Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 | 161416x 35x 161381x 161381x 161381x 161381x 161381x 161381x 161381x 161381x 161381x 161381x 161381x 161381x 161381x 161381x 7098x 7098x 5x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 7093x 212124x 58x 212066x 212066x 99149x 99149x 99149x 99149x 99149x 99149x 99149x 21990x 9x 21981x 21981x 77159x 77159x 77159x 99149x 1x 1x 99150x 99150x 99150x 99149x 99149x 99149x 99149x 99149x 99149x 99149x 99149x 99149x 99149x 99149x 99149x 9092x 12x 9080x 9080x 7098x 7098x 7098x 7098x 7098x 194x 6904x 6904x 6904x 6904x 1982x 1982x 1x 1981x 1981x 1982x 1982x 1143x 839x 9080x 9042x 9042x 9042x 9042x 38x 160x 160x 160x 160x 160x 160x 160x 160x 160x 102x 1x 13x 99140x 99139x 4x 15x 48x 47x 1x 19x 19x 19x 19x 18x 18x 18x 18x 18x 18x 18x 18x 18x 17x 1x 1x 1x 99050x 99049x 99048x 1x 8414x 1x 9076x 9076x 2x 9074x 1x 11x 11x 11x 11x 11x 11x 11x 11x 4x 11x 11x 11x 1x 1x 1x 1x 10x 2x 1x 1x 1x 1x 1x 8x 8x 8x 8x 8x 8x 53x 53x 53x 53x 8x 8x 8x 8x 1x 10x 10x 10x 10x 10x 10x 1x 9x 9x 9x 9x 9x 4x 4x 4x 4x 5x | import Cartesian3 from "./Cartesian3.js";
import Cartographic from "./Cartographic.js";
import Check from "./Check.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.js";
import Ellipsoid from "./Ellipsoid.js";
import CesiumMath from "./Math.js";
function calculateM(ellipticity, major, latitude) {
if (ellipticity === 0.0) {
// sphere
return major * latitude;
}
const e2 = ellipticity * ellipticity;
const e4 = e2 * e2;
const e6 = e4 * e2;
const e8 = e6 * e2;
const e10 = e8 * e2;
const e12 = e10 * e2;
const phi = latitude;
const sin2Phi = Math.sin(2 * phi);
const sin4Phi = Math.sin(4 * phi);
const sin6Phi = Math.sin(6 * phi);
const sin8Phi = Math.sin(8 * phi);
const sin10Phi = Math.sin(10 * phi);
const sin12Phi = Math.sin(12 * phi);
return (
major *
((1 -
e2 / 4 -
(3 * e4) / 64 -
(5 * e6) / 256 -
(175 * e8) / 16384 -
(441 * e10) / 65536 -
(4851 * e12) / 1048576) *
phi -
((3 * e2) / 8 +
(3 * e4) / 32 +
(45 * e6) / 1024 +
(105 * e8) / 4096 +
(2205 * e10) / 131072 +
(6237 * e12) / 524288) *
sin2Phi +
((15 * e4) / 256 +
(45 * e6) / 1024 +
(525 * e8) / 16384 +
(1575 * e10) / 65536 +
(155925 * e12) / 8388608) *
sin4Phi -
((35 * e6) / 3072 +
(175 * e8) / 12288 +
(3675 * e10) / 262144 +
(13475 * e12) / 1048576) *
sin6Phi +
((315 * e8) / 131072 + (2205 * e10) / 524288 + (43659 * e12) / 8388608) *
sin8Phi -
((693 * e10) / 1310720 + (6237 * e12) / 5242880) * sin10Phi +
((1001 * e12) / 8388608) * sin12Phi)
);
}
function calculateInverseM(M, ellipticity, major) {
const d = M / major;
if (ellipticity === 0.0) {
// sphere
return d;
}
const d2 = d * d;
const d3 = d2 * d;
const d4 = d3 * d;
const e = ellipticity;
const e2 = e * e;
const e4 = e2 * e2;
const e6 = e4 * e2;
const e8 = e6 * e2;
const e10 = e8 * e2;
const e12 = e10 * e2;
const sin2D = Math.sin(2 * d);
const cos2D = Math.cos(2 * d);
const sin4D = Math.sin(4 * d);
const cos4D = Math.cos(4 * d);
const sin6D = Math.sin(6 * d);
const cos6D = Math.cos(6 * d);
const sin8D = Math.sin(8 * d);
const cos8D = Math.cos(8 * d);
const sin10D = Math.sin(10 * d);
const cos10D = Math.cos(10 * d);
