From e159c70495cde6299adedb5e025c679263f170cf Mon Sep 17 00:00:00 2001
From: Matthias Boljen <2501-mboljen@users.noreply.gitlab.cc-asp.fraunhofer.de>
Date: Tue, 6 Aug 2024 20:45:48 +0200
Subject: [PATCH] Add option widths

---
 README.md          | 187 ++++++++--------
 bin/mkgrid         |  75 +++++--
 test/Makefile      |   6 +-
 test/testdata2.csv |  20 +-
 test/testdata3.csv |  62 +++---
 test/testdata4.csv | 534 ++++++++++++++++++++++-----------------------
 test/testdata4.png | Bin 171887 -> 169723 bytes
 7 files changed, 463 insertions(+), 421 deletions(-)

diff --git a/README.md b/README.md
index 9104c6a..6257eef 100644
--- a/README.md
+++ b/README.md
@@ -33,6 +33,10 @@ If output file `OUTFILE` is undefined, the output is directed to `STDOUT`.
 
   Set the filename of the input spreadsheet.
 
+- **-w**, **-\-width** *WIDTHS*
+
+  Set comma-separated list of column widths of the input spreadsheet if auto-detection fails.
+
 - **-m**, **-\-method** *METHOD*
 
   Set the interpolation method.  Select one of the following: `linear` (default), `nearest`, `cubic`.  The following options are available for 2D data only: `nearest-up`, `zero`, `slinear`, `quadratic`, `previous`, `next`.
@@ -65,44 +69,44 @@ If output file `OUTFILE` is undefined, the output is directed to `STDOUT`.
 Assume the following input file `testdata2.csv` containing scattered data points in 2D: 
 
 ```text
-           x            y
-       0.005        0.615
-       0.014        2.935
-       0.019        4.712
-       0.038       13.814
-       0.064       24.658
-       0.076       29.594
-       0.095       39.155
-       0.125       59.091
-       0.145       77.677
+         X         Y
+     0.005     0.615
+     0.014     2.935
+     0.019     4.712
+     0.038    13.814
+     0.064    24.658
+     0.076    29.594
+     0.095    39.155
+     0.125    59.091
+     0.145    77.677
 ```
 
 The following command will parse the file above and produce regular gridded data points using cubic spline interpolation along the first column in the interval `[0.0,0.15]` using `15` steps, i.e. every increment of `0.01` a data point is interpolated in the second column.
 
 ```bash
-$ mkgrid --infile testdata2.csv --range 0:0.15 --steps 15 --method cubic
+$ mkgrid -i testdata2.csv -r 0:0.15 -s 15 -m cubic
 ```
 
 The output will look like the following:
 
 ```text
-           x            y
-       0.000       -0.297
-       0.010        1.780
-       0.020        5.116
-       0.030        9.812
-       0.040       14.762
-       0.050       19.119
-       0.060       23.094
-       0.070       27.051
-       0.080       31.418
-       0.090       36.432
-       0.100       42.011
-       0.110       48.205
-       0.120       55.215
-       0.130       63.249
-       0.140       72.516
-       0.150       83.224
+         X         Y
+     0.000    -0.297
+     0.010     1.780
+     0.020     5.116
+     0.030     9.812
+     0.040    14.762
+     0.050    19.119
+     0.060    23.094
+     0.070    27.051
+     0.080    31.418
+     0.090    36.432
+     0.100    42.011
+     0.110    48.205
+     0.120    55.215
+     0.130    63.249
+     0.140    72.516
+     0.150    83.224
 ```
 
 An example plot for the above result would look like this:
@@ -114,69 +118,74 @@ An example plot for the above result would look like this:
 Assume the following input file `testdata3.csv` containing scattered data points in 3D:
 
 ```text
-           x            y            z
-       0.000        0.000        0.000
-       0.019        0.000        4.712
-       0.042        0.000       15.976
-       0.092        0.000       37.076
-       0.109        0.000       47.519
-       0.136        0.000       68.049
-       0.009        0.001        2.413
-       0.026        0.005       11.605
-       0.094        0.032       43.647
-       0.106        0.037       51.925
-       0.134        0.052       76.073
-       0.004        0.004        2.127
-       0.025        0.026       17.043
-       0.059        0.061       30.732
-       0.093        0.095       52.012
-       0.102        0.103       59.315
-       0.113        0.113       68.501
-       0.132        0.132       87.946
-       0.003        0.009        2.752
-       0.007        0.021        8.035
-       0.011        0.033       12.049
-       0.022        0.066       18.954
-       0.040        0.109       27.913
-       0.046        0.122       31.549
-       0.052        0.132       34.542
-       0.000        0.023        5.569
-       0.000        0.072       11.650
-       0.000        0.091       13.370
-       0.000        0.115       15.056
-       0.000        0.134       16.302
+         X         Y         Z
+     0.000     0.000     0.000
+     0.019     0.000     4.712
+     0.042     0.000    15.976
+     0.092     0.000    37.076
+     0.109     0.000    47.519
+     0.136     0.000    68.049
+
+     0.009     0.001     2.413
+     0.026     0.005    11.605
+     0.094     0.032    43.647
+     0.106     0.037    51.925
+     0.134     0.052    76.073
+
+     0.004     0.004     2.127
+     0.025     0.026    17.043
+     0.059     0.061    30.732
+     0.093     0.095    52.012
+     0.102     0.103    59.315
+     0.113     0.113    68.501
+     0.132     0.132    87.946
+
+     0.003     0.009     2.752
+     0.007     0.021     8.035
+     0.011     0.033    12.049
+     0.022     0.066    18.954
+     0.040     0.109    27.913
+     0.046     0.122    31.549
+     0.052     0.132    34.542
+
+     0.000     0.023     5.569
+     0.000     0.072    11.650
+     0.000     0.091    13.370
+     0.000     0.115    15.056
+     0.000     0.134    16.302
 ```
 
 The following command will parse the above input file and creates regular gridded data points along data columns 1 and 2 within the interval `[0.0,0.13]` in both dimensions.  The corresponding data in column 3 will be interpolated using `13` steps, i.e. `(13+1)×(13+1)=196` records will be created in total.
 
 ```bash
-$ mkgrid --infile testdata3.csv --range 0:0.13,0:0.13 --steps 13
+$ mkgrid -i testdata3.csv -r 0:0.13,0:0.13 -s 13
 ```
 
 The output will look like the following:
 
 ```text
-           x            y            z
-       0.000        0.000        0.000
-       0.010        0.000        2.480
-       0.020        0.000        5.202
-       0.030        0.000       10.099
-       0.040        0.000       14.997
-       0.050        0.000       19.352
-       0.060        0.000       23.572
-       0.070        0.000       27.792
-       0.080        0.000       32.012
-       0.090        0.000       36.232
-       0.100        0.000       41.990
-       0.110        0.000       48.279
-       0.120        0.000       55.883
-       0.130        0.000       63.487
-       0.000        0.010        2.421
-       0.010        0.010        5.438
-       0.020        0.010       10.451
-       0.030        0.010       14.423
-       0.040        0.010       17.364
-       0.050        0.010       20.807
+         X         Y         Z
+     0.000     0.000     0.000
+     0.010     0.000     2.480
+     0.020     0.000     5.202
+     0.030     0.000    10.099
+     0.040     0.000    14.997
+     0.050     0.000    19.352
+     0.060     0.000    23.572
+     0.070     0.000    27.792
+     0.080     0.000    32.012
+     0.090     0.000    36.232
+     0.100     0.000    41.990
+     0.110     0.000    48.279
+     0.120     0.000    55.883
+     0.130     0.000    63.487
+
+     0.000     0.010     2.421
+     0.010     0.010     5.438
+     0.020     0.010    10.451
+     0.030     0.010    14.423
+     0.040     0.010    17.364
+     0.050     0.010    20.807
 [...]
 ```
 An example plot for the above would look like this:
@@ -188,14 +197,14 @@ An example plot for the above would look like this:
 Assume an input file `testdata4.csv` containing 4 columns of scattered input data.  In this example, columns 1-3 describe spatial coordinates on the surface of a sphere wheras column 4 holds the surface temperature of that point:
 
 ```text
-          x          y          z          T
-      0.000      0.000     10.000        0.0
-      2.588      0.000      9.659        7.8
-      5.000      0.000      8.660       15.0
-      7.071      0.000      7.071       21.2
-      8.660      0.000      5.000       26.0
-      9.659      0.000      2.588       29.0
-     10.000      0.000      0.000       30.0
+         X         Y         Z         T
+     0.000     0.000    10.000       0.0
+     2.588     0.000     9.659       7.8
+     5.000     0.000     8.660      15.0
+     7.071     0.000     7.071      21.2
+     8.660     0.000     5.000      26.0
+     9.659     0.000     2.588      29.0
+    10.000     0.000     0.000      30.0
 [...]
 ```
 
