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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 44x 17x 27x 27x 27x 7x 20x 40698x 4x 40694x 40694x 6025x 40694x 215x 215x 215x 40479x 90x 90x 90x 30x 90x 90x 74x 90x 90x 76x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40389x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 40694x 20x 27x 1x 1x 1x 1x 1x 1x 1x 1x 101x 100x 100x 100x 100x 99x 1x 1x 1x 64x 64x 64x 64x 1x 1x 1x 1x 1x 1x 1x 2x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 13047x 13047x 35x 13047x 1x 13030x 1x 13029x 13029x 13029x 13029x 13029x 24x 13005x 13029x 13029x 13029x 13029x 13029x 13029x 13029x 13029x 4x 13025x 13025x 13025x 13025x 13025x 13025x 13025x 13025x 13025x 13025x 1x 1x 1x 1x 1x 8x 8x 8x 8x 8x 1x 13242x 1x 13241x 1x 13241x 13241x 37x 13204x 1x 1x 1x 1x 1x 1x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 1x 3x 1x 2x 2x 2x 2x 1x 1x 1x 1x 1x 13281x 2x 13279x 13279x 13279x 13279x 13279x 13279x 13279x 37x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 13242x 1x 1x 7x 4x 4x 1x 197x 1x 196x 1x 195x 1x 194x 10x 194x 194x 194x 194x 194x 1x 1x 1x 1x 15x 15x 15x 15x 15x 15x 15x 15x 15x 15x 15x 7x 15x 15x 15x 15x 15x 15x 15x 15x 15x 15x 1x 1x 1x 1x 1x 1x 1x 1x 168x 1x 167x 1x 166x 1x 165x 165x 165x 165x 165x 165x 165x 165x 165x 165x 165x 165x 165x 1x 4x 1x 3x 1x 2x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | import Cartesian2 from "./Cartesian2.js";
import Cartesian3 from "./Cartesian3.js";
import Cartesian4 from "./Cartesian4.js";
import Cartographic from "./Cartographic.js";
import Check from "./Check.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.js";
import EarthOrientationParameters from "./EarthOrientationParameters.js";
import EarthOrientationParametersSample from "./EarthOrientationParametersSample.js";
import Ellipsoid from "./Ellipsoid.js";
import HeadingPitchRoll from "./HeadingPitchRoll.js";
import Iau2006XysData from "./Iau2006XysData.js";
import Iau2006XysSample from "./Iau2006XysSample.js";
import JulianDate from "./JulianDate.js";
import CesiumMath from "./Math.js";
import Matrix3 from "./Matrix3.js";
import Matrix4 from "./Matrix4.js";
import Quaternion from "./Quaternion.js";
import TimeConstants from "./TimeConstants.js";
/**
* Contains functions for transforming positions to various reference frames.
*
* @namespace Transforms
*/
const Transforms = {};
const vectorProductLocalFrame = {
up: {
south: "east",
north: "west",
west: "south",
east: "north",
},
down: {
south: "west",
north: "east",
west: "north",
east: "south",
},
south: {
up: "west",
down: "east",
west: "down",
east: "up",
},
north: {
up: "east",
down: "west",
west: "up",
east: "down",
},
west: {
up: "north",
down: "south",
north: "down",
south: "up",
},
east: {
up: "south",
down: "north",
north: "up",
south: "down",
},
};
const degeneratePositionLocalFrame = {
north: [-1, 0, 0],
east: [0, 1, 0],
up: [0, 0, 1],
south: [1, 0, 0],
west: [0, -1, 0],
down: [0, 0, -1],
};
const localFrameToFixedFrameCache = {};
const scratchCalculateCartesian = {
east: new Cartesian3(),
north: new Cartesian3(),
up: new Cartesian3(),
west: new Cartesian3(),
south: new Cartesian3(),
down: new Cartesian3(),
};
let scratchFirstCartesian = new Cartesian3();
let scratchSecondCartesian = new Cartesian3();
let scratchThirdCartesian = new Cartesian3();
/**
* Generates a function that computes a 4x4 transformation matrix from a reference frame
* centered at the provided origin to the provided ellipsoid's fixed reference frame.
* @param {string} firstAxis name of the first axis of the local reference frame. Must be
* 'east', 'north', 'up', 'west', 'south' or 'down'.
* @param {string} secondAxis name of the second axis of the local reference frame. Must be
* 'east', 'north', 'up', 'west', 'south' or 'down'.
* @return {Transforms.LocalFrameToFixedFrame} The function that will computes a
* 4x4 transformation matrix from a reference frame, with first axis and second axis compliant with the parameters,
*/
Transforms.localFrameToFixedFrameGenerator = function (firstAxis, secondAxis) {
if (
!vectorProductLocalFrame.hasOwnProperty(firstAxis) ||
!vectorProductLocalFrame[firstAxis].hasOwnProperty(secondAxis)
) {
throw new DeveloperError(
"firstAxis and secondAxis must be east, north, up, west, south or down.",
);
}
const thirdAxis = vectorProductLocalFrame[firstAxis][secondAxis];
/**
* Computes a 4x4 transformation matrix from a reference frame
* centered at the provided origin to the provided ellipsoid's fixed reference frame.
* @callback Transforms.LocalFrameToFixedFrame
* @param {Cartesian3} origin The center point of the local reference frame.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if none was provided.
