添加法线

python/face.obj

@@ -958,6 +958,485 @@ v 0.566714 0.424674 -0.000015
 # 顶点 477
 v 0.580471 0.438213 -0.000013
 
+vn -0.157857 -0.117448 -0.980453
+vn -0.119837 0.273587 -0.954353
+vn -0.128373 0.314910 -0.940400
+vn -0.610928 -0.681921 -0.402182
+vn -0.132994 -0.246226 -0.960044
+vn -0.123946 -0.670973 -0.731049
+vn -0.108346 -0.777778 -0.619131
+vn -0.684593 -0.362166 -0.632589
+vn -0.163238 -0.084285 -0.982980
+vn -0.149706 -0.344610 -0.926732
+vn -0.146321 -0.575508 -0.804600
+vn -0.160774 0.221591 -0.961795
+vn -0.142939 0.540001 -0.829438
+vn -0.130929 0.701902 -0.700136
+vn -0.132220 -0.586515 -0.799073
+vn -0.129404 -0.572935 -0.809321
+vn -0.142849 -0.343520 -0.928218
+vn -0.153929 0.113041 -0.981594
+vn -0.128523 -0.010030 -0.991656
+vn -0.088288 0.729993 -0.677728
+vn -0.636811 0.578677 -0.509515
+vn -0.969362 -0.224245 -0.100262
+vn -0.218172 -0.395910 -0.891996
+vn -0.390156 -0.306586 -0.868207
+vn -0.556957 -0.311576 -0.769883
+vn -0.679451 -0.348525 -0.645660
+vn -0.194283 -0.580382 -0.790829
+vn -0.252431 0.252323 -0.934137
+vn -0.113347 0.265323 -0.957474
+vn -0.381453 0.264796 -0.885651
+vn -0.511917 0.309356 -0.801399
+vn -0.698691 -0.390333 -0.599559
+vn -0.654967 -0.076978 -0.751726
+vn -0.632232 0.100210 -0.768271
+vn -0.988822 -0.147172 -0.023900
+vn -0.811684 -0.022640 -0.583658
+vn -0.415885 -0.351885 -0.838580
+vn -0.362444 -0.111269 -0.925340
+vn -0.263204 0.656847 -0.706595
+vn -0.598851 0.007337 -0.800827
+vn -0.633756 0.262924 -0.727479
+vn -0.337229 0.640694 -0.689773
+vn -0.290734 0.743110 -0.602712
+vn -0.614569 -0.328323 -0.717293
+vn -0.465068 0.289013 -0.836769
+vn -0.624926 -0.303809 -0.719144
+vn -0.857381 0.038732 -0.513223
+vn -0.733323 -0.534735 -0.419875
+vn -0.917758 0.112721 -0.380806
+vn -0.971770 -0.232573 -0.039655
+vn -0.742226 -0.268963 -0.613807
+vn -0.571557 -0.650561 -0.500093
+vn -0.550789 -0.003127 -0.834639
+vn -0.676850 -0.017683 -0.735908
+vn -0.895687 -0.409162 -0.174157
+vn -0.465529 0.207493 -0.860366
+vn -0.099111 0.299117 -0.949055
+vn -0.475206 0.043895 -0.878779
+vn -0.967131 0.253160 0.023841
+vn -0.067552 0.591760 -0.803279
+vn -0.701432 0.163074 -0.693830
+vn -0.660510 -0.001308 -0.750816
+vn -0.697752 -0.297622 -0.651585
+vn -0.852534 -0.353566 -0.384938
+vn -0.862332 0.381581 -0.332835
+vn -0.386268 0.285397 -0.877123
+vn -0.466095 -0.365277 -0.805809
+vn -0.565578 -0.628499 -0.533957
+vn -0.908045 -0.388486 -0.156628
+vn -0.458071 -0.664675 -0.590236
+vn -0.960308 -0.194515 -0.199933
+vn -0.964776 -0.242581 -0.101793
+vn -0.380844 0.318965 -0.867882
+vn -0.492042 0.373384 -0.786435
+vn -0.478188 0.536839 -0.695083
+vn -0.404840 0.329011 -0.853145
+vn -0.815303 -0.135648 -0.562922
+vn -0.740418 -0.529167 -0.414444
+vn -0.526986 -0.682836 -0.505986
+vn -0.499321 0.751537 -0.431128
+vn -0.169673 0.838571 -0.517696
+vn -0.219605 0.797386 -0.562094
+vn -0.258173 0.737293 -0.624296
+vn -0.334590 0.135549 -0.932564
+vn -0.413710 0.025262 -0.910058
+vn -0.293211 -0.429325 -0.854229
+vn -0.290040 -0.635629 -0.715439
