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class="menu navigation"><div class="list-h"><a target="_blank" rel="external nofollow noopener noreferrer" href="https://github.com/MHuiG" active-action="action-https:githubcomMHuiG"><i class="fa-brands fa-github color-github fa-fw"></i><p>Github</p></a><a href="/pages/friends/" active-action="action-pagesfriends"><i class="fa-duotone fa-link color-friends fa-fw"></i><p>友链</p></a><a href="/pages/about/" active-action="action-pagesabout"><i class="fa-duotone fa-user-tie color-about fa-fw"></i><p>关于</p></a><a href="https://www.travellings.cn/go-by-clouds.html" target="_blank" active-action="action-https:wwwtravellingscngo-by-cloudshtml" rel="external nofollow noopener noreferrer"><i class="fa-duotone fa-subway color-travellings fa-fw"></i><p>Travelling</p></a></div></div></div></div><div id="scroll-down" style="display:none"><i class="fa fa-chevron-down scroll-down-effects"></i></div></div></div><div id="safearea"><div class="body-wrapper"><div id="l_main" class><article itemscope itemtype="http://schema.org/Article" class="article post white-box reveal md shadow floatable blur article-type-post" id="post" itemprop="blogPost"><link itemprop="mainEntityOfPage" href="https://blog.mhuig.top/p/5e7ad437/"><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="MHuiG"></span><span hidden itemprop="post" itemscope itemtype="http://schema.org/Post"><meta itemprop="name" content="MHuiG"><meta itemprop="description" content="MHuiG&#39;s Blog (MHuiG的博客) MHuiG&#39;s Neverland（MHuiG的梦幻岛） —— MHuiG(@MHuiG) 随便写写画画的地方 - 技术博客"></span><span hidden><meta itemprop="image" content="/lib/favicon/android-chrome-192x192.png"></span><div class="article-meta" id="top"><h1 class="title" itemprop="name headline"> LBS 球面距离公式</h1><div class="new-meta-box"><div class="new-meta-item author" itemprop="author" itemscope itemtype="http://schema.org/Person"> <a itemprop="url" class="author" target="_blank" href="https://mhuig.top/" rel="nofollow noopener"><img itemprop="image" src="/lib/avatar/avatar-16.webp?v=2199236952" class="lazyload" data-srcset="/lib/avatar/avatar-16.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw=="><p itemprop="name">MHuiG</p></a></div><div class="new-meta-item wordcount"><a class="notlink"><i class="fa-duotone fa-keyboard fa-fw" aria-hidden="true"></i><p>字数：313 字</p></a></div><div class="new-meta-item readtime"><a class="notlink"><i class="fa-duotone fa-hourglass-half fa-fw" aria-hidden="true"></i><p>时长：1 分钟</p></a></div></div></div><div id="layoutHelper-page-plugins"></div><div id="post-body" itemprop="articleBody"><p> 维基百科推荐使用<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.025ex" xmlns="http://www.w3.org/2000/svg" width="10.631ex" height="1.57ex" role="img" focusable="false" viewBox="0 -683 4699 694"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D43B" d="M228 637Q194 637 192 641 191 643 191 649 191 673 202 682 204 683 219 683 260 681 355 681 389 681 418 681T463 682 483 682Q499 682 499 672 499 670 497 658 492 641 487 638H485Q483 638 480 638T473 638 464 637 455 637Q416 636 405 634T387 623Q384 619 355 500 348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504 674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660 586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672 888 645 876 638H874Q872 638 869 638T862 638 853 637 844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51 646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2 533 2 504 2T458 2 437 1Q420 1 420 10 420 15 423 24 428 43 433 45 437 46 448 46H454Q481 46 514 49 520 50 522 50T528 55 534 64 540 82 547 110 558 153Q565 181 569 198 602 330 602 331T457 332H312L279 197Q245 63 245 58 245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2 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389Q284 441 347 441H350Q398 441 422 400 430 381 430 363 430 333 417 315T391 292 366 288Q346 288 334 299T322 328Q322 376 378 392 356 405 342 405 286 405 239 331 229 315 224 298T190 165Q156 25 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 114 189T154 366Q154 405 128 405 107 405 92 377T68 316 57 280Q55 278 41 278H27Q21 