*/
let resultat;
const hashAxis = firstAxis + secondAxis;
if (defined(localFrameToFixedFrameCache[hashAxis])) {
resultat = localFrameToFixedFrameCache[hashAxis];
} else {
resultat = function (origin, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(origin)) {
throw new DeveloperError("origin is required.");
}
Iif (isNaN(origin.x) || isNaN(origin.y) || isNaN(origin.z)) {
throw new DeveloperError("origin has a NaN component");
}
//>>includeEnd('debug');
if (!defined(result)) {
result = new Matrix4();
}
if (
Cartesian3.equalsEpsilon(origin, Cartesian3.ZERO, CesiumMath.EPSILON14)
) {
// If x, y, and z are zero, use the degenerate local frame, which is a special case
Cartesian3.unpack(
degeneratePositionLocalFrame[firstAxis],
0,
scratchFirstCartesian,
);
Cartesian3.unpack(
degeneratePositionLocalFrame[secondAxis],
0,
scratchSecondCartesian,
);
Cartesian3.unpack(
degeneratePositionLocalFrame[thirdAxis],
0,
scratchThirdCartesian,
);
} else if (
CesiumMath.equalsEpsilon(origin.x, 0.0, CesiumMath.EPSILON14) &&
CesiumMath.equalsEpsilon(origin.y, 0.0, CesiumMath.EPSILON14)
) {
// If x and y are zero, assume origin is at a pole, which is a special case.
const sign = CesiumMath.sign(origin.z);
Cartesian3.unpack(
degeneratePositionLocalFrame[firstAxis],
0,
scratchFirstCartesian,
);
if (firstAxis !== "east" && firstAxis !== "west") {
Cartesian3.multiplyByScalar(
scratchFirstCartesian,
sign,
scratchFirstCartesian,
);
}
Cartesian3.unpack(
degeneratePositionLocalFrame[secondAxis],
0,
scratchSecondCartesian,
);
if (secondAxis !== "east" && secondAxis !== "west") {
Cartesian3.multiplyByScalar(
scratchSecondCartesian,
sign,
scratchSecondCartesian,
);
}
Cartesian3.unpack(
degeneratePositionLocalFrame[thirdAxis],
0,
scratchThirdCartesian,
);
if (thirdAxis !== "east" && thirdAxis !== "west") {
Cartesian3.multiplyByScalar(
scratchThirdCartesian,
sign,
scratchThirdCartesian,
);
}
} else {
ellipsoid = ellipsoid ?? Ellipsoid.default;
ellipsoid.geodeticSurfaceNormal(origin, scratchCalculateCartesian.up);
const up = scratchCalculateCartesian.up;
const east = scratchCalculateCartesian.east;
east.x = -origin.y;
east.y = origin.x;
east.z = 0.0;
Cartesian3.normalize(east, scratchCalculateCartesian.east);
Cartesian3.cross(up, east, scratchCalculateCartesian.north);
Cartesian3.multiplyByScalar(
scratchCalculateCartesian.up,
-1,
scratchCalculateCartesian.down,
);
Cartesian3.multiplyByScalar(
scratchCalculateCartesian.east,
-1,
scratchCalculateCartesian.west,
);
Cartesian3.multiplyByScalar(
scratchCalculateCartesian.north,
-1,
scratchCalculateCartesian.south,
);
scratchFirstCartesian = scratchCalculateCartesian[firstAxis];
scratchSecondCartesian = scratchCalculateCartesian[secondAxis];
scratchThirdCartesian = scratchCalculateCartesian[thirdAxis];
}
result[0] = scratchFirstCartesian.x;
result[1] = scratchFirstCartesian.y;
result[2] = scratchFirstCartesian.z;
result[3] = 0.0;
result[4] = scratchSecondCartesian.x;
result[5] = scratchSecondCartesian.y;
result[6] = scratchSecondCartesian.z;
result[7] = 0.0;
result[8] = scratchThirdCartesian.x;
result[9] = scratchThirdCartesian.y;
result[10] = scratchThirdCartesian.z;
result[11] = 0.0;
result[12] = origin.x;
result[13] = origin.y;
result[14] = origin.z;
result[15] = 1.0;
return result;
};
localFrameToFixedFrameCache[hashAxis] = resultat;
}
return resultat;
};
/**
* Computes a 4x4 transformation matrix from a reference frame with an east-north-up axes
* centered at the provided origin to the provided ellipsoid's fixed reference frame.
* The local axes are defined as:
* <ul>
* <li>The <code>x</code> axis points in the local east direction.</li>
* <li>The <code>y</code> axis points in the local north direction.</li>
* <li>The <code>z</code> axis points in the direction of the ellipsoid surface normal which passes through the position.</li>
* </ul>
*
* @function
* @param {Cartesian3} origin The center point of the local reference frame.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if none was provided.
*
* @example
* // Get the transform from local east-north-up at cartographic (0.0, 0.0) to Earth's fixed frame.
* const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
* const transform = Cesium.Transforms.eastNorthUpToFixedFrame(center);
*/
Transforms.eastNorthUpToFixedFrame = Transforms.localFrameToFixedFrameGenerator(
"east",
"north",
);
/**
* Computes a 4x4 transformation matrix from a reference frame with an north-east-down axes
* centered at the provided origin to the provided ellipsoid's fixed reference frame.
* The local axes are defined as:
* <ul>
* <li>The <code>x</code> axis points in the local north direction.</li>
* <li>The <code>y</code> axis points in the local east direction.</li>
* <li>The <code>z</code> axis points in the opposite direction of the ellipsoid surface normal which passes through the position.</li>
* </ul>
*
* @function
* @param {Cartesian3} origin The center point of the local reference frame.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if none was provided.
*
* @example
* // Get the transform from local north-east-down at cartographic (0.0, 0.0) to Earth's fixed frame.
* const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
* const transform = Cesium.Transforms.northEastDownToFixedFrame(center);
*/
Transforms.northEastDownToFixedFrame =
Transforms.localFrameToFixedFrameGenerator("north", "east");
/**
* Computes a 4x4 transformation matrix from a reference frame with an north-up-east axes
* centered at the provided origin to the provided ellipsoid's fixed reference frame.