+vn -0.339300 -0.598067 -0.726079
+vn -0.484679 -0.817168 -0.311967
+vn -0.490798 -0.766282 -0.414642
+vn -0.647188 -0.502418 -0.573344
+vn -0.748078 -0.142671 -0.648092
+vn -0.679772 -0.065369 -0.730505
+vn -0.991413 0.068428 0.111434
+vn -0.054539 0.827746 -0.558446
+vn -0.522175 -0.822319 -0.226108
+vn -0.498764 -0.835104 -0.232025
+vn -0.573347 0.057293 -0.817307
+vn -0.752396 0.070652 -0.654912
+vn -0.695453 0.182717 -0.694953
+vn -0.554854 -0.525950 -0.644603
+vn -0.495384 -0.491707 -0.716114
+vn -0.996116 0.035619 -0.080529
+vn -0.807615 -0.518641 -0.280660
+vn -0.748369 -0.572540 -0.334875
+vn -0.654549 -0.488554 -0.576958
+vn -0.644511 -0.052985 -0.762757
+vn -0.287107 -0.341358 -0.895011
+vn -0.302272 -0.610020 -0.732466
+vn -0.332675 -0.566326 -0.754057
+vn -0.648946 -0.339719 -0.680779
+vn -0.814141 -0.316143 -0.487061
+vn -0.442642 -0.650887 -0.616777
+vn -0.695192 0.252386 -0.673060
+vn -0.839074 -0.493593 -0.228736
+vn -0.876677 -0.026484 -0.480350
+vn -0.952011 -0.168209 -0.255696
+vn -0.725635 -0.402182 -0.558304
+vn -0.528463 -0.468266 -0.708134
+vn -0.417297 -0.505946 -0.754905
+vn -0.448280 -0.554820 -0.700871
+vn -0.597240 -0.600283 -0.531944
+vn -0.732673 -0.566414 -0.377314
+vn -0.937537 -0.089135 -0.336272
+vn -0.849190 0.095406 -0.519398
+vn -0.367759 0.689946 -0.623481
+vn -0.785277 -0.386959 -0.483325
+vn -0.994313 -0.102014 0.030574
+vn -0.746438 -0.571671 -0.340622
+vn -0.932793 -0.157190 -0.324328
+vn -0.520931 0.112091 -0.846207
+vn -0.876588 -0.447940 -0.175908
+vn -0.984160 0.163837 0.067726
+vn -0.486312 -0.313467 -0.815622
+vn -0.811974 -0.518346 -0.268355
+vn -0.921857 0.269151 -0.278813
+vn -0.914605 0.363857 -0.176370
+vn -0.998523 0.050025 -0.021214
+vn -0.947370 0.250226 -0.199691
+vn -0.984160 -0.167800 -0.057210
+vn -0.763853 0.298501 -0.572211
+vn -0.244898 0.809943 -0.532933
+vn -0.503561 -0.332902 -0.797247
+vn -0.939590 -0.161793 -0.301652
+vn -0.533238 -0.331365 -0.778367
+vn -0.317318 -0.352295 -0.880453
+vn -0.785350 -0.410831 -0.463081
+vn -0.967689 0.064702 -0.243706
+vn -0.479638 0.627533 -0.613310
+vn -0.838152 0.422661 -0.344760
+vn -0.871368 0.408789 -0.271310
+vn -0.143140 -0.571383 -0.808105
+vn -0.148614 0.667385 -0.729733
+vn -0.132647 -0.409302 -0.902705
+vn -0.043635 -0.557089 -0.829306
+vn -0.196308 -0.738296 -0.645277
+vn -0.965742 -0.092485 -0.242465
+vn 0.039961 0.173970 -0.983940
+vn -0.112567 0.183385 -0.976575
+vn -0.243236 0.224570 -0.943613
+vn -0.388552 0.291555 -0.874084
+vn -0.508120 0.405064 -0.760090
+vn -0.991120 -0.117280 -0.062656
+vn -0.646358 -0.349248 -0.678415
+vn -0.143216 -0.234800 -0.961435
+vn -0.622317 -0.306458 -0.720281
+vn -0.345203 0.730598 -0.589119
+vn -0.423624 -0.217197 -0.879414
+vn -0.145231 -0.568718 -0.809610
+vn -0.875495 0.257934 -0.408630
+vn -0.850191 0.325159 -0.414061
+vn -0.511264 0.294961 -0.807222
+vn -0.940503 0.334942 -0.057174
+vn -0.074558 0.226929 -0.971053
+vn -0.860104 -0.461984 -0.216317
+vn -0.151581 0.530682 -0.833907
+vn -0.771131 0.483341 -0.414413
+vn -0.990077 0.131989 -0.048235
