273326264	1.146480127	0.7733262640
+
+-45	35	1.66070875226279	-0.5523700025	1.436877409	1.052370003
+-40	35	1.60524326524106	-0.4092819886	1.458772950	1.083640077
+-35	35	1.55418018255379	-0.2732711786	1.473271179	1.104345692
+-30	35	1.50734619980012	-0.1444433429	1.481577685	1.116208613
+-25	35	1.46449890614334	-0.02257852614	1.484703869	1.120673266
+-20	35	1.42533399789962	0.09275598917	1.483457820	1.118893724
+-15	35	1.38958485433767	0.2020901489	1.478501034	1.111814700
+-10	35	1.35695107438930	0.3060169194	1.470321222	1.100132718
+-5	35	1.32719652421997	0.4051277711	1.459301230	1.084394539
+0	35	1.30009299861040	0.5000000000	1.445702709	1.064973838
+5	35	1.27546506631818	0.5911742998	1.429705192	1.042127015
+10	35	1.25317217308937	0.6791473570	1.411407462	1.015995149
+15	35	1.23310710545051	0.7643629520	1.390835938	0.9866159685
+20	35	1.21522399949120	0.8472117387	1.367967471	0.9539564118
+25	35	1.19950797437723	0.9280215620	1.342717140	0.9178952018
+30	35	1.18598858756353	1.007051698	1.314949780	0.8782393029
+35	35	1.17476009557475	1.084493442	1.284493442	0.8347431435
+40	35	1.16593729647558	1.160439328	1.251120009	0.7870809420
+45	35	1.15970707014649	1.234891612	1.214576647	0.7348916122
+
+-45	40	1.60724734935080	-0.4773999049	1.520135900	0.9773999049
+-40	40	1.55334081464772	-0.3399165474	1.539916547	1.000973563
+-35	40	1.50452350565485	-0.2111643225	1.552229786	1.015647910
+-30	40	1.46036026931118	-0.09068907247	1.558485757	1.023103485
+-25	40	1.42041538804408	0.02218011853	1.559815359	1.024688043
+-20	40	1.38422708818299	0.1282334141	1.557073397	1.021420300
+-15	40	1.35141193425665	0.2282730040	1.550930059	1.014098955
+-10	40	1.32159242092354	0.3230933659	1.541858069	1.003287378
+-5	40	1.29447291786357	0.4134383473	1.530208714	0.9894042178
+0	40	1.26978592521641	0.5000000000	1.516202660	0.9727124520
+5	40	1.24732600842069	0.5834089298	1.499971098	0.9533684302
+10	40	1.22693724125659	0.6642362155	1.481562454	0.9314298629
+15	40	1.20850920310997	0.7429936921	1.460949923	0.9068648047
+20	40	1.19199024440570	0.8201368817	1.438045901	0.8795688536
+25	40	1.17737900397792	0.8960637859	1.412698946	0.8493615298
+30	40	1.16471305227459	0.9711051697	1.384686914	0.8159780897
+35	40	1.15411544062808	1.045532006	1.353742897	0.7791004464
+40	40	1.14575792361167	1.119529874	1.319529874	0.7383269532
+45	40	1.13987278285515	1.193179895	1.281646995	0.6931798954
+
+-45	45	1.55307589271538	-0.3966687847	1.596668785	0.8966687847
+-40	45	1.50171405257092	-0.2662850438	1.613222954	0.9132229540
+-35	45	1.45595524916908	-0.1460256982	1.622620313	0.9226203132
+-30	45	1.41512119477623	-0.03486553663	1.626414285	0.9264142847
+-25	45	1.37856149857591	0.06830951445	1.625763234	0.9257632338
+-20	45	1.34571125814001	0.1645901227	1.621531064	0.9215310642
+-15	45	1.31607880964690	0.2550029962	1.614341266	0.9143412660
+-10	45	1.28923960803368	0.3404900798	1.604625711	0.9046257105
+-5	45	1.26485420372645	0.4219005838	1.592680413	0.8926804125
+0	45	1.24263335785139	0.5000000000	1.578674474	0.8786744739
+5	45	1.22235552045383	0.5754753017	1.562686646	0.8626866457
+10	45	1.20385842563738	0.6489462162	1.544715968	0.8447159681
+15	45	1.18702630160278	0.7209730035	1.524682476	0.8246824760
+20	45	1.17179958781154	0.7920635118	1.502437904	0.8024379038
+25	45	1.15818117137418	0.8626793529	1.477768382	0.7777683822
+30	45	1.14622379537414	0.9332318728	1.450379615	0.7503796151
+35	45	1.13605266106893	1.004080887	1.419902114	0.7199021142
+40	45	1.12788121987200	1.075528016	1.385887581	0.6858875813
+45	45	1.12198931497928	1.147780833	1.347780833	0.6477808330
+
+
+### +x patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	-45	1.77648967562398	1.525656792	-0.3256567924	1.025656792
+45	-40	1.70988491999903	1.539815906	-0.1725091429	1.039815906
+45	-35	1.64918588906266	1.545068111	-0.03176456908	1.045068111
+45	-30	1.59387006748901	1.543432890	0.09757373990	1.043432890
+45	-25	1.54338591863648	1.536449908	0.2166954704	1.036449908
+45	-20	1.49713345640201	1.525223635	0.3268491135	1.025223635
+45	-15	1.45461504652962	1.510588844	0.4292135353	1.010588844
+45	-10	1.41533206190428	1.493101487	0.5248894132	0.9931014872
+45	-5	1.37890456099595	1.473172314	0.6148584549	0.9731723140
+45	0	1.34495720431479	1.451028360	0.7000000000	0.9510283596
+45	5	1.31324602750760	1.426833308	0.7810874074	0.9268333079
+45	10	1.28349222682848	1.400592923	0.8587988310	0.9005929235
+45	15	1.25552022374358	1.372268395	0.9337236120	0.8722683949
+45	20	1.22920690273172	1.341749921	1.006371916	0.8417499210
+45	25	1.20446049372284	1.308846934	1.077171520	0.8088469341
+45	30	1.18127562269348	1.273326423	1.146480218	0.7733264225
+45	35	1.15970697623078	1.234891553	1.214576605	0.7348915527
+45	40	1.13987241166119	1.193179670	1.281646805	0.6931796697
+45	45	1.12198954680079	1.147780967	1.347780967	0.6477809669
+
+50	-45	1.79039491432897	1.588775676	-0.3887756758	0.9135912680
+50	-40	1.72042484671478	1.608642593	-0.2302615908	0.9302615908
+50	-35	1.65592132588833	1.617850952	-0.08272766327	0.9379883216
+50	-30	1.59662374453545	1.618567351	0.05419483906	0.9385894513
+50	-25	1.54214472250494	1.612503617	0.1812310436	0.9335013748
+50	-20	1.49203832408020	1.600974143	0.2992781831	0.9238269977
+50	-15	1.44593457862114	1.585028708	0.4092674339	0.9104471887
+50	-10	1.40337484207692	1.565372533	0.5121460779	0.8939536996
+50	-5	1.36404835760750	1.542582799	0.6087858243	0.8748308423
+50	0	1.32759139831086	1.516994013	0.7000000000	0.8533593016
+50	5	1.29378813098874	1.488880815	0.7865158609	0.8297695270
+50	10	1.26237070988928	1.458329194	0.8689792933	0.8041336730
+50	15	1.23319327057341	1.425387719	0.9479568919	0.7764924935
+50	20	1.20614069426275	1.390010462	1.023937316	0.7468074501
+50	25	1.18113773128948	1.352073077	1.097328201	0.7149742044
+50	30	1.15820344713060	1.311417571	1.168472153	0.6808601849
+50	35	1.13737321190164	1.267798390	1.237618220	0.6442593458
+50	40	1.11876634645665	1.220933568	1.304935091	0.6049350910
+50	45	1.10259313976297	1.170509384	1.370509384	0.5626241767
+
+55	-45	1.80240635641800	1.642161971	-0.4421619710	0.7997504220
+55	-40	1.72979021989949	1.667717097	-0.2798309858	0.8176443141
+55	-35	1.66215770312465	1.681070715	-0.1269946179	0.8269946179
+55	-30	1.59943836202326	1.684404004	0.01618402931	0.8293286121
+55	-25	1.54144296548350	1.679552893	0.1499654526	0.8259318277
+55	-20	1.48790795623830	1.668014568	0.2748774640	0.8178526054
+55	-15	1.43855412542243	1.650995291	0.3915917413	0.8059355792
+55	-10	1.39301980729346	1.629375035	0.5008607100	0.7907969129
+55	-5	1.35107205535562	1.603902196	0.6034210722	0.7729606394
+55	0	1.31237190553196	1.575032129	0.7000000000	0.7527456007
+55	5	1.27674536407940	1.543173091	0.7912658195	0.7304376618
+55	10	1.24393660023953	1.508507513	0.8778270848	0.7061645629
+55	15	1.21381716363415	1.471181977	0.9602274264	0.6800289412
+55	20	1.18626863620723	1.431226319	1.038938661	0.6520516882
+55	25	1.16122601948566	1.388600838	1.114361376	0.6222050054
+55	30	1.13870380402307	1.343224332	1.186835795	0.5904320340
+55	35	1.11872554492514	1.294926966	1.256613854	0.5566138537
+55	40	1.10138444773251	1.243503713	1.323873691	0.5206069042
+55	45	1.08686181825884	1.188730503	1.388730503	0.4822542900
+
+60	-45	1.81257737020595	1.686610429	-0.4866104288	0.6850898505
+60	-40	1.73792269982038	1.717558987	-0.3216532973	0.7029580092
+60	-35	1.66773061814982	1.734975269	-0.1647389932	0.7130133043
+60	-30	1.60211940155204	1.740996352	-0.01648957799	0.7164895780
+60	-25	1.54109825193873	1.737530095	0.1229302396	0.7144883333
+60	-20	1.48458426954524	1.726214254	0.2536945106	0.7079551298
+60	-15	1.43237350837151	1.708364648	0.3762196683	0.6976496550
+60	-10	1.38421728845324	1.685030446	0.4910471593	0.6841776473
+60	-5	1.33994984331178	1.657114035	0.5987656395	0.6680600996
+60	0	1.29928373184947	1.625212719	0.7000000000	0.6496418659
+60	5	1.26208808302580	1.589876492	0.7953518377	0.6292404859
+60	10	1.22812092043092	1.551396117	0.8853895029	0.6070238314
+60	15	1.19727506942397	1.510033249	0.9706375933	0.5831429681
+60	20	1.16941257631043	1.465893550	1.051556502	0.5576589011
+60	25	1.14447110925491	1.419031242	1.128551306	0.5306029349
+60	30	1.12245003131056	1.369446056	1.201974914	0.5019749143
+60	35	1.10335553298346	1.317048498	1.272103517	0.4717231703
+60	40	1.08723824580955	1.261700562	1.339142661	0.4397680247
+60	45	1.07422008395700	1.203242121	1.403242121	0.4060170279
+
+65	-45	1.82101190655966	1.722887679	-0.5228876790	0.5702418898
+65	-40	1.74480908119266	1.758705740	-0.3561795222	0.5869441259
+65	-35	1.67255934484985	1.779886612	-0.1961862538	0.5968209287
+65	-30	1.60456623009085	1.788496042	-0.04391353698	0.6008355721
+65	-25	1.54101046358460	1.786461932	0.1001129493	0.5998870507
+65	-20	1.48196418284524	1.775510822	0.2357520272	0.5947804645
+65	-15	1.42729974838961	1.757037896	0.3631777109	0.5861663975
+65	-10	1.37688790002444	1.732248762	0.4827212964	0.5746070343
+65	-5	1.33062503023300	1.702182587	0.5948226522	0.5605869467
+65	0	1.28827619725671	1.667574749	0.7000000000	0.5444490471
+65	5	1.24975761191677	1.629121131	0.7987852987	0.5265178302
+65	10	1.21484403611892	1.587227260	0.8917075001	0.5069823975
+65	15	1.18345219644595	1.542278793	0.9792777609	0.4860225831
+65	20	1.15542422376389	1.494461350	1.061954331	0.4637249432
+65	25	1.13067625171823	1.443907903	1.140151484	0.4401514837
+65	30	1.10918189855074	1.390693360	1.214242051	0.4153371348
+65	35	1.09091548481442	1.334797359	1.284531404	0.3892724015
+65	40	1.07589907018856	1.276153878	1.351270433	0.3619264974
+65	45	1.06419267381502	1.214651071	1.414651071	0.3332472672
+
+70	-45	1.82778709605073	1.751652297	-0.5516522973	0.4555641799
+70	-40	1.75041434205126	1.791629645	-0.3838059587	0.4701147445
+70	-35	1.67656134375244	1.816108342	-0.2215489825	0.4790242617
+70	-30	1.60667583029354	1.827057578	-0.06617704996	0.4830094576
+70	-25	1.54108105672541	1.826392087	0.08149321191	0.4827672388
+70	-20	1.47994550197366	1.815858751	0.2210665823	0.4789334177