* The local axes are defined as:
* <ul>
* <li>The <code>x</code> axis points in the local north direction.</li>
* <li>The <code>y</code> axis points in the direction of the ellipsoid surface normal which passes through the position.</li>
* <li>The <code>z</code> axis points in the local east direction.</li>
* </ul>
*
* @function
* @param {Cartesian3} origin The center point of the local reference frame.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if none was provided.
*
* @example
* // Get the transform from local north-up-east at cartographic (0.0, 0.0) to Earth's fixed frame.
* const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
* const transform = Cesium.Transforms.northUpEastToFixedFrame(center);
*/
Transforms.northUpEastToFixedFrame = Transforms.localFrameToFixedFrameGenerator(
"north",
"up",
);
/**
* Computes a 4x4 transformation matrix from a reference frame with an north-west-up axes
* centered at the provided origin to the provided ellipsoid's fixed reference frame.
* The local axes are defined as:
* <ul>
* <li>The <code>x</code> axis points in the local north direction.</li>
* <li>The <code>y</code> axis points in the local west direction.</li>
* <li>The <code>z</code> axis points in the direction of the ellipsoid surface normal which passes through the position.</li>
* </ul>
*
* @function
* @param {Cartesian3} origin The center point of the local reference frame.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if none was provided.
*
* @example
* // Get the transform from local north-West-Up at cartographic (0.0, 0.0) to Earth's fixed frame.
* const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
* const transform = Cesium.Transforms.northWestUpToFixedFrame(center);
*/
Transforms.northWestUpToFixedFrame = Transforms.localFrameToFixedFrameGenerator(
"north",
"west",
);
const scratchHPRQuaternion = new Quaternion();
const scratchScale = new Cartesian3(1.0, 1.0, 1.0);
const scratchHPRMatrix4 = new Matrix4();
/**
* Computes a 4x4 transformation matrix from a reference frame with axes computed from the heading-pitch-roll angles
* centered at the provided origin to the provided ellipsoid's fixed reference frame. Heading is the rotation from the local east
* direction where a positive angle is increasing eastward. Pitch is the rotation from the local east-north plane. Positive pitch angles
* are above the plane. Negative pitch angles are below the plane. Roll is the first rotation applied about the local east axis.
*
* @param {Cartesian3} origin The center point of the local reference frame.
* @param {HeadingPitchRoll} headingPitchRoll The heading, pitch, and roll.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Transforms.LocalFrameToFixedFrame} [fixedFrameTransform=Transforms.eastNorthUpToFixedFrame] A 4x4 transformation
* matrix from a reference frame to the provided ellipsoid's fixed reference frame
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if none was provided.
*
* @example
* // Get the transform from local heading-pitch-roll at cartographic (0.0, 0.0) to Earth's fixed frame.
* const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
* const heading = -Cesium.Math.PI_OVER_TWO;
* const pitch = Cesium.Math.PI_OVER_FOUR;
* const roll = 0.0;
* const hpr = new Cesium.HeadingPitchRoll(heading, pitch, roll);
* const transform = Cesium.Transforms.headingPitchRollToFixedFrame(center, hpr);
*/
Transforms.headingPitchRollToFixedFrame = function (
origin,
headingPitchRoll,
ellipsoid,
fixedFrameTransform,
result,
) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("HeadingPitchRoll", headingPitchRoll);
//>>includeEnd('debug');
fixedFrameTransform =
fixedFrameTransform ?? Transforms.eastNorthUpToFixedFrame;
const hprQuaternion = Quaternion.fromHeadingPitchRoll(
headingPitchRoll,
scratchHPRQuaternion,
);
const hprMatrix = Matrix4.fromTranslationQuaternionRotationScale(
Cartesian3.ZERO,
hprQuaternion,
scratchScale,
scratchHPRMatrix4,
);
result = fixedFrameTransform(origin, ellipsoid, result);
return Matrix4.multiply(result, hprMatrix, result);
};
const scratchENUMatrix4 = new Matrix4();
const scratchHPRMatrix3 = new Matrix3();
/**
* Computes a quaternion from a reference frame with axes computed from the heading-pitch-roll angles
* centered at the provided origin. Heading is the rotation from the local east
* direction where a positive angle is increasing eastward. Pitch is the rotation from the local east-north plane. Positive pitch angles
* are above the plane. Negative pitch angles are below the plane. Roll is the first rotation applied about the local east axis.
*
* @param {Cartesian3} origin The center point of the local reference frame.
* @param {HeadingPitchRoll} headingPitchRoll The heading, pitch, and roll.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Transforms.LocalFrameToFixedFrame} [fixedFrameTransform=Transforms.eastNorthUpToFixedFrame] A 4x4 transformation
* matrix from a reference frame to the provided ellipsoid's fixed reference frame
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if none was provided.
*
* @example
* // Get the quaternion from local heading-pitch-roll at cartographic (0.0, 0.0) to Earth's fixed frame.
* const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
* const heading = -Cesium.Math.PI_OVER_TWO;
* const pitch = Cesium.Math.PI_OVER_FOUR;
* const roll = 0.0;
* const hpr = new HeadingPitchRoll(heading, pitch, roll);
* const quaternion = Cesium.Transforms.headingPitchRollQuaternion(center, hpr);
*/
Transforms.headingPitchRollQuaternion = function (
origin,
headingPitchRoll,
ellipsoid,
fixedFrameTransform,
result,
) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("HeadingPitchRoll", headingPitchRoll);
//>>includeEnd('debug');
const transform = Transforms.headingPitchRollToFixedFrame(
origin,
headingPitchRoll,
ellipsoid,
fixedFrameTransform,
scratchENUMatrix4,
);
const rotation = Matrix4.getMatrix3(transform, scratchHPRMatrix3);
return Quaternion.fromRotationMatrix(rotation, result);
};
const noScale = new Cartesian3(1.0, 1.0, 1.0);
const hprCenterScratch = new Cartesian3();
const ffScratch = new Matrix4();
const hprTransformScratch = new Matrix4();
const hprRotationScratch = new Matrix3();
const hprQuaternionScratch = new Quaternion();
/**
* Computes heading-pitch-roll angles from a transform in a particular reference frame. Heading is the rotation from the local east
* direction where a positive angle is increasing eastward. Pitch is the rotation from the local east-north plane. Positive pitch angles
* are above the plane. Negative pitch angles are below the plane. Roll is the first rotation applied about the local east axis.
