Okay. That explains a lot. The coordinates you've used above for the last point:

$Xl2 = -47.430
$Yl2 = -2.993
$Zl2 = -17.639

[download]

are different from those you supplied in Re^4: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?:

ATOM         CA  GLY A 101     -50.317  -4.262 -17.720

[download]

When I do the same thing using the line data from that post:

#! perl -slw
use strict;
use constant { X=>0, Y=>1, Z=>2, W=>3 };

my @first = (  -3.901,  ,9.352, ,-1.557 );
my @last  = ( -50.317,  -4.262, -17.720 );

my @v = (
    $last[X] - $first[X],
    $last[Y] - $first[Y],
    $last[Z] - $first[Z],
);

my $l = sqrt( $v[X]**2 + $v[Y]**2 + $v[Z]**2 );

my @unitVec = map $_ / $l, @v;

print "@unitVec";

__END__
[20:14:31.75] C:\test>unitVec.pl
-0.910112639703537 -0.266939707793087 -0.316919824963984

[download]

And put those in place of your supplied unit vector:0.906 0.258 0.335 and re-run the transforms, I get much better correspondence between rotation axis and the Z-axis:

[20:10:08.00] C:\test>979082 -LIM4A=15
[
  [0, 0, "1.54737342767147"],
  [ "1.06484137623042e-005", "-1.2776161742778e-005",   "4.54810050618
+484"],
  [ "0.000325405667775502",   "0.000255895356081837",   "7.54791747205
+851"],
  ["-0.000219093060060072",  "-0.000435009701289957",  "10.54715057839
+94" ],
  ["-0.000208444646297323",  "-0.000447785863032735",  "13.54787765691
+28" ],
  [ "0.000106312607715875",  "-0.000179114345206344",  "16.54769462278
+65" ],
  [ "0.000421069861728629",   "8.95571726164945e-005", "19.54751158866
+01" ],
  ["-0.000516734055701296",   "7.67810108754929e-005", "22.54792174734
+85" ],
  ["-0.000201976801687653",   "0.000345452528700108",  "25.54773871322
+22" ],
  [ "0.00020197680166989",   "-0.000345452528671686",  "28.54728873938
+81" ],
  [ "0.000212625215433082",  "-0.000358228690412687",  "31.54801581790
+14" ],
  ["-0.000421069861747281",  "-8.95571725898492e-005", "34.54751586395
+01" ],
  ["-0.000410421447985865",  "-0.000102333334330851",  "37.54824294246
+35" ],
  ["-9.56641939722225e-005",  "0.000166338183491987",  "40.54805990833
+72" ],
  ["-0.000640162921804244",  "-0.000524566873879806",  "43.54729301467
+81" ],
  ["-0.000629514508044604",  "-0.000537343035622584",  "46.54802009319
+14" ],
  ["-0.000314757254034514",  "-0.000268671517799746",  "49.54783705906
+51" ],
  ["-1.73194791841524e-014",  "2.66453525910038e-014", "52.54765402493
+88" ],
]

[download]

That's much more satisfying :)

And the affect that has on the collision results are small, but I think significant:

[20:19:34.18] C:\test>979082 -LIM4A=15

R:  0                   [ -18.731,  -0.135, -11.272 ] [   6.260,  52° 
+]
S:259 angle: -58.482°   [  -6.126,  -0.957,   0.400 ] [   9.888, 110° 
+]

R:  5                   [ -18.388,  -2.409,  -9.308 ] [   7.454,  75° 
+]
S:259 angle: -35.177°   [  -6.126,  -0.957,   0.400 ] [   9.888, 110° 
+]

R:  6                   [ -18.784,  -3.016,  -7.671 ] [   7.681,  89° 
+]
S:259 angle: -21.699°   [  -6.126,  -0.957,   0.400 ] [   9.888, 110° 
+]

R:  7                   [ -17.107,  -3.128,  -6.966 ] [   8.259,  90° 
+]
S:245 angle: -27.682°   [  -5.672,   3.533,   0.140 ] [   5.742, 118° 
+]
S:256 angle: -23.655°   [  -5.562,   1.600,   0.400 ] [   7.610, 114° 
+]
S:257 angle: -22.479°   [  -5.970,   0.493,   0.400 ] [   8.569, 112° 
+]
S:258 angle: -22.287°   [  -5.825,   0.591,   0.400 ] [   8.500, 112° 
+]
S:259 angle: -20.441°   [  -6.126,  -0.957,   0.400 ] [   9.888, 110° 
+]
S:254 angle: -20.325°   [  -4.738,   1.093,   0.400 ] [   8.200, 110° 
+]
S:255 angle: -20.193°   [  -4.814,   0.899,   0.400 ] [   8.368, 110° 
+]
S:  7 angle: -12.398°   [  -3.823,  -2.789,   0.030 ] [  11.951, 102° 
+]

R:140                   [ -18.510, -10.387,  -3.385 ] [  15.488, 107° 
+]
S:259 angle:  -3.661°   [  -6.126,  -0.957,   0.400 ] [   9.888, 110° 
+]

R:141                   [ -17.411, -10.096,  -2.922 ] [  15.540, 107° 
+]
S:256 angle:  -6.629°   [  -5.562,   1.600,   0.400 ] [   7.610, 114° 
+]
S:257 angle:  -5.453°   [  -5.970,   0.493,   0.400 ] [   8.569, 112° 
+]
S:258 angle:  -5.261°   [  -5.825,   0.591,   0.400 ] [   8.500, 112° 
+]
S:259 angle:  -3.414°   [  -6.126,  -0.957,   0.400 ] [   9.888, 110° 
+]

[download]
With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

The start of some sanity?

In reply to Re^13: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis? by BrowserUk
in thread Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis? by fraizerangus

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