+70	-15	1.42324719013640	1.796934976	0.3524873204	0.4720457272
+70	-10	1.37096325178923	1.770955630	0.4758962311	0.4625900184
+70	-5	1.32304714774193	1.739077302	0.5915947829	0.4509872557
+70	0	1.27932340333837	1.702170762	0.7000000000	0.4375543738
+70	5	1.23973859911824	1.661056097	0.8015792462	0.4225898598
+70	10	1.20408047216487	1.616246444	0.8968243652	0.4062804798
+70	15	1.17227964777295	1.568240632	0.9862342146	0.3888077930
+70	20	1.14416399174868	1.517306515	1.070269291	0.3702692905
+70	25	1.11963757410795	1.463660161	1.149362113	0.3507436145
+70	30	1.09863588911614	1.407434502	1.223907554	0.3302791483
+70	35	1.08110589319905	1.348673083	1.294247290	0.3088917410
+70	40	1.06703905308393	1.287367448	1.360679735	0.2865783145
+70	45	1.05643274615378	1.223435720	1.423435720	0.2633090684
+
+75	-45	1.83296842902426	1.773448567	-0.5734485668	0.3412195151
+75	-40	1.75475744132935	1.816769256	-0.4049005971	0.3528272588
+75	-35	1.67972133238724	1.843954537	-0.2410470979	0.3601115329
+75	-30	1.60841010762614	1.856870888	-0.08338977234	0.3635724586
+75	-25	1.54125116400328	1.857396106	0.06703580070	0.3637131904
+75	-20	1.47847956477797	1.847265516	0.2096354546	0.3609987069
+75	-15	1.42017410344377	1.828023446	0.3441571901	0.3558428099
+75	-10	1.36640649036770	1.801110602	0.4705790960	0.3486315351
+75	-5	1.31717962538836	1.767778932	0.5890837156	0.3397003411
+75	0	1.27237085788438	1.729015872	0.7000000000	0.3293138105
+75	5	1.23196172046051	1.685757117	0.8037403054	0.3177226618
+75	10	1.19574263382593	1.638602187	0.9007662858	0.3050875365
+75	15	1.16365668527872	1.588150641	0.9915690855	0.2915690855
+75	20	1.13551639432019	1.534740092	1.076614594	0.2772577720
+75	25	1.11121247577879	1.478656511	1.156355026	0.2622302219
+75	30	1.09064034707529	1.420075128	1.231205623	0.2465333876
+75	35	1.07372130433315	1.359090488	1.301541635	0.2301926024
+75	40	1.06041140718594	1.295732280	1.367698663	0.2132158218
+75	45	1.05066138728313	1.229943417	1.429943417	0.1955877490
+
+80	-45	1.83662398687858	1.788711011	-0.5887110113	0.2272345216
+80	-40	1.75784532215403	1.834468930	-0.4197523869	0.2353028772
+80	-35	1.68199140976333	1.863655489	-0.2548418532	0.2404492552
+80	-30	1.60968547090453	1.878054087	-0.09561989833	0.2429881165
+80	-25	1.54142148101910	1.879498441	0.05672931271	0.2432427949
+80	-20	1.47747990339549	1.869702214	0.2014691643	0.2415154559
+80	-15	1.41801946602483	1.850257170	0.3381996817	0.2380867700
+80	-10	1.36318517138831	1.822681566	0.4667755530	0.2332244470
+80	-5	1.31301677793486	1.788296136	0.5872886929	0.2271613679
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+135	40	1.13987241166118	1.193179670	1.281646805	-0.6931796697
+135	45	1.12198954680079	1.147780967	1.347780967	-0.6477809669
+
+
+### +y patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = 90 - dsigma = 90 - dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	45	1.12198951938101	1.147780951	1.347780951	0.6477809510
+40	45	1.12788175024096	1.075528287	1.385887904	0.6858879038
+35	45	1.13605256785396	1.004080846	1.419902055	0.7199020551
+30	45	1.14622403397791	0.9332319630	1.450379771	0.7503797713
+25	45	1.15818126338185	0.8626793817	1.477768444	0.7777684440
+20	45	1.17179955189614	0.7920635029	1.502437879	0.8024378792
+15	45	1.18702630680597	0.7209730044	1.524682480	0.8246824796
+10	45	1.20385844033324	0.6489462180	1.544715978	0.8447159784
+5	45	1.22235552516638	0.5754753020	1.562686649	0.8626866490
+0	45	1.24263337081977	0.5000000000	1.578674483	0.8786744830
+-5	45	1.26485423130356	0.4219005820	1.592680432	0.8926804320
+-10	45	1.28923965002703	0.3404900746	1.604625740	0.9046257400
+-15	45	1.31607886274645	0.2550029863	1.614341303	0.9143413029
+-20	45	1.34571139002997	0.1645900898	1.621531154	0.9215311545
+-25	45	1.37856141287799	0.06830954129	1.625763176	0.9257631762
+-30	45	1.41512182100761	-0.03486577332	1.626414695	0.9264146946
+-35	45	1.45595484118276	-0.1460255172	1.622620055	0.9226200547
+-40	45	1.50171430974745	-0.2662851751	1.613223110	0.9132231104
+-45	45	1.55307654758013	-0.3966691628	1.596669163	0.8966691628
+
+45	50	1.10259345494866	1.170509576	1.370509576	0.5626243375
+40	50	1.10635976256831	1.098226650	1.412938759	0.5982266500
+35	50	1.11278589161396	1.025996185	1.451200404	0.6303319817
+30	50	1.12161885674380	0.9536743543	1.485787032	0.6593536084
+25	50	1.13265430301113	0.8810186438	1.517097119	0.6856258908
+20	50	1.14575970696433	0.8077205887	1.545455369	0.7094212883
+15	50	1.16088621006509	0.7334181862	1.571128530	0.7309636286
+10	50	1.17802101832790	0.6576883538	1.594295094	0.7504026836
+5	50	1.19721329617504	0.5800578831	1.615065791	0.7678313679
+0	50	1.21857388110610	0.5000000000	1.633481750	0.7832841923
+-5	50	1.24225683994386	0.4169300465	1.649493914	0.7967199928
+-10	50	1.26847795609618	0.3302031987	1.662965512	0.8080240059
+-15	50	1.29751721106492	0.2391095601	1.673656377	0.8169947068
+-20	50	1.32969452279880	0.1428794110	1.681180754	0.8233084090
+-25	50	1.36541342945374	0.04068247323	1.685009615	0.8265212045
+-30	50	1.40510572898999	-0.06833961949	1.684393097	0.8260038846
+-35	50	1.44927967637653	-0.1850514434	1.678354853	0.8209371967
+-40	50	1.49845820673828	-0.3102406320	1.665607184	0.8102406320
+-45	50	1.55317606043746	-0.4445180509	1.644518051	0.7925447481
+
+45	55	1.08686184097155	1.188730517	1.388730517	0.4822543001
+40	55	1.08864148238479	1.116655502	1.434901410	0.5145835073
+35	55	1.09338355780872	1.044005130	1.476919842	0.5440051301
+30	55	1.10086413174004	0.9706580089	1.515203584	0.5708116950
+25	55	1.11091051970600	0.8964072487	1.550098088	0.5952450895
+20	55	1.12339676136936	0.8209750161	1.581871609	0.6174931482
+15	55	1.13828384314118	0.7440340143	1.610747340	0.6377121529
+10	55	1.15556336567246	0.6651936799	1.636859914	0.6559963738
+5	55	1.17527989911057	0.5840127454	1.660270074	0.6723883443
+0	55	1.19754221284986	0.5000000000	1.680969152	0.6868819948
+-5	55	1.22249772793256	0.4126119740	1.698849707	0.6994020946
+-10	55	1.25035284914594	0.3212556797	1.713709414	0.7098069732
+-15	55	1.28137385796716	0.2252892517	1.725234470	0.7178769044
+-20	55	1.31585396417051	0.1240364386	1.732951395	0.7232803537
+-25	55	1.35416319807313	0.01679266865	1.736241466	0.7255840860
+-30	55	1.39666170807391	-0.09712184246	1.734245369	0.7241864041
+-35	55	1.44379221282628	-0.2183484378	1.725907890	0.7183484378
+-40	55	1.49593880193140	-0.3473670241	1.709852695	0.7071064697
+-45	55	1.55348334263049	-0.4844226249	1.684422625	0.6893001428
+
+45	60	1.07422017741895	1.203242182	1.403242182	0.4060170633
+40	60	1.07422866064533	1.131494861	1.452586269	0.4345058850
+35	60	1.07741610226606	1.058653601	1.497840027	0.4606331543
+30	60	1.08359956012831	0.9846004554	1.539352610	0.4846004554
+25	60	1.09265424420508	0.9091482954	1.577421351	0.5065794532
+20	60	1.10447907859234	0.8320357664	1.612260771	0.5266940015
+15	60	1.11904693685313	0.7529545445	1.644039212	0.5450412932
+10	60	1.13635981634734	0.6715378168	1.672839302	0.5616690328
+5	60	1.15646164248395	0.5873716695	1.698662752	0.5765782085
+0	60	1.17945937509388	0.5000000000	1.721441782	0.5897296875
+-5	60	1.20550129600056	0.4089233426	1.741010957	0.6010279563
+-10	60	1.23478988030431	0.3136037924	1.757105424	0.6103201009
+-15	60	1.26756859794334	0.2134729324	1.769333574	0.6173800268
+-20	60	1.30409599393161	0.1079540833	1.777137303	0.6218855121
+-25	60	1.34469744247402	-0.003526773792	1.779816651	0.6234324342
+-30	60	1.38965935148308	-0.1214745551	1.776425505	0.6214745551
+-35	60	1.43933535474108	-0.2463132187	1.765845736	0.6153663224
+-40	60	1.49399560476425	-0.3782585877	1.746667827	0.6042939517
+-45	60	1.55388098060067	-0.5172538878	1.717253888	0.5873118060
+
+45	65	1.06419266291495	1.214651063	1.414651063	0.3332472638
+40	65	1.06267927413621	1.143268138	1.466617114	0.3574794311
+35	65	1.06450223751994	1.070378728	1.514585244	0.3798473376
+30	65	1.06952203770097	0.9958548342	1.558845766	0.4004863578
+25	65	1.07765591497165	0.9195116411	1.599645618	0.4195116411
+20	65	1.08883106221044	0.8410930029	1.637145324	0.4369980412
+15	65	1.10304079904870	0.7603018233	1.671459630	0.4529990650
+10	65	1.12030182894641	0.6767883421	1.702616510	0.4675277569
+5	65	1.14066063957460	0.5901618849	1.730555060	0.4805557168
+0	65	1.16424534867276	0.5000000000	1.755164626	0.4920313455
+-5	65	1.19120043486832	0.4058432694	1.776216355	0.5018479282
+-10	65	1.22171983036718	0.3072074706	1.793380767	0.5098518248
+-15	65	1.25601920470788	0.2035974650	1.806189320	0.5158245514
+-20	65	1.29431954165919	0.09453458433	1.814007074	0.5194700298
+-25	65	1.33689083871955	-0.02042703231	1.816059372	0.5204270323
+-30	65	1.38395003374785	-0.1416308316	1.811337200	0.5182250472
+-35	65	1.43575926476058	-0.2693046712	1.798680933	0.5123233328
+-40	65	1.49249588218773	-0.4034476062	1.776686930	0.5020673611
+-45	65	1.55428105894565	-0.5437664630	1.743766463	0.4867162950
+
+45	70	1.05643276857318	1.223435735	1.423435735	0.2633090740
+40	70	1.05365936097715	1.152395417	1.477494582	0.2829848850
+35	70	1.05432930491320	1.079529107	1.527653339	0.3012411796
+30	70	1.05834879847473	1.004695810	1.574158786	0.3181677781
+25	70	1.06567357790663	0.9277038764	1.617213923	0.3338385664
+20	70	1.07626095949601	0.8482948115	1.656932130	0.3482948115
+15	70	1.09012250771545	0.7661739973	1.693374882	0.3615588883
+10	70	1.10728843956143	0.6810023078	1.726515098	0.3736209406
+5	70	1.12782920272481	0.5924098357	1.756249256	0.3844432891
+0	70	1.15188296050603	0.5000000000	1.782415918	0.3939671752
+-5	70	1.17958966090571	0.4033491183	1.804724632	0.4020868833
+-10	70	1.21113043847322	0.3020232158	1.822782137	0.4086592774
+-15	70	1.24669684615182	0.1955954211	1.836053355	0.4134896056
+-20	70	1.28647451555249	0.08367680720	1.843838571	0.4163231928
+-25	70	1.33067421531452	-0.03406083432	1.845297155	0.4168540739
+-30	70	1.37945511671347	-0.1578220895	1.839381281	0.4147008719
+-35	70	1.43299419785289	-0.2876683724	1.824907016	0.4094326702
+-40	70	1.49139171408481	-0.4234266354	1.800497010	0.4005481546
