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Re^4: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?

by fraizerangus (Sexton)
on Jun 29, 2012 at 09:11 UTC ( [id://979082]=note: print w/replies, xml ) Need Help??


in reply to Re^3: 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 Again

The Line Unit Vector I've calculated as (0.906, 0.258, 0.335)

Here is the sample data for the line

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

and here are the Cartesian co-ordinates for the points I want to rotate by 1 degree intervals for each iteration

ATOM 183 N MET B 25 -18.731 -0.135 -11.272 ATOM 184 CA MET B 25 -19.287 -1.473 -11.499 ATOM 185 C MET B 25 -20.545 -1.396 -12.335 ATOM 186 O MET B 25 -21.421 -0.553 -12.114 ATOM 187 CB MET B 25 -19.594 -2.172 -10.170 ATOM 188 CG MET B 25 -18.388 -2.409 -9.308 ATOM 189 SD MET B 25 -18.784 -3.016 -7.671 ATOM 190 CE MET B 25 -17.107 -3.128 -6.966 ATOM 191 N PRO B 26 -20.681 -2.300 -13.307 ATOM 192 CA PRO B 26 -21.870 -2.245 -14.145 ATOM 193 C PRO B 26 -23.239 -2.337 -13.447 ATOM 194 O PRO B 26 -24.201 -1.730 -13.882 ATOM 195 CB PRO B 26 -21.604 -3.351 -15.184 ATOM 196 CG PRO B 26 -20.782 -4.304 -14.461 ATOM 197 CD PRO B 26 -19.827 -3.453 -13.654 ATOM 198 N GLU B 27 -23.296 -3.065 -12.345 ATOM 199 CA GLU B 27 -24.545 -3.199 -11.624 ATOM 200 C GLU B 27 -24.971 -1.907 -10.917 ATOM 201 O GLU B 27 -26.155 -1.714 -10.652 ATOM 202 CB GLU B 27 -24.417 -4.262 -10.541 ATOM 203 CG GLU B 27 -24.206 -5.670 -11.059 ATOM 204 CD GLU B 27 -22.756 -6.001 -11.359 ATOM 205 OE1 GLU B 27 -21.843 -5.132 -11.182 ATOM 206 OE2 GLU B 27 -22.549 -7.164 -11.773 ATOM 340 N VAL B 44 -28.758 -0.366 -7.293 ATOM 341 CA VAL B 44 -28.277 -1.382 -8.227 ATOM 342 C VAL B 44 -29.430 -2.020 -8.991 ATOM 343 O VAL B 44 -30.583 -2.037 -8.548 ATOM 344 CB VAL B 44 -27.545 -2.528 -7.509 ATOM 345 CG1 VAL B 44 -26.301 -2.027 -6.834 ATOM 346 CG2 VAL B 44 -28.453 -3.165 -6.499 ATOM 347 N GLU B 45 -29.101 -2.474 -10.197 ATOM 348 CA GLU B 45 -30.032 -3.224 -11.040 ATOM 349 C GLU B 45 -29.268 -4.484 -11.492 ATOM 350 O GLU B 45 -28.116 -4.412 -11.942 ATOM 351 CB GLU B 45 -30.496 -2.378 -12.258 ATOM 352 CG GLU B 45 -31.341 -1.173 -11.858 ATOM 353 CD GLU B 45 -31.677 -0.230 -13.021 ATOM 354 OE1 GLU B 45 -30.974 -0.274 -14.048 ATOM 355 OE2 GLU B 45 -32.633 0.552 -12.884 ATOM 356 N THR B 46 -29.918 -5.632 -11.352 ATOM 357 CA THR B 46 -29.341 -6.925 -11.736 ATOM 358 C THR B 46 -30.384 -7.735 -12.500 ATOM 359 O THR B 46 -31.579 -7.459 -12.407 ATOM 360 CB THR B 46 -28.853 -7.732 -10.500 ATOM 361 OG1 THR B 46 -29.953 -8.003 -9.622 ATOM 362 CG2 THR B 46 -27.735 -6.958 -9.755 ATOM 363 N ASP B 47 -29.939 -8.747 -13.241 ATOM 364 CA ASP B 47 -30.878 -9.551 -14.011 ATOM 365 C ASP B 47 -31.833 -10.352 -13.136 ATOM 366 O ASP B 47 -33.036 -10.461 -13.408 ATOM 367 CB ASP B 47 -30.088 -10.510 -14.903 ATOM 368 CG ASP B 47 -29.320 -9.797 -15.991 ATOM 369 OD1 ASP B 47 -29.582 -8.595 -16.229 ATOM 370 OD2 ASP B 47 -28.457 -10.451 -16.622 ATOM 371 N THR B 48 -31.275 -10.936 -12.094 ATOM 372 CA THR B 48 -31.996 -11.805 -11.190 ATOM 373 C THR B 48 -31.636 -11.519 -9.746 ATOM 374 O THR B 48 -30.654 -10.802 -9.448 ATOM 375 CB THR B 48 -31.599 -13.294 -11.440 ATOM 376 OG1 THR B 48 -30.210 -13.487 -11.070 ATOM 377 CG2 THR B 48 -31.741 -13.642 -12.949 ATOM 378 N LEU B 49 -32.428 -12.075 -8.840 ATOM 379 CA LEU B 49 -32.135 -11.978 -7.411 ATOM 380 C LEU B 49 -30.851 -12.716 -7.074 ATOM 381 O LEU B 49 -30.080 -12.298 -6.199 ATOM 382 CB LEU B 49 -33.281 -12.532 -6.554 ATOM 383 CG LEU B 49 -34.391 -11.563 -6.233 ATOM 384 CD1 LEU B 49 -35.291 -12.246 -5.196 ATOM 385 CD2 LEU B 49 -33.834 -10.232 -5.630 ATOM 386 N LYS B 50 -30.598 -13.835 -7.746 ATOM 387 CA LYS B 50 -29.385 -14.574 -7.494 ATOM 388 C LYS B 50 -28.185 -13.675 -7.804 ATOM 389 O LYS B 50 -27.196 -13.667 -7.069 ATOM 390 CB LYS B 50 -29.374 -15.839 -8.366 ATOM 391 CG LYS B 50 -28.083 -16.600 -8.281 ATOM 392 CD LYS B 50 -28.213 -17.957 -8.920 ATOM 393 CE LYS B 50 -26.851 -18.613 -9.055 ATOM 394 NZ LYS B 50 -26.976 -20.031 -9.478 ATOM 395 N ASP B 51 -28.281 -12.904 -8.884 ATOM 396 CA ASP B 51 -27.192 -11.993 -9.228 ATOM 397 C ASP B 51 -27.020 -10.918 -8.147 ATOM 398 O ASP B 51 -25.897 -10.550 -7.798 ATOM 399 CB ASP B 51 -27.447 -11.319 -10.586 ATOM 400 CG ASP B 51 -27.316 -12.286 -11.759 ATOM 401 OD1 ASP B 51 -26.408 -13.135 -11.716 ATOM 402 OD2 ASP B 51 -28.108 -12.169 -12.711 ATOM 403 N LEU B 52 -28.126 -10.396 -7.647 ATOM 404 CA LEU B 52 -28.039 -9.393 -6.586 ATOM 405 C LEU B 52 -27.400 -9.998 -5.331 ATOM 406 O LEU B 52 -26.592 -9.339 -4.682 ATOM 407 CB LEU B 52 -29.432 -8.849 -6.290 ATOM 408 CG LEU B 52 -29.515 -7.909 -5.079 ATOM 409 CD1 LEU B 52 -28.622 -6.677 -5.324 ATOM 410 CD2 LEU B 52 -30.990 -7.549 -4.806 ATOM 411 N ASP B 53 -27.788 -11.220 -4.974 ATOM 412 CA ASP B 53 -27.250 -11.886 -3.803 ATOM 413 C ASP B 53 -25.745 -12.043 -3.924 ATOM 414 O ASP B 53 -25.000 -11.783 -2.971 ATOM 415 CB ASP B 53 -27.931 -13.252 -3.645 ATOM 416 CG ASP B 53 -27.790 -13.802 -2.257 ATOM 417 OD1 ASP B 53 -27.786 -13.011 -1.288 ATOM 418 OD2 ASP B 53 -27.688 -15.033 -2.135 ATOM 419 N GLN B 54 -25.280 -12.456 -5.100 ATOM 420 CA GLN B 54 -23.859 -12.616 -5.309 ATOM 421 C GLN B 54 -23.145 -11.284 -5.250 ATOM 422 O GLN B 54 -22.033 -11.206 -4.727 ATOM 423 CB GLN B 54 -23.597 -13.346 -6.625 ATOM 424 CG GLN B 54 -24.127 -14.755 -6.529 ATOM 425 CD GLN B 54 -23.878 -15.578 -7.770 ATOM 426 OE1 GLN B 54 -23.247 -15.119 -8.724 ATOM 427 NE2 GLN B 54 -24.368 -16.813 -7.760 ATOM 428 N PHE B 55 -23.758 -10.226 -5.757 ATOM 429 CA PHE B 55 -23.128 -8.913 -5.673 ATOM 430 C PHE B 55 -22.938 -8.514 -4.211 ATOM 431 O PHE B 55 -21.864 -8.030 -3.828 ATOM 432 CB PHE B 55 -24.018 -7.892 -6.380 ATOM 433 CG PHE B 55 -23.448 -6.509 -6.415 ATOM 434 CD1 PHE B 55 -22.595 -6.140 -7.449 ATOM 435 CD2 PHE B 55 -23.733 -5.581 -5.409 ATOM 436 CE1 PHE B 55 -22.035 -4.860 -7.485 ATOM 437 CE2 PHE B 55 -23.167 -4.280 -5.431 ATOM 438 CZ PHE B 55 -22.322 -3.934 -6.480 ATOM 439 N ILE B 56 -23.984 -8.686 -3.405 ATOM 440 CA ILE B 56 -23.948 -8.313 -2.000 ATOM 441 C ILE B 56 -22.987 -9.148 -1.168 ATOM 442 O ILE B 56 -22.261 -8.598 -0.347 ATOM 443 CB ILE B 56 -25.376 -8.459 -1.390 ATOM 444 CG1 ILE B 56 -26.289 -7.371 -1.967 ATOM 445 CG2 ILE B 56 -25.329 -8.392 0.151 ATOM 446 CD1 ILE B 56 -27.739 -7.521 -1.574 ATOM 447 N THR B 57 -22.959 -10.461 -1.364 ATOM 448 CA THR B 57 -22.088 -11.246 -0.490 ATOM 449 C THR B 57 -20.683 -11.497 -1.042 ATOM 450 O THR B 57 -19.718 -11.631 -0.257 ATOM 451 CB THR B 57 -22.774 -12.556 -0.095 ATOM 452 OG1 THR B 57 -22.821 -13.385 -1.247 ATOM 453 CG2 THR B 57 -24.225 -12.310 0.420 ATOM 454 N GLU B 58 -20.531 -11.490 -2.358 ATOM 455 CA GLU B 58 -19.203 -11.666 -2.942 ATOM 456 C GLU B 58 -18.510 -10.387 -3.385 ATOM 457 O GLU B 58 -17.411 -10.096 -2.922 ATOM 458 CB GLU B 58 -19.234 -12.599 -4.139 ATOM 459 CG GLU B 58 -19.923 -13.930 -3.875 ATOM 460 CD GLU B 58 -19.918 -14.829 -5.113 ATOM 461 OE1 GLU B 58 -20.834 -15.660 -5.290 ATOM 462 OE2 GLU B 58 -18.981 -14.717 -5.920