284 21 287Z"/></g><g data-mml-node="mi" transform="translate(2819,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415 300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372 367 378Q368 378 368 379 368 382 361 388T336 399 297 405Q249 405 227 379T204 326Q204 301 223 291T278 274 330 259Q396 230 396 163 396 135 385 107T352 51 289 7 195-10Q118-10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34 201 27Q237 27 263 38T301 66 318 97 323 122Q323 150 302 164T254 181 195 196 148 231Q131 256 131 289Z"/></g><g data-mml-node="mi" transform="translate(3288,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369 98 420 158 442Q197 442 223 419T250 357Q250 340 236 301T196 196 154 83Q149 61 149 51 149 26 166 26 175 26 185 29T208 43 235 78 260 137Q263 149 265 151T282 153Q302 153 302 143 302 135 293 112T268 61 223 11 161-11Q129-11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281 56 279 53 278 49 278 41 278H27Q21 284 21 287Z"/></g><g data-mml-node="mi" transform="translate(3633,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341 56 388 89 425 135 442Q171 442 195 424T225 390 231 369Q231 367 232 367L243 378Q304 442 382 442 436 442 469 415T503 336 465 179 427 52Q427 26 444 26 450 26 453 27 482 32 505 65T540 145Q542 153 560 153 580 153 580 145 580 144 576 130 568 101 554 73T508 17 439-10Q392-10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291 189 157Q156 26 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 112 180T152 343Q153 348 153 366 153 405 129 405 91 405 66 305 60 285 60 284 58 278 41 278H27Q21 284 21 287Z"/></g><g data-mml-node="mi" transform="translate(4233,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350 174 402 244 433 307 442H310Q355 442 388 420T421 355Q421 265 310 237 261 224 176 223 139 223 138 221 138 219 132 186T125 128Q125 81 146 54T209 26 302 45 394 111Q403 121 406 121 410 121 419 112T429 98 420 82 390 55 344 24 281-1 205-11Q126-11 83 42T39 168ZM373 353Q367 405 305 405 272 405 244 391T199 357 170 316 154 280 149 261Q149 260 169 260 282 260 327 284T373 353Z"/></g></g></g></svg></mjx-container>公式，理由是<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.186ex" xmlns="http://www.w3.org/2000/svg" width="22.544ex" height="1.781ex" role="img" focusable="false" viewBox="0 -705 9964.4 787"><g stroke="currentColor" fill="currentColor" stroke-width="0" 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353Z"/></g></g></g></svg></mjx-container>公式用到了大量余弦函数， 而两点间距离很短时（比如地球表面上相距几百米的两点），余弦函数会得出 0.999… 的结果， 会导致较大的舍入误差。而<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.025ex" xmlns="http://www.w3.org/2000/svg" width="10.631ex" height="1.57ex" role="img" focusable="false" viewBox="0 -683 4699 694"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D43B" d="M228 637Q194 637 192 641 191 643 191 649 191 673 202 682 204 683 219 683 260 681 355 681 389 681 418 681T463 682 483 682Q499 682 499 672 499 670 497 658 492 641 487 638H485Q483 638 480 638T473 638 464 637 455 637Q416 636 405 634T387 623Q384 619 355 500 348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504 674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660 586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672 888 645 876 638H874Q872 638 869 638T862 638 853 637 844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51 646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2 533 2 504 2T458 2 437 1Q420 1 420 10 420 15 423 24 428 43 433 45 437 46 448 46H454Q481 46 514 49 520 50 522 50T528 55 534 64 540 82 547 110 558 153Q565 181 569 198 602 330 602 331T457 332H312L279 197Q245 63 245 58 245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2 144 2 115 2T69 2 48 1Q31 1 31 10 31 12 34 24 39 43 44 45 48 46 59 46H65Q92 46 125 49 139 52 144 61 147 65 216 339T285 628Q285 635 228 637Z"/></g><g data-mml-node="mi" transform="translate(888,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392 386 422 416 422 429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35 443 55 463 131 469 151 473 152 475 153 483 153H487Q506 153 506 144 506 138 501 117T481 63 449 13Q436 0 417-8 409-10 393-10 359-10 336 5T306 36L300 51Q299 52 296 50 294 48 292 46 233-10 