*
* @param {Matrix4} transform The transform
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Transforms.LocalFrameToFixedFrame} [fixedFrameTransform=Transforms.eastNorthUpToFixedFrame] A 4x4 transformation
* matrix from a reference frame to the provided ellipsoid's fixed reference frame
* @param {HeadingPitchRoll} [result] The object onto which to store the result.
* @returns {HeadingPitchRoll} The modified result parameter or a new HeadingPitchRoll instance if none was provided.
*/
Transforms.fixedFrameToHeadingPitchRoll = function (
transform,
ellipsoid,
fixedFrameTransform,
result,
) {
//>>includeStart('debug', pragmas.debug);
Check.defined("transform", transform);
//>>includeEnd('debug');
ellipsoid = ellipsoid ?? Ellipsoid.default;
fixedFrameTransform =
fixedFrameTransform ?? Transforms.eastNorthUpToFixedFrame;
Eif (!defined(result)) {
result = new HeadingPitchRoll();
}
const center = Matrix4.getTranslation(transform, hprCenterScratch);
Iif (Cartesian3.equals(center, Cartesian3.ZERO)) {
result.heading = 0;
result.pitch = 0;
result.roll = 0;
return result;
}
let toFixedFrame = Matrix4.inverseTransformation(
fixedFrameTransform(center, ellipsoid, ffScratch),
ffScratch,
);
let transformCopy = Matrix4.setScale(transform, noScale, hprTransformScratch);
transformCopy = Matrix4.setTranslation(
transformCopy,
Cartesian3.ZERO,
transformCopy,
);
toFixedFrame = Matrix4.multiply(toFixedFrame, transformCopy, toFixedFrame);
let quaternionRotation = Quaternion.fromRotationMatrix(
Matrix4.getMatrix3(toFixedFrame, hprRotationScratch),
hprQuaternionScratch,
);
quaternionRotation = Quaternion.normalize(
quaternionRotation,
quaternionRotation,
);
return HeadingPitchRoll.fromQuaternion(quaternionRotation, result);
};
const gmstConstant0 = 6 * 3600 + 41 * 60 + 50.54841;
const gmstConstant1 = 8640184.812866;
const gmstConstant2 = 0.093104;
const gmstConstant3 = -6.2e-6;
const rateCoef = 1.1772758384668e-19;
const wgs84WRPrecessing = 7.2921158553e-5;
const twoPiOverSecondsInDay = CesiumMath.TWO_PI / 86400.0;
let dateInUtc = new JulianDate();
/**
* The default function to compute a rotation matrix to transform a point or vector from the International Celestial
* Reference Frame (GCRF/ICRF) inertial frame axes to the central body, typically Earth, fixed frame axis at a given
* time for use in lighting and transformation from inertial reference frames. This function may return undefined if
* the data necessary to do the transformation is not yet loaded.
*
* @param {JulianDate} date The time at which to compute the rotation matrix.
* @param {Matrix3} [result] The object onto which to store the result. If this parameter is
* not specified, a new instance is created and returned.
* @returns {Matrix3|undefined} The rotation matrix, or undefined if the data necessary to do the
* transformation is not yet loaded.
*
* @example
* // Set the default ICRF to fixed transformation to that of the Moon.
* Cesium.Transforms.computeIcrfToCentralBodyFixedMatrix = Cesium.Transforms.computeIcrfToMoonFixedMatrix;
*
* @see Transforms.computeIcrfToFixedMatrix
* @see Transforms.computeTemeToPseudoFixedMatrix
* @see Transforms.computeIcrfToMoonFixedMatrix
*/
Transforms.computeIcrfToCentralBodyFixedMatrix = function (date, result) {
let transformMatrix = Transforms.computeIcrfToFixedMatrix(date, result);
if (!defined(transformMatrix)) {
transformMatrix = Transforms.computeTemeToPseudoFixedMatrix(date, result);
}
return transformMatrix;
};
/**
* Computes a rotation matrix to transform a point or vector from True Equator Mean Equinox (TEME) axes to the
* pseudo-fixed axes at a given time. This method treats the UT1 time standard as equivalent to UTC.
*
* @param {JulianDate} date The time at which to compute the rotation matrix.
* @param {Matrix3} [result] The object onto which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if none was provided.
*
* @example
* //Set the view to the inertial frame.
* scene.postUpdate.addEventListener(function(scene, time) {
* const now = Cesium.JulianDate.now();
* const offset = Cesium.Matrix4.multiplyByPoint(camera.transform, camera.position, new Cesium.Cartesian3());
* const transform = Cesium.Matrix4.fromRotationTranslation(Cesium.Transforms.computeTemeToPseudoFixedMatrix(now));
* const inverseTransform = Cesium.Matrix4.inverseTransformation(transform, new Cesium.Matrix4());
* Cesium.Matrix4.multiplyByPoint(inverseTransform, offset, offset);
* camera.lookAtTransform(transform, offset);
* });
*/
Transforms.computeTemeToPseudoFixedMatrix = function (date, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(date)) {
throw new DeveloperError("date is required.");
}
//>>includeEnd('debug');
// GMST is actually computed using UT1. We're using UTC as an approximation of UT1.
