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Re^6: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?

by fraizerangus (Sexton)
on Jun 29, 2012 at 16:33 UTC ( [id://979150]=note: print w/replies, xml ) Need Help??


in reply to Re^5: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?
in thread Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?

Hello

Apologies I'm really struggling to understand what you mean? any chance you could give me an equation or example code so I can get my head around it please?

many thanks and best wishes

Dan

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Re^7: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?
by BrowserUk (Patriarch) on Jun 29, 2012 at 20:45 UTC

    I'll try to clarify the approach with some 2D ascii art.

    Here is a diagram of the problem simplified so that we have 1 input point (x); 4 stopping points (o); and the rotational axis (+).

    Fortuitously, in this example all the z values are 0; and the axis of rotation happens to be parallel to the z-axis:

    + Axis of rotation: [-5, -2, *] x An input point to be rotated [+1, -2, *] o Several stopping points: [-7, +4, *] [-6, +3, *] [-5, +5, *] [-4, +4, *] o 5 o o | o | | | - - - 5 - - - - 0 - - - - 5 - - - - | + | x | | 5

    Using your described approach, you now have to rotate (x) around (+) and then compare the new position with each of the 4 (o)s; and do that 360 times. Or more, depending upon your allowable tolerance.

    In this example it is easy to see that by applying a simple translation transform to all the points, we can re-base the coordinates, and thus slide the z-axis until it is coincident with the axis of rotation. The 2D transform required is just [+5, +2], giving the points:

    + Axis of rotation: [ 0, 0, *] x An input point to be rotated [+6, 0, *] o Several stopping points: [-2, +6, *] [-1, +5, *] [ 0, +7, *] [+1, +6, *] | o o | o o 5 | | | | - - - + - - - - 5 x | | |

    And now we can convert the 3D cartesian points, to 2D polar vectors:

    [radius, angle] x An input point to be rotated [+6, 0, *] -> [6.00, 0.000] o Several stopping points: [-2, +6, *] -> [6.32, 108.4] [-1, +5, *] -> [5.09, 101.3] [ 0, +7, *] -> [7.00, 90.0] [+1, +6, *] -> [6.08, 80.5]

    And it is easy to see that if our tolerance on the radius, for a collision, were 0.1, then we only need look at 1 of the 4 stopping points.

    And we can directly obtain the rotation required to produce that collision by subtracting the angles. In this case 80.5 degrees.

    Obviously, real data is not so convenient, and the transform you'll need to apply to the points to align the axis of rotation with the z-axis will need to be a full Affine transform. But with the unit vector for the axis of rotation, you already have the major information required to construct it.

    The other part of the matrix will require you to find the closest point on the axis of rotation to the origin; in order to fill in the x,y,z translation values. But as I recall, that is simply derived directly from the equation of the axis, which is derived directly from is unit vector.

    But the major point is, once you have transformed the points to align the axis, you can exclude the z-coordinates and use 2D vectors to avoid having to iterate the rotation or do a full input points to stopping point cross comparison. You only need consider the z values again once you've found pairs that have the same radius in the X-Y plane.

    I'll need to refresh my memory of the math involved -- I always do -- but I'll try to post a worked example over the weekend.


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      Hello

      Thanks so much for your help! Its much appreciated! Once this wedding is over I will sit down and have a read! :) Just to put things in perspective if you download Jmol (http://jmol.sourceforge.net/download/) a molecular viewer and then copy this code into a text document and then open it in Jmol you'll see the test molecule, the blue balls are the co-ordinates I need to rotate around the axis (in grey) until they come into a distance of 4A of the red and then rotate in the other direction until it does the same