172-10 117-10 75 30T33 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transform="translate(3633,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341 56 388 89 425 135 442Q171 442 195 424T225 390 231 369Q231 367 232 367L243 378Q304 442 382 442 436 442 469 415T503 336 465 179 427 52Q427 26 444 26 450 26 453 27 482 32 505 65T540 145Q542 153 560 153 580 153 580 145 580 144 576 130 568 101 554 73T508 17 439-10Q392-10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291 189 157Q156 26 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 112 180T152 343Q153 348 153 366 153 405 129 405 91 405 66 305 60 285 60 284 58 278 41 278H27Q21 284 21 287Z"/></g><g data-mml-node="mi" transform="translate(4233,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350 174 402 244 433 307 442H310Q355 442 388 420T421 355Q421 265 310 237 261 224 176 223 139 223 138 221 138 219 132 186T125 128Q125 81 146 54T209 26 302 45 394 111Q403 121 406 121 410 121 419 112T429 98 420 82 390 55 344 24 281-1 205-11Q126-11 83 42T39 168ZM373 353Q367 405 305 405 272 405 244 391T199 357 170 316 154 280 149 261Q149 260 169 260 282 260 327 284T373 353Z"/></g></g></g></svg></mjx-container>公式采用了正弦函数，即使距离很小，也能保持足够的有效数字。 以前采用三角函数表计算时的确会有这个问题，但经过实际验证，采用计算机来计算时，两个公式的区别不大。 稳妥起见，这里还是采用<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.025ex" xmlns="http://www.w3.org/2000/svg" width="10.631ex" height="1.57ex" role="img" focusable="false" viewBox="0 -683 4699 694"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D43B" d="M228 637Q194 637 192 641 191 643 191 649 191 673 202 682 204 683 219 683 260 681 355 681 389 681 418 681T463 682 483 682Q499 682 499 672 499 670 497 658 492 641 487 638H485Q483 638 480 638T473 638 464 637 455 637Q416 636 405 634T387 623Q384 619 355 500 348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504 674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660 586 677 588 679T604 682Q609 682 646 681T740 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transform="translate(0,-750)"><g data-mml-node="mtext"><path data-c="28" d="M94 250Q94 319 104 381T127 488 164 576 202 643 244 695 277 729 302 750H315 319Q333 750 333 741 333 738 316 720T275 667 226 581 184 443 167 250 184 58 225-81 274-167 316-220 333-241Q333-250 318-250H315 302L274-226Q180-141 137-14T94 250Z"/><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315 301 241Q265 210 201 149L142 93 218 92Q375 92 385 97 392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19 31Q50 38 56 46T86 81Q115 113 136 137 145 147 170 174T204 211 233 244 261 278 284 308 305 340 320 369 333 401 340 431 343 464Q343 527 309 573T212 619Q179 619 154 602T119 569 109 550Q109 549 114 549 132 549 151 535T170 489Q170 464 154 447T109 429Z" transform="translate(389,0)"/><path data-c="29" d="M60 749 64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12 224-76 186-143 145-194 113-227 90-246Q87-249 86-250H74Q66-250 63-250T58-247 55-238Q56-237 66-225 221-64 221 250T66 725Q56 737 55 738 55 746 60 749Z" transform="translate(889,0)"/></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.048ex" xmlns="http://www.w3.org/2000/svg" width="1.717ex" height="1.593ex" role="img" focusable="false" viewBox="0 -683 759 704"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682 206 683 378 683 550 682 564 680 620 672 658 652T712 606 733 563 739 529Q739 484 710 445T643 385 576 351 538 338L545 333Q612 295 612 223 612 212 607 162T602 80V71Q602 53 603 43T614 25 640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93 755 75 731 36 693-21 641-21H632Q571-21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313 459 320 449 321T378 323H309L277 193Q244 61 244 59 244 55 245 54T252 50 269 48 302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2 146 2 117 2T71 2 50 1Q33 1 33 10 33 12 36 24 41 43 46 45 50 46 61 46H67Q94 46 127 49 141 52 146 61 149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627 385 624 352 494T319 361Q319 360 388 360 466 361 492 367 556 377 592 426 608 449 619 486T630 554Z"/></g></g></g></svg></mjx-container>为地球半径，可取平均值<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="11.713ex" height="1.62ex" role="img" focusable="false" viewBox="0 -694 5177 716"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601 351 623 311 626 240 626 194 566 147 500 147 364L148 360Q153 366 156 373 197 433 263 433H267Q313 433 348 414 372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149 440 90 387 34T253-22Q225-22 199-14T143 16 92 75 56 172 42 313ZM257 397Q227 397 205 380T171 335 154 278 148 216Q148 133 160 97T198 39Q222 21 251 21 302 21 329 59 342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z"/><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664 351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336 375 315Q457 262 457 175 457 96 395 37T238-22Q158-22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94 148 82 136 74 126 70 118 67L114 66Q165 21 238 21 293 21 321 74 338 107 338 175V195Q338 290 274 322 259 328 213 329L171 330 168 332Q166 335 166 348 166 366 174 366 202 366 232 371 266 376 294 413T322 525V533Q322 590 287 612 265 626 240 626 208 626 181 615T143 592 132 580H135Q138 579 143 578T153 573 165 566 175 555 183 540 186 520Q186 498 172 481T127 463Z" transform="translate(500,0)"/><path data-c="37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646 364 644H485V605L417 512Q408 500 387 472T360 435 339 403 319 367 305 330 292 284 284 230 278 162 275 80Q275 66 275 52T274 28V19Q270 2 255-10T221-22Q210-22 200-19T179 0 168 40Q168 198 265 368 285 400 349 489L395 552H302Q128 552 119 546 113 543 108 522T98 479L95 458V455H55V458Z" transform="translate(1000,0)"/><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 54 315 52T339 48 401 46H427V0H416Q395 3 257 3 121 3 100 0H88V46H114Q136 46 152 46T177 47 193 50 201 52 207 57 213 61V578Z" transform="translate(1500,0)"/><path data-c="2E" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0 96 17 78 60Z" transform="translate(2000,0)"/><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 54 315 52T339 48 401 46H427V0H416Q395 3 257 3 121 3 100 0H88V46H114Q136 46 152 46T177 47 193 50 201 52 207 57 213 61V578Z" transform="translate(2278,0)"/><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664 351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336 375 315Q457 262 457 175 457 96 395 37T238-22Q158-22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94 148 82 136 74 126 70 118 67L114 66Q165 21 238 21 293 21 321 74 338 107 338 175V195Q338 290 274 322 259 328 213 329L171 330 168 332Q166 335 166 348 166 366 174 366 202 366 232 371 266 376 294 413T322 525V533Q322 590 287 612 265 626 240 626 208 626 181 615T143 592 132 580H135Q138 579 143 578T153 573 165 566 175 555 183 540 186 520Q186 498 172 481T127 463Z" transform="translate(2778,0)"/><path data-c="37" d="M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646 364 644H485V605L417 512Q408 500 387 472T360 435 339 403 319 367 305 330 292 284 284 230 278 162 275 80Q275 66 275 52T274 28V19Q270 2 255-10T221-22Q210-22 200-19T179 0 168 40Q168 198 265 368 285 400 349 489L395 552H302Q128 552 119 546 113 543 108 522T98 479L95 458V455H55V458Z" transform="translate(3278,0)"/></g><g data-mml-node="mi" transform="translate(3778,0)"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686 294 679 244 477 194 279 194 272 213 282 223 291 247 309 292 354T362 415Q402 442 438 442 468 442 485 423T503 369Q503 344 496 327T477 302 456 291 438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316 228 255Q230 254 243 252T267 246 293 238 320 224 342 206 359 180 365 147Q365 130 360 106T354 66Q354 26 381 26 429 26 459 145 461 153 479 153H483Q499 153 499 144 499 139 496 130 455-11 378-11 333-11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206 200 217 182 220H180Q168 178 159 139T145 81 136 44 129 20 122 7 111-2Q98-11 83-11 66-11 57-1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640 121 647Z"/></g><g data-mml-node="mi" transform="translate(4299,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341 56 388 88 425 132 442 175 435 205 417 221 395 229 376L231 369Q231 367 232 367L243 378Q303 442 384 442 401 442 415 440T441 433 460 423 475 411 485 398 493 385 497 373 500 364 502 357L510 367Q573 442 659 442 713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145 