const sin12D = Math.sin(12 * d);
return (
d +
(d * e2) / 4 +
(7 * d * e4) / 64 +
(15 * d * e6) / 256 +
(579 * d * e8) / 16384 +
(1515 * d * e10) / 65536 +
(16837 * d * e12) / 1048576 +
((3 * d * e4) / 16 +
(45 * d * e6) / 256 -
(d * (32 * d2 - 561) * e8) / 4096 -
(d * (232 * d2 - 1677) * e10) / 16384 +
(d * (399985 - 90560 * d2 + 512 * d4) * e12) / 5242880) *
cos2D +
((21 * d * e6) / 256 +
(483 * d * e8) / 4096 -
(d * (224 * d2 - 1969) * e10) / 16384 -
(d * (33152 * d2 - 112599) * e12) / 1048576) *
cos4D +
((151 * d * e8) / 4096 +
(4681 * d * e10) / 65536 +
(1479 * d * e12) / 16384 -
(453 * d3 * e12) / 32768) *
cos6D +
((1097 * d * e10) / 65536 + (42783 * d * e12) / 1048576) * cos8D +
((8011 * d * e12) / 1048576) * cos10D +
((3 * e2) / 8 +
(3 * e4) / 16 +
(213 * e6) / 2048 -
(3 * d2 * e6) / 64 +
(255 * e8) / 4096 -
(33 * d2 * e8) / 512 +
(20861 * e10) / 524288 -
(33 * d2 * e10) / 512 +
(d4 * e10) / 1024 +
(28273 * e12) / 1048576 -
(471 * d2 * e12) / 8192 +
(9 * d4 * e12) / 4096) *
sin2D +
((21 * e4) / 256 +
(21 * e6) / 256 +
(533 * e8) / 8192 -
(21 * d2 * e8) / 512 +
(197 * e10) / 4096 -
(315 * d2 * e10) / 4096 +
(584039 * e12) / 16777216 -
(12517 * d2 * e12) / 131072 +
(7 * d4 * e12) / 2048) *
sin4D +
((151 * e6) / 6144 +
(151 * e8) / 4096 +
(5019 * e10) / 131072 -
(453 * d2 * e10) / 16384 +
(26965 * e12) / 786432 -
(8607 * d2 * e12) / 131072) *
sin6D +
((1097 * e8) / 131072 +
(1097 * e10) / 65536 +
(225797 * e12) / 10485760 -
(1097 * d2 * e12) / 65536) *
sin8D +
((8011 * e10) / 2621440 + (8011 * e12) / 1048576) * sin10D +
((293393 * e12) / 251658240) * sin12D
);
}
function calculateSigma(ellipticity, latitude) {
if (ellipticity === 0.0) {
// sphere
return Math.log(Math.tan(0.5 * (CesiumMath.PI_OVER_TWO + latitude)));
}
const eSinL = ellipticity * Math.sin(latitude);
return (
Math.log(Math.tan(0.5 * (CesiumMath.PI_OVER_TWO + latitude))) -
(ellipticity / 2.0) * Math.log((1 + eSinL) / (1 - eSinL))
);
}
function calculateHeading(
ellipsoidRhumbLine,
firstLongitude,
firstLatitude,
secondLongitude,
secondLatitude,
) {
const sigma1 = calculateSigma(ellipsoidRhumbLine._ellipticity, firstLatitude);
const sigma2 = calculateSigma(
ellipsoidRhumbLine._ellipticity,
secondLatitude,
);
return Math.atan2(
CesiumMath.negativePiToPi(secondLongitude - firstLongitude),
sigma2 - sigma1,
);
}
function calculateArcLength(
ellipsoidRhumbLine,
major,
minor,
firstLongitude,
firstLatitude,
secondLongitude,
secondLatitude,
) {
const heading = ellipsoidRhumbLine._heading;
const deltaLongitude = secondLongitude - firstLongitude;
let distance = 0.0;
//Check to see if the rhumb line has constant latitude
//This equation will diverge if heading gets close to 90 degrees
if (
CesiumMath.equalsEpsilon(
Math.abs(heading),
CesiumMath.PI_OVER_TWO,
CesiumMath.EPSILON8,
)
) {
//If heading is close to 90 degrees
if (major === minor) {
distance =
major *
Math.cos(firstLatitude) *
CesiumMath.negativePiToPi(deltaLongitude);
} else {
const sinPhi = Math.sin(firstLatitude);
distance =
(major *
Math.cos(firstLatitude) *
CesiumMath.negativePiToPi(deltaLongitude)) /