      REMARK #jmolscript: select all; wireframe off; spacefill off; color gr +ey ;background grey; REMARK #jmolscript: select 6- 23A, 29- 42A, 60- 71A REMARK #jmolscript: colour [255, 0 , 0] REMARK #jmolscript: select 24- 28A, 43- 59A REMARK #jmolscript: colour [0, 0 ,255] REMARK #jmolscript: select 23- 24A, 42- 43A, 28- 29A, 59- 67 +A REMARK #jmolscript: colour [0,255,0] REMARK #jmolscript: select all; wireframe off ; spacefill 250 REMARK #jmolscript: select all REMARK #jmolscript: anim mode loop 0.5 0.5;anim on; REMARK #jmolscript: set echo top left;color echo [xFF0D0D];echo DynDom REMARK #jmolscript: set antialiasDisplay ON MODEL 1 ATOM 1 N MET A 1 -35.886 -7.465 -14.571 ATOM 2 CA MET A 1 -34.664 -6.883 -13.939 ATOM 3 C MET A 1 -35.031 -6.598 -12.474 ATOM 4 O MET A 1 -36.183 -6.263 -12.186 ATOM 5 CB MET A 1 -34.293 -5.587 -14.662 ATOM 6 CG MET A 1 -33.150 -4.787 -14.060 ATOM 7 SD MET A 1 -32.948 -3.217 -14.990 ATOM 8 CE MET A 1 -34.066 -2.206 -14.093 ATOM 9 N VAL A 2 -34.068 -6.773 -11.568 ATOM 10 CA VAL A 2 -34.283 -6.504 -10.144 ATOM 11 C VAL A 2 -33.632 -5.165 -9.815 ATOM 12 O VAL A 2 -32.507 -4.897 -10.247 ATOM 13 CB VAL A 2 -33.628 -7.597 -9.278 ATOM 14 CG1 VAL A 2 -33.762 -7.248 -7.790 ATOM 15 CG2 VAL A 2 -34.313 -8.920 -9.513 ATOM 16 N THR A 3 -34.329 -4.335 -9.038 ATOM 17 CA THR A 3 -33.853 -3.026 -8.636 ATOM 18 C THR A 3 -33.758 -3.042 -7.112 ATOM 19 O THR A 3 -34.680 -3.483 -6.436 ATOM 20 CB THR A 3 -34.852 -1.943 -9.058 ATOM 21 OG1 THR A 3 -34.928 -1.954 -10.491 ATOM 22 CG2 THR A 3 -34.400 -0.570 -8.591 ATOM 23 N ALA A 4 -32.642 -2.559 -6.583 ATOM 24 CA ALA A 4 -32.483 -2.558 -5.130 ATOM 25 C ALA A 4 -31.614 -1.411 -4.657 ATOM 26 O ALA A 4 -30.839 -0.857 -5.418 ATOM 27 CB ALA A 4 -31.851 -3.910 -4.670 ATOM 28 N PHE A 5 -31.787 -1.029 -3.399 ATOM 29 CA PHE A 5 -30.940 -0.017 -2.792 ATOM 30 C PHE A 5 -30.146 -0.726 -1.710 ATOM 31 O PHE A 5 -30.725 -1.433 -0.875 ATOM 32 CB PHE A 5 -31.775 1.083 -2.141 ATOM 33 CG PHE A 5 -32.320 2.058 -3.118 ATOM 34 CD1 PHE A 5 -31.596 3.207 -3.447 ATOM 35 CD2 PHE A 5 -33.522 1.800 -3.763 ATOM 36 CE1 PHE A 5 -32.039 4.074 -4.407 ATOM 37 CE2 PHE A 5 -34.013 2.656 -4.741 ATOM 38 CZ PHE A 5 -33.266 3.810 -5.078 ATOM 39 N ILE A 6 -28.829 -0.577 -1.755 ATOM 40 CA ILE A 6 -27.978 -1.201 -0.739 ATOM 41 C ILE A 6 -27.490 -0.075 0.188 ATOM 42 O ILE A 6 -26.835 0.867 -0.296 ATOM 43 CB ILE A 6 -26.758 -1.900 -1.369 ATOM 44 CG1 ILE A 6 -27.164 -2.956 -2.409 ATOM 45 CG2 ILE A 6 -25.974 -2.620 -0.215 ATOM 46 CD1 ILE A 6 -25.963 -3.525 -3.177 ATOM 47 N LEU A 7 -27.820 -0.146 1.474 ATOM 48 CA LEU A 7 -27.416 0.862 2.461 ATOM 49 C LEU A 7 -26.158 0.325 3.110 ATOM 50 O LEU A 7 -26.141 -0.823 3.552 ATOM 51 CB LEU A 7 -28.531 1.081 3.503 ATOM 52 CG LEU A 7 -29.869 1.769 3.153 ATOM 53 CD1 LEU A 7 -29.658 3.236 2.903 ATOM 54 CD2 LEU A 7 -30.577 1.072 2.003 ATOM 55 N MET A 8 -25.113 1.144 3.175 ATOM 56 CA MET A 8 -23.820 0.694 3.663 ATOM 57 C MET A 8 -23.216 1.478 4.797 ATOM 58 O MET A 8 -23.355 2.705 4.863 ATOM 59 CB MET A 8 -22.805 0.716 2.520 ATOM 60 CG MET A 8 -23.303 0.038 1.207 ATOM 61 SD MET A 8 -21.963 0.079 -0.001 ATOM 62 CE MET A 8 -22.739 -0.888 -1.377 ATOM 63 N VAL A 9 -22.528 0.744 5.685 ATOM 64 CA VAL A 9 -21.751 1.321 6.795 ATOM 65 C VAL A 9 -20.324 1.148 6.307 ATOM 66 O VAL A 9 -19.916 0.079 5.859 ATOM 67 CB VAL A 9 -21.947 0.552 8.110 ATOM 68 CG1 VAL A 9 -20.963 1.089 9.173 ATOM 69 CG2 VAL A 9 -23.359 0.657 8.569 ATOM 70 N THR A 10 -19.534 2.207 6.312 ATOM 71 CA THR A 10 -18.168 2.079 5.859 ATOM 72 C THR A 10 -17.214 2.628 6.903 ATOM 73 O THR A 10 -17.622 3.396 7.773 ATOM 74 CB THR A 10 -17.901 2.869 4.558 ATOM 75 OG1 THR A 10 -18.005 4.272 4.826 ATOM 76 CG2 THR A 10 -18.900 2.537 3.474 ATOM 77 N ALA A 11 -15.965 2.214 6.805 ATOM 78 CA ALA A 11 -14.916 2.748 7.675 ATOM 79 C ALA A 11 -14.828 4.241 7.309 ATOM 80 O ALA A 11 -15.008 4.624 6.157 ATOM 81 CB ALA A 11 -13.606 2.065 7.351 ATOM 82 N ALA A 12 -14.525 5.086 8.288 ATOM 83 CA ALA A 12 -14.472 6.531 7.995 ATOM 84 C ALA A 12 -13.331 6.928 7.037 ATOM 85 O ALA A 12 -12.244 6.378 7.113 ATOM 86 CB ALA A 12 -14.390 7.321 9.338 ATOM 87 N GLY A 13 -13.634 7.862 6.126 ATOM 88 CA GLY A 13 -12.668 8.337 5.149 ATOM 89 C GLY A 13 -12.575 7.537 3.849 ATOM 90 O GLY A 13 -11.872 7.930 2.909 ATOM 91 N LYS A 14 -13.285 6.416 3.786 ATOM 92 CA LYS A 14 -13.261 5.574 2.593 ATOM 93 C LYS A 14 -14.493 5.686 1.683 ATOM 94 O LYS A 14 -14.576 5.016 0.650 ATOM 95 CB LYS A 14 -13.060 4.118 3.033 ATOM 96 CG LYS A 14 -11.780 3.953 3.841 ATOM 97 CD LYS A 14 -11.791 2.684 4.653 ATOM 98 CE LYS A 14 -10.578 2.594 5.573 ATOM 99 NZ LYS A 14 -10.464 1.242 6.222 ATOM 100 N GLU A 15 -15.441 6.536 2.060 ATOM 101 CA GLU A 15 -16.684 6.725 1.304 ATOM 102 C GLU A 15 -16.547 6.984 -0.191 ATOM 103 O GLU A 15 -17.155 6.274 -1.014 ATOM 104 CB GLU A 15 -17.505 7.876 1.911 ATOM 105 CG GLU A 15 -17.898 7.721 3.386 ATOM 106 CD GLU A 15 -16.815 8.171 4.341 ATOM 107 OE1 GLU A 15 -16.119 9.152 4.027 ATOM 108 OE2 GLU A 15 -16.673 7.566 5.426 ATOM 109 N ARG A 16 -15.778 8.010 -0.540 ATOM 110 CA ARG A 16 -15.585 8.390 -1.931 ATOM 111 C ARG