+-45	70	1.55465977945611	-0.5646171475	1.764617147	0.3874889526
+
+45	75	1.05066139253833	1.229943420	1.429943420	0.1955877500
+40	75	1.04691310299726	1.159199320	1.485603158	0.2105017318
+35	75	1.04667745020518	1.086390586	1.537452547	0.2243947337
+30	75	1.04989021073678	1.011357924	1.585697905	0.2373220383
+25	75	1.05654786466344	0.9339052510	1.630512814	0.2493301570
+20	75	1.06663644191714	0.8537693089	1.671973188	0.2604394308
+15	75	1.08018250704228	0.7706535611	1.710092841	0.2706535611
+10	75	1.09723861522063	0.6842273707	1.744805338	0.2799547466
+5	75	1.11789497415470	0.5941350402	1.775968433	0.2883048726
+0	75	1.14229905479049	0.5000000000	1.803376158	0.2956487506
+-5	75	1.17058857178051	0.4014277685	1.826685762	0.3018945400
+-10	75	1.20293431959479	0.2980262235	1.845450207	0.3069224578
+-15	75	1.23950156897400	0.1894270075	1.859074188	0.3105729925
+-20	75	1.28044392986836	0.07531756239	1.866805408	0.3126445667
+-25	75	1.32592020396201	-0.04453163756	1.867751865	0.3128981692
+-30	75	1.37604170123433	-0.1702127710	1.860842571	0.3110468295
+-35	75	1.43091311183745	-0.3016547777	1.844881673	0.3067701197
+-40	75	1.49057458016261	-0.4385552128	1.818526547	0.2997082849
+-45	75	1.55496184034649	-0.5803044371	1.780304437	0.2894667015
+
+45	80	1.04666752644809	1.234419226	1.434419226	0.1294979247
+40	80	1.04222241928785	1.163898596	1.491203537	0.1395105308
+35	80	1.04133307446823	1.091149513	1.544248999	0.1488638769
+30	80	1.04395895804973	1.015998023	1.593734792	0.1575895574
+25	80	1.05012584304658	0.9382417016	1.639812362	0.1657142762
+20	80	1.05984209967465	0.8576116105	1.682529825	0.1732465175
+15	80	1.07314510225010	0.7738074116	1.721863172	0.1801820477
+10	80	1.09011251051509	0.6865050272	1.757722570	0.1865050272
+5	80	1.11084607037772	0.5953566738	1.789931769	0.1921843781
+0	80	1.13550072514386	0.5000000000	1.818249918	0.1971776317
+-5	80	1.16421060519784	0.4000624354	1.842291591	0.2014168273
+-10	80	1.19713671551320	0.2951844295	1.861566821	0.2048155705
+-15	80	1.23442573545034	0.1850426706	1.875436755	0.2072612141
+-20	80	1.27620702809265	0.06938259882	1.883111586	0.2086144938
+-25	80	1.32260048752502	-0.05195164664	1.883664126	0.2087119215
+-30	80	1.37368141299134	-0.1789700758	1.876010668	0.2073624104
+-35	80	1.42949954813448	-0.3115059267	1.858950572	0.2043542551
+-40	80	1.49004815415101	-0.4491648418	1.831170610	0.1994558984
+-45	80	1.55520372095580	-0.5912457718	1.791245772	0.1924160721
+
+45	85	1.04432772525100	1.237042184	1.437042184	0.06448283563
+40	85	1.03946291724475	1.166658344	1.494492477	0.06950908497
+35	85	1.03817615514818	1.093950043	1.548248569	0.07421213367
+30	85	1.04044247351314	1.018734418	1.598474368	0.07860632168
+25	85	1.04630561383820	0.9408043258	1.645307927	0.08270372718
+20	85	1.05578799463550	0.8598865930	1.688780288	0.08650706589
+15	85	1.06893378253408	0.7756777918	1.728843526	0.09001214504
+10	85	1.08583868954214	0.6878579209	1.765395211	0.09321000318
+5	85	1.10661146451038	0.5960833042	1.798237192	0.09608330419
+0	85	1.13141201022694	0.5000000000	1.827106646	0.09860905410
+-5	85	1.16037299577820	0.3992487652	1.851591884	0.1007512348
+-10	85	1.19364944249635	0.2934900417	1.871176172	0.1024646381
+-15	85	1.23137444449619	0.1824287965	1.885191866	0.1036908524
+-20	85	1.27366174648181	0.06584675252	1.892826244	0.1043587739
+-25	85	1.32060738439736	-0.05636655299	1.893131923	0.1043855174
+-30	85	1.37226410145767	-0.1841710508	1.885019021	0.1036757304
+-35	85	1.42864707590520	-0.3173420159	1.867285371	0.1021242370
+-40	85	1.48972125621192	-0.4554310110	1.838638340	0.09961794660
+-45	85	1.55533278237721	-0.5976878645	1.797687865	0.09603524423
+
+45	90	1.04356012193811	1.237908439	1.437908439	0.000000000
+40	90	1.03855664419304	1.167571343	1.495580546	0.000000000
+35	90	1.03713838452095	1.094878139	1.549574028	0.000000000
+30	90	1.03928564132860	1.019642821	1.600047767	0.000000000
+25	90	1.04504820405665	0.9416564554	1.647135325	0.000000000
+20	90	1.05445323988819	0.8606442482	1.690861928	0.000000000
+15	90	1.06754718832124	0.7763015439	1.731171400	0.000000000
+10	90	1.08443219154136	0.6883096739	1.767957230	0.000000000
+5	90	1.10521938097328	0.5963262160	1.801013688	0.000000000
+0	90	1.13007019642116	0.5000000000	1.830070196	0.000000000
+-5	90	1.15911629842434	0.3989763581	1.854705511	0.000000000
+-10	90	1.19251035953649	0.2929227492	1.874393448	0.000000000
+-15	90	1.23038146537826	0.1815538440	1.888457234	0.000000000
+-20	90	1.27283809699851	0.06466373163	1.896076567	0.000000000
+-25	90	1.31996833941717	-0.05784272516	1.896297585	0.000000000
+-30	90	1.37181723450071	-0.1859086173	1.888028574	0.000000000
+-35	90	1.42838802600968	-0.3192897137	1.870066972	0.000000000
+-40	90	1.48963572327899	-0.4575193859	1.841127168	0.000000000
+-45	90	1.55539538830078	-0.5998306265	1.799830626	0.000000000
+
+45	95	1.04432772525100	1.237042184	1.437042184	-0.06448283563
+40	95	1.03946291724475	1.166658344	1.494492477	-0.06950908497
+35	95	1.03817615514818	1.093950043	1.548248569	-0.07421213367
+30	95	1.04044247351314	1.018734418	1.598474368	-0.07860632168
+25	95	1.04630561383820	0.9408043258	1.645307927	-0.08270372718
+20	95	1.05578799463550	0.8598865930	1.688780288	-0.08650706589
+15	95	1.06893378253408	0.7756777918	1.728843526	-0.09001214504
+10	95	1.08583868954214	0.6878579209	1.765395211	-0.09321000318
+5	95	1.10661146451038	0.5960833042	1.798237192	-0.09608330419
+0	95	1.13141201022694	0.5000000000	1.827106646	-0.09860905410
+-5	95	1.16037299577820	0.3992487652	1.851591884	-0.1007512348
+-10	95	1.19364944249635	0.2934900417	1.871176172	-0.1024646381
+-15	95	1.23137444449619	0.1824287965	1.885191866	-0.1036908524
+-20	95	1.27366174648181	0.06584675252	1.892826244	-0.1043587739
+-25	95	1.32060738439736	-0.05636655299	1.893131923	-0.1043855174
+-30	95	1.37226410145767	-0.1841710508	1.885019021	-0.1036757304
+-35	95	1.42864707590520	-0.3173420159	1.867285371	-0.1021242370
+-40	95	1.48972125621192	-0.4554310110	1.838638340	-0.09961794660
+-45	95	1.55533278237721	-0.5976878645	1.797687865	-0.09603524423
+
+45	100	1.04666752644809	1.234419226	1.434419226	-0.1294979247
+40	100	1.04222241928784	1.163898596	1.491203537	-0.1395105308
+35	100	1.04133307446823	1.091149513	1.544248999	-0.1488638769
+30	100	1.04395895804973	1.015998023	1.593734792	-0.1575895574
+25	100	1.05012584304658	0.9382417016	1.639812362	-0.1657142762
+20	100	1.05984209967466	0.8576116105	1.682529825	-0.1732465175
+15	100	1.07314510225010	0.7738074116	1.721863172	-0.1801820477
+10	100	1.09011251051509	0.6865050272	1.757722570	-0.1865050272
+5	100	1.11084607037772	0.5953566738	1.789931769	-0.1921843781
+0	100	1.13550072514386	0.5000000000	1.818249918	-0.1971776317
+-5	100	1.16421060519784	0.4000624354	1.842291591	-0.2014168273
+-10	100	1.19713671551320	0.2951844295	1.861566821	-0.2048155705
+-15	100	1.23442573545035	0.1850426706	1.875436755	-0.2072612141
+-20	100	1.27620702809265	0.06938259882	1.883111586	-0.2086144938
+-25	100	1.32260048752502	-0.05195164664	1.883664126	-0.2087119215
+-30	100	1.37368141299134	-0.1789700758	1.876010668	-0.2073624104
+-35	100	1.42949954813448	-0.3115059267	1.858950572	-0.2043542551
+-40	100	1.49004815415101	-0.4491648418	1.831170610	-0.1994558984
+-45	100	1.55520372095580	-0.5912457718	1.791245772	-0.1924160721
+
+45	105	1.05066139253833	1.229943420	1.429943420	-0.1955877500
+40	105	1.04691310299725	1.159199320	1.485603158	-0.2105017318
+35	105	1.04667745020517	1.086390586	1.537452547	-0.2243947337
+30	105	1.04989021073678	1.011357924	1.585697905	-0.2373220383
+25	105	1.05654786466344	0.9339052510	1.630512814	-0.2493301570
+20	105	1.06663644191714	0.8537693089	1.671973188	-0.2604394308
+15	105	1.08018250704228	0.7706535611	1.710092841	-0.2706535611
+10	105	1.09723861522063	0.6842273707	1.744805338	-0.2799547466
+5	105	1.11789497415470	0.5941350402	1.775968433	-0.2883048726
+0	105	1.14229905479049	0.5000000000	1.803376158	-0.2956487506
+-5	105	1.17058857178051	0.4014277685	1.826685762	-0.3018945400
+-10	105	1.20293431959479	0.2980262235	1.845450207	-0.3069224578
+-15	105	1.23950156897400	0.1894270075	1.859074188	-0.3105729925
+-20	105	1.28044392986836	0.07531756239	1.866805408	-0.3126445667
+-25	105	1.32592020396201	-0.04453163756	1.867751865	-0.3128981692
+-30	105	1.37604170123433	-0.1702127710	1.860842571	-0.3110468295
+-35	105	1.43091311183745	-0.3016547777	1.844881673	-0.3067701197
+-40	105	1.49057458016261	-0.4385552128	1.818526547	-0.2997082849
+-45	105	1.55496184034649	-0.5803044371	1.780304437	-0.2894667015
+
+45	110	1.05643276857318	1.223435735	1.423435735	-0.2633090740
+40	110	1.05365936097715	1.152395417	1.477494582	-0.2829848850
+35	110	1.05432930491320	1.079529107	1.527653339	-0.3012411796
+30	110	1.05834879847473	1.004695810	1.574158786	-0.3181677781
+25	110	1.06567357790662	0.9277038764	1.617213923	-0.3338385664
+20	110	1.07626095949601	0.8482948115	1.656932130	-0.3482948115
+15	110	1.09012250771545	0.7661739973	1.693374882	-0.3615588883
+10	110	1.10728843956143	0.6810023078	1.726515098	-0.3736209406
+5	110	1.12782920272481	0.5924098357	1.756249256	-0.3844432891
+0	110	1.15188296050603	0.5000000000	1.782415918	-0.3939671752
+-5	110	1.17958966090571	0.4033491183	1.804724632	-0.4020868833
+-10	110	1.21113043847323	0.3020232158	1.822782137	-0.4086592774
+-15	110	1.24669684615182	0.1955954211	1.836053355	-0.4134896056
+-20	110	1.28647451555249	0.08367680720	1.843838571	-0.4163231928
+-25	110	1.33067421531452	-0.03406083432	1.845297155	-0.4168540739
+-30	110	1.37945511671346	-0.1578220895	1.839381281	-0.4147008719
+-35	110	1.43299419785288	-0.2876683724	1.824907016	-0.4094326702
+-40	110	1.49139171408481	-0.4234266354	1.800497010	-0.4005481546
+-45	110	1.55465977945611	-0.5646171475	1.764617147	-0.3874889526
+
+45	115	1.06419266291495	1.214651063	1.414651063	-0.3332472638
+40	115	1.06267927413621	1.143268138	1.466617114	-0.3574794311
+35	115	1.06450223751993	1.070378728	1.514585244	-0.3798473376