+vn -0.402547 -0.718532 -0.567157
+vn -0.388516 -0.724702 -0.569088
+vn -0.490536 -0.432775 -0.756360
+vn -0.585094 0.031097 -0.810369
+vn -0.558811 -0.001352 -0.829294
+vn -0.351909 0.687982 -0.634697
+vn -0.501617 0.564033 -0.655933
+vn -0.528836 0.472406 -0.705099
+vn -0.624394 0.136338 -0.769119
+vn -0.888334 -0.019905 -0.458766
+vn -0.845489 -0.497892 -0.193010
+vn -0.750005 0.181199 -0.636129
+vn -0.411576 0.247242 -0.877198
+vn 0.038810 0.922572 -0.383868
+vn -0.931384 0.120842 -0.343396
+vn -0.802479 -0.144491 -0.578922
+vn -0.604929 -0.076977 -0.792550
+vn -0.096891 -0.820424 -0.563486
+vn -0.693446 -0.622774 -0.362333
+vn -0.098936 -0.807901 -0.580955
+vn -0.865886 -0.490948 -0.095978
+vn -0.147265 0.021839 -0.988856
+vn -0.124725 -0.240433 -0.962619
+vn -0.384776 -0.180825 -0.905124
+vn -0.678587 -0.052489 -0.732642
+vn -0.492760 -0.337015 -0.802252
+vn -0.669253 -0.053113 -0.741134
+vn -0.629533 -0.218747 -0.745545
+vn -0.536934 -0.239337 -0.808962
+vn -0.760821 -0.038319 -0.647830
+vn -0.426951 -0.114149 -0.897041
+vn -0.894277 -0.443768 -0.057783
+vn -0.788618 0.090049 -0.608255
+vn -0.765371 0.045103 -0.642007
+vn -0.662347 0.029016 -0.748635
+vn -0.951037 0.109388 -0.289071
+vn -0.861182 0.091132 -0.500061
+vn -0.974979 0.202443 -0.091834
+vn -0.642386 -0.042784 -0.765186
+vn -0.871669 -0.422453 -0.248449
+vn -0.580824 0.566204 -0.584856
+vn -0.404304 0.615481 -0.676551
+vn -0.843793 -0.112207 -0.524807
+vn -0.357124 0.445554 -0.820941
+vn -0.227522 0.325016 -0.917932
+vn -0.351121 0.186045 -0.917661
+vn -0.508493 0.163127 -0.845473
+vn -0.669192 0.225191 -0.708146
+vn -0.682635 -0.022622 -0.730409
+vn -0.997388 -0.072192 -0.002429
+vn -0.654244 -0.390045 -0.647943
+vn -0.543757 -0.404709 -0.735214
+vn -0.389752 -0.409587 -0.824822
+vn -0.311461 -0.461841 -0.830479
+vn -0.442690 -0.597730 -0.668389
+vn -0.665322 -0.567990 -0.484494
+vn -0.993700 -0.024428 0.109382
+vn -0.336571 0.515665 -0.787915
+vn -0.833255 -0.513401 -0.205196
+vn -0.655358 0.499906 -0.566216
+vn -0.636059 0.731171 -0.246614
+vn -0.636229 0.698436 -0.327720
+vn -0.532730 0.296960 -0.792473
+vn -0.543680 0.752620 -0.371450
+vn -0.616445 0.600503 -0.509306
+vn -0.700189 -0.272994 -0.659704
+vn -0.809167 -0.365862 -0.459775
+vn -0.874944 -0.418516 -0.243551
+vn -0.569283 0.534135 -0.624993
+vn -0.539129 0.436846 -0.720073
+vn 0.454850 -0.705475 -0.543522
+vn 0.408211 -0.433019 -0.803653
+vn 0.444474 0.660817 -0.604785
+vn 0.894262 -0.204831 -0.397918
+vn -0.114409 -0.363086 -0.924705
+vn 0.081504 -0.273941 -0.958287
+vn 0.264141 -0.284064 -0.921703
+vn 0.435588 -0.376506 -0.817622
+vn -0.125894 -0.533947 -0.836093
+vn -0.072754 0.174790 -0.981914
+vn -0.211495 0.199952 -0.956707
+vn 0.094753 0.214224 -0.972178
+vn 0.226207 0.328124 -0.917151
+vn 0.476069 -0.392222 -0.787096
+vn 0.386653 -0.071595 -0.919442
+vn 0.330539 0.074160 -0.940874
+vn 0.946905 -0.119587 -0.298445
+vn 0.540976 0.015395 -0.840897
+vn 0.100846 -0.309113 -0.945663
+vn 0.063171 -0.119717 -0.990796
+vn -0.017896 0.642546 -0.766038