The stopping point would be when any of the points come into contact with any of these Cartesian points after numerous iterations?

ATOM 39 N ILE A 6 -28.498 -0.713 -1.733 0.03 ATOM 40 CA ILE A 6 -27.704 -1.211 -0.641 0.03 ATOM 41 C ILE A 6 -27.201 -0.065 0.236 0.03 ATOM 42 O ILE A 6 -26.458 0.817 -0.235 0.03 ATOM 43 CB ILE A 6 -26.486 -1.991 -1.182 0.03 ATOM 44 CG1 ILE A 6 -26.936 -3.007 -2.231 0.03 ATOM 45 CG2 ILE A 6 -25.762 -2.672 -0.060 0.03 ATOM 46 CD1 ILE A 6 -25.781 -3.823 -2.789 0.03 ATOM 47 N LEU A 7 -27.587 -0.085 1.510 0.02 ATOM 48 CA LEU A 7 -27.153 0.909 2.483 0.02 ATOM 49 C LEU A 7 -25.832 0.351 2.982 0.02 ATOM 50 O LEU A 7 -25.725 -0.855 3.179 0.02 ATOM 51 CB LEU A 7 -28.150 0.965 3.635 0.02 ATOM 52 CG LEU A 7 -29.480 1.674 3.398 0.02 ATOM 53 CD1 LEU A 7 -30.088 1.292 2.072 0.02 ATOM 54 CD2 LEU A 7 -30.441 1.320 4.561 0.02 ATOM 55 N MET A 8 -24.844 1.208 3.209 0.02 ATOM 56 CA MET A 8 -23.528 0.721 3.622 0.02 ATOM 57 C MET A 8 -22.874 1.588 4.663 0.02 ATOM 58 O MET A 8 -23.051 2.789 4.654 0.02 ATOM 59 CB MET A 8 -22.538 0.723 2.437 0.02 ATOM 60 CG MET A 8 -22.909 -0.149 1.303 0.02 ATOM 61 SD MET A 8 -21.700 0.110 -0.066 0.02 ATOM 62 CE MET A 8 -22.383 -1.085 -1.224 0.02 ATOM 63 N VAL A 9 -22.103 0.946 5.551 0.04 ATOM 64 CA VAL A 9 -21.251 1.656 6.509 0.04 ATOM 65 C VAL A 9 -19.827 1.350 6.024 0.04 ATOM 66 O VAL A 9 -19.506 0.197 5.667 0.04 ATOM 67 CB VAL A 9 -21.425 1.146 7.936 0.04 ATOM 68 CG1 VAL A 9 -20.279 1.661 8.813 0.04 ATOM 69 CG2 VAL A 9 -22.738 1.625 8.459 0.04 ATOM 70 N THR A 10 -18.983 2.377 5.928 0.09 ATOM 71 CA THR A 10 -17.612 2.153 5.477 0.09 ATOM 72 C THR A 10 -16.618 2.492 6.565 0.09 ATOM 73 O THR A 10 -16.966 3.024 7.616 0.09 ATOM 74 CB THR A 10 -17.207 3.026 4.219 0.09 ATOM 75 OG1 THR A 10 -17.096 4.420 4.591 0.09 ATOM 76 CG2 THR A 10 -18.220 2.859 3.097 0.09 ATOM 77 N ALA A 11 -15.364 2.173 6.285 0.10 ATOM 78 CA ALA A 11 -14.313 2.532 7.215 0.10 ATOM 79 C ALA A 11 -14.258 4.060 7.162 0.10 ATOM 80 O ALA A 11 -14.598 4.689 6.142 0.10 ATOM 81 CB ALA A 11 -12.997 1.943 6.763 0.10 ATOM 82 N ALA A 12 -13.817 4.657 8.263 0.10 ATOM 83 CA ALA A 12 -13.702 6.102 8.382 0.10 ATOM 84 C ALA A 12 -12.862 6.679 7.260 0.10 ATOM 85 O ALA A 12 -11.763 6.198 6.975 0.10 ATOM 86 CB ALA A 12 -13.038 6.467 9.721 0.10 ATOM 87 N GLY A 13 -13.401 7.713 6.625 0.10 ATOM 88 CA GLY A 13 -12.709 8.403 5.560 0.10 ATOM 89 C GLY A 13 -12.679 7.741 4.199 0.10 ATOM 90 O GLY A 13 -12.124 