857 144 853 130 845 101 831 73T785 17 716-10Q669-10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291 466 157Q433 26 428 16 415-11 385-11 372-11 364-4T353 8 350 18Q350 29 384 161L420 307Q423 322 423 345 423 404 379 404H374Q288 404 229 303L222 291 189 157Q156 26 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 112 181 151 335 151 342 154 357 154 369 154 405 129 405 107 405 92 377T69 316 57 280Q55 278 41 278H27Q21 284 21 287Z"/></g></g></g></svg></mjx-container><br><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.493ex" xmlns="http://www.w3.org/2000/svg" width="2.467ex" height="1.493ex" role="img" focusable="false" viewBox="0 -442 1090.6 660"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D711" d="M92 210Q92 176 106 149T142 108 185 85 220 72L235 70 237 71 250 112Q268 170 283 211T322 299 370 375 429 423 502 442Q547 442 582 410T618 302Q618 224 575 152T457 35 299-10Q273-10 273-12L266-48Q260-83 252-125T241-179Q236-203 215-212 204-218 190-218 159-215 159-185 159-175 214-2L209 0Q204 2 195 5T173 14 147 28 120 46 94 71 71 103 56 142 50 190Q50 238 76 311T149 431H162Q183 431 183 423 183 417 175 409 134 361 114 300T92 210ZM574 278Q574 320 550 344T486 369Q437 369 394 329T323 218Q309 184 295 109L286 64Q304 62 306 62 423 62 498 131T574 278Z"/></g><g data-mml-node="mn" transform="translate(687,-150) scale(0.707)"><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 54 315 52T339 48 401 46H427V0H416Q395 3 257 3 121 3 100 0H88V46H114Q136 46 152 46T177 47 193 50 201 52 207 57 213 61V578Z"/></g></g></g></g></svg></mjx-container> ,<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.493ex" xmlns="http://www.w3.org/2000/svg" width="2.467ex" height="1.493ex" role="img" focusable="false" viewBox="0 -442 1090.6 660"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D711" d="M92 210Q92 176 106 149T142 108 185 85 220 72L235 70 237 71 250 112Q268 170 283 211T322 299 370 375 429 423 502 442Q547 442 582 410T618 302Q618 224 575 152T457 35 299-10Q273-10 273-12L266-48Q260-83 252-125T241-179Q236-203 215-212 204-218 190-218 159-215 159-185 159-175 214-2L209 0Q204 2 195 5T173 14 147 28 120 46 94 71 71 103 56 142 50 190Q50 238 76 311T149 431H162Q183 431 183 423 183 417 175 409 134 361 114 300T92 210ZM574 278Q574 320 550 344T486 369Q437 369 394 329T323 218Q309 184 295 109L286 64Q304 62 306 62 423 62 498 131T574 278Z"/></g><g data-mml-node="mn" transform="translate(687,-150) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315 301 241Q265 210 201 149L142 93 218 92Q375 92 385 97 392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19 31Q50 38 56 46T86 81Q115 113 136 137 145 147 170 174T204 211 233 244 261 278 284 308 305 340 320 369 333 401 340 431 343 464Q343 527 309 573T212 619Q179 619 154 602T119 569 109 550Q109 549 114 549 132 549 151 535T170 489Q170 464 154 447T109 429Z"/></g></g></g></g></svg></mjx-container> 表示两点的纬度；<br><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.027ex" xmlns="http://www.w3.org/2000/svg" width="3.204ex" height="1.647ex" role="img" focusable="false" viewBox="0 -716 1416 728"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D6E5" d="M574 715 582 716Q589 716 595 716 612 716 616 714 621 712 621 709 622 707 705 359T788 8Q786 5 785 3L781 0H416Q52 0 50 2T48 6Q48 9 305 358T567 711Q572 712 574 715ZM599 346 538 602 442 474Q347 345 252 217T157 87 409 86 661 88L654 120Q646 151 629 220T599 346Z"/></g><g data-mml-node="mi" transform="translate(833,0)"><path data-c="1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644 322 629 373 486T474 207 524 67Q531 47 537 34T546 15 551 6 555 2 556-2 550-11H482Q457 3 450 18T399 152L354 277 340 262Q327 246 293 207T236 141Q211 112 174 69 123 9 111-1T83-12Q47-12 47 20 47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657 166 657 166 673Z"/></g></g></g></svg></mjx-container> 表示两点经度的差值。