diff --git a/bin/mkgrid b/bin/mkgrid
index 6390124..745675e 100755
--- a/bin/mkgrid
+++ b/bin/mkgrid
@@ -1,7 +1,7 @@
 #!/usr/bin/env python3
 #
 # Created:   Mon 2024-07-15 18:40:27 CEST (boljen)
-# Modified:  So 2024-07-21 12:10:54 CEST (boljen)
+# Modified:  Tue 2024-08-06 20:17:12 CEST (boljen)
 #
 # mkgrid:
 #   Convert scattered data to regular gridded data in 2D, 3D and 4D
@@ -42,14 +42,15 @@ def execute_main():
         description='Convert scattered data to regular gridded data in 2D, 3D and 4D')
 
     # Add options
-    parser.add_argument('-i', '--infile',  help='Input filename', type=str, required=True)
-    parser.add_argument('-m', '--method',  help='Interpolation method', type=str, default='linear', choices=method.keys())
-    parser.add_argument('-p', '--plot',    help='Plot filename', nargs='?', const='***', type=str, default=None)
-    parser.add_argument('-u', '--usecols', help='Comma-separated list of data columns to use from input file', type=str, default=None)
-    parser.add_argument('-r', '--range',   help='Comma-separated list of range specifiers for output', type=str, default=None)
-    parser.add_argument('-s', '--steps',   help='Comma-separated list of discretization steps', type=str, default=None)
-    parser.add_argument('-y', '--yes',     help='Overwrite existing output file', default=False, action=argparse.BooleanOptionalAction)
-    parser.add_argument('outfile',         help='Output filename', nargs='?', type=str, default=sys.stdout.buffer)
+    parser.add_argument('-i', '--infile',   help='Input filename', type=str, required=True)
+    parser.add_argument('-m', '--method',   help='Interpolation method', type=str, default='linear', choices=method.keys())
+    parser.add_argument('-p', '--plot',     help='Plot filename', nargs='?', const='***', type=str, default=None)
+    parser.add_argument('-u', '--usecols',  help='Comma-separated list of data columns to use from input file', type=str, default=None)
+    parser.add_argument('-r', '--range',    help='Comma-separated list of range specifiers for output', type=str, default=None)
+    parser.add_argument('-s', '--steps',    help='Comma-separated list of discretization steps', type=str, default=None)
+    parser.add_argument('-w', '--widths',   help='Comma-separated list of column widths', type=str, default=None)
+    parser.add_argument('-y', '--yes',      help='Overwrite existing output file', default=False, action=argparse.BooleanOptionalAction)
+    parser.add_argument('outfile',          help='Output filename', nargs='?', type=str, default=sys.stdout.buffer)
 
     # Parse options
     args = parser.parse_args()
@@ -58,14 +59,33 @@ def execute_main():
     if args.outfile != sys.stdout.buffer and os.path.exists(args.outfile) and not args.yes:
         raise ValueError("File {:s} exists".format(args.outfile))
 
-    # Read input file
-    df = pd.read_fwf(args.infile)
+    if args.widths is None:
+
+        # Initialize list
+        widths = None
+
+    else:
+
+        # Split widths string in list of comma-seperated tokens
+        widths = [ x.strip() for x in args.widths.split(',') ]
+
+        # Loop over tokens
+        for i,x in enumerate(widths):
+
+            # Assert boundary values are floating-point data
+            try:
+                widths[i] = int(x)
+            except:
+                raise ValueError('Invalid token {:s} in widths list'.format(x))
+
+    # Read from input file
+    df = pd.read_fwf(args.infile, widths=widths, comment="#", skip_empty_rows=True)
     data = df.to_dict('list')
 
     # Initialize column list
     usecols = None
 
-    # Parse --usecols
+    # Parse usecols argument
     if args.usecols is None:
 
         # Use all available columns unless otherwise defined
@@ -75,6 +95,7 @@ def execute_main():
 
         # Use columns specified by comma-separated list only
         usecols = [ x.strip() for x in args.usecols.split(',') ]
+
         # Convert strings to integers
         for i,x in enumerate(usecols):
             try:
@@ -99,7 +120,7 @@ def execute_main():
     # Initialize range lists
     myrange = []
 
-    # Parse --range
+    # Parse range argument
     if args.range is not None:
 
         # Split comma-separated list of values
@@ -154,8 +175,12 @@ def execute_main():
             except:
                 raise ValueError('Invalid token {:s} in steps list'.format(x))
 
-    # Initialize labels list
+    # Initialize labels and formats list
     label = []
+    fmtlist = []
+
+    # Assemble header
+    headstr = ''
 
     # Loop over columns
     for i,x in enumerate(usecols):
@@ -163,6 +188,20 @@ def execute_main():
         # Assign column label
         label.append(df.columns[usecols[i]])
 
+        # Auto-determine column width
+        width = max(len(label[-1]),12)
+        if widths is not None and widths[usecols[i]] > width:
+            width = widths[usecols[i]]
+
+        # Set format string
+        fmtstr = '%{:d}.{:d}f'.format(width,width-6)
+        fmtlist.append(fmtstr)
+
+        # Set header
+        if headstr != '': headstr += ' '
+        fmtstr = '{:>' + '{:d}s'.format(width) + '}'
+        headstr += fmtstr.format(df.columns[usecols[i]])
+
         # Auto-detect array value
         if i >= len(steps):
             # Apply default or last element value
@@ -254,14 +293,8 @@ def execute_main():
         for i,j,k,l in np.nditer([xi,yi,zi,ci]):
             xout.append([i,j,k,l])
 
-    # Assemble header
-    headstr = ''
-    for i in label:
-        if headstr != '': headstr += ' '
-        headstr += '{:>16s}'.format(i)
-
     # Save regular gridded data to output file
-    np.savetxt(args.outfile, xout, header=headstr, comments='', fmt='%16.7f')
+    np.savetxt(args.outfile, xout, header=headstr, comments='', fmt=fmtlist)
 