8.301 3.256 0.10 ATOM 91 N LYS A 14 -13.292 6.567 4.099 0.10 ATOM 92 CA LYS A 14 -13.296 5.834 2.836 0.10 ATOM 93 C LYS A 14 -14.613 5.968 2.067 0.10 ATOM 94 O LYS A 14 -14.816 5.265 1.073 0.10 ATOM 95 CB LYS A 14 -13.052 4.340 3.097 0.10 ATOM 96 CG LYS A 14 -11.847 4.006 3.973 0.10 ATOM 97 CD LYS A 14 -10.669 3.514 3.192 0.10 ATOM 98 CE LYS A 14 -9.425 3.504 4.096 0.10 ATOM 99 NZ LYS A 14 -8.294 2.793 3.470 0.10 ATOM 100 N GLU A 15 -15.515 6.845 2.506 0.10 ATOM 101 CA GLU A 15 -16.819 6.965 1.812 0.10 ATOM 102 C GLU A 15 -16.734 7.312 0.338 0.10 ATOM 103 O GLU A 15 -17.331 6.638 -0.490 0.10 ATOM 104 CB GLU A 15 -17.727 8.003 2.502 0.10 ATOM 105 CG GLU A 15 -18.061 7.715 3.976 0.10 ATOM 106 CD GLU A 15 -17.016 8.228 4.947 0.10 ATOM 107 OE1 GLU A 15 -15.892 8.584 4.527 0.10 ATOM 108 OE2 GLU A 15 -17.340 8.275 6.164 0.10 ATOM 109 N ARG A 16 -15.982 8.340 -0.017 0.10 ATOM 110 CA ARG A 16 -15.900 8.706 -1.430 0.10 ATOM 111 C ARG A 16 -15.152 7.639 -2.208 0.10 ATOM 112 O ARG A 16 -15.500 7.374 -3.355 0.10 ATOM 113 CB ARG A 16 -15.213 10.071 -1.614 0.10 ATOM 114 CG ARG A 16 -15.066 10.477 -3.074 0.10 ATOM 115 CD ARG A 16 -14.327 11.819 -3.243 0.10 ATOM 116 NE ARG A 16 -13.901 11.961 -4.661 0.10 ATOM 117 CZ ARG A 16 -12.676 12.396 -4.952 0.10 ATOM 118 NH1 ARG A 16 -11.841 12.690 -3.980 0.10 ATOM 119 NH2 ARG A 16 -12.324 12.531 -6.223 0.10 ATOM 120 N GLU A 17 -14.127 7.041 -1.600 0.10 ATOM 121 CA GLU A 17 -13.340 5.994 -2.257 0.10 ATOM 122 C GLU A 17 -14.268 4.836 -2.644 0.10 ATOM 123 O GLU A 17 -14.220 4.331 -3.769 0.10 ATOM 124 CB GLU A 17 -12.243 5.483 -1.324 0.10 ATOM 125 CG GLU A 17 -11.398 4.389 -1.922 0.10 ATOM 126 CD GLU A 17 -10.374 3.854 -0.952 0.10 ATOM 127 OE1 GLU A 17 -9.787 4.637 -0.182 0.10 ATOM 128 OE2 GLU A 17 -10.145 2.634 -0.974 0.10 ATOM 129 N VAL A 18 -15.088 4.417 -1.687 0.05 ATOM 130 CA VAL A 18 -16.032 3.353 -1.954 0.05 ATOM 131 C VAL A 18 -17.052 3.764 -3.010 0.05 ATOM 132 O VAL A 18 -17.362 2.988 -3.934 0.05 ATOM 133 CB VAL A 18 -16.728 2.910 -0.642 0.05 ATOM 134 CG1 VAL A 18 -17.948 1.984 -0.944 0.05 ATOM 135 CG2 VAL A 18 -15.732 2.187 0.235 0.05 ATOM 136 N MET A 19 -17.576 4.985 -2.896 0.07 ATOM 137 CA MET A 19 -18.546 5.491 -3.868 0.07 ATOM 138 C MET A 19 -17.983 5.393 -5.290 0.07 ATOM 139 O MET A 19 -18.674 4.895 -6.177 0.07 ATOM 140 CB MET A 19 -18.893 6.968 -3.577 0.07 ATOM 141 CG MET A 19 -20.080 7.412 -4.413 0.07 ATOM 142 SD MET A 19 -20.383 9.219 -4.338 0.07 