// We do not want to use the function like convertTaiToUtc in JulianDate because
// we explicitly do not want to fail when inside the leap second.
dateInUtc = JulianDate.addSeconds(
date,
-JulianDate.computeTaiMinusUtc(date),
dateInUtc,
);
const utcDayNumber = dateInUtc.dayNumber;
const utcSecondsIntoDay = dateInUtc.secondsOfDay;
let t;
const diffDays = utcDayNumber - 2451545;
if (utcSecondsIntoDay >= 43200.0) {
t = (diffDays + 0.5) / TimeConstants.DAYS_PER_JULIAN_CENTURY;
} else {
t = (diffDays - 0.5) / TimeConstants.DAYS_PER_JULIAN_CENTURY;
}
const gmst0 =
gmstConstant0 +
t * (gmstConstant1 + t * (gmstConstant2 + t * gmstConstant3));
const angle = (gmst0 * twoPiOverSecondsInDay) % CesiumMath.TWO_PI;
const ratio = wgs84WRPrecessing + rateCoef * (utcDayNumber - 2451545.5);
const secondsSinceMidnight =
(utcSecondsIntoDay + TimeConstants.SECONDS_PER_DAY * 0.5) %
TimeConstants.SECONDS_PER_DAY;
const gha = angle + ratio * secondsSinceMidnight;
const cosGha = Math.cos(gha);
const sinGha = Math.sin(gha);
if (!defined(result)) {
return new Matrix3(
cosGha,
sinGha,
0.0,
-sinGha,
cosGha,
0.0,
0.0,
0.0,
1.0,
);
}
result[0] = cosGha;
result[1] = -sinGha;
result[2] = 0.0;
result[3] = sinGha;
result[4] = cosGha;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 1.0;
return result;
};
/**
* The source of IAU 2006 XYS data, used for computing the transformation between the
* Fixed and ICRF axes.
* @type {Iau2006XysData}
*
* @see Transforms.computeIcrfToFixedMatrix
* @see Transforms.computeFixedToIcrfMatrix
*
* @private
*/
Transforms.iau2006XysData = new Iau2006XysData();
/**
* The source of Earth Orientation Parameters (EOP) data, used for computing the transformation
* between the Fixed and ICRF axes. By default, zero values are used for all EOP values,
* yielding a reasonable but not completely accurate representation of the ICRF axes.
* @type {EarthOrientationParameters}
*
* @see Transforms.computeIcrfToFixedMatrix
* @see Transforms.computeFixedToIcrfMatrix
*
* @private
*/
Transforms.earthOrientationParameters = EarthOrientationParameters.NONE;
const ttMinusTai = 32.184;
const j2000ttDays = 2451545.0;
/**
* Preloads the data necessary to transform between the ICRF and Fixed axes, in either
* direction, over a given interval. This function returns a promise that, when resolved,
* indicates that the preload has completed.
*
* @param {TimeInterval} timeInterval The interval to preload.
* @returns {Promise<void>} A promise that, when resolved, indicates that the preload has completed
* and evaluation of the transformation between the fixed and ICRF axes will
* no longer return undefined for a time inside the interval.
*
*
* @example
* const interval = new Cesium.TimeInterval(...);
* await Cesium.Transforms.preloadIcrfFixed(interval));
* // the data is now loaded
*
* @see Transforms.computeIcrfToFixedMatrix
* @see Transforms.computeFixedToIcrfMatrix
*/
Transforms.preloadIcrfFixed = function (timeInterval) {
const startDayTT = timeInterval.start.dayNumber;
const startSecondTT = timeInterval.start.secondsOfDay + ttMinusTai;
const stopDayTT = timeInterval.stop.dayNumber;
const stopSecondTT = timeInterval.stop.secondsOfDay + ttMinusTai;
return Transforms.iau2006XysData.preload(
startDayTT,
startSecondTT,
stopDayTT,
stopSecondTT,
);
};
/**
* Computes a rotation matrix to transform a point or vector from the International Celestial
* Reference Frame (GCRF/ICRF) inertial frame axes to the Earth-Fixed frame axes (ITRF)
* at a given time. This function may return undefined if the data necessary to
* do the transformation is not yet loaded.
*
* @param {JulianDate} date The time at which to compute the rotation matrix.
* @param {Matrix3} [result] The object onto which to store the result. If this parameter is
* not specified, a new instance is created and returned.
* @returns {Matrix3|undefined} The rotation matrix, or undefined if the data necessary to do the
* transformation is not yet loaded.
*
*
* @example
* scene.postUpdate.addEventListener(function(scene, time) {
* // View in ICRF.
* const icrfToFixed = Cesium.Transforms.computeIcrfToFixedMatrix(time);
* if (Cesium.defined(icrfToFixed)) {
* const offset = Cesium.Cartesian3.clone(camera.position);
* const transform = Cesium.Matrix4.fromRotationTranslation(icrfToFixed);
* camera.lookAtTransform(transform, offset);
* }
* });
*
* @see Transforms.preloadIcrfFixed
*/
Transforms.computeIcrfToFixedMatrix = function (date, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(date)) {
throw new DeveloperError("date is required.");
}
//>>includeEnd('debug');
if (!defined(result)) {
result = new Matrix3();
}
const fixedToIcrfMtx = Transforms.computeFixedToIcrfMatrix(date, result);
if (!defined(fixedToIcrfMtx)) {
return undefined;
}
return Matrix3.transpose(fixedToIcrfMtx, result);
};
const TdtMinusTai = 32.184;
const J2000d = 2451545;
const scratchHpr = new HeadingPitchRoll();
const scratchRotationMatrix = new Matrix3();
const dateScratch = new JulianDate();
/**
* Computes a rotation matrix to transform a point or vector from the Moon-Fixed frame axes
* to the International Celestial Reference Frame (GCRF/ICRF) inertial frame axes
* at a given time.
*
* @param {JulianDate} date The time at which to compute the rotation matrix.