+30	115	1.06952203770097	0.9958548342	1.558845766	-0.4004863578
+25	115	1.07765591497165	0.9195116411	1.599645618	-0.4195116411
+20	115	1.08883106221044	0.8410930029	1.637145324	-0.4369980412
+15	115	1.10304079904870	0.7603018233	1.671459630	-0.4529990650
+10	115	1.12030182894642	0.6767883421	1.702616510	-0.4675277569
+5	115	1.14066063957460	0.5901618849	1.730555060	-0.4805557168
+0	115	1.16424534867277	0.5000000000	1.755164626	-0.4920313455
+-5	115	1.19120043486832	0.4058432694	1.776216355	-0.5018479282
+-10	115	1.22171983036719	0.3072074706	1.793380767	-0.5098518248
+-15	115	1.25601920470788	0.2035974650	1.806189320	-0.5158245514
+-20	115	1.29431954165919	0.09453458433	1.814007074	-0.5194700298
+-25	115	1.33689083871955	-0.02042703231	1.816059372	-0.5204270323
+-30	115	1.38395003374785	-0.1416308316	1.811337200	-0.5182250472
+-35	115	1.43575926476058	-0.2693046712	1.798680933	-0.5123233328
+-40	115	1.49249588218772	-0.4034476062	1.776686930	-0.5020673611
+-45	115	1.55428105894565	-0.5437664630	1.743766463	-0.4867162950
+
+45	120	1.07422017741895	1.203242182	1.403242182	-0.4060170633
+40	120	1.07422866064533	1.131494861	1.452586269	-0.4345058850
+35	120	1.07741610226605	1.058653601	1.497840027	-0.4606331543
+30	120	1.08359956012831	0.9846004554	1.539352610	-0.4846004554
+25	120	1.09265424420508	0.9091482954	1.577421351	-0.5065794532
+20	120	1.10447907859234	0.8320357664	1.612260771	-0.5266940015
+15	120	1.11904693685313	0.7529545445	1.644039212	-0.5450412932
+10	120	1.13635981634734	0.6715378168	1.672839302	-0.5616690328
+5	120	1.15646164248395	0.5873716695	1.698662752	-0.5765782085
+0	120	1.17945937509388	0.5000000000	1.721441782	-0.5897296875
+-5	120	1.20550129600057	0.4089233426	1.741010957	-0.6010279563
+-10	120	1.23478988030431	0.3136037924	1.757105424	-0.6103201009
+-15	120	1.26756859794334	0.2134729324	1.769333574	-0.6173800268
+-20	120	1.30409599393161	0.1079540833	1.777137303	-0.6218855121
+-25	120	1.34469744247402	-0.003526773792	1.779816651	-0.6234324342
+-30	120	1.38965935148308	-0.1214745551	1.776425505	-0.6214745551
+-35	120	1.43933535474108	-0.2463132187	1.765845736	-0.6153663224
+-40	120	1.49399560476424	-0.3782585877	1.746667827	-0.6042939517
+-45	120	1.55388098060067	-0.5172538878	1.717253888	-0.5873118060
+
+45	125	1.08686184097155	1.188730517	1.388730517	-0.4822543001
+40	125	1.08864148238479	1.116655502	1.434901410	-0.5145835073
+35	125	1.09338355780872	1.044005130	1.476919842	-0.5440051301
+30	125	1.10086413174003	0.9706580089	1.515203584	-0.5708116950
+25	125	1.11091051970600	0.8964072487	1.550098088	-0.5952450895
+20	125	1.12339676136936	0.8209750161	1.581871609	-0.6174931482
+15	125	1.13828384314118	0.7440340143	1.610747340	-0.6377121529
+10	125	1.15556336567246	0.6651936799	1.636859914	-0.6559963738
+5	125	1.17527989911057	0.5840127454	1.660270074	-0.6723883443
+0	125	1.19754221284986	0.5000000000	1.680969152	-0.6868819948
+-5	125	1.22249772793256	0.4126119740	1.698849707	-0.6994020946
+-10	125	1.25035284914594	0.3212556797	1.713709414	-0.7098069732
+-15	125	1.28137385796716	0.2252892517	1.725234470	-0.7178769044
+-20	125	1.31585396417051	0.1240364386	1.732951395	-0.7232803537
+-25	125	1.35416319807313	0.01679266865	1.736241466	-0.7255840860
+-30	125	1.39666170807391	-0.09712184246	1.734245369	-0.7241864041
+-35	125	1.44379221282627	-0.2183484378	1.725907890	-0.7183484378
+-40	125	1.49593880193140	-0.3473670241	1.709852695	-0.7071064697
+-45	125	1.55348334263049	-0.4844226249	1.684422625	-0.6893001428
+
+45	130	1.10259345494866	1.170509576	1.370509576	-0.5626243375
+40	130	1.10635976256831	1.098226650	1.412938759	-0.5982266500
+35	130	1.11278589161396	1.025996185	1.451200404	-0.6303319817
+30	130	1.12161885674380	0.9536743543	1.485787032	-0.6593536084
+25	130	1.13265430301113	0.8810186438	1.517097119	-0.6856258908
+20	130	1.14575970696433	0.8077205887	1.545455369	-0.7094212883
+15	130	1.16088621006509	0.7334181862	1.571128530	-0.7309636286
+10	130	1.17802101832790	0.6576883538	1.594295094	-0.7504026836
+5	130	1.19721329617504	0.5800578831	1.615065791	-0.7678313679
+0	130	1.21857388110610	0.5000000000	1.633481750	-0.7832841923
+-5	130	1.24225683994387	0.4169300465	1.649493914	-0.7967199928
+-10	130	1.26847795609618	0.3302031987	1.662965512	-0.8080240059
+-15	130	1.29751721106492	0.2391095601	1.673656377	-0.8169947068
+-20	130	1.32969452279880	0.1428794110	1.681180754	-0.8233084090
+-25	130	1.36541342945374	0.04068247323	1.685009615	-0.8265212045
+-30	130	1.40510572898999	-0.06833961949	1.684393097	-0.8260038846
+-35	130	1.44927967637653	-0.1850514434	1.678354853	-0.8209371967
+-40	130	1.49845820673828	-0.3102406320	1.665607184	-0.8102406320
+-45	130	1.55317606043746	-0.4445180509	1.644518051	-0.7925447481
+
+45	135	1.12198951938101	1.147780951	1.347780951	-0.6477809510
+40	135	1.12788175024096	1.075528287	1.385887904	-0.6858879038
+35	135	1.13605256785396	1.004080846	1.419902055	-0.7199020551
+30	135	1.14622403397791	0.9332319630	1.450379771	-0.7503797713
+25	135	1.15818126338185	0.8626793817	1.477768444	-0.7777684440
+20	135	1.17179955189614	0.7920635029	1.502437879	-0.8024378792
+15	135	1.18702630680597	0.7209730044	1.524682480	-0.8246824796
+10	135	1.20385844033324	0.6489462180	1.544715978	-0.8447159784
+5	135	1.22235552516638	0.5754753020	1.562686649	-0.8626866490
+0	135	1.24263337081977	0.5000000000	1.578674483	-0.8786744830
+-5	135	1.26485423130356	0.4219005820	1.592680432	-0.8926804320
+-10	135	1.28923965002704	0.3404900746	1.604625740	-0.9046257400
+-15	135	1.31607886274645	0.2550029863	1.614341303	-0.9143413029
+-20	135	1.34571139002997	0.1645900898	1.621531154	-0.9215311545
+-25	135	1.37856141287799	0.06830954129	1.625763176	-0.9257631762
+-30	135	1.41512182100761	-0.03486577332	1.626414695	-0.9264146946
+-35	135	1.45595484118276	-0.1460255172	1.622620055	-0.9226200547
+-40	135	1.50171430974745	-0.2662851751	1.613223110	-0.9132231104
+-45	135	1.55307654758013	-0.3966691628	1.596669163	-0.8966691628
+
+
+### -x patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = 180 - dsigma = 180 - dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-135	45	1.55307669083840	-0.3966692455	1.596669246	-0.8966692455
+-135	40	1.60724782678259	-0.4774001952	1.520136143	-0.9774001952
+-135	35	1.66070773707550	-0.5523693592	1.436876958	-1.052369359
+-135	30	1.71335482065713	-0.6216540226	1.347587252	-1.121654023
+-135	25	1.76516599340672	-0.6853847506	1.252753987	-1.185384751
+-135	20	1.81619309146095	-0.7437128264	1.152674449	-1.243712826
+-135	15	1.86655280445547	-0.7967811971	1.047471475	-1.296781197
+-135	10	1.91634552528601	-0.8446495295	0.9370979917	-1.344649530
+-135	5	1.96575226233816	-0.8873445140	0.8213769174	-1.387344514
+-135	-2.84217e-14	2.01490466144001	-0.9247527495	0.7000000000	-1.424752750
+-135	-5	2.06403602257640	-0.9567090205	0.5725544747	-1.456709020
+-135	-10	2.11321362277730	-0.9827867241	0.4385446939	-1.482786724
+-135	-15	2.16252659436943	-1.002407979	0.2974309954	-1.502407979
+-135	-20	2.21210093687743	-1.014826987	0.1486480667	-1.514826987
+-135	-25	2.26191580784798	-1.018973579	-0.008309012237	-1.518973579
+-135	-30	2.31186215386092	-1.013469045	-0.1738017607	-1.513469045
+-135	-35	2.36168894063541	-0.9965722274	-0.3479111551	-1.496572227
+-135	-40	2.41096294902780	-0.9661557588	-0.5302507564	-1.466155759
+-135	-45	2.45902042093682	-0.9197161020	-0.7197161020	-1.419716102
+
+-130	45	1.55317612704970	-0.4445180914	1.644518091	-0.7925447821
+-130	40	1.61072048717089	-0.5379490512	1.570942666	-0.8709426660
+-130	35	1.66828438538341	-0.6261967942	1.488571485	-0.9449913146
+-130	30	1.72560163789978	-0.7089270617	1.397974365	-1.014410252
+-130	25	1.78252972026748	-0.7859174191	1.299633140	-1.079012832
+-130	20	1.83898808535515	-0.8569881546	1.193903297	-1.138648260
+-130	15	1.89494282310402	-0.9219643084	1.081014188	-1.193169727
+-130	10	1.95042335131257	-0.9806646123	0.9610811205	-1.242425130
+-130	5	2.00546348019430	-1.032835487	0.8341057282	-1.286201692
+-130	-2.84217e-14	2.06007381791222	-1.078108101	0.7000000000	-1.324189925
+-130	-5	2.11438492491677	-1.116087393	0.5586106739	-1.356058335
+-130	-10	2.16833985804388	-1.146096009	0.4097488607	-1.381238554
+-130	-15	2.22188431599945	-1.167301069	0.2532480250	-1.399031712
+-130	-20	2.27495355907383	-1.178686804	0.08900797063	-1.408585478
+-130	-25	2.32739733316274	-1.178985061	-0.08292359209	-1.408835746
+-130	-30	2.37889813177883	-1.166615437	-0.2622208714	-1.398456399
+-130	-35	2.42898698552048	-1.139718851	-0.4481435003	-1.375887483
+-130	-40	2.47701964252477	-1.096192641	-0.6393646560	-1.339364656
+-130	-45	2.52209391353809	-1.033736766	-0.8337367656	-1.286957954
+
+-125	45	1.55348325603983	-0.4844225701	1.684422570	-0.6893001043
+-125	40	1.61397524751689	-0.5895347134	1.614228176	-0.7629004194
+-125	35	1.67523074088794	-0.6903599552	1.533499014	-0.8334990138
+-125	30	1.73685320808421	-0.7861614072	1.442565635	-0.9005799127
+-125	25	1.79858362702702	-0.8763237232	1.341790292	-0.9637122460
+-125	20	1.86020151952977	-0.9602667225	1.231493621	-1.022489767
+-125	15	1.92153951851896	-1.037434635	1.111954369	-1.076523321
+-125	10	1.98249820771010	-1.107287973	0.9834082354	-1.125435155
+-125	5	2.04289584983757	-1.169161320	0.8460326931	-1.168759339
+-125	-2.84217e-14	2.10267091999790	-1.222407183	0.7000000000	-1.206042493
+-125	-5	2.16184349670114	-1.266348268	0.5454645507	-1.236810372
+-125	-10	2.22018192525481	-1.299987356	0.3826136643	-1.260364715
+-125	-15	2.27743465248292	-1.322188345	0.2117461046	-1.275910015
+-125	-20	2.33336309277893	-1.331700727	0.03331545727	-1.282570657
+-125	-25	2.38763853492431	-1.327084106	-0.1519833107	-1.279338064
+-125	-30	2.43976614156135	-1.306677179	-0.3430855555	-1.265048980
+-125	-35	2.48912428728610	-1.268684040	-0.5384458977	-1.238445898
+-125	-40	2.53496000802218	-1.211257301	-0.7359153700	-1.198235262
+-125	-45	2.57632089670170	-1.132581767	-0.9325817666	-1.143146060
+
+-120	45	1.55388017072355	-0.5172533576	1.717253358	-0.5873114998