ATOM 143 CE MET A 19 -19.063 9.830 -5.317 0.07 ATOM 144 N GLU A 20 -16.756 5.884 -5.511 0.09 ATOM 145 CA GLU A 20 -16.196 5.861 -6.857 0.09 ATOM 146 C GLU A 20 -15.772 4.495 -7.343 0.09 ATOM 147 O GLU A 20 -15.901 4.220 -8.534 0.09 ATOM 148 CB GLU A 20 -15.044 6.862 -6.987 0.09 ATOM 149 CG GLU A 20 -15.543 8.306 -6.956 0.09 ATOM 150 CD GLU A 20 -16.363 8.708 -8.202 0.09 ATOM 151 OE1 GLU A 20 -16.970 9.796 -8.155 0.09 ATOM 152 OE2 GLU A 20 -16.379 7.971 -9.220 0.09 ATOM 153 N LYS A 21 -15.252 3.643 -6.462 0.10 ATOM 154 CA LYS A 21 -14.915 2.272 -6.858 0.10 ATOM 155 C LYS A 21 -16.180 1.564 -7.282 0.10 ATOM 156 O LYS A 21 -16.169 0.784 -8.252 0.10 ATOM 157 CB LYS A 21 -14.303 1.491 -5.708 0.10 ATOM 158 CG LYS A 21 -12.832 1.764 -5.525 0.10 ATOM 159 CD LYS A 21 -12.327 1.210 -4.178 0.10 ATOM 160 CE LYS A 21 -10.801 1.122 -4.130 0.10 ATOM 161 NZ LYS A 21 -10.349 0.604 -2.784 0.10 ATOM 162 N LEU A 22 -17.288 1.806 -6.579 0.11 ATOM 163 CA LEU A 22 -18.534 1.162 -6.994 0.11 ATOM 164 C LEU A 22 -19.072 1.736 -8.301 0.11 ATOM 165 O LEU A 22 -19.512 0.989 -9.171 0.11 ATOM 166 CB LEU A 22 -19.598 1.245 -5.873 0.11 ATOM 167 CG LEU A 22 -19.223 0.453 -4.620 0.11 ATOM 168 CD1 LEU A 22 -20.205 0.865 -3.502 0.11 ATOM 169 CD2 LEU A 22 -19.288 -1.055 -4.861 0.11 ATOM 223 N GLU A 30 -26.173 4.298 -9.604 0.06 ATOM 224 CA GLU A 30 -26.154 5.548 -8.818 0.06 ATOM 225 C GLU A 30 -25.520 5.244 -7.485 0.06 ATOM 226 O GLU A 30 -25.520 4.099 -7.058 0.06 ATOM 227 CB GLU A 30 -27.568 6.089 -8.553 0.06 ATOM 228 CG GLU A 30 -28.375 6.303 -9.811 0.06 ATOM 229 CD GLU A 30 -29.809 6.722 -9.535 0.06 ATOM 230 OE1 GLU A 30 -30.598 6.782 -10.509 0.06 ATOM 231 OE2 GLU A 30 -30.165 6.966 -8.358 0.06 ATOM 232 N ALA A 31 -24.951 6.248 -6.833 0.05 ATOM 233 CA ALA A 31 -24.363 6.006 -5.506 0.05 ATOM 234 C ALA A 31 -24.301 7.338 -4.796 0.05 ATOM 235 O ALA A 31 -24.077 8.365 -5.437 0.05 ATOM 236 CB ALA A 31 -22.978 5.359 -5.608 0.05 ATOM 237 N TYR A 32 -24.572 7.316 -3.488 0.04 ATOM 238 CA TYR A 32 -24.652 8.533 -2.696 0.04 ATOM 239 C TYR A 32 -23.980 8.358 -1.362 0.04 ATOM 240 O TYR A 32 -24.240 7.361 -0.691 0.04 ATOM 241 CB TYR A 32 -26.131 8.855 -2.372 0.04 ATOM 242 CG TYR A 32 -27.052 8.910 -3.572 0.04 ATOM 243 CD1 TYR A 32 -27.483 10.132 -4.088 0.04 ATOM 244 CD2 TYR A 32 -27.498 7.734 -4.193 0.04 ATOM 245 CE1 TYR A 32 -28.332 10.204 -5.226 0.04 ATOM 246 CE2 TYR A 32 -28.364 7.805 -5.341 0.04 ATOM 247 CZ TYR A 32 -28.750 9.031 -5.829 0.04 ATOM 248 OH TYR A 32 -29.576 9.155 -6.940 0.04 ATOM 249 N VAL A 33 -23.111 9.305 -0.989 0.05 ATOM 250 CA VAL A 33 -22.554 9.322 0.369 0.05 ATOM 251 C VAL A 33 -23.675 10.096 1.073 0.05 ATOM 252 O VAL A 33 -24.156 11.136 0.594 0.05 ATOM 253 CB VAL A 33 -21.220 10.083 0.445 0.05 ATOM 254 CG1 VAL A 33 -20.755 10.141 1.920 0.05 ATOM 255 CG2 VAL A 33 -20.178 9.346 -0.413 0.05 ATOM 256 N VAL A 34 -24.084 9.606 2.238 0.04 ATOM 257 CA VAL A 34 -25.214 10.222 2.922 0.04 ATOM 258 C VAL A 34 -24.914 10.490 4.371 0.04 ATOM 259 O VAL A 34 -23.962 9.945 4.913 0.04 ATOM 260 CB VAL A 34 -26.489 9.301 2.849 0.04 ATOM 261 CG1 VAL A 34 -26.909 9.102 1.409 0.04 ATOM 262 CG2 VAL A 34 -26.195 7.910 3.440 0.04 ATOM 263 N TYR A 35 -25.732 11.375 4.933 0.04 ATOM 264 CA TYR A 35 -25.675 11.728 6.350 0.04 ATOM 265 C TYR A 35 -26.947 11.098 6.898 0.04 ATOM 266 O TYR A 35 -28.070 11.485 6.523 0.04 ATOM 267 CB TYR A 35 -25.713 13.247 6.505 0.04 ATOM 268 CG TYR A 35 -25.506 13.693 7.918 0.04 ATOM 269 CD1 TYR A 35 -24.229 13.810 8.453 0.04 ATOM 270 CD2 TYR A 35 -26.602 14.002 8.703 0.04 ATOM 271 CE1 TYR A 35 -24.064 14.240 9.769 0.04 ATOM 272 CE2 TYR A 35 -26.438 14.440 10.025 0.04 ATOM 273 CZ TYR A 35 -25.179 14.547 10.528 0.04 ATOM 274 OH TYR A 35 -25.061 15.008 11.825 0.04 ATOM 275 N GLY A 36 -26.755 10.167 7.815 0.05 ATOM 276 CA GLY A 36 -27.878 9.430 8.387 0.05 ATOM 277 C GLY A 36 -27.317 8.205 9.102 0.05 ATOM 278 O GLY A 36 -26.136 8.180 9.497 0.05 ATOM 279 N GLU A 37 -28.152 7.181 9.241 0.06 ATOM 280 CA GLU A 37 -27.716 5.986 9.945 0.06 ATOM 281 C GLU A 37 -26.676 5.184 9.210 0.06 ATOM 282 O GLU A 37 -25.909 4.448 9.828 0.06 ATOM 283 CB GLU A 37 -28.913 5.123 10.324 0.06 ATOM 284 CG GLU A 37 -29.626 5.662 11.596 0.06 ATOM 285 CD GLU A 37 -28.641 5.978 12.759 0.06 ATOM 286 OE1 GLU A 37 -28.100 7.102 12.829 0.06 ATOM 287 OE2 GLU A 37 -28.369 5.099 13.599 0.06 ATOM 288 N TYR A 38 -26.637 5.312 7.885 0.06 ATOM 289 CA TYR A 38 -25.628 4.630 7.088 0.06 ATOM 290 C TYR A 38 -24.754 5.692 6.410 0.06 ATOM 291 O TYR A 38 -25.087 6.891 6.460 0.06 ATOM 292 CB TYR A 38 -26.302 3.702 6.043 0.06 ATOM 293 CG TYR A 38 -26.774 2.386 6.623 0.06 ATOM 294 CD1 TYR A 38 -25.935 1.280 6.620 0.06 ATOM 295 CD2 TYR A 38 -28.064 2.253 7.172 0.06 ATOM 296 CE1 TYR A 38 -26.345 0.074 7.134 0.06 ATOM 297 CE2 TYR A 38 -28.480 1.039 7.696 0.06 ATOM 298 CZ TYR A 38 -27.612 -0.032 7.671 0.06 ATOM 299 OH TYR A 38 -27.972 -1.249 8.206 