</p></div><div class="story post-story"><h2 id="距离计算函数"><a href="#距离计算函数" class="headerlink" title="距离计算函数"></a>距离计算函数</h2><p>下面就是计算球面间两点<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="23.289ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10293.8 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="28" d="M94 250Q94 319 104 381T127 488 164 576 202 643 244 695 277 729 302 750H315 319Q333 750 333 741 333 738 316 720T275 667 226 581 184 443 167 250 184 58 225-81 274-167 316-220 333-241Q333-250 318-250H315 302L274-226Q180-141 137-14T94 250Z"/></g><g data-mml-node="mi" transform="translate(389,0)"><path data-c="1D459" d="M117 59Q117 26 142 26 179 26 205 131 211 151 215 152 217 153 225 153H229Q238 153 241 153T246 151 248 144Q247 138 245 128T234 90 214 43 183 6 137-11Q101-11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623 167 626 166 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166 540T173 566 179 586 187 603 197 615 211 624 229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420 330 398 317 385H210L174 240Q135 80 135 68 135 26 162 26 197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145 322 142 319 133 314 117 301 95T267 48 216 6 155-11Q125-11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383 128 385 77 385H26Z"/></g><g data-mml-node="mn" transform="translate(1577,0)"><path data-c="30" d="M96 585Q152 666 249 666 297 666 345 640T423 548Q460 465 460 320 460 165 417 83 397 41 362 16T301-15 250-22Q224-22 198-16T137 16 82 83Q39 165 39 320 39 494 96 585ZM321 597Q291 629 250 629 208 629 178 597 153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16 290 16 318 46 347 76 354 130T362 333Q362 478 354 524T321 597Z"/></g><g data-mml-node="mo" transform="translate(2077,0)"><path data-c="2C" d="M78 35T78 60 94 103 137 121Q165 121 187 96T210 8Q210-27 201-60T180-117 154-158 130-185 117-194Q113-194 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634 149 635 141 636 132 637 122 637Q112 637 109 637T101 638 95 641 94 647Q94 649 96 661 101 680 107 682T179 688Q194 689 213 690T243 693 254 694Q266 694 266 686 266 675 193 386T118 83Q118 81 118 75T117 65V59Z"/></g><g data-mml-node="mi" transform="translate(6195.1,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392 386 422 416 422 429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35 443 55 463 131 469 151 473 152 475 153 483 153H487Q506 153 506 144 506 138 501 117T481 63 449 13Q436 0 417-8 409-10 393-10 359-10 336 5T306 36L300 51Q299 52 296 50 294 48 292 46 233-10 172-10 117-10 75 30T33 157ZM351 328Q351 334 346 350T323 385 277 405Q242 405 210 374T160 293Q131 214 119 129 119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"/></g><g data-mml-node="mi" transform="translate(6724.1,0)"><path data-c="1D461" d="M26 385Q19 392 19 395 19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566 179 586 187 603 197 615 211 624 229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420 330 398 317 385H210L174 240Q135 80 135 68 135 26 162 26 197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145 322 142 319 133 314 117 301 95T267 48 216 6 155-11Q125-11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383 128 385 77 385H26Z"/></g><g data-mml-node="mn" transform="translate(7085.1,0)"><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 54 315 52T339 48 401 46H427V0H416Q395 3 257 3 121 3 100 0H88V46H114Q136 46 152 46T177 47 193 50 201 52 207 57 213 61V578Z"/></g><g data-mml-node="mo" transform="translate(7585.1,0)"><path data-c="2C" d="M78 35T78 60 94 103 137 121Q165 121 187 96T210 8Q210-27 201-60T180-117 154-158 130-185 117-194Q113-194 104-185T95-172Q95-168 106-156T131-126 157-76 173-3V9L172 8Q170 7 167 6T161 3 152 1 140 0Q113 0 96 17Z"/></g><g data-mml-node="mi" transform="translate(8029.8,0)"><path data-c="1D459" d="M117 59Q117 26 142 26 179 26 205 131 211 151 215 152 217 153 225 153H229Q238 153 241 153T246 151 248 144Q247 138 245 128T234 90 214 43 183 6 137-11Q101-11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623 167 626 166 628T162 632 157 634 149 635 141 636 132 637 122 637Q112 637 109 637T101 638 95 641 94 647Q94 649 96 661 101 680 107 682T179 688Q194 689 213 690T243 693 254 694Q266 694 266 686 266 675 193 386T118 83Q118 81 118 75T117 65V59Z"/></g><g data-mml-node="mi" transform="translate(8327.8,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341 56 388 89 425 135 442Q171 442 195 424T225 390 231 369Q231 367 232 367L243 378Q304 442 