Math.sqrt(1 - ellipsoidRhumbLine._ellipticitySquared * sinPhi * sinPhi);
}
} else {
const M1 = calculateM(
ellipsoidRhumbLine._ellipticity,
major,
firstLatitude,
);
const M2 = calculateM(
ellipsoidRhumbLine._ellipticity,
major,
secondLatitude,
);
distance = (M2 - M1) / Math.cos(heading);
}
return Math.abs(distance);
}
const scratchCart1 = new Cartesian3();
const scratchCart2 = new Cartesian3();
function computeProperties(ellipsoidRhumbLine, start, end, ellipsoid) {
const firstCartesian = Cartesian3.normalize(
ellipsoid.cartographicToCartesian(start, scratchCart2),
scratchCart1,
);
const lastCartesian = Cartesian3.normalize(
ellipsoid.cartographicToCartesian(end, scratchCart2),
scratchCart2,
);
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number.greaterThanOrEquals(
"value",
Math.abs(
Math.abs(Cartesian3.angleBetween(firstCartesian, lastCartesian)) -
Math.PI,
),
0.0125,
);
//>>includeEnd('debug');
const major = ellipsoid.maximumRadius;
const minor = ellipsoid.minimumRadius;
const majorSquared = major * major;
const minorSquared = minor * minor;
ellipsoidRhumbLine._ellipticitySquared =
(majorSquared - minorSquared) / majorSquared;
ellipsoidRhumbLine._ellipticity = Math.sqrt(
ellipsoidRhumbLine._ellipticitySquared,
);
ellipsoidRhumbLine._start = Cartographic.clone(
start,
ellipsoidRhumbLine._start,
);
ellipsoidRhumbLine._start.height = 0;
ellipsoidRhumbLine._end = Cartographic.clone(end, ellipsoidRhumbLine._end);
ellipsoidRhumbLine._end.height = 0;
ellipsoidRhumbLine._heading = calculateHeading(
ellipsoidRhumbLine,
start.longitude,
start.latitude,
end.longitude,
end.latitude,
);
ellipsoidRhumbLine._distance = calculateArcLength(
ellipsoidRhumbLine,
ellipsoid.maximumRadius,
ellipsoid.minimumRadius,
start.longitude,
start.latitude,
end.longitude,
end.latitude,
);
}
function interpolateUsingSurfaceDistance(
start,
heading,
distance,
major,
ellipticity,
result,
) {
if (distance === 0.0) {
return Cartographic.clone(start, result);
}
const ellipticitySquared = ellipticity * ellipticity;
let longitude;
let latitude;
let deltaLongitude;
//Check to see if the rhumb line has constant latitude
//This won't converge if heading is close to 90 degrees
if (
Math.abs(CesiumMath.PI_OVER_TWO - Math.abs(heading)) > CesiumMath.EPSILON8
) {
//Calculate latitude of the second point
const M1 = calculateM(ellipticity, major, start.latitude);
const deltaM = distance * Math.cos(heading);
const M2 = M1 + deltaM;
latitude = calculateInverseM(M2, ellipticity, major);
//Now find the longitude of the second point
// Check to see if the rhumb line has constant longitude
if (Math.abs(heading) < CesiumMath.EPSILON10) {
longitude = CesiumMath.negativePiToPi(start.longitude);
} else {
const sigma1 = calculateSigma(ellipticity, start.latitude);
const sigma2 = calculateSigma(ellipticity, latitude);
deltaLongitude = Math.tan(heading) * (sigma2 - sigma1);
longitude = CesiumMath.negativePiToPi(start.longitude + deltaLongitude);
}
} else {
//If heading is close to 90 degrees
latitude = start.latitude;
let localRad;
if (ellipticity === 0.0) {
// sphere
localRad = major * Math.cos(start.latitude);
} else {