+-120	40	1.61692167382562	-0.6327877334	1.650521769	-0.6540153028
+-120	35	1.68140642751476	-0.7451023765	1.571830070	-0.7188601922
+-120	30	1.74692660951612	-0.8531635331	1.481249330	-0.7812493301
+-120	25	1.81305142425747	-0.9559134682	1.378903600	-0.8405720328
+-120	20	1.87946281951236	-1.052370012	1.265016477	-0.8962612441
+-120	15	1.94583378747248	-1.141524886	1.139845268	-0.9477348349
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+-65	15	1.96734480170233	-1.232661253	1.164265183	0.8079532112
+-65	10	2.03805770461903	-1.323964088	1.021614081	0.8505284223
+-65	5	2.10803895685584	-1.404554377	0.8666269171	0.8881082916
+-65	-2.84217e-14	2.17692184567345	-1.472961221	0.7000000000	0.9200069264
+-65	-5	2.24437398785344	-1.527729274	0.5225966758	0.9455456890
+-65	-10	2.30983226004597	-1.567189306	0.3354987512	0.9639462040
+-65	-15	2.37274777066200	-1.589703910	0.1400655248	0.9744449366
+-65	-20	2.43252369334396	-1.593647291	-0.06202529492	0.9762837652
+-65	-25	2.48852115053884	-1.577460084	-0.2687355465	0.9687355465
+-65	-30	2.54004426840366	-1.539702024	-0.4776225128	0.9511286743
+-65	-35	2.58632606932389	-1.479125058	-0.6857982847	0.9228811710
+-65	-40	2.62656099120836	-1.394801805	-0.8899274955	0.8835605922
+-65	-45	2.65993527061974	-1.286260737	-1.086260737	0.8329470609
+
+-60	45	1.55388017072355	-0.5172533576	1.717253358	0.5873114998
+-60	40	1.61692167382562	-0.6327877334	1.650521769	0.6540153028
+-60	35	1.68140642751477	-0.7451023765	1.571830070	0.7188601922
+-60	30	1.74692660951612	-0.8531635331	1.481249330	0.7812493301
+-60	25	1.81305142425747	-0.9559134682	1.378903600	0.8405720328
+-60	20	1.87946281951236	-1.052370012	1.265016477	0.8962612441
+-60	15	1.94583378747248	-1.141524886	1.139845268	0.9477348349
+-60	10	2.01189734807707	-1.222388264	1.003703522	0.9944213279
+-60	5	2.07734980715749	-1.293895965	0.8569455605	1.035706318
+-60	-2.84217e-14	2.14192130899117	-1.354958266	0.7000000000	1.070960654
+-60	-5	2.20549229017337	-1.404553440	0.5333731649	1.099594441
+-60	-10	2.26766430877440	-1.441350733	0.3576874867	1.120839369
+-60	-15	2.32803909462439	-1.463957114	0.1737592773	1.133891168
+-60	-20	2.38618538302242	-1.470904980	-0.01735074732	1.137902521
+-60	-25	2.44159954581500	-1.460649111	-0.2142656953	1.131981292
+-60	-30	2.49367079300926	-1.431589090	-0.4152034813	1.115203481
+-60	-35	2.54168624045127	-1.382150280	-0.6178958140	1.086659971
+-60	-40	2.58482716137630	-1.310885802	-0.8195136082	1.045515405
+-60	-45	2.62213520141378	-1.216590435	-1.016590435	0.9910739496
+
+-55	45	1.55348325603983	-0.4844225701	1.684422570	0.6893001043
+-55	40	1.61397524751689	-0.5895347134	1.614228176	0.7629004194
+-55	35	1.67523074088794	-0.6903599552	1.533499014	0.8334990138
+-55	30	1.73685320808421	-0.7861614072	1.442565635	0.9005799127
+-55	25	1.79858362702702	-0.8763237232	1.341790292	0.9637122460
+-55	20	1.86020151952977	-0.9602667225	1.231493621	1.022489767
+-55	15	1.92153951851896	-1.037434635	1.111954369	1.076523321
+-55	10	1.98249820771010	-1.107287973	0.9834082354	1.125435155
+-55	5	2.04289584983757	-1.169161320	0.8460326931	1.168759339
+-55	-2.84217e-14	2.10267091999790	-1.222407183	0.7000000000	1.206042493
+-55	-5	2.16184349670114	-1.266348268	0.5454645507	1.236810372
+-55	-10	2.22018192525481	-1.299987356	0.3826136643	1.260364715
+-55	-15	2.27743465248293	-1.322188345	0.2117461046	1.275910015
+-55	-20	2.33336309277894	-1.331700727	0.03331545727	1.282570657
+-55	-25	2.38763853492432	-1.327084106	-0.1519833107	1.279338064
+-55	-30	2.43976614156136	-1.306677179	-0.3430855555	1.265048980
+-55	-35	2.48912428728611	-1.268684040	-0.5384458977	1.238445898
+-55	-40	2.53496000802219	-1.211257301	-0.7359153700	1.198235262
+-55	-45	2.57632089670170	-1.132581767	-0.9325817666	1.143146060
+
+-50	45	1.55317612704970	-0.4445180914	1.644518091	0.7925447821
+-50	40	1.61072048717089	-0.5379490512	1.570942666	0.8709426660
+-50	35	1.66828438538341	-0.6261967942	1.488571485	0.9449913146
+-50	30	1.72560163789978	-0.7089270617	1.397974365	1.014410252
+-50	25	1.78252972026748	-0.7859174191	1.299633140	1.079012832
+-50	20	1.83898808535515	-0.8569881546	1.193903297	1.138648260
+-50	15	1.89494282310403	-0.9219643084	1.081014188	1.193169727
+-50	10	1.95042335131257	-0.9806646123	0.9610811205	1.242425130
+-50	5	2.00546348019431	-1.032835487	0.8341057282	1.286201692
+-50	-2.84217e-14	2.06007381791222	-1.078108101	0.7000000000	1.324189925
+-50	-5	2.11438492491677	-1.116087393	0.5586106739	1.356058335
+-50	-10	2.16833985804388	-1.146096009	0.4097488607	1.381238554
+-50	-15	2.22188431599945	-1.167301069	0.2532480250	1.399031712
+-50	-20	2.27495355907384	-1.178686804	0.08900797063	1.408585478
+-50	-25	2.32739733316274	-1.178985061	-0.08292359209	1.408835746
+-50	-30	2.37889813177883	-1.166615437	-0.2622208714	1.398456399
+-50	-35	2.42898698552049	-1.139718851	-0.4481435003	1.375887483
+-50	-40	2.47701964252478	-1.096192641	-0.6393646560	1.339364656
+-50	-45	2.52209391353809	-1.033736766	-0.8337367656	1.286957954
+
+-45	45	1.55307669083840	-0.3966692455	1.596669246	0.8966692455
+-45	40	1.60724782678259	-0.4774001952	1.520136143	0.9774001952
+-45	35	1.66070773707550	-0.5523693592	1.436876958	1.052369359
+-45	30	1.71335482065713	-0.6216540226	1.347587252	1.121654023
+-45	25	1.76516599340672	-0.6853847506	1.252753987	1.185384751
+-45	20	1.81619309146096	-0.7437128264	1.152674449	1.243712826
+-45	15	1.86655280445548	-0.7967811971	1.047471475	1.296781197
+-45	10	1.91634552528602	-0.8446495295	0.9370979917	1.344649530
+-45	5	1.96575226233816	-0.8873445140	0.8213769174	1.387344514
+-45	-2.84217e-14	2.01490466144001	-0.9247527495	0.7000000000	1.424752750
+-45	-5	2.06403602257641	-0.9567090205	0.5725544747	1.456709020
+-45	-10	2.11321362277731	-0.9827867241	0.4385446939	1.482786724
+-45	-15	2.16252659436944	-1.002407979	0.2974309954	1.502407979
+-45	-20	2.21210093687744	-1.014826987	0.1486480667	1.514826987
+-45	-25	2.26191580784799	-1.018973579	-0.008309012237	1.518973579
+-45	-30	2.31186215386093	-1.013469045	-0.1738017607	1.513469045
+-45	-35	2.36168894063542	-0.9965722274	-0.3479111551	1.496572227
+-45	-40	2.41096294902780	-0.9661557588	-0.5302507564	1.466155759
+-45	-45	2.45902042093683	-0.9197161020	-0.7197161020	1.419716102
+
+
+### -y patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = 90 + dsigma = 90 + dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-135	2.45902708372356	-0.9197199487	-0.7197199487	-1.419719949
+-40	-135	2.43665280645099	-0.7433596126	-0.7817782852	-1.481778285
+-35	-135	2.41092613450877	-0.5697583187	-0.8277732105	-1.527773211
+-30	-135	2.38264885179568	-0.4005566176	-0.8598098168	-1.559809817
+-25	-135	2.35242017034242	-0.2366500563	-0.8797511438	-1.579751144
+-20	-135	2.32064172883383	-0.07840502771	-0.8891547529	-1.589154753
+-15	-135	2.28757242799693	0.07415286472	-0.8892831451	-1.589283145
+-10	-135	2.25332021710917	0.2212101414	-0.8810958566	-1.581095857
+-5	-135	2.21789913766772	0.3630540758	-0.8652990766	-1.565299077
+-2.84217e-14	-135	2.18130161379306	0.5000000000	-0.8424131629	-1.542413163
+5	-135	2.14346229252596	0.6323497628	-0.8127647107	-1.512764711
+10	-135	2.10420494125444	0.7603407157	-0.7764655679	-1.476465568
+15	-135	2.06340162209847	0.8841162181	-0.7335412420	-1.433541242
+20	-135	2.02090126471248	1.003696645	-0.6838951572	-1.383895157
+25	-135	1.97653466050048	1.118943158	-0.6273278855	-1.327327886
+30	-135	1.93004548694468	1.229488625	-0.5635113627	-1.263511363
+35	-135	1.88127541797210	1.334745619	-0.4921402917	-1.192140292
+40	-135	1.83012840141095	1.433866218	-0.4129384199	-1.112938420
+45	-135	1.77648935900540	1.525656610	-0.3256566096	-1.025656610
+
+-45	-130	2.52208895050095	-1.033733747	-0.8337337475	-1.286955422
+-40	-130	2.50482947789638	-0.8544018846	-0.9141133118	-1.354401885
+-35	-130	2.48273436614084	-0.6735490319	-0.9760017107	-1.406332417
+-30	-130	2.45665259654433	-0.4936711332	-1.021088889	-1.444165052
+-25	-130	2.42728261729714	-0.3165244493	-1.051042332	-1.469298975
+-20	-130	2.39516872758201	-0.1432786268	-1.067393502	-1.483019235
+-15	-130	2.36068134291102	0.02534025075	-1.071454301	-1.486426650
+-10	-130	2.32405114800248	0.1889055510	-1.064304293	-1.480427082
+-5	-130	2.28544358070030	0.3471719487	-1.046832620	-1.465766607
+-2.84217e-14	-130	2.24496114555327	0.5000000000	-1.019740011	-1.443033209
+5	-130	2.20262866124614	0.6472902017	-0.9835347094	-1.412653354
+10	-130	2.15838294223717	0.7889183196	-0.9385372130	-1.374895971
+15	-130	2.11220145390916	0.9246981557	-0.8849950949	-1.329968800
+20	-130	2.06399710487794	1.054334736	-0.8230221689	-1.277967340
+25	-130	2.01364456352303	1.177378895	-0.7526437292	-1.218912817
+30	-130	1.96111951968439	1.293237049	-0.6739268708	-1.152861531
+35	-130	1.90636733213100	1.401109506	-0.5869177442	-1.079852205
+40	-130	1.84941072013409	1.500006342	-0.4917611513	-1.000006342
+45	-130	1.79039302738868	1.588774528	-0.3887745283	-0.9135903051
+
+-45	-125	2.57632552098710	-1.132584697	-0.9325846969	-1.143148112
+-40	-125	2.56470482465213	-0.9527641720	-1.031336921	-1.212295163
+-35	-125	2.54690278524993	-0.7671931741	-1.109739406	-1.267193174
+-30	-125	2.52378820861935	-0.5790079347	-1.168896565	-1.308615463
+-25	-125	2.49603788464905	-0.3906635529	-1.210034153	-1.337420312
+-20	-125	2.46427535064478	-0.2040885709	-1.234467450	-1.354528691
+-15	-125	2.42897753858267	-0.02074282079	-1.243438665	-1.360810403
+-10	-125	2.39050137457522	0.1582656299	-1.238071920	-1.357052568
+-5	-125	2.34914018462357	0.3320759878	-1.219380243	-1.343964515
+-2.84217e-14	-125	2.30509822560579	0.5000000000	-1.188225924	-1.322150026
+5	-125	2.25848798822742	0.6614439049	-1.145312277	-1.292101567
+10	-125	2.20936133687622	0.8158394774	-1.091214686	-1.254222026
+15	-125	2.15784072055377	0.9626144317	-1.026500563	-1.208908709
+20	-125	2.10396413927604	1.101141063	-0.9516214967	-1.156477822
+25	-125	2.04775708889720	1.230703094	-0.8669978412	-1.097223701