* @param {Matrix3} [result] The object onto which to store the result. If this parameter is
* not specified, a new instance is created and returned.
* @returns {Matrix3} The rotation matrix.
*
* @example
* // Transform a point from the Fixed axes to the ICRF axes.
* const now = Cesium.JulianDate.now();
* const pointInFixed = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
* const fixedToIcrf = Cesium.Transforms.computeMoonFixedToIcrfMatrix(now);
* let pointInInertial = new Cesium.Cartesian3();
* if (Cesium.defined(fixedToIcrf)) {
* pointInInertial = Cesium.Matrix3.multiplyByVector(fixedToIcrf, pointInFixed, pointInInertial);
* }
*/
Transforms.computeMoonFixedToIcrfMatrix = function (date, result) {
//>>includeStart('debug', pragmas.debug);
Iif (!defined(date)) {
throw new DeveloperError("date is required.");
}
//>>includeEnd('debug');
Iif (!defined(result)) {
result = new Matrix3();
}
// Converts TAI to TT
const secondsTT = JulianDate.addSeconds(date, TdtMinusTai, dateScratch);
// Converts TT to TDB, interval in days since the standard epoch
const d = JulianDate.totalDays(secondsTT) - J2000d;
// Compute the approximate rotation, using https://articles.adsabs.harvard.edu//full/1980CeMec..22..205D/0000209.000.html
const e1 = CesiumMath.toRadians(12.112) - CesiumMath.toRadians(0.052992) * d;
const e2 = CesiumMath.toRadians(24.224) - CesiumMath.toRadians(0.105984) * d;
const e3 = CesiumMath.toRadians(227.645) + CesiumMath.toRadians(13.012) * d;
const e4 =
CesiumMath.toRadians(261.105) + CesiumMath.toRadians(13.340716) * d;
const e5 = CesiumMath.toRadians(358.0) + CesiumMath.toRadians(0.9856) * d;
scratchHpr.pitch =
CesiumMath.toRadians(270.0 - 90) -
CesiumMath.toRadians(3.878) * Math.sin(e1) -
CesiumMath.toRadians(0.12) * Math.sin(e2) +
CesiumMath.toRadians(0.07) * Math.sin(e3) -
CesiumMath.toRadians(0.017) * Math.sin(e4);
scratchHpr.roll =
CesiumMath.toRadians(66.53 - 90) +
CesiumMath.toRadians(1.543) * Math.cos(e1) +
CesiumMath.toRadians(0.24) * Math.cos(e2) -
CesiumMath.toRadians(0.028) * Math.cos(e3) +
CesiumMath.toRadians(0.007) * Math.cos(e4);
scratchHpr.heading =
CesiumMath.toRadians(244.375 - 90) +
CesiumMath.toRadians(13.17635831) * d +
CesiumMath.toRadians(3.558) * Math.sin(e1) +
CesiumMath.toRadians(0.121) * Math.sin(e2) -
CesiumMath.toRadians(0.064) * Math.sin(e3) +
CesiumMath.toRadians(0.016) * Math.sin(e4) +
CesiumMath.toRadians(0.025) * Math.sin(e5);
return Matrix3.fromHeadingPitchRoll(scratchHpr, scratchRotationMatrix);
};
/**
* Computes a rotation matrix to transform a point or vector from the International Celestial
* Reference Frame (GCRF/ICRF) inertial frame axes to the Moon-Fixed frame axes
* at a given time.
*
* @param {JulianDate} date The time at which to compute the rotation matrix.
* @param {Matrix3} [result] The object onto which to store the result. If this parameter is
* not specified, a new instance is created and returned.
* @returns {Matrix3} The rotation matrix.
*
* @example
* // Set the default ICRF to fixed transformation to that of the Moon.
* Cesium.Transforms.computeIcrfToCentralBodyFixedMatrix = Cesium.Transforms.computeIcrfToMoonFixedMatrix;
*/
Transforms.computeIcrfToMoonFixedMatrix = function (date, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(date)) {
throw new DeveloperError("date is required.");
}
//>>includeEnd('debug');
Iif (!defined(result)) {
result = new Matrix3();
}
const fixedToIcrfMtx = Transforms.computeMoonFixedToIcrfMatrix(date, result);
Iif (!defined(fixedToIcrfMtx)) {
return undefined;
}
return Matrix3.transpose(fixedToIcrfMtx, result);
};
const xysScratch = new Iau2006XysSample(0.0, 0.0, 0.0);
const eopScratch = new EarthOrientationParametersSample(
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
);
const rotation1Scratch = new Matrix3();
const rotation2Scratch = new Matrix3();
/**
* Computes a rotation matrix to transform a point or vector from the Earth-Fixed frame axes (ITRF)
* to the International Celestial Reference Frame (GCRF/ICRF) inertial frame axes
* at a given time. This function may return undefined if the data necessary to
* do the transformation is not yet loaded.
*
* @param {JulianDate} date The time at which to compute the rotation matrix.
* @param {Matrix3} [result] The object onto which to store the result. If this parameter is
* not specified, a new instance is created and returned.
* @returns {Matrix3|undefined} The rotation matrix, or undefined if the data necessary to do the
* transformation is not yet loaded.
*
*
* @example
* // Transform a point from the Fixed axes to the ICRF axes.
* const now = Cesium.JulianDate.now();
* const pointInFixed = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
* const fixedToIcrf = Cesium.Transforms.computeFixedToIcrfMatrix(now);
* let pointInInertial = new Cesium.Cartesian3();
* if (Cesium.defined(fixedToIcrf)) {
* pointInInertial = Cesium.Matrix3.multiplyByVector(fixedToIcrf, pointInFixed, pointInInertial);
* }
*
* @see Transforms.preloadIcrfFixed
*/
Transforms.computeFixedToIcrfMatrix = function (date, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(date)) {
throw new DeveloperError("date is required.");
}
//>>includeEnd('debug');
Iif (!defined(result)) {
result = new Matrix3();
}
// Compute pole wander
const eop = Transforms.earthOrientationParameters.compute(date, eopScratch);
Iif (!defined(eop)) {
return undefined;
}
// There is no external conversion to Terrestrial Time (TT).