const sinPhi = Math.sin(start.latitude);
localRad =
(major * Math.cos(start.latitude)) /
Math.sqrt(1 - ellipticitySquared * sinPhi * sinPhi);
}
deltaLongitude = distance / localRad;
if (heading > 0.0) {
longitude = CesiumMath.negativePiToPi(start.longitude + deltaLongitude);
} else {
longitude = CesiumMath.negativePiToPi(start.longitude - deltaLongitude);
}
}
if (defined(result)) {
result.longitude = longitude;
result.latitude = latitude;
result.height = 0;
return result;
}
return new Cartographic(longitude, latitude, 0);
}
/**
* Initializes a rhumb line on the ellipsoid connecting the two provided planetodetic points.
*
* @alias EllipsoidRhumbLine
* @constructor
*
* @param {Cartographic} [start] The initial planetodetic point on the path.
* @param {Cartographic} [end] The final planetodetic point on the path.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid on which the rhumb line lies.
*
* @exception {DeveloperError} angle between start and end must be at least 0.0125 radians.
*/
function EllipsoidRhumbLine(start, end, ellipsoid) {
const e = ellipsoid ?? Ellipsoid.default;
this._ellipsoid = e;
this._start = new Cartographic();
this._end = new Cartographic();
this._heading = undefined;
this._distance = undefined;
this._ellipticity = undefined;
this._ellipticitySquared = undefined;
if (defined(start) && defined(end)) {
computeProperties(this, start, end, e);
}
}
Object.defineProperties(EllipsoidRhumbLine.prototype, {
/**
* Gets the ellipsoid.
* @memberof EllipsoidRhumbLine.prototype
* @type {Ellipsoid}
* @readonly
*/
ellipsoid: {
get: function () {
return this._ellipsoid;
},
},
/**
* Gets the surface distance between the start and end point
* @memberof EllipsoidRhumbLine.prototype
* @type {number}
* @readonly
*/
surfaceDistance: {
get: function () {
//>>includeStart('debug', pragmas.debug);
Check.defined("distance", this._distance);
//>>includeEnd('debug');
return this._distance;
},
},
/**
* Gets the initial planetodetic point on the path.
* @memberof EllipsoidRhumbLine.prototype
* @type {Cartographic}
* @readonly
*/
start: {
get: function () {
return this._start;
},
},
/**
* Gets the final planetodetic point on the path.
* @memberof EllipsoidRhumbLine.prototype
* @type {Cartographic}
* @readonly
*/
end: {
get: function () {
return this._end;
},
},
/**
* Gets the heading from the start point to the end point.
* @memberof EllipsoidRhumbLine.prototype
* @type {number}
* @readonly
*/
heading: {
get: function () {
//>>includeStart('debug', pragmas.debug);
Check.defined("distance", this._distance);
//>>includeEnd('debug');
return this._heading;
},
},
});
/**
* Create a rhumb line using an initial position with a heading and distance.
*
* @param {Cartographic} start The initial planetodetic point on the path.
* @param {number} heading The heading in radians.
* @param {number} distance The rhumb line distance between the start and end point.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid on which the rhumb line lies.
* @param {EllipsoidRhumbLine} [result] The object in which to store the result.
* @returns {EllipsoidRhumbLine} The EllipsoidRhumbLine object.