     # =================
     #    Create plot
diff --git a/test/Makefile b/test/Makefile
index bd2de87..370e134 100644
--- a/test/Makefile
+++ b/test/Makefile
@@ -5,13 +5,13 @@ OUTFILES = $(addsuffix .out, testdata2 testdata3 testdata4)
 default: $(OUTFILES)
 
 testdata2.out: testdata2.csv
-	$(MKGRID) -y -i $< -p $(subst .csv,.png,$<) -s 15 -r 0:0.15 -m cubic $@
+	$(MKGRID) -y -i $< -p $(subst .csv,.png,$<) -s 15 -r 0:0.15 -m cubic -w 12,12 $@
 
 testdata3.out: testdata3.csv
-	$(MKGRID) -y -i $< -p $(subst .csv,.png,$<) -s 13 -r 0:0.13,0:0.13 $@
+	$(MKGRID) -y -i $< -p $(subst .csv,.png,$<) -s 13 -r 0:0.13,0:0.13 -w 12,12,12 $@
 
 testdata4.out: testdata4.csv
-	$(MKGRID) -y -i $< -p $(subst .csv,.png,$<) -s 10 -u 4,5,6,7 $@
+	$(MKGRID) -y -i $< -p $(subst .csv,.png,$<) -s 10 -u 4,5,6,7 -w 10,10,10,10,10,10,10 $@
 
 clean:
 	$(RM) $(OUTFILES) $(subst .out,.png,$(OUTFILES))
diff --git a/test/testdata2.csv b/test/testdata2.csv
index 774c0d3..c757038 100644
--- a/test/testdata2.csv
+++ b/test/testdata2.csv
@@ -1,10 +1,10 @@
-           x            y
-       0.005        0.615
-       0.014        2.935
-       0.019        4.712
-       0.038       13.814
-       0.064       24.658
-       0.076       29.594
-       0.095       39.155
-       0.125       59.091
-       0.145       77.677
+           x           y
+       0.005       0.615
+       0.014       2.935
+       0.019       4.712
+       0.038      13.814
+       0.064      24.658
+       0.076      29.594
+       0.095      39.155
+       0.125      59.091
+       0.145      77.677
diff --git a/test/testdata3.csv b/test/testdata3.csv
index cb7b804..0765956 100644
--- a/test/testdata3.csv
+++ b/test/testdata3.csv
@@ -1,31 +1,31 @@
-           x            y            z
-       0.000        0.000        0.000
-       0.019        0.000        4.712
-       0.042        0.000       15.976
-       0.092        0.000       37.076
-       0.109        0.000       47.519
-       0.136        0.000       68.049
-       0.009        0.001        2.413
-       0.026        0.005       11.605
-       0.094        0.032       43.647
-       0.106        0.037       51.925
-       0.134        0.052       76.073
-       0.004        0.004        2.127
-       0.025        0.026       17.043
-       0.059        0.061       30.732
-       0.093        0.095       52.012
-       0.102        0.103       59.315
-       0.113        0.113       68.501
-       0.132        0.132       87.946
-       0.003        0.009        2.752
-       0.007        0.021        8.035
-       0.011        0.033       12.049
-       0.022        0.066       18.954
-       0.040        0.109       27.913
-       0.046        0.122       31.549
-       0.052        0.132       34.542
-       0.000        0.023        5.569
-       0.000        0.072       11.650
-       0.000        0.091       13.370
-       0.000        0.115       15.056
-       0.000        0.134       16.302
+           x           y           z
+       0.000       0.000       0.000
+       0.019       0.000       4.712
+       0.042       0.000      15.976
+       0.092       0.000      37.076
+       0.109       0.000      47.519
+       0.136       0.000      68.049
+       0.009       0.001       2.413
+       0.026       0.005      11.605
+       0.094       0.032      43.647
+       0.106       0.037      51.925
+       0.134       0.052      76.073
+       0.004       0.004       2.127
+       0.025       0.026      17.043
+       0.059       0.061      30.732
+       0.093       0.095      52.012
+       0.102       0.103      59.315
+       0.113       0.113      68.501
+       0.132       0.132      87.946
+       0.003       0.009       2.752
+       0.007       0.021       8.035
+       0.011       0.033      12.049
+       0.022       0.066      18.954
+       0.040       0.109      27.913
+       0.046       0.122      31.549
+       0.052       0.132      34.542
+       0.000       0.023       5.569
+       0.000       0.072      11.650
+       0.000       0.091      13.370
+       0.000       0.115      15.056
+       0.000       0.134      16.302
diff --git a/test/testdata4.csv b/test/testdata4.csv
index 17edfff..a4a8bf5 100644
--- a/test/testdata4.csv
+++ b/test/testdata4.csv
@@ -1,290 +1,290 @@
-          r      theta        phi          x          y          z          T
-       10.0        0.0        0.0      0.000      0.000     10.000        0.0
-       10.0       15.0        0.0      2.588      0.000      9.659        7.8
-       10.0       30.0        0.0      5.000      0.000      8.660       15.0
-       10.0       45.0        0.0      7.071      0.000      7.071       21.2
-       10.0       60.0        0.0      8.660      0.000      5.000       26.0
-       10.0       75.0        0.0      9.659      0.000      2.588       29.0
-       10.0       90.0        0.0     10.000      0.000      0.000       30.0
-       10.0      105.0        0.0      9.659      0.000     -2.588       29.0
-       10.0      120.0        0.0      8.660      0.000     -5.000       26.0
-       10.0      135.0        0.0      7.071      0.000     -7.071       21.2
-       10.0      150.0        0.0      5.000      0.000     -8.660       15.0
-       10.0      165.0        0.0      2.588      0.000     -9.659        7.8
-       10.0      180.0        0.0      0.000      0.000    -10.000        0.0
+         r     theta       phi         x         y         z         T
+      10.0       0.0       0.0     0.000     0.000    10.000       0.0
+      10.0      15.0       0.0     2.588     0.000     9.659       7.8
+      10.0      30.0       0.0     5.000     0.000     8.660      15.0
+      10.0      45.0       0.0     7.071     0.000     7.071      21.2
+      10.0      60.0       0.0     8.660     0.000     5.000      26.0
+      10.0      75.0       0.0     9.659     0.000     2.588      29.0
+      10.0      90.0       0.0    10.000     0.000     0.000      30.0
+      10.0     105.0       0.0     9.659     0.000    -2.588      29.0
+      10.0     120.0       0.0     8.660     0.000    -5.000      26.0
+      10.0     135.0       0.0     7.071     0.000    -7.071      21.2
+      10.0     150.0       0.0     5.000     0.000    -8.660      15.0
+      10.0     165.0       0.0     2.588     0.000    -9.659       7.8
+      10.0     180.0       0.0     0.000     0.000   -10.000       0.0
 
-       10.0       15.0       15.0      2.500      0.670      9.659        7.8
-       10.0       30.0       15.0      4.830      1.294      8.660       15.0
-       10.0       45.0       15.0      6.830      1.830      7.071       21.2
-       10.0       60.0       15.0      8.365      2.241      5.000       26.0
-       10.0       75.0       15.0      9.330      2.500      2.588       29.0
-       10.0       90.0       15.0      9.659      2.588      0.000       30.0
-       10.0      105.0       15.0      9.330      2.500     -2.588       29.0
-       10.0      120.0       15.0      8.365      2.241     -5.000       26.0
-       10.0      135.0       15.0      6.830      1.830     -7.071       21.2
-       10.0      150.0       15.0      4.830      1.294     -8.660       15.0
-       10.0      165.0       15.0      2.500      0.670     -9.659        7.8
+      10.0      15.0      15.0     2.500     0.670     9.659       7.8
+      10.0      30.0      15.0     4.830     1.294     8.660      15.0
+      10.0      45.0      15.0     6.830     1.830     7.071      21.2
+      10.0      60.0      15.0     8.365     2.241     5.000      26.0
+      10.0      75.0      15.0     9.330     2.500     2.588      29.0
+      10.0      90.0      15.0     9.659     2.588     0.000      30.0
+      10.0     105.0      15.0     9.330     2.500    -2.588      29.0
+      10.0     120.0      15.0     8.365     2.241    -5.000      26.0
+      10.0     135.0      15.0     6.830     1.830    -7.071      21.2
+      10.0     150.0      15.0     4.830     1.294    -8.660      15.0
+      10.0     165.0      15.0     2.500     0.670    -9.659       7.8
 