A 16 -14.770 7.369 -2.716 ATOM 112 O ARG A 16 -15.072 7.133 -3.896 ATOM 113 CB ARG A 16 -14.920 9.778 -2.024 ATOM 114 CG ARG A 16 -15.794 10.970 -1.597 ATOM 115 CD ARG A 16 -15.078 12.286 -1.949 ATOM 116 NE ARG A 16 -15.933 13.472 -1.867 ATOM 117 CZ ARG A 16 -15.551 14.701 -2.218 ATOM 118 NH1 ARG A 16 -14.326 14.915 -2.681 ATOM 119 NH2 ARG A 16 -16.395 15.722 -2.108 ATOM 120 N GLU A 17 -13.740 6.793 -2.077 ATOM 121 CA GLU A 17 -12.879 5.767 -2.693 ATOM 122 C GLU A 17 -13.745 4.592 -3.092 ATOM 123 O GLU A 17 -13.643 4.074 -4.211 ATOM 124 CB GLU A 17 -11.817 5.252 -1.703 ATOM 125 CG GLU A 17 -11.189 3.900 -2.124 ATOM 126 CD GLU A 17 -10.201 3.317 -1.106 ATOM 127 OE1 GLU A 17 -9.919 2.102 -1.173 ATOM 128 OE2 GLU A 17 -9.693 4.060 -0.248 ATOM 129 N VAL A 18 -14.576 4.163 -2.146 ATOM 130 CA VAL A 18 -15.511 3.061 -2.336 ATOM 131 C VAL A 18 -16.577 3.482 -3.346 ATOM 132 O VAL A 18 -16.956 2.706 -4.198 ATOM 133 CB VAL A 18 -16.228 2.666 -0.974 ATOM 134 CG1 VAL A 18 -17.482 1.813 -1.246 ATOM 135 CG2 VAL A 18 -15.255 1.883 -0.091 ATOM 136 N MET A 19 -17.073 4.712 -3.210 ATOM 137 CA MET A 19 -18.116 5.241 -4.095 ATOM 138 C MET A 19 -17.607 5.175 -5.541 ATOM 139 O MET A 19 -18.313 4.741 -6.441 ATOM 140 CB MET A 19 -18.443 6.693 -3.689 ATOM 141 CG MET A 19 -19.907 7.021 -3.252 ATOM 142 SD MET A 19 -20.630 8.353 -4.316 ATOM 143 CE MET A 19 -19.320 9.541 -4.402 ATOM 144 N GLU A 20 -16.364 5.566 -5.772 ATOM 145 CA GLU A 20 -15.874 5.502 -7.137 ATOM 146 C GLU A 20 -15.661 4.083 -7.619 ATOM 147 O GLU A 20 -15.915 3.777 -8.792 ATOM 148 CB GLU A 20 -14.631 6.350 -7.301 ATOM 149 CG GLU A 20 -14.993 7.838 -7.209 ATOM 150 CD GLU A 20 -16.269 8.191 -8.004 ATOM 151 OE1 GLU A 20 -17.311 8.483 -7.361 ATOM 152 OE2 GLU A 20 -16.229 8.170 -9.269 ATOM 153 N LYS A 21 -15.212 3.189 -6.738 ATOM 154 CA LYS A 21 -15.069 1.808 -7.163 ATOM 155 C LYS A 21 -16.442 1.220 -7.422 ATOM 156 O LYS A 21 -16.614 0.415 -8.335 ATOM 157 CB LYS A 21 -14.377 0.948 -6.110 ATOM 158 CG LYS A 21 -12.870 1.159 -6.013 ATOM 159 CD LYS A 21 -12.303 0.191 -4.944 ATOM 160 CE LYS A 21 -10.776 0.225 -4.886 ATOM 161 NZ LYS A 21 -10.171 1.453 -4.308 ATOM 162 N LEU A 22 -17.422 1.617 -6.606 ATOM 163 CA LEU A 22 -18.777 1.109 -6.788 ATOM 164 C LEU A 22 -19.388 1.608 -8.079 ATOM 165 O LEU A 22 -19.926 0.841 -8.837 ATOM 166 CB LEU A 22 -19.691 1.501 -5.604 ATOM 167 CG LEU A 22 -19.424 0.794 -4.277 ATOM 168 CD1 LEU A 22 -20.198 1.493 -3.187 ATOM 169 CD2 LEU A 22 -19.818 -0.665 -4.387 ATOM 170 N LEU A 23 -19.294 2.917 -8.322 ATOM 171 CA LEU A 23 -19.883 3.479 -9.521 ATOM 172 C LEU A 23 -19.309 2.887 -10.801 ATOM 173 O LEU A 23 -19.974 2.868 -11.834 ATOM 174 CB LEU A 23 -19.699 4.998 -9.520 ATOM 175 CG LEU A 23 -20.846 5.676 -8.780 ATOM 176 CD1 LEU A 23 -20.499 7.161 -8.561 ATOM 177 CD2 LEU A 23 -22.172 5.469 -9.562 ATOM 178 N ALA A 24 -18.071 2.393 -10.733 ATOM 179 CA ALA A 24 -17.442 1.813 -11.921 ATOM 180 C ALA A 24 -18.004 0.436 -12.236 ATOM 181 O ALA A 24 -17.811 -0.097 -13.320 ATOM 182 CB ALA A 24 -15.933 1.741 -11.732 ATOM 183 N MET A 25 -18.731 -0.135 -11.272 ATOM 184 CA MET A 25 -19.287 -1.473 -11.499 ATOM 185 C MET A 25 -20.545 -1.396 -12.335 ATOM 186 O MET A 25 -21.421 -0.553 -12.114 ATOM 187 CB MET A 25 -19.594 -2.172 -10.170 ATOM 188 CG MET A 25 -18.388 -2.409 -9.308 ATOM 189 SD MET A 25 -18.784 -3.016 -7.671 ATOM 190 CE MET A 25 -17.107 -3.128 -6.966 ATOM 191 N PRO A 26 -20.681 -2.300 -13.307 ATOM 192 CA PRO A 26 -21.870 -2.245 -14.145 ATOM 193 C PRO A 26 -23.239 -2.337 -13.447 ATOM 194 O PRO A 26 -24.201 -1.730 -13.882 ATOM 195 CB PRO A 26 -21.604 -3.351 -15.184 ATOM 196 CG PRO A 26 -20.782 -4.304 -14.461 ATOM 197 CD PRO A 26 -19.827 -3.453 -13.654 ATOM 198 N GLU A 27 -23.296 -3.065 -12.345 ATOM 199 CA GLU A 27 -24.545 -3.199 -11.624 ATOM 200 C GLU A 27 -24.971 -1.907 -10.917 ATOM 201 O GLU A 27 -26.155 -1.714 -10.652 ATOM 202 CB GLU A 27 -24.417 -4.262 -10.541 ATOM 203 CG GLU A 27 -24.206 -5.670 -11.059 ATOM 204 CD GLU A 27 -22.756 -6.001 -11.359 ATOM 205 OE1 GLU A 27 -21.843 -5.132 -11.182 ATOM 206 OE2 GLU A 27 -22.549 -7.164 -11.773 ATOM 207 N VAL A 28 -23.988 -1.076 -10.565 ATOM 208 CA VAL A 28 -24.238 0.131 -9.804 ATOM 209 C VAL A 28 -24.657 1.283 -10.689 ATOM 210 O VAL A 28 -23.881 1.717 -11.562 ATOM 211 CB VAL A 28 -23.016 0.519 -8.959 ATOM 212 CG1 VAL A 28 -23.273 1.851 -8.250 ATOM 213 CG2 VAL A 28 -22.735 -0.583 -7.947 ATOM 214 N LYS A 29 -25.869 1.775 -10.441 ATOM 215 CA LYS A 29 -26.419 2.844 -11.260 ATOM 216 C LYS A 29 -26.323 4.220 -10.665 ATOM 217 O LYS A 29 -26.220 5.215 -11.406 ATOM 218 CB LYS A 29 -27.876 2.547 -11.613 ATOM 219 CG LYS A 29 -28.077 1.163 -12.253 ATOM 220 CD LYS A 29 -27.098 0.895 -13.421 ATOM 221 CE LYS A 29 -27.163 -0.549 -14.013 ATOM 222 NZ LYS A 29 -28.349 -0.812 -14.826 ATOM 223 N GLU A 30 -26.362 4.301 -9.336 ATOM 224 CA GLU A 30 -26.272 5.579 -8.638 ATOM 225 C GLU A 30 -25.651 5.284 -7.288 ATOM 226 O GLU A 30 -25.820 4.190 -6.757 ATOM 227 CB GLU A 30 -27.655 6.176 -8.332 ATOM 228 CG GLU A 30 -28.525 6.343 -9.533 ATOM 229 CD GLU A 30 -29.932 6.747 -9.170 ATOM 230 OE1 GLU A 30 -30.171 7.178 -8.021 