+30	-125	1.98932447019233	1.350505950	-0.7731195176	-1.031489391
+35	-125	1.92879222320645	1.459656707	-0.6705318130	-0.9596567068
+40	-125	1.86639656749069	1.557210966	-0.5599349663	-0.8822159611
+45	-125	1.80240529322583	1.642161297	-0.4421612973	-0.7997499502
+
+-45	-120	2.62213009933529	-1.216587095	-1.016587095	-0.9910720212
+-40	-120	2.61618050504002	-1.037944950	-1.132851419	-1.058197260
+-35	-120	2.60299058474725	-0.8496828763	-1.227546909	-1.112869727
+-30	-120	2.58324930300220	-0.6552642089	-1.300976306	-1.155264209
+-25	-120	2.55765514006792	-0.4577231282	-1.353843876	-1.185787315
+-20	-120	2.52681538065408	-0.2596278623	-1.387060399	-1.204964883
+-15	-120	2.49125934442365	-0.06313578274	-1.401651353	-1.213388974
+-10	-120	2.45143913400086	0.1299459810	-1.398680630	-1.211673827
+-5	-120	2.40774839878398	0.3180925424	-1.379211755	-1.200433466
+-2.84217e-14	-120	2.36048904336462	0.5000000000	-1.344243477	-1.180244522
+5	-120	2.30989430984826	0.6745144972	-1.294709831	-1.151646258
+10	-120	2.25615777492933	0.8405755585	-1.231499973	-1.115152029
+15	-120	2.19948955473053	0.9971827902	-1.155511434	-1.071280026
+20	-120	2.14014725745976	1.143385147	-1.067686165	-1.020574083
+25	-120	2.07834287060690	1.278242932	-0.9689473538	-0.9635672040
+30	-120	2.01431259507779	1.400827978	-0.8602798270	-0.9008279781
+35	-120	1.94841790211150	1.510278828	-0.7428276950	-0.8330169581
+40	-120	1.88101323174759	1.605770338	-0.6178057724	-0.7608355175
+45	-120	1.81257706051694	1.686610226	-0.4866102261	-0.6850897335
+
+-45	-115	2.65993726575774	-1.286262076	-1.086262076	-0.8329476857
+-40	-115	2.65934612902596	-1.109773215	-1.218453012	-0.8945893313
+-35	-115	2.65065579144244	-0.9202672635	-1.328351861	-0.9458360064
+-30	-115	2.63445912908358	-0.7213953977	-1.415518885	-0.9864826570
+-25	-115	2.61132408212655	-0.5165404707	-1.479978074	-1.016540471
+-20	-115	2.58179864178110	-0.3087879583	-1.522126653	-1.036194675
+-15	-115	2.54641521034786	-0.1009175025	-1.542654650	-1.045767038
+-10	-115	2.50569945026910	0.1045900845	-1.542481065	-1.045686094
+-5	-115	2.46010388289158	0.3055446156	-1.522635215	-1.036431822
+-2.84217e-14	-115	2.41001562783372	0.5000000000	-1.484215930	-1.018516615
+5	-115	2.35578718272244	0.6862098204	-1.428387987	-0.9924836177
+10	-115	2.29777182366091	0.8625980612	-1.356395792	-0.9589131061
+15	-115	2.23634902572674	1.027746326	-1.269576101	-0.9184284194
+20	-115	2.17194013284591	1.180393504	-1.169365790	-0.8716995836
+25	-115	2.10497052084426	1.319426336	-1.057265448	-0.8194263357
+30	-115	2.03583228924149	1.443858328	-0.9348105791	-0.7623246927
+35	-115	1.96509301717360	1.552930860	-0.8037411090	-0.7012059950
+40	-115	1.89326408345586	1.646043299	-0.6658012185	-0.6368835677
+45	-115	1.82101302999240	1.722888433	-0.5228884334	-0.5702422416
+
+-45	-110	2.69017742478109	-1.342209501	-1.142209501	-0.6705094236
+-40	-110	2.69427515032362	-1.168217286	-1.288103943	-0.7236106580
+-35	-110	2.68975007064775	-0.9784645071	-1.411466139	-0.7685108252
+-30	-110	2.67694931884621	-0.7765593988	-1.511065738	-0.8047621145
+-25	-110	2.65628071841350	-0.5660877624	-1.586232584	-0.8321206093
+-20	-110	2.62824313938183	-0.3505404204	-1.636840599	-0.8505404204
+-15	-110	2.59333136412204	-0.1332108278	-1.663174981	-0.8601253515
+-10	-110	2.55206384175154	0.08282825995	-1.665898505	-0.8611166331
+-5	-110	2.50494296528854	0.2947549439	-1.645961726	-0.8538602389
+-2.84217e-14	-110	2.45247447427004	0.5000000000	-1.604572166	-0.8387956712
+5	-110	2.39512033203575	0.6962466266	-1.543109207	-0.8164249834
+10	-110	2.33335015314445	0.8814198248	-1.463139318	-0.7873183244
+15	-110	2.26769292146063	1.053700052	-1.366436727	-0.7521214597
+20	-110	2.19877672806427	1.211558400	-1.254990636	-0.7115583998
+25	-110	2.12724215699262	1.353760228	-1.130894717	-0.6663911790
+30	-110	2.05370739567560	1.479353423	-0.9962898870	-0.6173990276
+35	-110	1.97876798292987	1.587661736	-0.8533419399	-0.5653702298
+40	-110	1.90318593125280	1.678397710	-0.7043597048	-0.5111451308
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+30	-55	1.98932447019233	1.350505950	-0.7731195176	1.031489391
+35	-55	1.92879222320645	1.459656707	-0.6705318130	0.9596567068
+40	-55	1.86639656749069	1.557210966	-0.5599349663	0.8822159611
+45	-55	1.80240529322583	1.642161297	-0.4421612973	0.7997499502
+
+-45	-50	2.52208895050096	-1.033733747	-0.8337337475	1.286955422
+-40	-50	2.50482947789638	-0.8544018846	-0.9141133118	1.354401885
+-35	-50	2.48273436614085	-0.6735490319	-0.9760017107	1.406332417
+-30	-50	2.45665259654433	-0.4936711332	-1.021088889	1.444165052
+-25	-50	2.42728261729714	-0.3165244493	-1.051042332	1.469298975
+-20	-50	2.39516872758202	-0.1432786268	-1.067393502	1.483019235
+-15	-50	2.36068134291102	0.02534025075	-1.071454301	1.486426650
+-10	-50	2.32405114800248	0.1889055510	-1.064304293	1.480427082
+-5	-50	2.28544358070031	0.3471719487	-1.046832620	1.465766607
+-2.84217e-14	-50	2.24496114555327	0.5000000000	-1.019740011	1.443033209
+5	-50	2.20262866124615	0.6472902017	-0.9835347094	1.412653354
+10	-50	2.15838294223718	0.7889183196	-0.9385372130	1.374895971
+15	-50	2.11220145390917	0.9246981557	-0.8849950949	1.329968800
+20	-50	2.06399710487794	1.054334736	-0.8230221689	1.277967340
+25	-50	2.01364456352303	1.177378895	-0.7526437292	1.218912817
+30	-50	1.96111951968440	1.293237049	-0.6739268708	1.152861531
+35	-50	1.90636733213100	1.401109506	-0.5869177442	1.079852205
+40	-50	1.84941072013409	1.500006342	-0.4917611513	1.000006342
+45	-50	1.79039302738868	1.588774528	-0.3887745283	0.9135903051
+
+-45	-45	2.45902708372356	-0.9197199487	-0.7197199487	1.419719949
+-40	-45	2.43665280645100	-0.7433596126	-0.7817782852	1.481778285
+-35	-45	2.41092613450878	-0.5697583187	-0.8277732105	1.527773211
+-30	-45	2.38264885179568	-0.4005566176	-0.8598098168	1.559809817
+-25	-45	2.35242017034243	-0.2366500563	-0.8797511438	1.579751144
+-20	-45	2.32064172883383	-0.07840502771	-0.8891547529	1.589154753
+-15	-45	2.28757242799694	0.07415286472	-0.8892831451	1.589283145
+-10	-45	2.25332021710917	0.2212101414	-0.8810958566	1.581095857
+-5	-45	2.21789913766773	0.3630540758	-0.8652990766	1.565299077
+-2.84217e-14	-45	2.18130161379306	0.5000000000	-0.8424131629	1.542413163
+5	-45	2.14346229252596	0.6323497628	-0.8127647107	1.512764711
+10	-45	2.10420494125444	0.7603407157	-0.7764655679	1.476465568
+15	-45	2.06340162209847	0.8841162181	-0.7335412420	1.433541242
+20	-45	2.02090126471248	1.003696645	-0.6838951572	1.383895157
+25	-45	1.97653466050049	1.118943158	-0.6273278855	1.327327886
+30	-45	1.93004548694468	1.229488625	-0.5635113627	1.263511363
+35	-45	1.88127541797210	1.334745619	-0.4921402917	1.192140292
+40	-45	1.83012840141095	1.433866218	-0.4129384199	1.112938420
+45	-45	1.77648935900539	1.525656610	-0.3256566096	1.025656610
+
+
+### -z patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = dsigma = dnu
+# dpy = 180 - drho = 180 - dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+135	45	1.12198931497928	1.147780833	1.347780833	-0.6477808330
+140	45	1.12788121987200	1.075528016	1.385887581	-0.6858875813
+145	45	1.13605266106893	1.004080887	1.419902114	-0.7199021142
+150	45	1.14622379537414	0.9332318728	1.450379615	-0.7503796151
+155	45	1.15818117137418	0.8626793529	1.477768382	-0.7777683822
+160	45	1.17179958781154	0.7920635118	1.502437904	-0.8024379038
+165	45	1.18702630160278	0.7209730035	1.524682476	-0.8246824760
+170	45	1.20385842563738	0.6489462162	1.544715968	-0.8447159681
+175	45	1.22235552045383	0.5754753017	1.562686646	-0.8626866457
+180	45	1.24263335785139	0.5000000000	1.578674474	-0.8786744739
+185	45	1.26485420372645	0.4219005838	1.592680413	-0.8926804125
+190	45	1.28923960803368	0.3404900798	1.604625711	-0.9046257105
+195	45	1.31607880964690	0.2550029962	1.614341266	-0.9143412660
+200	45	1.34571125814001	0.1645901227	1.621531064	-0.9215310642
+205	45	1.37856149857591	0.06830951445	1.625763234	-0.9257632338
+210	45	1.41512119477623	-0.03486553663	1.626414285	-0.9264142847
+215	45	1.45595524916908	-0.1460256982	1.622620313	-0.9226203132
+220	45	1.50171405257092	-0.2662850438	1.613222954	-0.9132229540
+225	45	1.55307589271537	-0.3966687847	1.596668785	-0.8966687847
+
+135	40	1.13987278285515	1.193179895	1.281646995	-0.6931798954
+140	40	1.14575792361167	1.119529874	1.319529874	-0.7383269532
+145	40	1.15411544062808	1.045532006	1.353742897	-0.7791004464
+150	40	1.16471305227459	0.9711051697	1.384686914	-0.8159780897
+155	40	1.17737900397792	0.8960637859	1.412698946	-0.8493615298
+160	40	1.19199024440570	0.8201368817	1.438045901	-0.8795688536
+165	40	1.20850920310997	0.7429936921	1.460949923	-0.9068648047
+170	40	1.22693724125659	0.6642362155	1.481562454	-0.9314298629
+175	40	1.24732600842068	0.5834089298	1.499971098	-0.9533684302
+180	40	1.26978592521641	0.5000000000	1.516202660	-0.9727124520
+185	40	1.29447291786357	0.4134383473	1.530208714	-0.9894042178
+190	40	1.32159242092354	0.3230933659	1.541858069	-1.003287378
+195	40	1.35141193425665	0.2282730040	1.550930059	-1.014098955
+200	40	1.38422708818299	0.1282334141	1.557073397	-1.021420300
+205	40	1.42041538804408	0.02218011853	1.559815359	-1.024688043
+210	40	1.46036026931118	-0.09068907247	1.558485757	-1.023103485
+215	40	1.50452350565485	-0.2111643225	1.552229786	-1.015647910
+220	40	1.55334081464772	-0.3399165474	1.539916547	-1.000973563
+225	40	1.60724734935080	-0.4773999049	1.520135900	-0.9773999049
+
+135	35	1.15970707014649	1.234891612	1.214576647	-0.7348916122
+140	35	1.16593729647558	1.160439328	1.251120009	-0.7870809420
+145	35	1.17476009557475	1.084493442	1.284493442	-0.8347431435
+150	35	1.18598858756353	1.007051698	1.314949780	-0.8782393029
+155	35	1.19950797437723	0.9280215620	1.342717140	-0.9178952018
+160	35	1.21522399949120	0.8472117387	1.367967471	-0.9539564118
+165	35	1.23310710545051	0.7643629520	1.390835938	-0.9866159685
+170	35	1.25317217308937	0.6791473570	1.411407462	-1.015995149
+175	35	1.27546506631818	0.5911742998	1.429705192	-1.042127015