-       10.0       15.0       30.0      2.241      1.294      9.659        7.8
-       10.0       30.0       30.0      4.330      2.500      8.660       15.0
-       10.0       45.0       30.0      6.124      3.536      7.071       21.2
-       10.0       60.0       30.0      7.500      4.330      5.000       26.0
-       10.0       75.0       30.0      8.365      4.830      2.588       29.0
-       10.0       90.0       30.0      8.660      5.000      0.000       30.0
-       10.0      105.0       30.0      8.365      4.830     -2.588       29.0
-       10.0      120.0       30.0      7.500      4.330     -5.000       26.0
-       10.0      135.0       30.0      6.124      3.536     -7.071       21.2
-       10.0      150.0       30.0      4.330      2.500     -8.660       15.0
-       10.0      165.0       30.0      2.241      1.294     -9.659        7.8
+      10.0      15.0      30.0     2.241     1.294     9.659       7.8
+      10.0      30.0      30.0     4.330     2.500     8.660      15.0
+      10.0      45.0      30.0     6.124     3.536     7.071      21.2
+      10.0      60.0      30.0     7.500     4.330     5.000      26.0
+      10.0      75.0      30.0     8.365     4.830     2.588      29.0
+      10.0      90.0      30.0     8.660     5.000     0.000      30.0
+      10.0     105.0      30.0     8.365     4.830    -2.588      29.0
+      10.0     120.0      30.0     7.500     4.330    -5.000      26.0
+      10.0     135.0      30.0     6.124     3.536    -7.071      21.2
+      10.0     150.0      30.0     4.330     2.500    -8.660      15.0
+      10.0     165.0      30.0     2.241     1.294    -9.659       7.8
 
-       10.0       15.0       45.0      1.830      1.830      9.659        7.8
-       10.0       30.0       45.0      3.536      3.536      8.660       15.0
-       10.0       45.0       45.0      5.000      5.000      7.071       21.2
-       10.0       60.0       45.0      6.124      6.124      5.000       26.0
-       10.0       75.0       45.0      6.830      6.830      2.588       29.0
-       10.0       90.0       45.0      7.071      7.071      0.000       30.0
-       10.0      105.0       45.0      6.830      6.830     -2.588       29.0
-       10.0      120.0       45.0      6.124      6.124     -5.000       26.0
-       10.0      135.0       45.0      5.000      5.000     -7.071       21.2
-       10.0      150.0       45.0      3.536      3.536     -8.660       15.0
-       10.0      165.0       45.0      1.830      1.830     -9.659        7.8
+      10.0      15.0      45.0     1.830     1.830     9.659       7.8
+      10.0      30.0      45.0     3.536     3.536     8.660      15.0
+      10.0      45.0      45.0     5.000     5.000     7.071      21.2
+      10.0      60.0      45.0     6.124     6.124     5.000      26.0
+      10.0      75.0      45.0     6.830     6.830     2.588      29.0
+      10.0      90.0      45.0     7.071     7.071     0.000      30.0
+      10.0     105.0      45.0     6.830     6.830    -2.588      29.0
+      10.0     120.0      45.0     6.124     6.124    -5.000      26.0
+      10.0     135.0      45.0     5.000     5.000    -7.071      21.2
+      10.0     150.0      45.0     3.536     3.536    -8.660      15.0
+      10.0     165.0      45.0     1.830     1.830    -9.659       7.8
 
-       10.0       15.0       60.0      1.294      2.241      9.659        7.8
-       10.0       30.0       60.0      2.500      4.330      8.660       15.0
-       10.0       45.0       60.0      3.536      6.124      7.071       21.2
-       10.0       60.0       60.0      4.330      7.500      5.000       26.0
-       10.0       75.0       60.0      4.830      8.365      2.588       29.0
-       10.0       90.0       60.0      5.000      8.660      0.000       30.0
-       10.0      105.0       60.0      4.830      8.365     -2.588       29.0
-       10.0      120.0       60.0      4.330      7.500     -5.000       26.0
-       10.0      135.0       60.0      3.536      6.124     -7.071       21.2
-       10.0      150.0       60.0      2.500      4.330     -8.660       15.0
-       10.0      165.0       60.0      1.294      2.241     -9.659        7.8
+      10.0      15.0      60.0     1.294     2.241     9.659       7.8
+      10.0      30.0      60.0     2.500     4.330     8.660      15.0
+      10.0      45.0      60.0     3.536     6.124     7.071      21.2
+      10.0      60.0      60.0     4.330     7.500     5.000      26.0
+      10.0      75.0      60.0     4.830     8.365     2.588      29.0
+      10.0      90.0      60.0     5.000     8.660     0.000      30.0
+      10.0     105.0      60.0     4.830     8.365    -2.588      29.0
+      10.0     120.0      60.0     4.330     7.500    -5.000      26.0
+      10.0     135.0      60.0     3.536     6.124    -7.071      21.2
+      10.0     150.0      60.0     2.500     4.330    -8.660      15.0
+      10.0     165.0      60.0     1.294     2.241    -9.659       7.8
 
-       10.0       15.0       75.0      0.670      2.500      9.659        7.8
-       10.0       30.0       75.0      1.294      4.830      8.660       15.0
-       10.0       45.0       75.0      1.830      6.830      7.071       21.2
-       10.0       60.0       75.0      2.241      8.365      5.000       26.0
-       10.0       75.0       75.0      2.500      9.330      2.588       29.0
-       10.0       90.0       75.0      2.588      9.659      0.000       30.0
-       10.0      105.0       75.0      2.500      9.330     -2.588       29.0
-       10.0      120.0       75.0      2.241      8.365     -5.000       26.0
-       10.0      135.0       75.0      1.830      6.830     -7.071       21.2
-       10.0      150.0       75.0      1.294      4.830     -8.660       15.0
-       10.0      165.0       75.0      0.670      2.500     -9.659        7.8
+      10.0      15.0      75.0     0.670     2.500     9.659       7.8
+      10.0      30.0      75.0     1.294     4.830     8.660      15.0
+      10.0      45.0      75.0     1.830     6.830     7.071      21.2
+      10.0      60.0      75.0     2.241     8.365     5.000      26.0
+      10.0      75.0      75.0     2.500     9.330     2.588      29.0
+      10.0      90.0      75.0     2.588     9.659     0.000      30.0
+      10.0     105.0      75.0     2.500     9.330    -2.588      29.0
+      10.0     120.0      75.0     2.241     8.365    -5.000      26.0
+      10.0     135.0      75.0     1.830     6.830    -7.071      21.2
+      10.0     150.0      75.0     1.294     4.830    -8.660      15.0
+      10.0     165.0      75.0     0.670     2.500    -9.659       7.8
 