ATOM 231 OE2 GLU A 30 -30.803 6.641 -10.055 ATOM 232 N ALA A 31 -24.938 6.262 -6.746 ATOM 233 CA ALA A 31 -24.319 6.133 -5.432 ATOM 234 C ALA A 31 -24.314 7.518 -4.774 ATOM 235 O ALA A 31 -24.133 8.570 -5.436 ATOM 236 CB ALA A 31 -22.888 5.621 -5.536 ATOM 237 N TYR A 32 -24.549 7.526 -3.461 ATOM 238 CA TYR A 32 -24.565 8.761 -2.701 ATOM 239 C TYR A 32 -23.894 8.595 -1.367 ATOM 240 O TYR A 32 -24.190 7.657 -0.630 ATOM 241 CB TYR A 32 -25.989 9.187 -2.388 ATOM 242 CG TYR A 32 -26.876 9.311 -3.586 ATOM 243 CD1 TYR A 32 -27.158 10.552 -4.139 ATOM 244 CD2 TYR A 32 -27.470 8.181 -4.134 ATOM 245 CE1 TYR A 32 -28.049 10.649 -5.245 ATOM 246 CE2 TYR A 32 -28.342 8.266 -5.211 ATOM 247 CZ TYR A 32 -28.618 9.496 -5.754 ATOM 248 OH TYR A 32 -29.477 9.505 -6.837 ATOM 249 N VAL A 33 -22.982 9.503 -1.074 ATOM 250 CA VAL A 33 -22.396 9.584 0.279 ATOM 251 C VAL A 33 -23.486 10.311 1.070 ATOM 252 O VAL A 33 -24.027 11.348 0.646 ATOM 253 CB VAL A 33 -21.120 10.425 0.282 ATOM 254 CG1 VAL A 33 -20.626 10.611 1.713 ATOM 255 CG2 VAL A 33 -20.073 9.731 -0.563 ATOM 256 N VAL A 34 -23.811 9.786 2.248 ATOM 257 CA VAL A 34 -24.871 10.366 3.062 ATOM 258 C VAL A 34 -24.518 10.376 4.535 ATOM 259 O VAL A 34 -23.584 9.663 5.006 ATOM 260 CB VAL A 34 -26.228 9.567 2.973 ATOM 261 CG1 VAL A 34 -26.859 9.748 1.575 ATOM 262 CG2 VAL A 34 -25.978 8.057 3.231 ATOM 263 N TYR A 35 -25.260 11.212 5.260 ATOM 264 CA TYR A 35 -25.148 11.281 6.719 ATOM 265 C TYR A 35 -26.449 10.771 7.333 ATOM 266 O TYR A 35 -27.545 11.151 6.913 ATOM 267 CB TYR A 35 -24.915 12.706 7.208 ATOM 268 CG TYR A 35 -23.506 13.206 7.110 ATOM 269 CD1 TYR A 35 -23.210 14.484 7.541 ATOM 270 CD2 TYR A 35 -22.466 12.409 6.622 ATOM 271 CE1 TYR A 35 -21.914 14.979 7.499 ATOM 272 CE2 TYR A 35 -21.164 12.889 6.561 ATOM 273 CZ TYR A 35 -20.895 14.173 6.998 ATOM 274 OH TYR A 35 -19.618 14.716 6.904 ATOM 275 N GLY A 36 -26.318 9.920 8.342 ATOM 276 CA GLY A 36 -27.477 9.342 8.981 ATOM 277 C GLY A 36 -27.063 7.977 9.519 ATOM 278 O GLY A 36 -25.903 7.784 9.852 ATOM 279 N GLU A 37 -27.995 7.038 9.570 ATOM 280 CA GLU A 37 -27.748 5.673 10.050 ATOM 281 C GLU A 37 -26.720 4.941 9.166 ATOM 282 O GLU A 37 -25.946 4.083 9.619 ATOM 283 CB GLU A 37 -29.079 4.922 10.062 ATOM 284 CG GLU A 37 -28.987 3.484 10.482 ATOM 285 CD GLU A 37 -30.343 2.845 10.620 ATOM 286 OE1 GLU A 37 -31.363 3.567 10.556 ATOM 287 OE2 GLU A 37 -30.398 1.606 10.798 ATOM 288 N TYR A 38 -26.728 5.252 7.872 ATOM 289 CA TYR A 38 -25.789 4.663 6.938 ATOM 290 C TYR A 38 -24.908 5.746 6.328 ATOM 291 O TYR A 38 -25.248 6.944 6.376 ATOM 292 CB TYR A 38 -26.559 3.928 5.844 ATOM 293 CG TYR A 38 -27.332 2.733 6.376 ATOM 294 CD1 TYR A 38 -26.701 1.501 6.565 ATOM 295 CD2 TYR A 38 -28.671 2.854 6.716 ATOM 296 CE1 TYR A 38 -27.397 0.399 7.097 ATOM 297 CE2 TYR A 38 -29.385 1.757 7.247 ATOM 298 CZ TYR A 38 -28.737 0.552 7.425 ATOM 299 OH TYR A 38 -29.444 -0.517 7.915 ATOM 300 N ASP A 39 -23.775 5.324 5.778 ATOM 301 CA ASP A 39 -22.790 6.202 5.158 ATOM 302 C ASP A 39 -22.869 6.337 3.666 ATOM 303 O ASP A 39 -22.399 7.334 3.094 ATOM 304 CB ASP A 39 -21.379 5.703 5.506 ATOM 305 CG ASP A 39 -21.153 5.632 6.998 ATOM 306 OD1 ASP A 39 -21.261 6.697 7.656 ATOM 307 OD2 ASP A 39 -20.855 4.535 7.506 ATOM 308 N LEU A 40 -23.378 5.284 3.028 ATOM 309 CA LEU A 40 -23.461 5.277 1.577 ATOM 310 C LEU A 40 -24.726 4.569 1.148 ATOM 311 O LEU A 40 -25.139 3.603 1.775 ATOM 312 CB LEU A 40 -22.228 4.543 0.980 ATOM 313 CG LEU A 40 -21.925 4.479 -0.525 ATOM 314 CD1 LEU A 40 -21.848 5.890 -1.106 ATOM 315 CD2 LEU A 40 -20.596 3.732 -0.744 ATOM 316 N ILE A 41 -25.371 5.081 0.102 ATOM 317 CA ILE A 41 -26.561 4.434 -0.453 ATOM 318 C ILE A 41 -26.275 4.217 -1.932 ATOM 319 O ILE A 41 -25.878 5.133 -2.641 ATOM 320 CB ILE A 41 -27.800 5.286 -0.368 ATOM 321 CG1 ILE A 41 -28.189 5.489 1.076 ATOM 322 CG2 ILE A 41 -28.981 4.551 -1.132 ATOM 323 CD1 ILE A 41 -29.424 6.323 1.226 ATOM 324 N VAL A 42 -26.496 2.998 -2.396 ATOM 325 CA VAL A 42 -26.228 2.671 -3.786 ATOM 326 C VAL A 42 -27.460 2.022 -4.412 ATOM 327 O VAL A 42 -28.150 1.215 -3.769 ATOM 328 CB VAL A 42 -25.006 1.734 -3.870 ATOM 329 CG1 VAL A 42 -23.889 2.291 -2.946 ATOM 330 CG2 VAL A 42 -25.361 0.316 -3.496 ATOM 331 N LYS A 43 -27.798 2.430 -5.633 ATOM 332 CA LYS A 43 -28.941 1.853 -6.347 ATOM 333 C LYS A 43 -28.323 0.890 -7.347 ATOM 334 O LYS A 43 -27.464 1.269 -8.144 ATOM 335 CB LYS A 43 -29.793 2.903 -7.123 ATOM 336 CG LYS A 43 -31.116 2.304 -7.684 ATOM 337 CD LYS A 43 -31.938 3.302 -8.543 ATOM 338 CE LYS A 43 -33.303 2.731 -8.911 ATOM 339 NZ LYS A 43 -33.907 3.574 -9.998 ATOM 340 N VAL A 44 -28.758 -0.366 -7.293 ATOM 341 CA VAL A 44 -28.277 -1.382 -8.227 ATOM 342 C VAL A 44 -29.430 -2.020 -8.991 ATOM 343 O VAL A 44 -30.583 -2.037 -8.548 ATOM 344 CB VAL A 44 -27.545 -2.528 -7.509 ATOM 345 CG1 VAL A 44 -26.301 -2.027 -6.834 ATOM 346 CG2 VAL A 44 -28.453 -3.165 -6.499 ATOM 347 N GLU A 45 -29.101 -2.474 -10.197 ATOM 348 CA GLU A 45 -30.032 -3.224 -11.040 ATOM 349 C GLU A 45 -29.268 -4.484 -11.492 ATOM 350 O GLU A 45 -28.116 -4.412 -11.942 ATOM 351 CB GLU A 45 -30.496 -2.378 -12.258 ATOM 352 CG GLU A 