0.06 ATOM 300 N ASP A 39 -23.666 5.240 5.773 0.07 ATOM 301 CA ASP A 39 -22.715 6.122 5.095 0.07 ATOM 302 C ASP A 39 -22.972 6.280 3.599 0.07 ATOM 303 O ASP A 39 -22.630 7.313 3.035 0.07 ATOM 304 CB ASP A 39 -21.268 5.626 5.263 0.07 ATOM 305 CG ASP A 39 -20.814 5.604 6.699 0.07 ATOM 306 OD1 ASP A 39 -21.158 6.535 7.462 0.07 ATOM 307 OD2 ASP A 39 -20.061 4.677 7.044 0.07 ATOM 308 N LEU A 40 -23.514 5.243 2.964 0.05 ATOM 309 CA LEU A 40 -23.828 5.322 1.528 0.05 ATOM 310 C LEU A 40 -25.104 4.579 1.239 0.05 ATOM 311 O LEU A 40 -25.514 3.699 1.976 0.05 ATOM 312 CB LEU A 40 -22.778 4.630 0.631 0.05 ATOM 313 CG LEU A 40 -21.479 5.351 0.353 0.05 ATOM 314 CD1 LEU A 40 -20.465 4.981 1.407 0.05 ATOM 315 CD2 LEU A 40 -21.005 4.968 -1.063 0.05 ATOM 316 N ILE A 41 -25.715 4.944 0.130 0.04 ATOM 317 CA ILE A 41 -26.837 4.195 -0.420 0.04 ATOM 318 C ILE A 41 -26.429 4.027 -1.883 0.04 ATOM 319 O ILE A 41 -26.037 4.995 -2.562 0.04 ATOM 320 CB ILE A 41 -28.223 4.858 -0.239 0.04 ATOM 321 CG1 ILE A 41 -29.288 3.916 -0.824 0.04 ATOM 322 CG2 ILE A 41 -28.325 6.173 -0.938 0.04 ATOM 323 CD1 ILE A 41 -30.749 4.243 -0.427 0.04 ATOM 541 N MET A 68 -20.563 -2.717 6.892 0.13 ATOM 542 CA MET A 68 -21.918 -3.188 7.191 0.13 ATOM 543 C MET A 68 -22.777 -2.880 5.974 0.13 ATOM 544 O MET A 68 -22.516 -1.911 5.266 0.13 ATOM 545 CB MET A 68 -22.532 -2.425 8.376 0.13 ATOM 546 CG MET A 68 -21.642 -2.257 9.591 0.13 ATOM 547 SD MET A 68 -22.647 -1.596 10.958 0.13 ATOM 548 CE MET A 68 -21.570 -1.866 12.362 0.13 ATOM 549 N THR A 69 -23.759 -3.734 5.714 0.14 ATOM 550 CA THR A 69 -24.695 -3.461 4.626 0.14 ATOM 551 C THR A 69 -26.114 -3.843 5.016 0.14 ATOM 552 O THR A 69 -26.355 -4.624 5.935 0.14 ATOM 553 CB THR A 69 -24.373 -4.249 3.311 0.14 ATOM 554 OG1 THR A 69 -24.469 -5.672 3.533 0.14 ATOM 555 CG2 THR A 69 -22.981 -3.930 2.810 0.14 ATOM 556 N SER A 70 -27.059 -3.260 4.303 0.20 ATOM 557 CA SER A 70 -28.483 -3.591 4.459 0.20 ATOM 558 C SER A 70 -28.977 -3.509 3.019 0.20 ATOM 559 O SER A 70 -28.971 -2.437 2.406 0.20 ATOM 560 CB SER A 70 -29.213 -2.581 5.344 0.20 ATOM 561 OG SER A 70 -30.606 -2.925 5.446 0.20 ATOM 562 N THR A 71 -29.427 -4.639 2.480 0.40 ATOM 563 CA THR A 71 -29.837 -4.738 1.093 0.40 ATOM 564 C THR A 71 -31.352 -4.814 0.899 0.40 ATOM 565 O THR A 71 -32.039 -5.562 1.600 0.40 ATOM 566 CB THR A 71 -29.178 -5.970 0.493 0.40 ATOM 567 OG1 THR A 71 -27.743 -5.825 0.591 0.40 ATOM 568 CG2 THR A 71 -29.593 -6.126 -0.957 0.40