382 442 436 442 469 415T503 336 465 179 427 52Q427 26 444 26 450 26 453 27 482 32 505 65T540 145Q542 153 560 153 580 153 580 145 580 144 576 130 568 101 554 73T508 17 439-10Q392-10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291 189 157Q156 26 151 16 138-11 108-11 95-11 87-5T76 7 74 17Q74 30 112 180T152 343Q153 348 153 366 153 405 129 405 91 405 66 305 60 285 60 284 58 278 41 278H27Q21 284 21 287Z"/></g><g data-mml-node="mi" transform="translate(8927.8,0)"><path data-c="1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412 431 419 447 422Q461 422 470 413T480 394Q480 379 423 152T363-80Q345-134 286-169T151-205Q10-205 10-137 10-111 28-91T74-71Q89-71 102-80T116-111Q116-121 114-130T107-144 99-154 92-162L90-164H91Q101-167 151-167 189-167 211-155 234-144 254-122T282-75Q288-56 298-13 311 35 311 43ZM384 328 380 339Q377 350 375 354T369 368 359 382 346 393 328 402 306 405Q262 405 221 352 191 313 171 233T151 117Q151 38 213 38 269 38 323 108L331 118 384 328Z"/></g><g data-mml-node="mn" transform="translate(9404.8,0)"><path data-c="31" d="M213 578 200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641 273 663Q275 666 285 666 294 666 302 660V361L303 61Q310 54 315 52T339 48 401 46H427V0H416Q395 3 257 3 121 3 100 0H88V46H114Q136 46 152 46T177 47 193 50 201 52 207 57 213 61V578Z"/></g><g data-mml-node="mo" transform="translate(9904.8,0)"><path data-c="29" d="M60 749 64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12 224-76 186-143 145-194 113-227 90-246Q87-249 86-250H74Q66-250 63-250T58-247 55-238Q56-237 66-225 221-64 221 250T66 725Q56 737 55 738 55 746 60 749Z"/></g></g></g></svg></mjx-container>之间距离的函数。</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">from</span> math <span class="keyword">import</span> sin, asin, cos, radians, fabs, sqrt</span><br><span class="line"> </span><br><span class="line">EARTH_RADIUS=<span class="number">6371</span> <span class="comment"># 地球平均半径，6371km</span></span><br><span class="line"> </span><br><span class="line"><span class="keyword">def</span> <span class="title function_">hav</span>(<span class="params">theta</span>):</span><br><span class="line"> s = sin(theta / <span class="number">2</span>)</span><br><span class="line"> <span class="keyword">return</span> s * s</span><br><span class="line"> </span><br><span class="line"><span class="keyword">def</span> <span class="title function_">get_distance_hav</span>(<span class="params">lat0, lng0, lat1, lng1</span>):</span><br><span class="line"> <span class="string">"用haversine公式计算球面两点间的距离。"</span></span><br><span class="line"> <span class="comment"># 经纬度转换成弧度</span></span><br><span class="line"> lat0 = radians(lat0)</span><br><span class="line"> lat1 = radians(lat1)</span><br><span class="line"> lng0 = radians(lng0)</span><br><span class="line"> lng1 = radians(lng1)</span><br><span class="line"> </span><br><span class="line"> dlng = fabs(lng0 - lng1)</span><br><span class="line"> dlat = fabs(lat0 - lat1)</span><br><span class="line"> h = hav(dlat) + cos(lat0) * cos(lat1) * hav(dlng)</span><br><span class="line"> distance = <span class="number">2</span> * EARTH_RADIUS * asin(sqrt(h))</span><br><span class="line"> </span><br><span class="line"> <span class="keyword">return</span> distance</span><br></pre></td></tr></tbody></table></figure></div><div class="story post-story"><h2 id="相关文献"><a href="#相关文献" class="headerlink" title="相关文献"></a>相关文献</h2><p><a target="_blank" rel="external nofollow noopener noreferrer" href="http://oracle-abc.wikidot.com/zh-blog:20">LBS 球面距离公式</a></p></div></div><div class="footer"><div class="copyright license"><div class="license-title">LBS 球面距离公式</div><div class="license-link"><a href="https://blog.mhuig.top/p/5e7ad437/">https://blog.mhuig.top/p/5e7ad437/</a></div><div class="license-meta"><div class="license-meta-item"><div class="license-meta-title">本文作者</div><div class="license-meta-text">MHuiG</div></div><div class="license-meta-item"><div class="license-meta-title">发布于</div><div class="license-meta-text">2020年2月23日</div></div><div class="license-meta-item"><div 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