45 -31.341 -1.173 -11.858 ATOM 353 CD GLU A 45 -31.677 -0.230 -13.021 ATOM 354 OE1 GLU A 45 -30.974 -0.274 -14.048 ATOM 355 OE2 GLU A 45 -32.633 0.552 -12.884 ATOM 356 N THR A 46 -29.918 -5.632 -11.352 ATOM 357 CA THR A 46 -29.341 -6.925 -11.736 ATOM 358 C THR A 46 -30.384 -7.735 -12.500 ATOM 359 O THR A 46 -31.579 -7.459 -12.407 ATOM 360 CB THR A 46 -28.853 -7.732 -10.500 ATOM 361 OG1 THR A 46 -29.953 -8.003 -9.622 ATOM 362 CG2 THR A 46 -27.735 -6.958 -9.755 ATOM 363 N ASP A 47 -29.939 -8.747 -13.241 ATOM 364 CA ASP A 47 -30.878 -9.551 -14.011 ATOM 365 C ASP A 47 -31.833 -10.352 -13.136 ATOM 366 O ASP A 47 -33.036 -10.461 -13.408 ATOM 367 CB ASP A 47 -30.088 -10.510 -14.903 ATOM 368 CG ASP A 47 -29.320 -9.797 -15.991 ATOM 369 OD1 ASP A 47 -29.582 -8.595 -16.229 ATOM 370 OD2 ASP A 47 -28.457 -10.451 -16.622 ATOM 371 N THR A 48 -31.275 -10.936 -12.094 ATOM 372 CA THR A 48 -31.996 -11.805 -11.190 ATOM 373 C THR A 48 -31.636 -11.519 -9.746 ATOM 374 O THR A 48 -30.654 -10.802 -9.448 ATOM 375 CB THR A 48 -31.599 -13.294 -11.440 ATOM 376 OG1 THR A 48 -30.210 -13.487 -11.070 ATOM 377 CG2 THR A 48 -31.741 -13.642 -12.949 ATOM 378 N LEU A 49 -32.428 -12.075 -8.840 ATOM 379 CA LEU A 49 -32.135 -11.978 -7.411 ATOM 380 C LEU A 49 -30.851 -12.716 -7.074 ATOM 381 O LEU A 49 -30.080 -12.298 -6.199 ATOM 382 CB LEU A 49 -33.281 -12.532 -6.554 ATOM 383 CG LEU A 49 -34.391 -11.563 -6.233 ATOM 384 CD1 LEU A 49 -35.291 -12.246 -5.196 ATOM 385 CD2 LEU A 49 -33.834 -10.232 -5.630 ATOM 386 N LYS A 50 -30.598 -13.835 -7.746 ATOM 387 CA LYS A 50 -29.385 -14.574 -7.494 ATOM 388 C LYS A 50 -28.185 -13.675 -7.804 ATOM 389 O LYS A 50 -27.196 -13.667 -7.069 ATOM 390 CB LYS A 50 -29.374 -15.839 -8.366 ATOM 391 CG LYS A 50 -28.083 -16.600 -8.281 ATOM 392 CD LYS A 50 -28.213 -17.957 -8.920 ATOM 393 CE LYS A 50 -26.851 -18.613 -9.055 ATOM 394 NZ LYS A 50 -26.976 -20.031 -9.478 ATOM 395 N ASP A 51 -28.281 -12.904 -8.884 ATOM 396 CA ASP A 51 -27.192 -11.993 -9.228 ATOM 397 C ASP A 51 -27.020 -10.918 -8.147 ATOM 398 O ASP A 51 -25.897 -10.550 -7.798 ATOM 399 CB ASP A 51 -27.447 -11.319 -10.586 ATOM 400 CG ASP A 51 -27.316 -12.286 -11.759 ATOM 401 OD1 ASP A 51 -26.408 -13.135 -11.716 ATOM 402 OD2 ASP A 51 -28.108 -12.169 -12.711 ATOM 403 N LEU A 52 -28.126 -10.396 -7.647 ATOM 404 CA LEU A 52 -28.039 -9.393 -6.586 ATOM 405 C LEU A 52 -27.400 -9.998 -5.331 ATOM 406 O LEU A 52 -26.592 -9.339 -4.682 ATOM 407 CB LEU A 52 -29.432 -8.849 -6.290 ATOM 408 CG LEU A 52 -29.515 -7.909 -5.079 ATOM 409 CD1 LEU A 52 -28.622 -6.677 -5.324 ATOM 410 CD2 LEU A 52 -30.990 -7.549 -4.806 ATOM 411 N ASP A 53 -27.788 -11.220 -4.974 ATOM 412 CA ASP A 53 -27.250 -11.886 -3.803 ATOM 413 C ASP A 53 -25.745 -12.043 -3.924 ATOM 414 O ASP A 53 -25.000 -11.783 -2.971 ATOM 415 CB ASP A 53 -27.931 -13.252 -3.645 ATOM 416 CG ASP A 53 -27.790 -13.802 -2.257 ATOM 417 OD1 ASP A 53 -27.786 -13.011 -1.288 ATOM 418 OD2 ASP A 53 -27.688 -15.033 -2.135 ATOM 419 N GLN A 54 -25.280 -12.456 -5.100 ATOM 420 CA GLN A 54 -23.859 -12.616 -5.309 ATOM 421 C GLN A 54 -23.145 -11.284 -5.250 ATOM 422 O GLN A 54 -22.033 -11.206 -4.727 ATOM 423 CB GLN A 54 -23.597 -13.346 -6.625 ATOM 424 CG GLN A 54 -24.127 -14.755 -6.529 ATOM 425 CD GLN A 54 -23.878 -15.578 -7.770 ATOM 426 OE1 GLN A 54 -23.247 -15.119 -8.724 ATOM 427 NE2 GLN A 54 -24.368 -16.813 -7.760 ATOM 428 N PHE A 55 -23.758 -10.226 -5.757 ATOM 429 CA PHE A 55 -23.128 -8.913 -5.673 ATOM 430 C PHE A 55 -22.938 -8.514 -4.211 ATOM 431 O PHE A 55 -21.864 -8.030 -3.828 ATOM 432 CB PHE A 55 -24.018 -7.892 -6.380 ATOM 433 CG PHE A 55 -23.448 -6.509 -6.415 ATOM 434 CD1 PHE A 55 -22.595 -6.140 -7.449 ATOM 435 CD2 PHE A 55 -23.733 -5.581 -5.409 ATOM 436 CE1 PHE A 55 -22.035 -4.860 -7.485 ATOM 437 CE2 PHE A 55 -23.167 -4.280 -5.431 ATOM 438 CZ PHE A 55 -22.322 -3.934 -6.480 ATOM 439 N ILE A 56 -23.984 -8.686 -3.405 ATOM 440 CA ILE A 56 -23.948 -8.313 -2.000 ATOM 441 C ILE A 56 -22.987 -9.148 -1.168 ATOM 442 O ILE A 56 -22.261 -8.598 -0.347 ATOM 443 CB ILE A 56 -25.376 -8.459 -1.390 ATOM 444 CG1 ILE A 56 -26.289 -7.371 -1.967 ATOM 445 CG2 ILE A 56 -25.329 -8.392 0.151 ATOM 446 CD1 ILE A 56 -27.739 -7.521 -1.574 ATOM 447 N THR A 57 -22.959 -10.461 -1.364 ATOM 448 CA THR A 57 -22.088 -11.246 -0.490 ATOM 449 C THR A 57 -20.683 -11.497 -1.042 ATOM 450 O THR A 57 -19.718 -11.631 -0.257 ATOM 451 CB THR A 57 -22.774 -12.556 -0.095 ATOM 452 OG1 THR A 57 -22.821 -13.385 -1.247 ATOM 453 CG2 THR A 57 -24.225 -12.310 0.420 ATOM 454 N GLU A 58 -20.531 -11.490 -2.358 ATOM 455 CA GLU A 58 -19.203 -11.666 -2.942 ATOM 456 C GLU A 58 -18.510 -10.387 -3.385 ATOM 457 O GLU A 58 -17.411 -10.096 -2.922 ATOM 458 CB GLU A 58 -19.234 -12.599 -4.139 ATOM 459 CG GLU A 58 -19.923 -13.930 -3.875 ATOM 460 CD GLU A 58 -19.918 -14.829 -5.113 ATOM 461 OE1 GLU A 58 -20.834 -15.660 -5.290 ATOM 462 OE2 GLU A 58 -18.981 -14.717 -5.920 ATOM 463 N LYS A 59 -19.140 -9.637 -4.283 ATOM 464 CA LYS A 59 -18.491 -8.426 -4.791 ATOM 465 C LYS A 59 -18.197 -7.401 -3.711 ATOM 466 O LYS A 59 -17.119 -6.827 -3.688 ATOM 467 CB LYS A 59 -19.335 -7.797 -5.895 ATOM 468 CG LYS A 