// So use International Atomic Time (TAI) and convert using offsets.
// Here we are assuming that dayTT and secondTT are positive
const dayTT = date.dayNumber;
// It's possible here that secondTT could roll over 86400
// This does not seem to affect the precision (unit tests check for this)
const secondTT = date.secondsOfDay + ttMinusTai;
const xys = Transforms.iau2006XysData.computeXysRadians(
dayTT,
secondTT,
xysScratch,
);
if (!defined(xys)) {
return undefined;
}
const x = xys.x + eop.xPoleOffset;
const y = xys.y + eop.yPoleOffset;
// Compute XYS rotation
const a = 1.0 / (1.0 + Math.sqrt(1.0 - x * x - y * y));
const rotation1 = rotation1Scratch;
rotation1[0] = 1.0 - a * x * x;
rotation1[3] = -a * x * y;
rotation1[6] = x;
rotation1[1] = -a * x * y;
rotation1[4] = 1 - a * y * y;
rotation1[7] = y;
rotation1[2] = -x;
rotation1[5] = -y;
rotation1[8] = 1 - a * (x * x + y * y);
const rotation2 = Matrix3.fromRotationZ(-xys.s, rotation2Scratch);
const matrixQ = Matrix3.multiply(rotation1, rotation2, rotation1Scratch);
// Similar to TT conversions above
// It's possible here that secondTT could roll over 86400
// This does not seem to affect the precision (unit tests check for this)
const dateUt1day = date.dayNumber;
const dateUt1sec =
date.secondsOfDay - JulianDate.computeTaiMinusUtc(date) + eop.ut1MinusUtc;
// Compute Earth rotation angle
// The IERS standard for era is
// era = 0.7790572732640 + 1.00273781191135448 * Tu
// where
// Tu = JulianDateInUt1 - 2451545.0
// However, you get much more precision if you make the following simplification
// era = a + (1 + b) * (JulianDayNumber + FractionOfDay - 2451545)
// era = a + (JulianDayNumber - 2451545) + FractionOfDay + b (JulianDayNumber - 2451545 + FractionOfDay)
// era = a + FractionOfDay + b (JulianDayNumber - 2451545 + FractionOfDay)
// since (JulianDayNumber - 2451545) represents an integer number of revolutions which will be discarded anyway.
const daysSinceJ2000 = dateUt1day - 2451545;
const fractionOfDay = dateUt1sec / TimeConstants.SECONDS_PER_DAY;
let era =
0.779057273264 +
fractionOfDay +
0.00273781191135448 * (daysSinceJ2000 + fractionOfDay);
era = (era % 1.0) * CesiumMath.TWO_PI;
const earthRotation = Matrix3.fromRotationZ(era, rotation2Scratch);
// pseudoFixed to ICRF
const pfToIcrf = Matrix3.multiply(matrixQ, earthRotation, rotation1Scratch);
// Compute pole wander matrix
const cosxp = Math.cos(eop.xPoleWander);
const cosyp = Math.cos(eop.yPoleWander);
const sinxp = Math.sin(eop.xPoleWander);
const sinyp = Math.sin(eop.yPoleWander);
let ttt = dayTT - j2000ttDays + secondTT / TimeConstants.SECONDS_PER_DAY;
ttt /= 36525.0;
// approximate sp value in rad
const sp = (-47.0e-6 * ttt * CesiumMath.RADIANS_PER_DEGREE) / 3600.0;
const cossp = Math.cos(sp);
const sinsp = Math.sin(sp);
const fToPfMtx = rotation2Scratch;
fToPfMtx[0] = cosxp * cossp;
fToPfMtx[1] = cosxp * sinsp;
fToPfMtx[2] = sinxp;
fToPfMtx[3] = -cosyp * sinsp + sinyp * sinxp * cossp;
fToPfMtx[4] = cosyp * cossp + sinyp * sinxp * sinsp;
fToPfMtx[5] = -sinyp * cosxp;
fToPfMtx[6] = -sinyp * sinsp - cosyp * sinxp * cossp;
fToPfMtx[7] = sinyp * cossp - cosyp * sinxp * sinsp;
fToPfMtx[8] = cosyp * cosxp;
return Matrix3.multiply(pfToIcrf, fToPfMtx, result);
};
const pointToWindowCoordinatesTemp = new Cartesian4();
/**
* Transform a point from model coordinates to window coordinates.
*
* @param {Matrix4} modelViewProjectionMatrix The 4x4 model-view-projection matrix.
* @param {Matrix4} viewportTransformation The 4x4 viewport transformation.
* @param {Cartesian3} point The point to transform.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if none was provided.
*/
Transforms.pointToWindowCoordinates = function (
modelViewProjectionMatrix,
viewportTransformation,
point,
result,
) {
result = Transforms.pointToGLWindowCoordinates(
modelViewProjectionMatrix,
viewportTransformation,
point,
result,
);
result.y = 2.0 * viewportTransformation[5] - result.y;
return result;
};
/**
* @private
*/
Transforms.pointToGLWindowCoordinates = function (
modelViewProjectionMatrix,
viewportTransformation,
point,
result,
) {
//>>includeStart('debug', pragmas.debug);
if (!defined(modelViewProjectionMatrix)) {
throw new DeveloperError("modelViewProjectionMatrix is required.");
}
if (!defined(viewportTransformation)) {
throw new DeveloperError("viewportTransformation is required.");
}
if (!defined(point)) {
throw new DeveloperError("point is required.");
}
//>>includeEnd('debug');
if (!defined(result)) {
result = new Cartesian2();
}
const tmp = pointToWindowCoordinatesTemp;
Matrix4.multiplyByVector(
modelViewProjectionMatrix,
Cartesian4.fromElements(point.x, point.y, point.z, 1, tmp),
tmp,
);
Cartesian4.multiplyByScalar(tmp, 1.0 / tmp.w, tmp);
Matrix4.multiplyByVector(viewportTransformation, tmp, tmp);
return Cartesian2.fromCartesian4(tmp, result);
};
const normalScratch = new Cartesian3();
const rightScratch = new Cartesian3();
const upScratch = new Cartesian3();
/**
* Transform a position and velocity to a rotation matrix.