+vn 0.333980 -0.014725 -0.942465
+vn 0.380697 0.257309 -0.888179
+vn 0.068112 0.650019 -0.756860
+vn 0.065937 0.735296 -0.674531
+vn 0.400581 -0.278998 -0.872751
+vn 0.194475 0.270930 -0.942749
+vn 0.381649 -0.269766 -0.884065
+vn 0.615574 0.046015 -0.786734
+vn 0.545476 -0.536828 -0.643639
+vn 0.727145 0.144279 -0.671151
+vn 0.927940 -0.242782 -0.282814
+vn 0.466986 -0.253795 -0.847061
+vn 0.391417 -0.650509 -0.650869
+vn 0.223812 -0.034118 -0.974035
+vn 0.366096 -0.046639 -0.929408
+vn 0.790992 -0.412150 -0.452178
+vn 0.168181 0.209548 -0.963226
+vn -0.197093 0.225498 -0.954099
+vn 0.188290 0.093752 -0.977629
+vn 0.939692 0.249236 -0.234223
+vn -0.063834 0.644034 -0.762329
+vn 0.428616 0.283999 -0.857690
+vn 0.419036 0.086465 -0.903843
+vn 0.445596 -0.144931 -0.883425
+vn 0.670143 -0.372842 -0.641793
+vn 0.713407 0.416837 -0.563291
+vn 0.089433 0.265664 -0.959909
+vn 0.164903 -0.358844 -0.918715
+vn 0.316171 -0.624061 -0.714551
+vn 0.811159 -0.392839 -0.433242
+vn 0.212527 -0.652151 -0.727689
+vn 0.857619 -0.209164 -0.469830
+vn 0.893408 -0.232951 -0.384129
+vn 0.065972 0.316731 -0.946218
+vn 0.218147 0.357328 -0.908146
+vn 0.210255 0.562562 -0.799573
+vn 0.048769 0.353226 -0.934266
+vn 0.597955 -0.031114 -0.800926
+vn 0.598886 -0.562365 -0.570158
+vn 0.433311 -0.636236 -0.638315
+vn 0.304301 0.774954 -0.553938
+vn -0.020878 0.795868 -0.605110
+vn 0.002533 0.783921 -0.620855
+vn 0.008736 0.683967 -0.729461
+vn 0.023435 0.165341 -0.985958
+vn 0.097846 0.057449 -0.993542
+vn 0.026655 -0.409331 -0.911997
+vn 0.070020 -0.618934 -0.782315
+vn 0.092721 -0.630847 -0.770347
+vn 0.409819 -0.791039 -0.454209
+vn 0.382164 -0.757518 -0.529261
+vn 0.493523 -0.476034 -0.727892
+vn 0.539205 -0.137380 -0.830894
+vn 0.418831 -0.070980 -0.905286
+vn 0.986933 0.055707 -0.151193
+vn 0.493470 -0.771912 -0.400797
+vn 0.465506 -0.805744 -0.366171
+vn 0.315981 0.035930 -0.948085
+vn 0.518716 0.081342 -0.851068
+vn 0.462785 0.182249 -0.867534
+vn 0.297107 -0.507853 -0.808587
+vn 0.210386 -0.458985 -0.863174
+vn 0.960656 0.014050 -0.277384
+vn 0.656210 -0.518111 -0.548589
+vn 0.577419 -0.577784 -0.576847
+vn 0.399230 -0.494824 -0.771858
+vn 0.400883 -0.033284 -0.915525
+vn -0.008315 -0.335603 -0.941967
+vn 0.023684 -0.603233 -0.797214
+vn 0.034899 -0.569581 -0.821194
+vn 0.377257 -0.367745 -0.849965
+vn 0.594885 -0.330477 -0.732733
+vn 0.151774 -0.645015 -0.748947
+vn 0.375446 0.291550 -0.879795
+vn 0.711923 -0.513977 -0.478533
+vn 0.688950 -0.004557 -0.724795
+vn 0.824694 -0.176503 -0.537333
+vn 0.492354 -0.409779 -0.767899
+vn 0.252615 -0.458422 -0.852076
+vn 0.131510 -0.485245 -0.864432
+vn 0.173988 -0.540706 -0.823022
+vn 0.370374 -0.600183 -0.708945
+vn 0.561193 -0.585737 -0.584786
+vn 0.779313 -0.098650 -0.618821
+vn 0.593701 0.153003 -0.790006
+vn 0.196140 0.692132 -0.694610
+vn 0.591967 -0.372306 -0.714817
+vn 0.969067 -0.077038 -0.234465
+vn 0.581669 -0.595887 -0.553696
+vn 0.819149 -0.133497 -0.557829
+vn 0.238421 0.063984 -0.969052
+vn 0.789920 -0.441515 -0.425549
+vn 0.972040 0.139257 -0.189067