59 -18.552 -6.826 -6.770 ATOM 469 CD LYS A 59 -19.017 -6.963 -8.217 ATOM 470 CE LYS A 59 -18.155 -6.208 -9.202 ATOM 471 NZ LYS A 59 -18.806 -6.201 -10.566 ATOM 472 N ILE A 60 -19.147 -7.160 -2.812 ATOM 473 CA ILE A 60 -18.916 -6.184 -1.756 ATOM 474 C ILE A 60 -17.775 -6.606 -0.830 ATOM 475 O ILE A 60 -17.060 -5.746 -0.310 ATOM 476 CB ILE A 60 -20.197 -5.919 -0.939 ATOM 477 CG1 ILE A 60 -21.222 -5.223 -1.841 ATOM 478 CG2 ILE A 60 -19.882 -5.043 0.294 ATOM 479 CD1 ILE A 60 -20.723 -3.973 -2.539 ATOM 480 N ARG A 61 -17.570 -7.916 -0.646 ATOM 481 CA ARG A 61 -16.459 -8.356 0.191 ATOM 482 C ARG A 61 -15.070 -8.087 -0.400 ATOM 483 O ARG A 61 -14.060 -8.281 0.285 ATOM 484 CB ARG A 61 -16.637 -9.849 0.560 ATOM 485 CG ARG A 61 -17.531 -10.009 1.767 ATOM 486 CD ARG A 61 -17.521 -11.462 2.270 ATOM 487 NE ARG A 61 -18.164 -11.608 3.562 ATOM 488 CZ ARG A 61 -19.466 -11.862 3.719 ATOM 489 NH1 ARG A 61 -20.237 -11.991 2.632 ATOM 490 NH2 ARG A 61 -19.979 -12.023 4.948 ATOM 491 N LYS A 62 -15.008 -7.638 -1.656 ATOM 492 CA LYS A 62 -13.709 -7.284 -2.261 ATOM 493 C LYS A 62 -13.272 -5.933 -1.708 ATOM 494 O LYS A 62 -12.115 -5.539 -1.882 ATOM 495 CB LYS A 62 -13.806 -7.196 -3.803 ATOM 496 CG LYS A 62 -14.168 -8.529 -4.471 ATOM 497 CD LYS A 62 -14.249 -8.438 -5.999 ATOM 498 CE LYS A 62 -12.894 -8.113 -6.582 ATOM 499 NZ LYS A 62 -11.842 -8.953 -5.950 ATOM 500 N MET A 63 -14.190 -5.225 -1.040 ATOM 501 CA MET A 63 -13.900 -3.916 -0.455 ATOM 502 C MET A 63 -14.114 -3.999 1.047 ATOM 503 O MET A 63 -15.190 -3.693 1.554 ATOM 504 CB MET A 63 -14.819 -2.848 -1.069 ATOM 505 CG MET A 63 -14.547 -2.656 -2.551 ATOM 506 SD MET A 63 -15.844 -1.729 -3.405 ATOM 507 CE MET A 63 -17.064 -3.026 -3.458 ATOM 508 N PRO A 64 -13.080 -4.400 1.802 ATOM 509 CA PRO A 64 -13.272 -4.497 3.253 ATOM 510 C PRO A 64 -13.588 -3.190 3.977 ATOM 511 O PRO A 64 -13.926 -3.183 5.158 ATOM 512 CB PRO A 64 -11.986 -5.180 3.731 ATOM 513 CG PRO A 64 -10.956 -4.756 2.707 ATOM 514 CD PRO A 64 -11.727 -4.814 1.390 ATOM 515 N GLU A 65 -13.513 -2.091 3.232 ATOM 516 CA GLU A 65 -13.866 -0.796 3.797 ATOM 517 C GLU A 65 -15.381 -0.773 4.079 ATOM 518 O GLU A 65 -15.880 0.013 4.890 ATOM 519 CB GLU A 65 -13.536 0.330 2.806 ATOM 520 CG GLU A 65 -12.054 0.539 2.501 ATOM 521 CD GLU A 65 -11.484 -0.426 1.491 ATOM 522 OE1 GLU A 65 -12.241 -1.211 0.899 ATOM 523 OE2 GLU A 65 -10.252 -0.393 1.274 ATOM 524 N ILE A 66 -16.122 -1.630 3.382 ATOM 525 CA ILE A 66 -17.567 -1.708 3.590 ATOM 526 C ILE A 66 -17.805 -2.724 4.720 ATOM 527 O ILE A 66 -17.584 -3.932 4.546 ATOM 528 CB ILE A 66 -18.293 -2.139 2.306 ATOM 529 CG1 ILE A 66 -18.028 -1.128 1.180 ATOM 530 CG2 ILE A 66 -19.781 -2.233 2.590 ATOM 531 CD1 ILE A 66 -18.520 -1.539 -0.198 ATOM 532 N GLN A 67 -18.248 -2.243 5.864 ATOM 533 CA GLN A 67 -18.430 -3.074 7.070 ATOM 534 C GLN A 67 -19.784 -3.720 7.266 ATOM 535 O GLN A 67 -19.890 -4.783 7.922 ATOM 536 CB GLN A 67 -18.069 -2.223 8.324 ATOM 537 CG GLN A 67 -16.693 -1.635 8.272 ATOM 538 CD GLN A 67 -16.426 -0.674 9.412 ATOM 539 OE1 GLN A 67 -17.352 -0.119 10.000 ATOM 540 NE2 GLN A 67 -15.156 -0.458 9.715 ATOM 541 N MET A 68 -20.837 -3.106 6.715 ATOM 542 CA MET A 68 -22.168 -3.641 6.888 ATOM 543 C MET A 68 -23.048 -3.161 5.751 ATOM 544 O MET A 68 -22.880 -2.047 5.266 ATOM 545 CB MET A 68 -22.768 -3.180 8.235 ATOM 546 CG MET A 68 -24.097 -3.834 8.626 ATOM 547 SD MET A 68 -25.560 -2.952 8.022 ATOM 548 CE MET A 68 -26.000 -1.917 9.483 ATOM 549 N THR A 69 -23.893 -4.050 5.257 ATOM 550 CA THR A 69 -24.878 -3.648 4.261 ATOM 551 C THR A 69 -26.242 -4.194 4.643 ATOM 552 O THR A 69 -26.353 -5.262 5.292 ATOM 553 CB THR A 69 -24.568 -4.140 2.818 ATOM 554 OG1 THR A 69 -24.710 -5.577 2.726 ATOM 555 CG2 THR A 69 -23.153 -3.727 2.372 ATOM 556 N SER A 70 -27.269 -3.427 4.271 ATOM 557 CA SER A 70 -28.682 -3.815 4.435 ATOM 558 C SER A 70 -29.306 -3.468 3.082 ATOM 559 O SER A 70 -29.280 -2.301 2.671 ATOM 560 CB SER A 70 -29.390 -3.044 5.549 ATOM 561 OG SER A 70 -30.727 -3.509 5.712 ATOM 562 N THR A 71 -29.890 -4.449 2.411 ATOM 563 CA THR A 71 -30.435 -4.218 1.065 ATOM 564 C THR A 71 -31.963 -4.208 1.028 ATOM 565 O THR A 71 -32.615 -5.057 1.656 ATOM 566 CB THR A 71 -29.886 -5.275 0.133 ATOM 567 OG1 THR A 71 -28.453 -5.196 0.125 ATOM 568 CG2 THR A 71 -30.388 -5.079 -1.318 ATOM 569 N MET A 72 -32.524 -3.227 0.322 ATOM 570 CA MET A 72 -33.995 -3.073 0.198 ATOM 571 C MET A 72 -34.353 -3.412 -1.261 ATOM 572 O MET A 72 -33.935 -2.675 -2.150 ATOM 573 CB MET A 72 -34.389 -1.611 0.460 ATOM 574 CG MET A 72 -33.849 -0.965 1.741 ATOM 575 SD MET A 72 -34.588 -1.646 3.220 ATOM 576 CE MET A 72 -33.212 -1.300 4.390 ATOM 577 N ILE A 73 -35.065 -4.526 -1.524 ATOM 578 CA ILE A 73 -35.458 -4.899 -2.914 ATOM 579 C ILE A 73 -36.737 -4.172 -3.312 ATOM 580 O ILE A 73 -37.749 -4.268 -2.627 ATOM 581 CB ILE A 73 -35.718 -6.428 -3.044 ATOM 582 CG1 ILE A 73 -34.460 -7.220 -2.704 ATOM 583 CG2 ILE A 73 -36.170 -6.763 -4.450 ATOM 584 CD1 ILE A 73 -34.717 -8.711 -2.452 ATOM 585 N ALA A 74 -36.704 -3.445 -4.420 ATOM 586 CA ALA A 74 -37.914 -2.732 -4.857 ATOM 587 C ALA A 74 -38.966 -3.723 -5.375 ATOM 588 O ALA A 74 -38.656 -4.567 -6.232 ATOM 589 CB ALA A 74 -37.535 -1.736 -5.949 ATOM 590 N ILE A 75 -40.176 -3.622 -4.824 ATOM 591 CA ILE A 75 -41.284 -4.455 -5.283 ATOM 592 C ILE A 75 -42.388 -3.589 -5.900 ATOM 593 O ILE A 75 -43.306 -4.118 -6.500 ATOM 594 CB ILE A 75 -41.823 -5.376 -4.173 ATOM 595 CG1 ILE A 75 -42.162 -4.600 -2.894 ATOM 596 CG2 ILE A 75 -40.758 -6.430 -3.866 ATOM 597 CD1 ILE A 75 -42.893 -5.488 -1.846 ATOM 598 N LEU A 76 -42.299 -2.263 -5.742 ATOM 599 CA LEU A 76 -43.234 -1.336 -6.379 ATOM 600 C LEU A 76 -42.499 0.018 -6.353 ATOM 601 O LEU A 76 -41.762 0.336 -5.416 ATOM 602 CB LEU A 76 -44.539 -1.223 -5.579 ATOM 603 CG LEU A 76 -45.702 -0.616 -6.412 ATOM 604 CD1 LEU A 76 -46.246 -1.651 -7.384 ATOM 605 CD2 LEU A 76 -46.802 -0.110 -5.498 ATOM 606 N GLU A 77 -42.698 0.843 -7.379 ATOM 607 CA GLU A 77 -42.070 2.161 -7.370 ATOM 608 C GLU A 77 -42.816 3.179 -8.210 ATOM 609 O GLU A 77 -43.936 2.912 -8.651 ATOM 610 CB GLU A 77 -40.557 2.095 -7.691 ATOM 611 CG GLU A 77 -40.131 1.228 -8.841 ATOM 612 CD GLU A 77 -40.392 1.886 -10.142 ATOM 613 OE1 GLU A 77 -39.450 2.464 -10.703 ATOM 614 OE2 GLU A 77 -41.557 1.830 -10.574 ATOM 615 N HIS A 78 -42.185 4.322 -8.460 ATOM 616 CA HIS A 78 -42.881 5.431 -9.089 ATOM 617 C HIS A 78 -43.326 5.273 -10.505 ATOM 618 O HIS A 78 -44.065 6.109 -11.014 ATOM 619 CB HIS A 78 -42.087 6.727 -8.870 ATOM 620 CG HIS A 78 -40.667 6.614 -9.267 ATOM 621 ND1 HIS A 78 -39.739 5.992 -8.468 ATOM 622 CD2 HIS A 78 -40.012 6.981 -10.397 ATOM 623 CE1 HIS A 78 -38.570 5.981 -9.081 ATOM 624 NE2 HIS A 78 -38.712 6.577 -10.257 ATOM 625 N HIS A 79 -42.905 4.201 -11.146 ATOM 626 CA HIS A 79 -43.385 3.936 -12.485 ATOM 627 C HIS A 79 -44.668 3.147 -12.454 ATOM 628 O HIS A 79 -45.245 2.876 -13.508 ATOM 629 CB HIS A 79 -42.330 3.201 -13.299 ATOM 630 CG HIS A 79 -41.144 4.040 -13.621 ATOM 631 ND1 HIS A 79 -39.978 3.982 -12.882 ATOM 632 CD2 HIS A 79 -40.961 5.009 -14.556 ATOM 633 CE1 HIS A 79 -39.125 4.882 -13.357 ATOM 634 NE2 HIS A 79 -39.694 5.514 -14.372 ATOM 635 N HIS A 80 -45.124 2.720 -11.279 ATOM 636 CA HIS A 80 -46.389 1.977 -11.220 ATOM 637 C HIS A 80 -47.512 2.909 -11.700 ATOM 638 O HIS A 80 -47.743 3.985 -11.148 ATOM 639 CB HIS A 80 -46.625 1.503 -9.785 ATOM 640 CG HIS A 80 -47.867 0.684 -9.610 ATOM 641 ND1 HIS A 80 -48.029 -0.570 -10.162 ATOM 642 CD2 HIS A 80 -48.990 0.938 -8.899 ATOM 643 CE1 HIS A 80 -49.201 -1.056 -9.788 ATOM 644 NE2 HIS A 80 -49.803 -0.163 -9.020 ATOM 645 N HIS A 81 -48.164 2.442 -12.751 ATOM 646 CA HIS A 81 -49.227 3.132 -13.487 ATOM 647 C HIS A 81 -48.734 4.411 -14.156 ATOM 648 O HIS A 81 -49.518 5.184 -14.700 ATOM 649 CB HIS A 81 -50.435 3.450 -12.599 ATOM 650 CG HIS A 81 -51.069 2.239 -11.956 ATOM 651 ND1 HIS A 81 -51.034 0.971 -12.510 ATOM 652 CD2 HIS A 81 -51.802 2.134 -10.822 ATOM 653 CE1 HIS A 81 -51.724 0.143 -11.735 ATOM 654 NE2 HIS A 81 -52.199 0.828 -10.706 ATOM 655 N HIS A 82 -47.432 4.663 -14.052 ATOM 656 CA HIS A 82 -46.826 5.874 -14.630 ATOM 657 C HIS A 82 -45.571 5.535 -15.387 ATOM 658 O HIS A 82 -44.442 5.833 -14.953 ATOM 659 CB HIS A 82 -46.561 6.919 -13.532 ATOM 660 CG HIS A 82 -47.819 7.519 -13.000 ATOM 661 ND1 HIS A 82 -48.466 8.571 -13.633 ATOM 662 CD2 HIS A 82 -48.603 7.168 -11.952 ATOM 663 CE1 HIS A 82 -49.585 8.842 -12.982 ATOM 664 NE2 HIS A 82 -49.687 8.008 -11.958 ATOM 665 N HIS A 83 -45.761 4.898 -16.534 ATOM 666 CA HIS A 83 -44.616 4.527 -17.347 ATOM 667 C HIS A 83 -44.852 4.845 -18.813 ATOM 668 O HIS A 83 -45.554 5.850 -19.032 ATOM 669 CB HIS A 83 -44.277 3.028 -17.154 ATOM 670 CG HIS A 83 -45.387 2.120 -17.548 ATOM 671 ND1 HIS A 83 -45.562 1.651 -18.833 ATOM 672 CD2 HIS A 83 -46.366 1.558 -16.800 ATOM 673 CE1 HIS A 83 -46.604 0.834 -18.858 ATOM 674 NE2 HIS A 83 -47.107 0.763 -17.637 ATOM 675 OXT HIS A 83 -44.324 4.123 -19.672 ATOM CA GLY A 84 -3.901 9.352 -1.557 + ATOM CA GLY A 85 -6.632 8.551 -2.508 + ATOM CA GLY A 86 -9.362 7.750 -3.459 + ATOM CA GLY A 87 -12.092 6.950 -4.409 + ATOM CA GLY A 88 -14.823 6.149 -5.360 + ATOM CA GLY A 89 -17.553 5.348 -6.311 + ATOM CA GLY A 90 -20.283 4.547 -7.262 + ATOM CA GLY A 91 -23.014 3.746 -8.212 + ATOM CA GLY A 92 -25.744 2.945 -9.163 + ATOM CA GLY A 93 -28.474 2.145 -10.114 + ATOM CA GLY A 94 -31.205 1.344 -11.065 + ATOM CA GLY A 95 -33.935 0.543 -12.015 + ATOM CA GLY A 96 -36.666 -0.258 -12.966 + ATOM CA GLY A 97 -39.396 -1.059 -13.917 + ATOM CA GLY A 98 -42.126 -1.859 -14.867 + ATOM CA GLY A 99 -44.857 -2.660 -15.818 + ATOM CA GLY A 100 -47.587 -3.461 -16.769 + ATOM CA GLY A 101 -50.317 -4.262 -17.720 + ATOM CA GLY A 102 -47.430 -2.993 -17.639 + ATOM CA GLY A 103 -50.317 -4.262 -17.720 + ATOM CA GLY A 104 -47.430 -2.993 -17.639 + ATOM CA GLY A 105 -47.208 -4.303 -17.154 + ATOM CA GLY A 106 -50.317 -4.262 -17.720 + ATOM CA GLY A 107 -47.208 -4.303 -17.154 + ATOM CA GLY A 108 -47.752 -3.932 -15.902 + ATOM CA GLY A 109 -50.317 -4.262 -17.720 + ATOM CA GLY A 110 -47.752 -3.932 -15.902 + ATOM CA GLY A 111 -47.975 -2.622 -16.387 + ATOM CA GLY A 112 -50.317 -4.262 -17.720 + ATOM CA GLY A 113 -47.975 -2.622 -16.387 + ATOM CA GLY A 114 -47.430 -2.993 -17.639 + TER ARROW HEAD END ENDMDL