+180	35	1.30009299861041	0.5000000000	1.445702709	-1.064973838
+185	35	1.32719652421997	0.4051277711	1.459301230	-1.084394539
+190	35	1.35695107438930	0.3060169194	1.470321222	-1.100132718
+195	35	1.38958485433767	0.2020901489	1.478501034	-1.111814700
+200	35	1.42533399789962	0.09275598917	1.483457820	-1.118893724
+205	35	1.46449890614334	-0.02257852614	1.484703869	-1.120673266
+210	35	1.50734619980012	-0.1444433429	1.481577685	-1.116208613
+215	35	1.55418018255379	-0.2732711786	1.473271179	-1.104345692
+220	35	1.60524326524106	-0.4092819886	1.458772950	-1.083640077
+225	35	1.66070875226279	-0.5523700025	1.436877409	-1.052370003
+
+135	30	1.18127538058853	1.273326264	1.146480127	-0.7733262640
+140	30	1.18823389254863	1.198513849	1.180618920	-0.8324563890
+145	30	1.19784295902803	1.121096419	1.212119857	-0.8870176125
+150	30	1.20997015916060	1.041115105	1.241115105	-0.9372388552
+155	30	1.22454636393857	0.9585357721	1.267727651	-0.9833331365
+160	30	1.24152257207831	0.8732346830	1.292046064	-1.025453864
+165	30	1.26087753181753	0.7850145881	1.314121086	-1.063688924
+170	30	1.28264333758706	0.6936198682	1.333972649	-1.098072838
+175	30	1.30685765453972	0.5987342172	1.351561295	-1.128537267
+180	30	1.33362120269366	0.5000000000	1.366810601	-1.154949841
+185	30	1.36305693515197	0.3970198789	1.379580625	-1.177068170
+190	30	1.39530237422146	0.2893738237	1.389656677	-1.194520405
+195	30	1.43053312987362	0.1766356760	1.396753283	-1.206812087
+200	30	1.46891521690785	0.05840504426	1.400483014	-1.213272169
+205	30	1.51062943411956	-0.06566060240	1.400362294	-1.213063077
+210	30	1.55584576336370	-0.1957953779	1.395795378	-1.205152946
+215	30	1.60468158381739	-0.3320472876	1.386057632	-1.188286675
+220	30	1.65720595058857	-0.4742032393	1.370309557	-1.161010210
+225	30	1.71335490238684	-0.6216540761	1.347587283	-1.121654076
+
+135	25	1.20446054417189	1.308846968	1.077171535	-0.8088469680
+140	25	1.21253957802745	1.233982581	1.107891609	-0.8747263774
+145	25	1.22327622218706	1.155452578	1.136502808	-0.9360832932
+150	25	1.23660472493754	1.073318183	1.163051069	-0.9930162210
+155	25	1.25248265413494	0.9875684774	1.187568477	-1.045593974
+160	25	1.27090792045738	0.8981313668	1.210073868	-1.093856940
+165	25	1.29186345237487	0.8048612639	1.230545141	-1.137757726
+170	25	1.31540155153412	0.7075758991	1.248947365	-1.177221423
+175	25	1.34156795258360	0.6060423154	1.265197156	-1.212069212
+180	25	1.37043971747934	0.5000000000	1.279172851	-1.242040188
+185	25	1.40211509051583	0.3891718229	1.290705420	-1.266771861
+190	25	1.43668422687899	0.2732851844	1.299561419	-1.285763612
+195	25	1.47425184378738	0.1520976892	1.305448781	-1.298389100
+200	25	1.51491166024517	0.02543072537	1.308003804	-1.303868366
+205	25	1.55871711747993	-0.1067799256	1.306779926	-1.301243750
+210	25	1.60573612740378	-0.2444559281	1.301273644	-1.289435491
+215	25	1.65591379450595	-0.3872672797	1.290881281	-1.267148997
+220	25	1.70913926321688	-0.5345876290	1.274944996	-1.232973524
+225	25	1.76516593545057	-0.6853847117	1.252753969	-1.185384712
+
+135	20	1.22920674763986	1.341749815	1.006371877	-0.8417498147
+140	20	1.23882049813018	1.267041840	1.032714243	-0.9141248685
+145	20	1.25104575871674	1.187657478	1.057446671	-0.9820766570
+150	20	1.26588824936709	1.103665348	1.080559653	-1.045579054
+155	20	1.28332761828553	1.015058465	1.102022027	-1.104546442
+160	20	1.30339718452647	0.9217996321	1.121799632	-1.158884965
+165	20	1.32611297735760	0.8237955271	1.139829405	-1.208421359
+170	20	1.35152174005239	0.7209257726	1.156030069	-1.252932318
+175	20	1.37966656267845	0.6130443866	1.170287123	-1.292103252
+180	20	1.41058894083879	0.5000000000	1.182449832	-1.325520019
+185	20	1.44436338913042	0.3816546129	1.192340339	-1.352693964
+190	20	1.48103036607711	0.2579041696	1.199728832	-1.372993681
+195	20	1.52062129556442	0.1287115937	1.204341614	-1.385667197
+200	20	1.56316681402039	-0.005865130651	1.205865131	-1.389853024
+205	20	1.60859681556008	-0.1456039709	1.203917584	-1.384502184
+210	20	1.65684198743808	-0.2900998336	1.198090738	-1.368493055
+215	20	1.70773903115876	-0.4386863012	1.187932298	-1.340582970
+220	20	1.76099525739659	-0.5903573556	1.172956497	-1.299437296
+225	20	1.81619387020303	-0.7437133596	1.152674643	-1.243713360
+
+135	15	1.25552026721029	1.372268425	0.9337236201	-0.8722684251
+140	15	1.26706628033318	1.297820973	0.9547677029	-0.9508060112
+145	15	1.28115632076441	1.217755031	0.9746641110	-1.025060417
+150	15	1.29784273309956	1.132125301	0.9933703731	-1.094873138
+155	15	1.31713023492699	1.040921755	1.010823862	-1.160010447
+160	15	1.33907343190998	0.9441279746	1.026960067	-1.220231582
+165	15	1.36370940119432	0.8416948556	1.041694856	-1.275222562
+170	15	1.39106510739560	0.7335611084	1.054923053	-1.324590868
+175	15	1.42117834179031	0.6196737470	1.066521588	-1.367877187
+180	15	1.45408056956291	0.5000000000	1.076343745	-1.404533976
+185	15	1.48981016950814	0.3745469446	1.084221721	-1.433934985
+190	15	1.52834266159311	0.2433898642	1.089948710	-1.455308398
+195	15	1.56963203032587	0.1067085924	1.093291408	-1.467783515
+200	15	1.61364678143237	-0.03519520269	1.094002336	-1.470436734
+205	15	1.66020621687619	-0.1818169052	1.091784878	-1.462161072
+210	15	1.70911268557677	-0.3324378163	1.086335735	-1.441824592
+215	15	1.76009462925491	-0.4860754346	1.077342576	-1.408261666
+220	15	1.81275125230814	-0.6414169810	1.064488014	-1.360287788
+225	15	1.86655232779717	-0.7967808659	1.047471386	-1.296780866
+
+135	10	1.28349223529647	1.400592929	0.8587988321	-0.9005929294
+140	10	1.29734524428539	1.326412549	0.8736609387	-0.9848801245
+145	10	1.31366611390032	1.245748985	0.8877952746	-1.065039926
+150	10	1.33251145611078	1.158620984	0.9011476495	-1.140765008
+155	10	1.35393495066060	1.065028240	0.9136566316	-1.211706971
+160	10	1.37797894731431	0.9649572523	0.9252505857	-1.277459552
+165	10	1.40467716613517	0.8583960997	0.9358465856	-1.337552453
+170	10	1.43405357905616	0.7453491719	0.9453491719	-1.391444298
+175	10	1.46614641809927	0.6258561825	0.9536538995	-1.438542749
+180	10	1.50094500701831	0.5000000000	0.9606363652	-1.478142280
+185	10	1.53844660423091	0.3679374623	0.9661623529	-1.509481713
+190	10	1.57856479992115	0.2299267111	0.9700732889	-1.531661733
+195	10	1.62119306981720	0.08636098955	0.9721998046	-1.543721803
+200	10	1.66622679757171	-0.06221775743	0.9723688652	-1.544680593
+205	10	1.71342623584017	-0.2150522332	0.9703858689	-1.533434463
+210	10	1.76247204316855	-0.3711377801	0.9660518281	-1.508854896
+215	10	1.81297334220135	-0.5291983751	0.9591737908	-1.469847608
+220	10	1.86446286622342	-0.6876680606	0.9495745623	-1.415407678
+225	10	1.91634559614301	-0.8446495793	0.9370980004	-1.344649579
+
+135	5	1.31324602665406	1.426833307	0.7810874074	-0.9268333073
+140	5	1.32978564596926	1.352856492	0.7889230216	-1.016394788
+145	5	1.34870385754763	1.271605772	0.7964096415	-1.101967245
+150	5	1.37003395290345	1.183059163	0.8035072408	-1.183093176
+155	5	1.39386181513831	1.087228349	0.8101758088	-1.259315257
+160	5	1.42019721801524	0.9841028130	0.8163653072	-1.330061547
+165	5	1.44908352615448	0.8737183287	0.8220235703	-1.394735790
+170	5	1.48054237407217	0.7561445037	0.8270919527	-1.452667667
+175	5	1.51457543704122	0.6315054263	0.8315054263	-1.503113901
+180	5	1.55111988036382	0.5000000000	0.8351890053	-1.545217401
+185	5	1.59016518306663	0.3619313735	0.8380686265	-1.578131623
+190	5	1.63157943006702	0.2177249969	0.8400571976	-1.600861093
+195	5	1.67518228928033	0.06797084910	0.8410627615	-1.612354741
+200	5	1.72078631622751	-0.08656465853	0.8409943814	-1.611573154
+205	5	1.76813002175779	-0.2449060312	0.8397593026	-1.597456139
+210	5	1.81680514779380	-0.4058063136	0.8372611879	-1.568902557
+215	5	1.86634884472280	-0.5677551879	0.8334125517	-1.524912443
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+
+
diff --git a/test/Kerr-carpet-mask/emask.xy.asc b/test/Kerr-carpet-mask/emask.xy.asc
new file mode 100644
index 0000000..de5b723
--- /dev/null
+++ b/test/Kerr-carpet-mask/emask.xy.asc
@@ -0,0 +1,1201 @@
+# 2D ASCII output created by CarpetIOASCII
+# created on carbon.aei.mpg.de by jonathan on Jun 09 2006 at 12:59:25
+# parameter filename: "Kerr-carpet-mask.par"
+#
+# SPACEMASK::emask x y (emask)
+#
+# iteration 0
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it	2:tl 3:rl 4:c 5:ml	6:ix 7:iy 8:iz	9:time	10:x 11:y 12:z	13:data
+0	0 0 0 0	0 0 2	0	-3.3 -3.3 0.1	1
+0	0 0 0 0	1 0 2	0	-3.1 -3.3 0.1	1
+0	0 0 0 0	2 0 2	0	-2.9 -3.3 0.1	1
+0	0 0 0 0	3 0 2	0	-2.7 -3.3 0.1	1
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+0	0 0 0 0	29 33 2	0	2.5 3.3 0.1	1
+0	0 0 0 0	30 33 2	0	2.7 3.3 0.1	1
+0	0 0 0 0	31 33 2	0	2.9 3.3 0.1	1
+0	0 0 0 0	32 33 2	0	3.1 3.3 0.1	1
+0	0 0 0 0	33 33 2	0	3.3 3.3 0.1	1
+
+
+
diff --git a/test/Kerr-carpet-mask/emask.xz.asc b/test/Kerr-carpet-mask/emask.xz.asc
new file mode 100644
index 0000000..1158aa7
--- /dev/null
+++ b/test/Kerr-carpet-mask/emask.xz.asc
@@ -0,0 +1,676 @@
+# 2D ASCII output created by CarpetIOASCII
+# created on carbon.aei.mpg.de by jonathan on Jun 09 2006 at 12:59:25
+# parameter filename: "Kerr-carpet-mask.par"
+#
+# SPACEMASK::emask x z (emask)
+#
+# iteration 0
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it	2:tl 3:rl 4:c 5:ml	6:ix 7:iy 8:iz	9:time	10:x 11:y 12:z	13:data
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+0	0 0 0 0	21 17 16	0	0.9 0.1 2.9	1
+0	0 0 0 0	22 17 16	0	1.1 0.1 2.9	1
+0	0 0 0 0	23 17 16	0	1.3 0.1 2.9	1
+0	0 0 0 0	24 17 16	0	1.5 0.1 2.9	1
+0	0 0 0 0	25 17 16	0	1.7 0.1 2.9	1
+0	0 0 0 0	26 17 16	0	1.9 0.1 2.9	1
+0	0 0 0 0	27 17 16	0	2.1 0.1 2.9	1
+0	0 0 0 0	28 17 16	0	2.3 0.1 2.9	1
+0	0 0 0 0	29 17 16	0	2.5 0.1 2.9	1
+0	0 0 0 0	30 17 16	0	2.7 0.1 2.9	1
+0	0 0 0 0	31 17 16	0	2.9 0.1 2.9	1
+0	0 0 0 0	32 17 16	0	3.1 0.1 2.9	1
+0	0 0 0 0	33 17 16	0	3.3 0.1 2.9	1
+
+0	0 0 0 0	0 17 17	0	-3.3 0.1 3.1	1
+0	0 0 0 0	1 17 17	0	-3.1 0.1 3.1	1
+0	0 0 0 0	2 17 17	0	-2.9 0.1 3.1	1
+0	0 0 0 0	3 17 17	0	-2.7 0.1 3.1	1