-       10.0       15.0       90.0      0.000      2.588      9.659        7.8
-       10.0       30.0       90.0      0.000      5.000      8.660       15.0
-       10.0       45.0       90.0      0.000      7.071      7.071       21.2
-       10.0       60.0       90.0      0.000      8.660      5.000       26.0
-       10.0       75.0       90.0      0.000      9.659      2.588       29.0
-       10.0       90.0       90.0      0.000     10.000      0.000       30.0
-       10.0      105.0       90.0      0.000      9.659     -2.588       29.0
-       10.0      120.0       90.0      0.000      8.660     -5.000       26.0
-       10.0      135.0       90.0      0.000      7.071     -7.071       21.2
-       10.0      150.0       90.0      0.000      5.000     -8.660       15.0
-       10.0      165.0       90.0      0.000      2.588     -9.659        7.8
+      10.0      15.0      90.0     0.000     2.588     9.659       7.8
+      10.0      30.0      90.0     0.000     5.000     8.660      15.0
+      10.0      45.0      90.0     0.000     7.071     7.071      21.2
+      10.0      60.0      90.0     0.000     8.660     5.000      26.0
+      10.0      75.0      90.0     0.000     9.659     2.588      29.0
+      10.0      90.0      90.0     0.000    10.000     0.000      30.0
+      10.0     105.0      90.0     0.000     9.659    -2.588      29.0
+      10.0     120.0      90.0     0.000     8.660    -5.000      26.0
+      10.0     135.0      90.0     0.000     7.071    -7.071      21.2
+      10.0     150.0      90.0     0.000     5.000    -8.660      15.0
+      10.0     165.0      90.0     0.000     2.588    -9.659       7.8
 
-       10.0       15.0      105.0     -0.670      2.500      9.659        7.8
-       10.0       30.0      105.0     -1.294      4.830      8.660       15.0
-       10.0       45.0      105.0     -1.830      6.830      7.071       21.2
-       10.0       60.0      105.0     -2.241      8.365      5.000       26.0
-       10.0       75.0      105.0     -2.500      9.330      2.588       29.0
-       10.0       90.0      105.0     -2.588      9.659      0.000       30.0
-       10.0      105.0      105.0     -2.500      9.330     -2.588       29.0
-       10.0      120.0      105.0     -2.241      8.365     -5.000       26.0
-       10.0      135.0      105.0     -1.830      6.830     -7.071       21.2
-       10.0      150.0      105.0     -1.294      4.830     -8.660       15.0
-       10.0      165.0      105.0     -0.670      2.500     -9.659        7.8
+      10.0      15.0     105.0    -0.670     2.500     9.659       7.8
+      10.0      30.0     105.0    -1.294     4.830     8.660      15.0
+      10.0      45.0     105.0    -1.830     6.830     7.071      21.2
+      10.0      60.0     105.0    -2.241     8.365     5.000      26.0
+      10.0      75.0     105.0    -2.500     9.330     2.588      29.0
+      10.0      90.0     105.0    -2.588     9.659     0.000      30.0
+      10.0     105.0     105.0    -2.500     9.330    -2.588      29.0
+      10.0     120.0     105.0    -2.241     8.365    -5.000      26.0
+      10.0     135.0     105.0    -1.830     6.830    -7.071      21.2
+      10.0     150.0     105.0    -1.294     4.830    -8.660      15.0
+      10.0     165.0     105.0    -0.670     2.500    -9.659       7.8
 
-       10.0       15.0      120.0     -1.294      2.241      9.659        7.8
-       10.0       30.0      120.0     -2.500      4.330      8.660       15.0
-       10.0       45.0      120.0     -3.536      6.124      7.071       21.2
-       10.0       60.0      120.0     -4.330      7.500      5.000       26.0
-       10.0       75.0      120.0     -4.830      8.365      2.588       29.0
-       10.0       90.0      120.0     -5.000      8.660      0.000       30.0
-       10.0      105.0      120.0     -4.830      8.365     -2.588       29.0
-       10.0      120.0      120.0     -4.330      7.500     -5.000       26.0
-       10.0      135.0      120.0     -3.536      6.124     -7.071       21.2
-       10.0      150.0      120.0     -2.500      4.330     -8.660       15.0
-       10.0      165.0      120.0     -1.294      2.241     -9.659        7.8
+      10.0      15.0     120.0    -1.294     2.241     9.659       7.8
+      10.0      30.0     120.0    -2.500     4.330     8.660      15.0
+      10.0      45.0     120.0    -3.536     6.124     7.071      21.2
+      10.0      60.0     120.0    -4.330     7.500     5.000      26.0
+      10.0      75.0     120.0    -4.830     8.365     2.588      29.0
+      10.0      90.0     120.0    -5.000     8.660     0.000      30.0
+      10.0     105.0     120.0    -4.830     8.365    -2.588      29.0
+      10.0     120.0     120.0    -4.330     7.500    -5.000      26.0
+      10.0     135.0     120.0    -3.536     6.124    -7.071      21.2
+      10.0     150.0     120.0    -2.500     4.330    -8.660      15.0
+      10.0     165.0     120.0    -1.294     2.241    -9.659       7.8
 
-       10.0       15.0      135.0     -1.830      1.830      9.659        7.8
-       10.0       30.0      135.0     -3.536      3.536      8.660       15.0
-       10.0       45.0      135.0     -5.000      5.000      7.071       21.2
-       10.0       60.0      135.0     -6.124      6.124      5.000       26.0
-       10.0       75.0      135.0     -6.830      6.830      2.588       29.0
-       10.0       90.0      135.0     -7.071      7.071      0.000       30.0
-       10.0      105.0      135.0     -6.830      6.830     -2.588       29.0
-       10.0      120.0      135.0     -6.124      6.124     -5.000       26.0
-       10.0      135.0      135.0     -5.000      5.000     -7.071       21.2
-       10.0      150.0      135.0     -3.536      3.536     -8.660       15.0
-       10.0      165.0      135.0     -1.830      1.830     -9.659        7.8
+      10.0      15.0     135.0    -1.830     1.830     9.659       7.8
+      10.0      30.0     135.0    -3.536     3.536     8.660      15.0
+      10.0      45.0     135.0    -5.000     5.000     7.071      21.2
+      10.0      60.0     135.0    -6.124     6.124     5.000      26.0
+      10.0      75.0     135.0    -6.830     6.830     2.588      29.0
+      10.0      90.0     135.0    -7.071     7.071     0.000      30.0
+      10.0     105.0     135.0    -6.830     6.830    -2.588      29.0
+      10.0     120.0     135.0    -6.124     6.124    -5.000      26.0
+      10.0     135.0     135.0    -5.000     5.000    -7.071      21.2
+      10.0     150.0     135.0    -3.536     3.536    -8.660      15.0
+      10.0     165.0     135.0    -1.830     1.830    -9.659       7.8
 
-       10.0       15.0      150.0     -2.241      1.294      9.659        7.8
-       10.0       30.0      150.0     -4.330      2.500      8.660       15.0
-       10.0       45.0      150.0     -6.124      3.536      7.071       21.2
-       10.0       60.0      150.0     -7.500      4.330      5.000       26.0
-       10.0       75.0      150.0     -8.365      4.830      2.588       29.0
-       10.0       90.0      150.0     -8.660      5.000      0.000       30.0
-       10.0      105.0      150.0     -8.365      4.830     -2.588       29.0
-       10.0      120.0      150.0     -7.500      4.330     -5.000       26.0
-       10.0      135.0      150.0     -6.124      3.536     -7.071       21.2
-       10.0      150.0      150.0     -4.330      2.500     -8.660       15.0
-       10.0      165.0      150.0     -2.241      1.294     -9.659        7.8
+      10.0      15.0     150.0    -2.241     1.294     9.659       7.8
+      10.0      30.0     150.0    -4.330     2.500     8.660      15.0
+      10.0      45.0     150.0    -6.124     3.536     7.071      21.2
+      10.0      60.0     150.0    -7.500     4.330     5.000      26.0
+      10.0      75.0     150.0    -8.365     4.830     2.588      29.0
+      10.0      90.0     150.0    -8.660     5.000     0.000      30.0
+      10.0     105.0     150.0    -8.365     4.830    -2.588      29.0
+      10.0     120.0     150.0    -7.500     4.330    -5.000      26.0
+      10.0     135.0     150.0    -6.124     3.536    -7.071      21.2
+      10.0     150.0     150.0    -4.330     2.500    -8.660      15.0
+      10.0     165.0     150.0    -2.241     1.294    -9.659       7.8
 