*/
EllipsoidRhumbLine.fromStartHeadingDistance = function (
start,
heading,
distance,
ellipsoid,
result,
) {
//>>includeStart('debug', pragmas.debug);
Check.defined("start", start);
Check.defined("heading", heading);
Check.defined("distance", distance);
Check.typeOf.number.greaterThan("distance", distance, 0.0);
//>>includeEnd('debug');
const e = ellipsoid ?? Ellipsoid.default;
const major = e.maximumRadius;
const minor = e.minimumRadius;
const majorSquared = major * major;
const minorSquared = minor * minor;
const ellipticity = Math.sqrt((majorSquared - minorSquared) / majorSquared);
heading = CesiumMath.negativePiToPi(heading);
const end = interpolateUsingSurfaceDistance(
start,
heading,
distance,
e.maximumRadius,
ellipticity,
);
if (
!defined(result) ||
(defined(ellipsoid) && !ellipsoid.equals(result.ellipsoid))
) {
return new EllipsoidRhumbLine(start, end, e);
}
result.setEndPoints(start, end);
return result;
};
/**
* Sets the start and end points of the rhumb line.
*
* @param {Cartographic} start The initial planetodetic point on the path.
* @param {Cartographic} end The final planetodetic point on the path.
*/
EllipsoidRhumbLine.prototype.setEndPoints = function (start, end) {
//>>includeStart('debug', pragmas.debug);
Check.defined("start", start);
Check.defined("end", end);
//>>includeEnd('debug');
computeProperties(this, start, end, this._ellipsoid);
};
/**
* Provides the location of a point at the indicated portion along the rhumb line.
*
* @param {number} fraction The portion of the distance between the initial and final points.
* @param {Cartographic} [result] The object in which to store the result.
* @returns {Cartographic} The location of the point along the rhumb line.
*/
EllipsoidRhumbLine.prototype.interpolateUsingFraction = function (
fraction,
result,
) {
return this.interpolateUsingSurfaceDistance(
fraction * this._distance,
result,
);
};
/**
* Provides the location of a point at the indicated distance along the rhumb line.
*
* @param {number} distance The distance from the initial point to the point of interest along the rhumbLine.
* @param {Cartographic} [result] The object in which to store the result.
* @returns {Cartographic} The location of the point along the rhumb line.
*
* @exception {DeveloperError} start and end must be set before calling function interpolateUsingSurfaceDistance
*/
EllipsoidRhumbLine.prototype.interpolateUsingSurfaceDistance = function (
distance,
result,
) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number("distance", distance);
if (!defined(this._distance) || this._distance === 0.0) {
throw new DeveloperError(
"EllipsoidRhumbLine must have distinct start and end set.",
);
}
//>>includeEnd('debug');
return interpolateUsingSurfaceDistance(
this._start,
this._heading,
distance,
this._ellipsoid.maximumRadius,
this._ellipticity,
result,
);
};
/**
* Provides the location of a point at the indicated longitude along the rhumb line.
* If the longitude is outside the range of start and end points, the first intersection with the longitude from the start point in the direction of the heading is returned. This follows the spiral property of a rhumb line.
*
* @param {number} intersectionLongitude The longitude, in radians, at which to find the intersection point from the starting point using the heading.
* @param {Cartographic} [result] The object in which to store the result.
* @returns {Cartographic} The location of the intersection point along the rhumb line, undefined if there is no intersection or infinite intersections.
*
* @exception {DeveloperError} start and end must be set before calling function findIntersectionWithLongitude.