*
* @param {Cartesian3} position The position to transform.
* @param {Cartesian3} velocity The velocity vector to transform.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid whose fixed frame is used in the transformation.
* @param {Matrix3} [result] The object onto which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if none was provided.
*/
Transforms.rotationMatrixFromPositionVelocity = function (
position,
velocity,
ellipsoid,
result,
) {
//>>includeStart('debug', pragmas.debug);
Iif (!defined(position)) {
throw new DeveloperError("position is required.");
}
Iif (!defined(velocity)) {
throw new DeveloperError("velocity is required.");
}
//>>includeEnd('debug');
const normal = (ellipsoid ?? Ellipsoid.default).geodeticSurfaceNormal(
position,
normalScratch,
);
let right = Cartesian3.cross(velocity, normal, rightScratch);
Iif (Cartesian3.equalsEpsilon(right, Cartesian3.ZERO, CesiumMath.EPSILON6)) {
right = Cartesian3.clone(Cartesian3.UNIT_X, right);
}
const up = Cartesian3.cross(right, velocity, upScratch);
Cartesian3.normalize(up, up);
Cartesian3.cross(velocity, up, right);
Cartesian3.negate(right, right);
Cartesian3.normalize(right, right);
if (!defined(result)) {
result = new Matrix3();
}
result[0] = velocity.x;
result[1] = velocity.y;
result[2] = velocity.z;
result[3] = right.x;
result[4] = right.y;
result[5] = right.z;
result[6] = up.x;
result[7] = up.y;
result[8] = up.z;
return result;
};
/**
* An immutable matrix that swaps x, y, z for 2D.
*
* @type {Matrix4}
* @constant
* @private
*/
Transforms.SWIZZLE_3D_TO_2D_MATRIX = Object.freeze(
new Matrix4(
0.0,
0.0,
1.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
1.0,
),
);
const scratchCartographic = new Cartographic();
const scratchCartesian3Projection = new Cartesian3();
const scratchCenter = new Cartesian3();
const scratchRotation = new Matrix3();
const scratchFromENU = new Matrix4();
const scratchToENU = new Matrix4();
/**
* @private
*/
Transforms.basisTo2D = function (projection, matrix, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(projection)) {
throw new DeveloperError("projection is required.");
}
if (!defined(matrix)) {
throw new DeveloperError("matrix is required.");
}
if (!defined(result)) {
throw new DeveloperError("result is required.");
}
//>>includeEnd('debug');
const rtcCenter = Matrix4.getTranslation(matrix, scratchCenter);
const ellipsoid = projection.ellipsoid;
let projectedPosition;
Iif (Cartesian3.equals(rtcCenter, Cartesian3.ZERO)) {
projectedPosition = Cartesian3.clone(
Cartesian3.ZERO,
scratchCartesian3Projection,
);
} else {
// Get the 2D Center
const cartographic = ellipsoid.cartesianToCartographic(
rtcCenter,
scratchCartographic,
);
projectedPosition = projection.project(
cartographic,
scratchCartesian3Projection,
);
Cartesian3.fromElements(
projectedPosition.z,
projectedPosition.x,
projectedPosition.y,
projectedPosition,
);
}
// Assuming the instance are positioned on the ellipsoid, invert the ellipsoidal transform to get the local transform and then convert to 2D
const fromENU = Transforms.eastNorthUpToFixedFrame(
rtcCenter,
ellipsoid,
scratchFromENU,
);
const toENU = Matrix4.inverseTransformation(fromENU, scratchToENU);
const rotation = Matrix4.getMatrix3(matrix, scratchRotation);
const local = Matrix4.multiplyByMatrix3(toENU, rotation, result);
Matrix4.multiply(Transforms.SWIZZLE_3D_TO_2D_MATRIX, local, result); // Swap x, y, z for 2D
Matrix4.setTranslation(result, projectedPosition, result); // Use the projected center
return result;
};
/**
* @private
*/
Transforms.ellipsoidTo2DModelMatrix = function (projection, center, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(projection)) {
throw new DeveloperError("projection is required.");
}
if (!defined(center)) {
throw new DeveloperError("center is required.");
}
if (!defined(result)) {
throw new DeveloperError("result is required.");
}
//>>includeEnd('debug');
const ellipsoid = projection.ellipsoid;
const fromENU = Transforms.eastNorthUpToFixedFrame(
center,
ellipsoid,
scratchFromENU,
);
const toENU = Matrix4.inverseTransformation(fromENU, scratchToENU);
const cartographic = ellipsoid.cartesianToCartographic(
center,
scratchCartographic,
);
const projectedPosition = projection.project(
cartographic,
scratchCartesian3Projection,
);
Cartesian3.fromElements(
projectedPosition.z,
projectedPosition.x,
projectedPosition.y,
projectedPosition,
);
const translation = Matrix4.fromTranslation(
projectedPosition,
scratchFromENU,
);
Matrix4.multiply(Transforms.SWIZZLE_3D_TO_2D_MATRIX, toENU, result);
Matrix4.multiply(translation, result, result);
return result;
};
export default Transforms;
|