+vn 0.057462 -0.314078 -0.947657
+vn 0.693157 -0.522721 -0.496282
+vn 0.739950 0.272322 -0.615072
+vn 0.790496 0.361690 -0.494263
+vn 0.958590 0.040656 -0.281872
+vn 0.819688 0.255140 -0.512850
+vn 0.932700 -0.157964 -0.324218
+vn 0.499548 0.299430 -0.812892
+vn 0.083532 0.820153 -0.566014
+vn 0.186487 -0.280786 -0.941479
+vn 0.787146 -0.136486 -0.601476
+vn 0.238126 -0.364158 -0.900380
+vn 0.007287 -0.363717 -0.931481
+vn 0.645009 -0.420021 -0.638393
+vn 0.839904 0.068556 -0.538387
+vn 0.197300 0.636047 -0.746001
+vn 0.626750 0.432393 -0.648244
+vn 0.690255 0.402132 -0.601530
+vn -0.170048 -0.417506 -0.892621
+vn -0.247796 -0.515074 -0.820546
+vn -0.080811 -0.694954 -0.714499
+vn 0.844324 -0.066101 -0.531741
+vn -0.340340 0.068977 -0.937769
+vn -0.200540 0.109107 -0.973591
+vn -0.100527 0.181664 -0.978209
+vn 0.094829 0.280911 -0.955037
+vn 0.229554 0.387707 -0.892742
+vn 0.930935 -0.080592 -0.356180
+vn 0.366088 -0.414320 -0.833258
+vn 0.373518 -0.311428 -0.873783
+vn 0.101419 0.749991 -0.653626
+vn 0.156448 -0.234954 -0.959333
+vn 0.643712 0.248871 -0.723670
+vn 0.630486 0.320510 -0.706938
+vn 0.214515 0.300675 -0.929289
+vn 0.878408 0.335787 -0.340068
+vn -0.262455 0.138240 -0.954991
+vn 0.741140 -0.487892 -0.461164
+vn 0.536215 0.491979 -0.685880
+vn 0.943726 0.117453 -0.309171
+vn 0.252325 -0.681862 -0.686583
+vn 0.241799 -0.694384 -0.677764
+vn 0.256437 -0.424027 -0.868586
+vn 0.306119 0.053652 -0.950480
+vn 0.270754 0.029516 -0.962196
+vn 0.091458 0.705352 -0.702932
+vn 0.222280 0.605321 -0.764315
+vn 0.257340 0.499918 -0.826957
+vn 0.348374 0.140406 -0.926780
+vn 0.653396 0.002004 -0.757014
+vn 0.726583 -0.526114 -0.441906
+vn 0.457252 0.192072 -0.868348
+vn 0.024687 0.216176 -0.976042
+vn -0.160486 0.893703 -0.418973
+vn 0.737559 0.139254 -0.660768
+vn 0.577788 -0.157188 -0.800908
+vn 0.338594 -0.046212 -0.939797
+vn 0.540829 -0.644375 -0.540634
+vn 0.793925 -0.513592 -0.325434
+vn 0.112988 -0.172200 -0.978561
+vn 0.380219 -0.028586 -0.924455
+vn 0.181942 -0.311670 -0.932609
+vn 0.405675 -0.040496 -0.913120
+vn 0.311617 -0.183545 -0.932312
+vn 0.229757 -0.215696 -0.949045
+vn 0.448979 -0.011642 -0.893467
+vn 0.157043 -0.116421 -0.980706
+vn 0.849173 -0.441846 -0.289270
+vn 0.509987 0.101136 -0.854216
+vn 0.502497 0.042382 -0.863539
+vn 0.346830 0.049796 -0.936605
+vn 0.789142 0.131175 -0.600041
+vn 0.593830 0.110576 -0.796956
+vn 0.903119 0.207614 -0.375863
+vn 0.335467 -0.027738 -0.941644
+vn 0.749363 -0.431754 -0.502040
+vn 0.398722 0.556700 -0.728770
+vn 0.159415 0.619185 -0.768893
+vn 0.633699 -0.103057 -0.766684
+vn 0.068828 0.420231 -0.904803
+vn -0.088663 0.243948 -0.965727
+vn 0.028039 0.088562 -0.995676
+vn 0.196340 0.128200 -0.972119
+vn 0.351608 0.234772 -0.906231
+vn 0.401167 -0.024876 -0.915667
+vn 0.960510 -0.059404 -0.271829
+vn 0.403250 -0.363753 -0.839686
+vn 0.263046 -0.370792 -0.890685
+vn 0.088544 -0.372991 -0.923600
+vn -0.020440 -0.422138 -0.906301
+vn 0.171241 -0.593300 -0.786557
+vn 0.447940 -0.597460 -0.665125
+vn 0.988307 -0.005346 -0.152383
+vn 0.048883 0.565646 -0.823198