-       10.0       15.0      165.0     -2.500      0.670      9.659        7.8
-       10.0       30.0      165.0     -4.830      1.294      8.660       15.0
-       10.0       45.0      165.0     -6.830      1.830      7.071       21.2
-       10.0       60.0      165.0     -8.365      2.241      5.000       26.0
-       10.0       75.0      165.0     -9.330      2.500      2.588       29.0
-       10.0       90.0      165.0     -9.659      2.588      0.000       30.0
-       10.0      105.0      165.0     -9.330      2.500     -2.588       29.0
-       10.0      120.0      165.0     -8.365      2.241     -5.000       26.0
-       10.0      135.0      165.0     -6.830      1.830     -7.071       21.2
-       10.0      150.0      165.0     -4.830      1.294     -8.660       15.0
-       10.0      165.0      165.0     -2.500      0.670     -9.659        7.8
+      10.0      15.0     165.0    -2.500     0.670     9.659       7.8
+      10.0      30.0     165.0    -4.830     1.294     8.660      15.0
+      10.0      45.0     165.0    -6.830     1.830     7.071      21.2
+      10.0      60.0     165.0    -8.365     2.241     5.000      26.0
+      10.0      75.0     165.0    -9.330     2.500     2.588      29.0
+      10.0      90.0     165.0    -9.659     2.588     0.000      30.0
+      10.0     105.0     165.0    -9.330     2.500    -2.588      29.0
+      10.0     120.0     165.0    -8.365     2.241    -5.000      26.0
+      10.0     135.0     165.0    -6.830     1.830    -7.071      21.2
+      10.0     150.0     165.0    -4.830     1.294    -8.660      15.0
+      10.0     165.0     165.0    -2.500     0.670    -9.659       7.8
 
-       10.0       15.0      180.0     -2.588      0.000      9.659        7.8
-       10.0       30.0      180.0     -5.000      0.000      8.660       15.0
-       10.0       45.0      180.0     -7.071      0.000      7.071       21.2
-       10.0       60.0      180.0     -8.660      0.000      5.000       26.0
-       10.0       75.0      180.0     -9.659      0.000      2.588       29.0
-       10.0       90.0      180.0    -10.000      0.000      0.000       30.0
-       10.0      105.0      180.0     -9.659      0.000     -2.588       29.0
-       10.0      120.0      180.0     -8.660      0.000     -5.000       26.0
-       10.0      135.0      180.0     -7.071      0.000     -7.071       21.2
-       10.0      150.0      180.0     -5.000      0.000     -8.660       15.0
-       10.0      165.0      180.0     -2.588      0.000     -9.659        7.8
+      10.0      15.0     180.0    -2.588     0.000     9.659       7.8
+      10.0      30.0     180.0    -5.000     0.000     8.660      15.0
+      10.0      45.0     180.0    -7.071     0.000     7.071      21.2
+      10.0      60.0     180.0    -8.660     0.000     5.000      26.0
+      10.0      75.0     180.0    -9.659     0.000     2.588      29.0
+      10.0      90.0     180.0   -10.000     0.000     0.000      30.0
+      10.0     105.0     180.0    -9.659     0.000    -2.588      29.0
+      10.0     120.0     180.0    -8.660     0.000    -5.000      26.0
+      10.0     135.0     180.0    -7.071     0.000    -7.071      21.2
+      10.0     150.0     180.0    -5.000     0.000    -8.660      15.0
+      10.0     165.0     180.0    -2.588     0.000    -9.659       7.8
 
-       10.0       15.0      195.0     -2.500     -0.670      9.659        7.8
-       10.0       30.0      195.0     -4.830     -1.294      8.660       15.0
-       10.0       45.0      195.0     -6.830     -1.830      7.071       21.2
-       10.0       60.0      195.0     -8.365     -2.241      5.000       26.0
-       10.0       75.0      195.0     -9.330     -2.500      2.588       29.0
-       10.0       90.0      195.0     -9.659     -2.588      0.000       30.0
-       10.0      105.0      195.0     -9.330     -2.500     -2.588       29.0
-       10.0      120.0      195.0     -8.365     -2.241     -5.000       26.0
-       10.0      135.0      195.0     -6.830     -1.830     -7.071       21.2
-       10.0      150.0      195.0     -4.830     -1.294     -8.660       15.0
-       10.0      165.0      195.0     -2.500     -0.670     -9.659        7.8
+      10.0      15.0     195.0    -2.500    -0.670     9.659       7.8
+      10.0      30.0     195.0    -4.830    -1.294     8.660      15.0
+      10.0      45.0     195.0    -6.830    -1.830     7.071      21.2
+      10.0      60.0     195.0    -8.365    -2.241     5.000      26.0
+      10.0      75.0     195.0    -9.330    -2.500     2.588      29.0
+      10.0      90.0     195.0    -9.659    -2.588     0.000      30.0
+      10.0     105.0     195.0    -9.330    -2.500    -2.588      29.0
+      10.0     120.0     195.0    -8.365    -2.241    -5.000      26.0
+      10.0     135.0     195.0    -6.830    -1.830    -7.071      21.2
+      10.0     150.0     195.0    -4.830    -1.294    -8.660      15.0
+      10.0     165.0     195.0    -2.500    -0.670    -9.659       7.8
 
-       10.0       15.0      210.0     -2.241     -1.294      9.659        7.8
-       10.0       30.0      210.0     -4.330     -2.500      8.660       15.0
-       10.0       45.0      210.0     -6.124     -3.536      7.071       21.2
-       10.0       60.0      210.0     -7.500     -4.330      5.000       26.0
-       10.0       75.0      210.0     -8.365     -4.830      2.588       29.0
-       10.0       90.0      210.0     -8.660     -5.000      0.000       30.0
-       10.0      105.0      210.0     -8.365     -4.830     -2.588       29.0
-       10.0      120.0      210.0     -7.500     -4.330     -5.000       26.0
-       10.0      135.0      210.0     -6.124     -3.536     -7.071       21.2
-       10.0      150.0      210.0     -4.330     -2.500     -8.660       15.0
-       10.0      165.0      210.0     -2.241     -1.294     -9.659        7.8
+      10.0      15.0     210.0    -2.241    -1.294     9.659       7.8
+      10.0      30.0     210.0    -4.330    -2.500     8.660      15.0
+      10.0      45.0     210.0    -6.124    -3.536     7.071      21.2
+      10.0      60.0     210.0    -7.500    -4.330     5.000      26.0
+      10.0      75.0     210.0    -8.365    -4.830     2.588      29.0
+      10.0      90.0     210.0    -8.660    -5.000     0.000      30.0
+      10.0     105.0     210.0    -8.365    -4.830    -2.588      29.0
+      10.0     120.0     210.0    -7.500    -4.330    -5.000      26.0
+      10.0     135.0     210.0    -6.124    -3.536    -7.071      21.2
+      10.0     150.0     210.0    -4.330    -2.500    -8.660      15.0
+      10.0     165.0     210.0    -2.241    -1.294    -9.659       7.8
 