      best wishes and many thanks

      Dan

        until they come into a distance of 4A

        What is the distance "4A", in the units used by the data?


        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?

      Here's the code I promised:

      And output from a sample run with the 4A limit set manually to an arbitrary value that produces limited output:

      [17:54:13.90] C:\test>979082 -LIM4A=15 R: 5 [ -18.388, -2.409, -9.308 ] [ 7.506, 282° +] S:259 angle: 32.607° [ -6.126, -0.957, 0.400 ] [ 9.944, 249° +] R: 6 [ -18.784, -3.016, -7.671 ] [ 7.821, 269° +] S:259 angle: 19.401° [ -6.126, -0.957, 0.400 ] [ 9.944, 249° +] R: 7 [ -17.107, -3.128, -6.966 ] [ 8.391, 268° +] S: 7 angle: 10.377° [ -3.823, -2.789, 0.030 ] [ 11.980, 258° +] S:255 angle: 18.214° [ -4.814, 0.899, 0.400 ] [ 8.401, 250° +] S:254 angle: 18.338° [ -4.738, 1.093, 0.400 ] [ 8.231, 250° +] S:259 angle: 18.570° [ -6.126, -0.957, 0.400 ] [ 9.944, 249° +] S:258 angle: 20.395° [ -5.825, 0.591, 0.400 ] [ 8.548, 248° +] S:257 angle: 20.599° [ -5.970, 0.493, 0.400 ] [ 8.620, 247° +] S:256 angle: 21.740° [ -5.562, 1.600, 0.400 ] [ 7.653, 246° +] S:245 angle: 25.796° [ -5.672, 3.533, 0.140 ] [ 5.782, 242° +] R:140 [ -18.510, -10.387, -3.385 ] [ 15.732, 252° +] S:259 angle: 2.897° [ -6.126, -0.957, 0.400 ] [ 9.944, 249° +] R:141 [ -17.411, -10.096, -2.922 ] [ 15.769, 252° +] S:259 angle: 2.729° [ -6.126, -0.957, 0.400 ] [ 9.944, 249° +] S:258 angle: 4.554° [ -5.825, 0.591, 0.400 ] [ 8.548, 248° +] S:257 angle: 4.758° [ -5.970, 0.493, 0.400 ] [ 8.620, 247° +] S:256 angle: 5.899° [ -5.562, 1.600, 0.400 ] [ 7.653, 246° +] [17:54:14.34] C:\test>

      As you can see, the run takes around 1/2 a second to process the 146 rotation points against the 254 stop point of your sample data. The runtime will be linear in the number of points.

      The output shows that rotatable point 5 [original 3D cartesian coords] [2D polar coords (radius/angle) about z-axis]

      will collide with stop point 259 after being rotated 32.607°</c>

      Rot point: 6 will collide with stop point 6 after being rotated 19.401°.

      Rot point 7 will collide with stop point 7 after being rotated 10.377°, and stop point 245 after being rotated 334.204° the opposite way.

      And so on.


      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?

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