+vn 0.731655 -0.535076 -0.422345
+vn 0.448720 0.492887 -0.745461
+vn 0.512870 0.781166 -0.356011
+vn 0.473893 0.738222 -0.480055
+vn 0.221524 0.339691 -0.914077
+vn 0.377685 0.773714 -0.508645
+vn 0.373587 0.663078 -0.648661
+vn 0.342115 -0.286605 -0.894883
+vn 0.604377 -0.400864 -0.688503
+vn 0.746569 -0.450215 -0.489838
+vn 0.284146 0.505382 -0.814770
+vn 0.233946 0.442438 -0.865747
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+vn 0.000000 1.000000 0.000000
+
 # 面 127 34 139
 f 128 35 140
 # 面 11 0 37

python/generate_normal.py

@@ -0,0 +1,179 @@
+import numpy as np
+import sys
+import os
+
+def compute_vertex_normals(vertices, faces):
+    """
+    计算顶点法线
+    Args:
+        vertices: 顶点列表，每个顶点是[x, y, z]
+        faces: 面列表，每个面是顶点索引列表（三角形面为3个索引）
+    
+    Returns:
+        normals: 顶点法线列表，每个法线是[nx, ny, nz]
+    """
+    # 初始化法线数组
+    normals = np.zeros_like(vertices, dtype=np.float64)
+    
+    # 计算每个面的法线并累加到对应的顶点
+    for face in faces:
+        if len(face) < 3:
+            continue
+            
+        # 获取三角形的三个顶点
+        v0 = vertices[face[0]]
+        v1 = vertices[face[1]]
+        v2 = vertices[face[2]]
+        
+        # 计算两条边向量
+        edge1 = v1 - v0
+        edge2 = v2 - v0
+        
+        # 计算面法线（叉积）
+        face_normal = np.cross(edge1, edge2)
+        
+        # 面法线长度（用于加权平均）
+        face_area = np.linalg.norm(face_normal)
+        
+        # 如果面法线长度不为零，则归一化并加权
+        if face_area > 1e-10:
+            face_normal_normalized = face_normal / face_area
+            
+            # 将面法线累加到每个顶点
+            for vertex_index in face:
+                normals[vertex_index] += face_normal_normalized
+    
+    # 归一化所有顶点法线
+    for i in range(len(normals)):
+        length = np.linalg.norm(normals[i])
+        if length > 1e-10:
+            normals[i] /= length
+        else:
+            # 如果法线长度为零（可能是孤立顶点），设置为默认向上法线
+            normals[i] = np.array([0.0, 1.0, 0.0])
+    
+    return normals
+
+def parse_obj_file(filename):
+    """
+    解析OBJ文件
+    Returns:
+        vertices: 顶点列表
+        faces: 面索引列表
+        has_normals: 是否已经包含法线
+    """
+    vertices = []
+    faces = []
+    existing_normals = []
+    has_normals = False
+    
+    try:
+        with open(filename, 'r', encoding='utf-8') as file:
+            for line in file:
+                line = line.strip()
+                if not line or line.startswith('#'):
+                    continue
+                
+                parts = line.split()
+                if not parts:
+                    continue
+                
+                if parts[0] == 'v':  # 顶点
+                    if len(parts) >= 4:
+                        vertex = [float(parts[1]), float(parts[2]), float(parts[3])]
+                        vertices.append(vertex)
+                
+                elif parts[0] == 'vn':  # 法线
+                    if len(parts) >= 4:
+                        normal = [float(parts[1]), float(parts[2]), float(parts[3])]
+                        existing_normals.append(normal)