-       10.0       15.0      225.0     -1.830     -1.830      9.659        7.8
-       10.0       30.0      225.0     -3.536     -3.536      8.660       15.0
-       10.0       45.0      225.0     -5.000     -5.000      7.071       21.2
-       10.0       60.0      225.0     -6.124     -6.124      5.000       26.0
-       10.0       75.0      225.0     -6.830     -6.830      2.588       29.0
-       10.0       90.0      225.0     -7.071     -7.071      0.000       30.0
-       10.0      105.0      225.0     -6.830     -6.830     -2.588       29.0
-       10.0      120.0      225.0     -6.124     -6.124     -5.000       26.0
-       10.0      135.0      225.0     -5.000     -5.000     -7.071       21.2
-       10.0      150.0      225.0     -3.536     -3.536     -8.660       15.0
-       10.0      165.0      225.0     -1.830     -1.830     -9.659        7.8
+      10.0      15.0     225.0    -1.830    -1.830     9.659       7.8
+      10.0      30.0     225.0    -3.536    -3.536     8.660      15.0
+      10.0      45.0     225.0    -5.000    -5.000     7.071      21.2
+      10.0      60.0     225.0    -6.124    -6.124     5.000      26.0
+      10.0      75.0     225.0    -6.830    -6.830     2.588      29.0
+      10.0      90.0     225.0    -7.071    -7.071     0.000      30.0
+      10.0     105.0     225.0    -6.830    -6.830    -2.588      29.0
+      10.0     120.0     225.0    -6.124    -6.124    -5.000      26.0
+      10.0     135.0     225.0    -5.000    -5.000    -7.071      21.2
+      10.0     150.0     225.0    -3.536    -3.536    -8.660      15.0
+      10.0     165.0     225.0    -1.830    -1.830    -9.659       7.8
 
-       10.0       15.0      240.0     -1.294     -2.241      9.659        7.8
-       10.0       30.0      240.0     -2.500     -4.330      8.660       15.0
-       10.0       45.0      240.0     -3.536     -6.124      7.071       21.2
-       10.0       60.0      240.0     -4.330     -7.500      5.000       26.0
-       10.0       75.0      240.0     -4.830     -8.365      2.588       29.0
-       10.0       90.0      240.0     -5.000     -8.660      0.000       30.0
-       10.0      105.0      240.0     -4.830     -8.365     -2.588       29.0
-       10.0      120.0      240.0     -4.330     -7.500     -5.000       26.0
-       10.0      135.0      240.0     -3.536     -6.124     -7.071       21.2
-       10.0      150.0      240.0     -2.500     -4.330     -8.660       15.0
-       10.0      165.0      240.0     -1.294     -2.241     -9.659        7.8
+      10.0      15.0     240.0    -1.294    -2.241     9.659       7.8
+      10.0      30.0     240.0    -2.500    -4.330     8.660      15.0
+      10.0      45.0     240.0    -3.536    -6.124     7.071      21.2
+      10.0      60.0     240.0    -4.330    -7.500     5.000      26.0
+      10.0      75.0     240.0    -4.830    -8.365     2.588      29.0
+      10.0      90.0     240.0    -5.000    -8.660     0.000      30.0
+      10.0     105.0     240.0    -4.830    -8.365    -2.588      29.0
+      10.0     120.0     240.0    -4.330    -7.500    -5.000      26.0
+      10.0     135.0     240.0    -3.536    -6.124    -7.071      21.2
+      10.0     150.0     240.0    -2.500    -4.330    -8.660      15.0
+      10.0     165.0     240.0    -1.294    -2.241    -9.659       7.8
 
-       10.0       15.0      255.0     -0.670     -2.500      9.659        7.8
-       10.0       30.0      255.0     -1.294     -4.830      8.660       15.0
-       10.0       45.0      255.0     -1.830     -6.830      7.071       21.2
-       10.0       60.0      255.0     -2.241     -8.365      5.000       26.0
-       10.0       75.0      255.0     -2.500     -9.330      2.588       29.0
-       10.0       90.0      255.0     -2.588     -9.659      0.000       30.0
-       10.0      105.0      255.0     -2.500     -9.330     -2.588       29.0
-       10.0      120.0      255.0     -2.241     -8.365     -5.000       26.0
-       10.0      135.0      255.0     -1.830     -6.830     -7.071       21.2
-       10.0      150.0      255.0     -1.294     -4.830     -8.660       15.0
-       10.0      165.0      255.0     -0.670     -2.500     -9.659        7.8
+      10.0      15.0     255.0    -0.670    -2.500     9.659       7.8
+      10.0      30.0     255.0    -1.294    -4.830     8.660      15.0
+      10.0      45.0     255.0    -1.830    -6.830     7.071      21.2
+      10.0      60.0     255.0    -2.241    -8.365     5.000      26.0
+      10.0      75.0     255.0    -2.500    -9.330     2.588      29.0
+      10.0      90.0     255.0    -2.588    -9.659     0.000      30.0
+      10.0     105.0     255.0    -2.500    -9.330    -2.588      29.0
+      10.0     120.0     255.0    -2.241    -8.365    -5.000      26.0
+      10.0     135.0     255.0    -1.830    -6.830    -7.071      21.2
+      10.0     150.0     255.0    -1.294    -4.830    -8.660      15.0
+      10.0     165.0     255.0    -0.670    -2.500    -9.659       7.8
 
-       10.0       15.0      270.0      0.000     -2.588      9.659        7.8
-       10.0       30.0      270.0      0.000     -5.000      8.660       15.0
-       10.0       45.0      270.0      0.000     -7.071      7.071       21.2
-       10.0       60.0      270.0      0.000     -8.660      5.000       26.0
-       10.0       75.0      270.0      0.000     -9.659      2.588       29.0
-       10.0       90.0      270.0      0.000    -10.000      0.000       30.0
-       10.0      105.0      270.0      0.000     -9.659     -2.588       29.0
-       10.0      120.0      270.0      0.000     -8.660     -5.000       26.0
-       10.0      135.0      270.0      0.000     -7.071     -7.071       21.2
-       10.0      150.0      270.0      0.000     -5.000     -8.660       15.0
-       10.0      165.0      270.0      0.000     -2.588     -9.659        7.8
+      10.0      15.0     270.0     0.000    -2.588     9.659       7.8
+      10.0      30.0     270.0     0.000    -5.000     8.660      15.0
+      10.0      45.0     270.0     0.000    -7.071     7.071      21.2
+      10.0      60.0     270.0     0.000    -8.660     5.000      26.0
+      10.0      75.0     270.0     0.000    -9.659     2.588      29.0
+      10.0      90.0     270.0     0.000   -10.000     0.000      30.0
+      10.0     105.0     270.0     0.000    -9.659    -2.588      29.0
+      10.0     120.0     270.0     0.000    -8.660    -5.000      26.0
+      10.0     135.0     270.0     0.000    -7.071    -7.071      21.2
+      10.0     150.0     270.0     0.000    -5.000    -8.660      15.0
+      10.0     165.0     270.0     0.000    -2.588    -9.659       7.8
 
-       10.0       15.0      285.0      0.670     -2.500      9.659        7.8
-       10.0       30.0      285.0      1.294     -4.830      8.660       15.0
-       10.0       45.0      285.0      1.830     -6.830      7.071       21.2
-       10.0       60.0      285.0      2.241     -8.365      5.000       26.0
-       10.0       75.0      285.0      2.500     -9.330      2.588       29.0
-       10.0       90.0      285.0      2.588     -9.659      0.000       30.0
-       10.0      105.0      285.0      2.500     -9.330     -2.588       29.0
-       10.0      120.0      285.0      2.241     -8.365     -5.000       26.0
-       10.0      135.0      285.0      1.830     -6.830     -7.071       21.2
-       10.0      150.0      285.0      1.294     -4.830     -8.660       15.0
-       10.0      165.0      285.0      0.670     -2.500     -9.659        7.8
+      10.0      15.0     285.0     0.670    -2.500     9.659       7.8
+      10.0      30.0     285.0     1.294    -4.830     8.660      15.0
+      10.0      45.0     285.0     1.830    -6.830     7.071      21.2
+      10.0      60.0     285.0     2.241    -8.365     5.000      26.0
+      10.0      75.0     285.0     2.500    -9.330     2.588      29.0
+      10.0      90.0     285.0     2.588    -9.659     0.000      30.0
+      10.0     105.0     285.0     2.500    -9.330    -2.588      29.0
+      10.0     120.0     285.0     2.241    -8.365    -5.000      26.0
+      10.0     135.0     285.0     1.830    -6.830    -7.071      21.2
+      10.0     150.0     285.0     1.294    -4.830    -8.660      15.0
+      10.0     165.0     285.0     0.670    -2.500    -9.659       7.8
 