Many Thanks again!

Dan

Replies are listed 'Best First'.
Re^5: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?
by BrowserUk (Patriarch) on Jun 29, 2012 at 15:17 UTC

    The whole problem becomes far simpler if you re-base your points (both those you need to rotate, and those that form stopping points) so that they are relative to your axis of rotation. Ie. move the entire field of view so that the axis unit vector lines up with the Z-axis of your re-based coordinate system.

    You can then subset your stopping points against your input points by their radius.

    That is, once the points are re-based, sqrt( x2 + y2 ) for each of the points will give you their radius of rotation. Now you only need compare any given input point against those stopping points that have that same radius (+-some tolorance).

    And if once you've re-based the points, you convert them to 2D vectors, the length is the radius directly, and the difference between their angles tells you how far you would have to rotate them before they collided.

    So now you don't need to rotate all the points incrementally at all, you simply find all the pairs of input/stopping points that can collide; and choose the minimum or maximum angle (depending upon which direction you are rotating them, as your "first collision point".

    This is a much simpler, and far more computationally efficient way of folding your molecule.


    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?

      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

        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.


        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?

Re^5: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?
by salva (Canon) on Jun 29, 2012 at 11:44 UTC
    This script below does what you have asked for. It uses Math::Vector::Real::kdTree for fast lookups.

    But anyway, I am not sure that this is really what you need. If by doing 1deg rotation you are trying to simulate a continuous rotation, 1deg may be not fine enough. Even going for 0.1deg may not be fine enough and the computational cost grows exponentially with the precision.

    If you are on the continuous simulation problem there are better ways to do it...

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