+                        has_normals = True
+                
+                elif parts[0] == 'f':  # 面
+                    face_vertices = []
+                    for part in parts[1:]:
+                        # 处理 f v1/vt1/vn1 v2/vt2/vn2 格式
+                        vertex_data = part.split('/')
+                        if vertex_data[0]:  # 顶点索引
+                            # OBJ索引从1开始，转换为从0开始
+                            vertex_index = int(vertex_data[0]) - 1
+                            face_vertices.append(vertex_index)
+                    
+                    if len(face_vertices) >= 3:
+                        # 如果是四边形或多边形，分解为三角形
+                        for i in range(1, len(face_vertices) - 1):
+                            faces.append([face_vertices[0], face_vertices[i], face_vertices[i + 1]])
+    
+    except UnicodeDecodeError:
+        print(f"错误: 无法读取文件 {filename}，请确保文件是UTF-8编码。")
+        sys.exit(1)
+    
+    return np.array(vertices), faces, has_normals
+
+def write_obj_file(filename, vertices, faces, normals, original_has_normals=False):
+    """
+    写入OBJ文件
+    """
+    with open(filename, 'w', encoding='utf-8') as file:
+        file.write("# OBJ文件 - 自动计算法线\n")
+        file.write(f"# 顶点数: {len(vertices)}\n")
+        file.write(f"# 面数: {len(faces)}\n\n")
+        
+        # 写入顶点
+        for i, vertex in enumerate(vertices):
+            file.write(f"v {vertex[0]:.6f} {vertex[1]:.6f} {vertex[2]:.6f}\n")
+        
+        file.write("\n")
+        
+        # 写入法线
+        for i, normal in enumerate(normals):
+            file.write(f"vn {normal[0]:.6f} {normal[1]:.6f} {normal[2]:.6f}\n")
+        
+        file.write("\n")
+        
+        # 写入面（使用顶点索引/法线索引格式）
+        for face in faces:
+            face_line = "f"
+            for vertex_index in face:
+                # 如果原始文件有法线或者我们计算了法线，使用 v//vn 格式
+                face_line += f" {vertex_index + 1}//{vertex_index + 1}"
+            file.write(face_line + "\n")
+
+def process_obj_file(input_file, output_file=None):
+    """
+    处理OBJ文件的主要函数
+    """
+    if output_file is None:
+        base_name = os.path.splitext(input_file)[0]
+        output_file = f"{base_name}_with_normals.obj"
+    
+    print(f"读取文件: {input_file}")
+    vertices, faces, has_normals = parse_obj_file(input_file)
+    
+    print(f"找到 {len(vertices)} 个顶点, {len(faces)} 个面")
+    
+    if has_normals:
+        print("警告: 输入文件已包含法线数据，将被重新计算")
+    
+    if len(vertices) == 0:
+        print("错误: 没有找到顶点数据")
+        return False
+    
+    if len(faces) == 0:
+        print("错误: 没有找到面数据")
+        return False
+    
+    print("计算顶点法线中...")
+    normals = compute_vertex_normals(vertices, faces)
+    
+    print("写入输出文件...")
+    write_obj_file(output_file, vertices, faces, normals, has_normals)
+    
+    print(f"完成! 输出文件: {output_file}")
+    return True
+
+
+if __name__ == "__main__":
+    input_file = "face.obj"  # 默认输入文件
+    output_file = "face_with_normals.obj"  # 默认输出文件
+    process_obj_file(input_file, output_file)