Re^12: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?

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Re^13: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis? by BrowserUk (Patriarch) on Jul 02, 2012 at 19:21 UTC
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?	[reply] [d/l] [select]

Replies are listed 'Best First'.

Re^13: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?
by BrowserUk (Patriarch) on Jul 02, 2012 at 19:21 UTC

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?

[reply]
[d/l]
[select]