*/
EllipsoidRhumbLine.prototype.findIntersectionWithLongitude = function (
intersectionLongitude,
result,
) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number("intersectionLongitude", intersectionLongitude);
Iif (!defined(this._distance) || this._distance === 0.0) {
throw new DeveloperError(
"EllipsoidRhumbLine must have distinct start and end set.",
);
}
//>>includeEnd('debug');
const ellipticity = this._ellipticity;
const heading = this._heading;
const absHeading = Math.abs(heading);
const start = this._start;
intersectionLongitude = CesiumMath.negativePiToPi(intersectionLongitude);
if (
CesiumMath.equalsEpsilon(
Math.abs(intersectionLongitude),
Math.PI,
CesiumMath.EPSILON14,
)
) {
intersectionLongitude = CesiumMath.sign(start.longitude) * Math.PI;
}
Eif (!defined(result)) {
result = new Cartographic();
}
// If heading is -PI/2 or PI/2, this is an E-W rhumb line
// If heading is 0 or PI, this is an N-S rhumb line
if (Math.abs(CesiumMath.PI_OVER_TWO - absHeading) <= CesiumMath.EPSILON8) {
result.longitude = intersectionLongitude;
result.latitude = start.latitude;
result.height = 0;
return result;
} else if (
CesiumMath.equalsEpsilon(
Math.abs(CesiumMath.PI_OVER_TWO - absHeading),
CesiumMath.PI_OVER_TWO,
CesiumMath.EPSILON8,
)
) {
if (
CesiumMath.equalsEpsilon(
intersectionLongitude,
start.longitude,
CesiumMath.EPSILON12,
)
) {
return undefined;
}
result.longitude = intersectionLongitude;
result.latitude =
CesiumMath.PI_OVER_TWO *
CesiumMath.sign(CesiumMath.PI_OVER_TWO - heading);
result.height = 0;
return result;
}
// Use iterative solver from Equation 9 from http://edwilliams.org/ellipsoid/ellipsoid.pdf
const phi1 = start.latitude;
const eSinPhi1 = ellipticity * Math.sin(phi1);
const leftComponent =
Math.tan(0.5 * (CesiumMath.PI_OVER_TWO + phi1)) *
Math.exp((intersectionLongitude - start.longitude) / Math.tan(heading));
const denominator = (1 + eSinPhi1) / (1 - eSinPhi1);
let newPhi = start.latitude;
let phi;
do {
phi = newPhi;
const eSinPhi = ellipticity * Math.sin(phi);
const numerator = (1 + eSinPhi) / (1 - eSinPhi);
newPhi =
2 *
Math.atan(
leftComponent * Math.pow(numerator / denominator, ellipticity / 2),
) -
CesiumMath.PI_OVER_TWO;
} while (!CesiumMath.equalsEpsilon(newPhi, phi, CesiumMath.EPSILON12));
result.longitude = intersectionLongitude;
result.latitude = newPhi;
result.height = 0;
return result;
};
/**
* Provides the location of a point at the indicated latitude along the rhumb line.
* If the latitude is outside the range of start and end points, the first intersection with the latitude from that start point in the direction of the heading is returned. This follows the spiral property of a rhumb line.
*
* @param {number} intersectionLatitude The latitude, in radians, at which to find the intersection point from the starting point using the heading.
* @param {Cartographic} [result] The object in which to store the result.
* @returns {Cartographic} The location of the intersection point along the rhumb line, undefined if there is no intersection or infinite intersections.
*
* @exception {DeveloperError} start and end must be set before calling function findIntersectionWithLongitude.
*/
EllipsoidRhumbLine.prototype.findIntersectionWithLatitude = function (
intersectionLatitude,
result,
) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.number("intersectionLatitude", intersectionLatitude);
Iif (!defined(this._distance) || this._distance === 0.0) {
throw new DeveloperError(
"EllipsoidRhumbLine must have distinct start and end set.",
);
}
//>>includeEnd('debug');
const ellipticity = this._ellipticity;
const heading = this._heading;
const start = this._start;
// If start and end have same latitude, return undefined since it's either no intersection or infinite intersections
if (
CesiumMath.equalsEpsilon(
Math.abs(heading),
CesiumMath.PI_OVER_TWO,
CesiumMath.EPSILON8,
)
) {
return;
}
// Can be solved using the same equations from interpolateUsingSurfaceDistance
const sigma1 = calculateSigma(ellipticity, start.latitude);
const sigma2 = calculateSigma(ellipticity, intersectionLatitude);
const deltaLongitude = Math.tan(heading) * (sigma2 - sigma1);
const longitude = CesiumMath.negativePiToPi(start.longitude + deltaLongitude);
if (defined(result)) {
result.longitude = longitude;
result.latitude = intersectionLatitude;
result.height = 0;
return result;
}
return new Cartographic(longitude, intersectionLatitude, 0);
};
export default EllipsoidRhumbLine;
|