+0	0 0 0 0	4 17 17	0	-2.5 0.1 3.1	1
+0	0 0 0 0	5 17 17	0	-2.3 0.1 3.1	1
+0	0 0 0 0	6 17 17	0	-2.1 0.1 3.1	1
+0	0 0 0 0	7 17 17	0	-1.9 0.1 3.1	1
+0	0 0 0 0	8 17 17	0	-1.7 0.1 3.1	1
+0	0 0 0 0	9 17 17	0	-1.5 0.1 3.1	1
+0	0 0 0 0	10 17 17	0	-1.3 0.1 3.1	1
+0	0 0 0 0	11 17 17	0	-1.1 0.1 3.1	1
+0	0 0 0 0	12 17 17	0	-0.9 0.1 3.1	1
+0	0 0 0 0	13 17 17	0	-0.7 0.1 3.1	1
+0	0 0 0 0	14 17 17	0	-0.5 0.1 3.1	1
+0	0 0 0 0	15 17 17	0	-0.3 0.1 3.1	1
+0	0 0 0 0	16 17 17	0	-0.1 0.1 3.1	1
+0	0 0 0 0	17 17 17	0	0.1 0.1 3.1	1
+0	0 0 0 0	18 17 17	0	0.3 0.1 3.1	1
+0	0 0 0 0	19 17 17	0	0.5 0.1 3.1	1
+0	0 0 0 0	20 17 17	0	0.7 0.1 3.1	1
+0	0 0 0 0	21 17 17	0	0.9 0.1 3.1	1
+0	0 0 0 0	22 17 17	0	1.1 0.1 3.1	1
+0	0 0 0 0	23 17 17	0	1.3 0.1 3.1	1
+0	0 0 0 0	24 17 17	0	1.5 0.1 3.1	1
+0	0 0 0 0	25 17 17	0	1.7 0.1 3.1	1
+0	0 0 0 0	26 17 17	0	1.9 0.1 3.1	1
+0	0 0 0 0	27 17 17	0	2.1 0.1 3.1	1
+0	0 0 0 0	28 17 17	0	2.3 0.1 3.1	1
+0	0 0 0 0	29 17 17	0	2.5 0.1 3.1	1
+0	0 0 0 0	30 17 17	0	2.7 0.1 3.1	1
+0	0 0 0 0	31 17 17	0	2.9 0.1 3.1	1
+0	0 0 0 0	32 17 17	0	3.1 0.1 3.1	1
+0	0 0 0 0	33 17 17	0	3.3 0.1 3.1	1
+
+0	0 0 0 0	0 17 18	0	-3.3 0.1 3.3	1
+0	0 0 0 0	1 17 18	0	-3.1 0.1 3.3	1
+0	0 0 0 0	2 17 18	0	-2.9 0.1 3.3	1
+0	0 0 0 0	3 17 18	0	-2.7 0.1 3.3	1
+0	0 0 0 0	4 17 18	0	-2.5 0.1 3.3	1
+0	0 0 0 0	5 17 18	0	-2.3 0.1 3.3	1
+0	0 0 0 0	6 17 18	0	-2.1 0.1 3.3	1
+0	0 0 0 0	7 17 18	0	-1.9 0.1 3.3	1
+0	0 0 0 0	8 17 18	0	-1.7 0.1 3.3	1
+0	0 0 0 0	9 17 18	0	-1.5 0.1 3.3	1
+0	0 0 0 0	10 17 18	0	-1.3 0.1 3.3	1
+0	0 0 0 0	11 17 18	0	-1.1 0.1 3.3	1
+0	0 0 0 0	12 17 18	0	-0.9 0.1 3.3	1
+0	0 0 0 0	13 17 18	0	-0.7 0.1 3.3	1
+0	0 0 0 0	14 17 18	0	-0.5 0.1 3.3	1
+0	0 0 0 0	15 17 18	0	-0.3 0.1 3.3	1
+0	0 0 0 0	16 17 18	0	-0.1 0.1 3.3	1
+0	0 0 0 0	17 17 18	0	0.1 0.1 3.3	1
+0	0 0 0 0	18 17 18	0	0.3 0.1 3.3	1
+0	0 0 0 0	19 17 18	0	0.5 0.1 3.3	1
+0	0 0 0 0	20 17 18	0	0.7 0.1 3.3	1
+0	0 0 0 0	21 17 18	0	0.9 0.1 3.3	1
+0	0 0 0 0	22 17 18	0	1.1 0.1 3.3	1
+0	0 0 0 0	23 17 18	0	1.3 0.1 3.3	1
+0	0 0 0 0	24 17 18	0	1.5 0.1 3.3	1
+0	0 0 0 0	25 17 18	0	1.7 0.1 3.3	1
+0	0 0 0 0	26 17 18	0	1.9 0.1 3.3	1
+0	0 0 0 0	27 17 18	0	2.1 0.1 3.3	1
+0	0 0 0 0	28 17 18	0	2.3 0.1 3.3	1
+0	0 0 0 0	29 17 18	0	2.5 0.1 3.3	1
+0	0 0 0 0	30 17 18	0	2.7 0.1 3.3	1
+0	0 0 0 0	31 17 18	0	2.9 0.1 3.3	1
+0	0 0 0 0	32 17 18	0	3.1 0.1 3.3	1
+0	0 0 0 0	33 17 18	0	3.3 0.1 3.3	1
+
+
+
diff --git a/test/Kerr-carpet-mask/emask.yz.asc b/test/Kerr-carpet-mask/emask.yz.asc
new file mode 100644
index 0000000..ac95648
--- /dev/null
+++ b/test/Kerr-carpet-mask/emask.yz.asc
@@ -0,0 +1,676 @@
+# 2D ASCII output created by CarpetIOASCII
+# created on carbon.aei.mpg.de by jonathan on Jun 09 2006 at 12:59:25
+# parameter filename: "Kerr-carpet-mask.par"
+#
+# SPACEMASK::emask y z (emask)
+#
+# iteration 0
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it	2:tl 3:rl 4:c 5:ml	6:ix 7:iy 8:iz	9:time	10:x 11:y 12:z	13:data
+0	0 0 0 0	17 0 0	0	0.1 -3.3 -0.3	1
+0	0 0 0 0	17 1 0	0	0.1 -3.1 -0.3	1
+0	0 0 0 0	17 2 0	0	0.1 -2.9 -0.3	1
+0	0 0 0 0	17 3 0	0	0.1 -2.7 -0.3	1
+0	0 0 0 0	17 4 0	0	0.1 -2.5 -0.3	1
+0	0 0 0 0	17 5 0	0	0.1 -2.3 -0.3	1
+0	0 0 0 0	17 6 0	0	0.1 -2.1 -0.3	1
+0	0 0 0 0	17 7 0	0	0.1 -1.9 -0.3	1
+0	0 0 0 0	17 8 0	0	0.1 -1.7 -0.3	1
+0	0 0 0 0	17 9 0	0	0.1 -1.5 -0.3	1
+0	0 0 0 0	17 10 0	0	0.1 -1.3 -0.3	0.5
+0	0 0 0 0	17 11 0	0	0.1 -1.1 -0.3	0.5
+0	0 0 0 0	17 12 0	0	0.1 -0.9 -0.3	0.5
+0	0 0 0 0	17 13 0	0	0.1 -0.7 -0.3	0.5
+0	0 0 0 0	17 14 0	0	0.1 -0.5 -0.3	0.5
+0	0 0 0 0	17 15 0	0	0.1 -0.3 -0.3	0
+0	0 0 0 0	17 16 0	0	0.1 -0.1 -0.3	0
+0	0 0 0 0	17 17 0	0	0.1 0.1 -0.3	0
+0	0 0 0 0	17 18 0	0	0.1 0.3 -0.3	0
+0	0 0 0 0	17 19 0	0	0.1 0.5 -0.3	0
+0	0 0 0 0	17 20 0	0	0.1 0.7 -0.3	0
+0	0 0 0 0	17 21 0	0	0.1 0.9 -0.3	0.5
+0	0 0 0 0	17 22 0	0	0.1 1.1 -0.3	0.5
+0	0 0 0 0	17 23 0	0	0.1 1.3 -0.3	0.5
+0	0 0 0 0	17 24 0	0	0.1 1.5 -0.3	0.5
+0	0 0 0 0	17 25 0	0	0.1 1.7 -0.3	1
+0	0 0 0 0	17 26 0	0	0.1 1.9 -0.3	1
+0	0 0 0 0	17 27 0	0	0.1 2.1 -0.3	1
+0	0 0 0 0	17 28 0	0	0.1 2.3 -0.3	1
+0	0 0 0 0	17 29 0	0	0.1 2.5 -0.3	1
+0	0 0 0 0	17 30 0	0	0.1 2.7 -0.3	1
+0	0 0 0 0	17 31 0	0	0.1 2.9 -0.3	1
+0	0 0 0 0	17 32 0	0	0.1 3.1 -0.3	1
+0	0 0 0 0	17 33 0	0	0.1 3.3 -0.3	1
+
+0	0 0 0 0	17 0 1	0	0.1 -3.3 -0.1	1
+0	0 0 0 0	17 1 1	0	0.1 -3.1 -0.1	1
+0	0 0 0 0	17 2 1	0	0.1 -2.9 -0.1	1
+0	0 0 0 0	17 3 1	0	0.1 -2.7 -0.1	1
+0	0 0 0 0	17 4 1	0	0.1 -2.5 -0.1	1
+0	0 0 0 0	17 5 1	0	0.1 -2.3 -0.1	1
+0	0 0 0 0	17 6 1	0	0.1 -2.1 -0.1	1
+0	0 0 0 0	17 7 1	0	0.1 -1.9 -0.1	1
+0	0 0 0 0	17 8 1	0	0.1 -1.7 -0.1	1
+0	0 0 0 0	17 9 1	0	0.1 -1.5 -0.1	1
+0	0 0 0 0	17 10 1	0	0.1 -1.3 -0.1	0.5
+0	0 0 0 0	17 11 1	0	0.1 -1.1 -0.1	0.5
+0	0 0 0 0	17 12 1	0	0.1 -0.9 -0.1	0.5
+0	0 0 0 0	17 13 1	0	0.1 -0.7 -0.1	0.5
+0	0 0 0 0	17 14 1	0	0.1 -0.5 -0.1	0.5
+0	0 0 0 0	17 15 1	0	0.1 -0.3 -0.1	0
+0	0 0 0 0	17 16 1	0	0.1 -0.1 -0.1	0
+0	0 0 0 0	17 17 1	0	0.1 0.1 -0.1	0
+0	0 0 0 0	17 18 1	0	0.1 0.3 -0.1	0
+0	0 0 0 0	17 19 1	0	0.1 0.5 -0.1	0
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+0	0 0 0 0	17 21 1	0	0.1 0.9 -0.1	0.5
+0	0 0 0 0	17 22 1	0	0.1 1.1 -0.1	0.5
+0	0 0 0 0	17 23 1	0	0.1 1.3 -0.1	0.5
+0	0 0 0 0	17 24 1	0	0.1 1.5 -0.1	0.5
+0	0 0 0 0	17 25 1	0	0.1 1.7 -0.1	1
+0	0 0 0 0	17 26 1	0	0.1 1.9 -0.1	1
+0	0 0 0 0	17 27 1	0	0.1 2.1 -0.1	1
+0	0 0 0 0	17 28 1	0	0.1 2.3 -0.1	1
+0	0 0 0 0	17 29 1	0	0.1 2.5 -0.1	1
+0	0 0 0 0	17 30 1	0	0.1 2.7 -0.1	1
+0	0 0 0 0	17 31 1	0	0.1 2.9 -0.1	1
+0	0 0 0 0	17 32 1	0	0.1 3.1 -0.1	1
+0	0 0 0 0	17 33 1	0	0.1 3.3 -0.1	1
+
+0	0 0 0 0	17 0 2	0	0.1 -3.3 0.1	1
+0	0 0 0 0	17 1 2	0	0.1 -3.1 0.1	1
+0	0 0 0 0	17 2 2	0	0.1 -2.9 0.1	1
+0	0 0 0 0	17 3 2	0	0.1 -2.7 0.1	1
+0	0 0 0 0	17 4 2	0	0.1 -2.5 0.1	1
+0	0 0 0 0	17 5 2	0	0.1 -2.3 0.1	1
+0	0 0 0 0	17 6 2	0	0.1 -2.1 0.1	1
+0	0 0 0 0	17 7 2	0	0.1 -1.9 0.1	1
+0	0 0 0 0	17 8 2	0	0.1 -1.7 0.1	1
+0	0 0 0 0	17 9 2	0	0.1 -1.5 0.1	1
+0	0 0 0 0	17 10 2	0	0.1 -1.3 0.1	0.5
+0	0 0 0 0	17 11 2	0	0.1 -1.1 0.1	0.5
+0	0 0 0 0	17 12 2	0	0.1 -0.9 0.1	0.5
+0	0 0 0 0	17 13 2	0	0.1 -0.7 0.1	0.5
+0	0 0 0 0	17 14 2	0	0.1 -0.5 0.1	0.5
+0	0 0 0 0	17 15 2	0	0.1 -0.3 0.1	0
+0	0 0 0 0	17 16 2	0	0.1 -0.1 0.1	0
+0	0 0 0 0	17 17 2	0	0.1 0.1 0.1	0
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+0	0 0 0 0	17 19 2	0	0.1 0.5 0.1	0
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+0	0 0 0 0	17 22 2	0	0.1 1.1 0.1	0.5
+0	0 0 0 0	17 23 2	0	0.1 1.3 0.1	0.5
+0	0 0 0 0	17 24 2	0	0.1 1.5 0.1	0.5
+0	0 0 0 0	17 25 2	0	0.1 1.7 0.1	1
+0	0 0 0 0	17 26 2	0	0.1 1.9 0.1	1
+0	0 0 0 0	17 27 2	0	0.1 2.1 0.1	1
+0	0 0 0 0	17 28 2	0	0.1 2.3 0.1	1
+0	0 0 0 0	17 29 2	0	0.1 2.5 0.1	1
+0	0 0 0 0	17 30 2	0	0.1 2.7 0.1	1
+0	0 0 0 0	17 31 2	0	0.1 2.9 0.1	1
+0	0 0 0 0	17 32 2	0	0.1 3.1 0.1	1
+0	0 0 0 0	17 33 2	0	0.1 3.3 0.1	1
+
+0	0 0 0 0	17 0 3	0	0.1 -3.3 0.3	1
+0	0 0 0 0	17 1 3	0	0.1 -3.1 0.3	1
+0	0 0 0 0	17 2 3	0	0.1 -2.9 0.3	1
+0	0 0 0 0	17 3 3	0	0.1 -2.7 0.3	1
+0	0 0 0 0	17 4 3	0	0.1 -2.5 0.3	1
+0	0 0 0 0	17 5 3	0	0.1 -2.3 0.3	1
+0	0 0 0 0	17 6 3	0	0.1 -2.1 0.3	1
+0	0 0 0 0	17 7 3	0	0.1 -1.9 0.3	1
+0	0 0 0 0	17 8 3	0	0.1 -1.7 0.3	1
+0	0 0 0 0	17 9 3	0	0.1 -1.5 0.3	1
+0	0 0 0 0	17 10 3	0	0.1 -1.3 0.3	0.5
+0	0 0 0 0	17 11 3	0	0.1 -1.1 0.3	0.5
+0	0 0 0 0	17 12 3	0	0.1 -0.9 0.3	0.5
+0	0 0 0 0	17 13 3	0	0.1 -0.7 0.3	0.5
+0	0 0 0 0	17 14 3	0	0.1 -0.5 0.3	0.5
+0	0 0 0 0	17 15 3	0	0.1 -0.3 0.3	0
+0	0 0 0 0	17 16 3	0	0.1 -0.1 0.3	0
+0	0 0 0 0	17 17 3	0	0.1 0.1 0.3	0
+0	0 0 0 0	17 18 3	0	0.1 0.3 0.3	0
+0	0 0 0 0	17 19 3	0	0.1 0.5 0.3	0
+0	0 0 0 0	17 20 3	0	0.1 0.7 0.3	0
+0	0 0 0 0	17 21 3	0	0.1 0.9 0.3	0.5
+0	0 0 0 0	17 22 3	0	0.1 1.1 0.3	0.5
+0	0 0 0 0	17 23 3	0	0.1 1.3 0.3	0.5
+0	0 0 0 0	17 24 3	0	0.1 1.5 0.3	0.5
+0	0 0 0 0	17 25 3	0	0.1 1.7 0.3	1
+0	0 0 0 0	17 26 3	0	0.1 1.9 0.3	1
+0	0 0 0 0	17 27 3	0	0.1 2.1 0.3	1
+0	0 0 0 0	17 28 3	0	0.1 2.3 0.3	1
+0	0 0 0 0	17 29 3	0	0.1 2.5 0.3	1
+0	0 0 0 0	17 30 3	0	0.1 2.7 0.3	1
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+0	0 0 0 0	17 32 3	0	0.1 3.1 0.3	1
+0	0 0 0 0	17 33 3	0	0.1 3.3 0.3	1
+
+0	0 0 0 0	17 0 4	0	0.1 -3.3 0.5	1
+0	0 0 0 0	17 1 4	0	0.1 -3.1 0.5	1
+0	0 0 0 0	17 2 4	0	0.1 -2.9 0.5	1
+0	0 0 0 0	17 3 4	0	0.1 -2.7 0.5	1
+0	0 0 0 0	17 4 4	0	0.1 -2.5 0.5	1
+0	0 0 0 0	17 5 4	0	0.1 -2.3 0.5	1
+0	0 0 0 0	17 6 4	0	0.1 -2.1 0.5	1
+0	0 0 0 0	17 7 4	0	0.1 -1.9 0.5	1
+0	0 0 0 0	17 8 4	0	0.1 -1.7 0.5	1
+0	0 0 0 0	17 9 4	0	0.1 -1.5 0.5	1
+0	0 0 0 0	17 10 4	0	0.1 -1.3 0.5	1
+0	0 0 0 0	17 11 4	0	0.1 -1.1 0.5	0.5
+0	0 0 0 0	17 12 4	0	0.1 -0.9 0.5	0.5
+0	0 0 0 0	17 13 4	0	0.1 -0.7 0.5	0.5
+0	0 0 0 0	17 14 4	0	0.1 -0.5 0.5	0.5
+0	0 0 0 0	17 15 4	0	0.1 -0.3 0.5	0.5
+0	0 0 0 0	17 16 4	0	0.1 -0.1 0.5	0
+0	0 0 0 0	17 17 4	0	0.1 0.1 0.5	0
+0	0 0 0 0	17 18 4	0	0.1 0.3 0.5	0
+0	0 0 0 0	17 19 4	0	0.1 0.5 0.5	0
+0	0 0 0 0	17 20 4	0	0.1 0.7 0.5	0.5
+0	0 0 0 0	17 21 4	0	0.1 0.9 0.5	0.5
+0	0 0 0 0	17 22 4	0	0.1 1.1 0.5	0.5
+0	0 0 0 0	17 23 4	0	0.1 1.3 0.5	0.5
+0	0 0 0 0	17 24 4	0	0.1 1.5 0.5	0.5
+0	0 0 0 0	17 25 4	0	0.1 1.7 0.5	1
+0	0 0 0 0	17 26 4	0	0.1 1.9 0.5	1
+0	0 0 0 0	17 27 4	0	0.1 2.1 0.5	1
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+0	0 0 0 0	17 32 4	0	0.1 3.1 0.5	1
+0	0 0 0 0	17 33 4	0	0.1 3.3 0.5	1
+
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+0	0 0 0 0	17 2 5	0	0.1 -2.9 0.7	1
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+0	0 0 0 0	17 4 5	0	0.1 -2.5 0.7	1
+0	0 0 0 0	17 5 5	0	0.1 -2.3 0.7	1
+0	0 0 0 0	17 6 5	0	0.1 -2.1 0.7	1
+0	0 0 0 0	17 7 5	0	0.1 -1.9 0.7	1
+0	0 0 0 0	17 8 5	0	0.1 -1.7 0.7	1
+0	0 0 0 0	17 9 5	0	0.1 -1.5 0.7	1
+0	0 0 0 0	17 10 5	0	0.1 -1.3 0.7	1
+0	0 0 0 0	17 11 5	0	0.1 -1.1 0.7	0.5
+0	0 0 0 0	17 12 5	0	0.1 -0.9 0.7	0.5
+0	0 0 0 0	17 13 5	0	0.1 -0.7 0.7	0.5
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+0	0 0 0 0	17 17 5	0	0.1 0.1 0.7	0.5
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author	jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5>	2006-06-09 11:00:47 +0000
committer	jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5>	2006-06-09 11:00:47 +0000
commit	49e55a961198c44b9930d3f04a46684d9daf1f8f (patch)
tree	33a6176231fd8a46d99f762453ceac0ce8db3bbb /test
parent	fe4e962d3e30527e164e194af8f360c701134e04 (diff)