-       10.0       15.0      300.0      1.294     -2.241      9.659        7.8
-       10.0       30.0      300.0      2.500     -4.330      8.660       15.0
-       10.0       45.0      300.0      3.536     -6.124      7.071       21.2
-       10.0       60.0      300.0      4.330     -7.500      5.000       26.0
-       10.0       75.0      300.0      4.830     -8.365      2.588       29.0
-       10.0       90.0      300.0      5.000     -8.660      0.000       30.0
-       10.0      105.0      300.0      4.830     -8.365     -2.588       29.0
-       10.0      120.0      300.0      4.330     -7.500     -5.000       26.0
-       10.0      135.0      300.0      3.536     -6.124     -7.071       21.2
-       10.0      150.0      300.0      2.500     -4.330     -8.660       15.0
-       10.0      165.0      300.0      1.294     -2.241     -9.659        7.8
+      10.0      15.0     300.0     1.294    -2.241     9.659       7.8
+      10.0      30.0     300.0     2.500    -4.330     8.660      15.0
+      10.0      45.0     300.0     3.536    -6.124     7.071      21.2
+      10.0      60.0     300.0     4.330    -7.500     5.000      26.0
+      10.0      75.0     300.0     4.830    -8.365     2.588      29.0
+      10.0      90.0     300.0     5.000    -8.660     0.000      30.0
+      10.0     105.0     300.0     4.830    -8.365    -2.588      29.0
+      10.0     120.0     300.0     4.330    -7.500    -5.000      26.0
+      10.0     135.0     300.0     3.536    -6.124    -7.071      21.2
+      10.0     150.0     300.0     2.500    -4.330    -8.660      15.0
+      10.0     165.0     300.0     1.294    -2.241    -9.659       7.8
 
-       10.0       15.0      315.0      1.830     -1.830      9.659        7.8
-       10.0       30.0      315.0      3.536     -3.536      8.660       15.0
-       10.0       45.0      315.0      5.000     -5.000      7.071       21.2
-       10.0       60.0      315.0      6.124     -6.124      5.000       26.0
-       10.0       75.0      315.0      6.830     -6.830      2.588       29.0
-       10.0       90.0      315.0      7.071     -7.071      0.000       30.0
-       10.0      105.0      315.0      6.830     -6.830     -2.588       29.0
-       10.0      120.0      315.0      6.124     -6.124     -5.000       26.0
-       10.0      135.0      315.0      5.000     -5.000     -7.071       21.2
-       10.0      150.0      315.0      3.536     -3.536     -8.660       15.0
-       10.0      165.0      315.0      1.830     -1.830     -9.659        7.8
+      10.0      15.0     315.0     1.830    -1.830     9.659       7.8
+      10.0      30.0     315.0     3.536    -3.536     8.660      15.0
+      10.0      45.0     315.0     5.000    -5.000     7.071      21.2
+      10.0      60.0     315.0     6.124    -6.124     5.000      26.0
+      10.0      75.0     315.0     6.830    -6.830     2.588      29.0
+      10.0      90.0     315.0     7.071    -7.071     0.000      30.0
+      10.0     105.0     315.0     6.830    -6.830    -2.588      29.0
+      10.0     120.0     315.0     6.124    -6.124    -5.000      26.0
+      10.0     135.0     315.0     5.000    -5.000    -7.071      21.2
+      10.0     150.0     315.0     3.536    -3.536    -8.660      15.0
+      10.0     165.0     315.0     1.830    -1.830    -9.659       7.8
 
-       10.0       15.0      330.0      2.241     -1.294      9.659        7.8
-       10.0       30.0      330.0      4.330     -2.500      8.660       15.0
-       10.0       45.0      330.0      6.124     -3.536      7.071       21.2
-       10.0       60.0      330.0      7.500     -4.330      5.000       26.0
-       10.0       75.0      330.0      8.365     -4.830      2.588       29.0
-       10.0       90.0      330.0      8.660     -5.000      0.000       30.0
-       10.0      105.0      330.0      8.365     -4.830     -2.588       29.0
-       10.0      120.0      330.0      7.500     -4.330     -5.000       26.0
-       10.0      135.0      330.0      6.124     -3.536     -7.071       21.2
-       10.0      150.0      330.0      4.330     -2.500     -8.660       15.0
-       10.0      165.0      330.0      2.241     -1.294     -9.659        7.8
+      10.0      15.0     330.0     2.241    -1.294     9.659       7.8
+      10.0      30.0     330.0     4.330    -2.500     8.660      15.0
+      10.0      45.0     330.0     6.124    -3.536     7.071      21.2
+      10.0      60.0     330.0     7.500    -4.330     5.000      26.0
+      10.0      75.0     330.0     8.365    -4.830     2.588      29.0
+      10.0      90.0     330.0     8.660    -5.000     0.000      30.0
+      10.0     105.0     330.0     8.365    -4.830    -2.588      29.0
+      10.0     120.0     330.0     7.500    -4.330    -5.000      26.0
+      10.0     135.0     330.0     6.124    -3.536    -7.071      21.2
+      10.0     150.0     330.0     4.330    -2.500    -8.660      15.0
+      10.0     165.0     330.0     2.241    -1.294    -9.659       7.8
 
-       10.0       15.0      345.0      2.500     -0.670      9.659        7.8
-       10.0       30.0      345.0      4.830     -1.294      8.660       15.0
-       10.0       45.0      345.0      6.830     -1.830      7.071       21.2
-       10.0       60.0      345.0      8.365     -2.241      5.000       26.0
-       10.0       75.0      345.0      9.330     -2.500      2.588       29.0
-       10.0       90.0      345.0      9.659     -2.588      0.000       30.0
-       10.0      105.0      345.0      9.330     -2.500     -2.588       29.0
-       10.0      120.0      345.0      8.365     -2.241     -5.000       26.0
-       10.0      135.0      345.0      6.830     -1.830     -7.071       21.2
-       10.0      150.0      345.0      4.830     -1.294     -8.660       15.0
-       10.0      165.0      345.0      2.500     -0.670     -9.659        7.8
+      10.0      15.0     345.0     2.500    -0.670     9.659       7.8
+      10.0      30.0     345.0     4.830    -1.294     8.660      15.0
+      10.0      45.0     345.0     6.830    -1.830     7.071      21.2
+      10.0      60.0     345.0     8.365    -2.241     5.000      26.0
+      10.0      75.0     345.0     9.330    -2.500     2.588      29.0
+      10.0      90.0     345.0     9.659    -2.588     0.000      30.0
+      10.0     105.0     345.0     9.330    -2.500    -2.588      29.0
+      10.0     120.0     345.0     8.365    -2.241    -5.000      26.0
+      10.0     135.0     345.0     6.830    -1.830    -7.071      21.2
+      10.0     150.0     345.0     4.830    -1.294    -8.660      15.0
+      10.0     165.0     345.0     2.500    -0.670    -9.659       7.8
diff --git a/test/testdata4.png b/test/testdata4.png
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