/**
 * @license
 * Cesium - https://github.com/CesiumGS/cesium
 * Version 1.133
 *
 * Copyright 2011-2022 Cesium Contributors
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * Columbus View (Pat. Pend.)
 *
 * Portions licensed separately.
 * See https://github.com/CesiumGS/cesium/blob/main/LICENSE.md for full licensing details.
 */

import {
  Cartesian3_default,
  Cartographic_default,
  Ellipsoid_default
} from "./chunk-IHUXLSNT.js";
import {
  Math_default
} from "./chunk-4O5SZ2RE.js";
import {
  Check_default,
  DeveloperError_default
} from "./chunk-O2O4FYNI.js";
import {
  defined_default
} from "./chunk-NJYFQE5B.js";

// packages/engine/Source/Core/EllipsoidRhumbLine.js
function calculateM(ellipticity, major, latitude) {
  if (ellipticity === 0) {
    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) {
    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) {
    return Math.log(Math.tan(0.5 * (Math_default.PI_OVER_TWO + latitude)));
  }
  const eSinL = ellipticity * Math.sin(latitude);
  return Math.log(Math.tan(0.5 * (Math_default.PI_OVER_TWO + latitude))) - ellipticity / 2 * 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(
    Math_default.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;
  if (Math_default.equalsEpsilon(
    Math.abs(heading),
    Math_default.PI_OVER_TWO,
    Math_default.EPSILON8
  )) {
    if (major === minor) {
      distance = major * Math.cos(firstLatitude) * Math_default.negativePiToPi(deltaLongitude);
    } else {
      const sinPhi = Math.sin(firstLatitude);
      distance = major * Math.cos(firstLatitude) * Math_default.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);
}
var scratchCart1 = new Cartesian3_default();
var scratchCart2 = new Cartesian3_default();
function computeProperties(ellipsoidRhumbLine, start, end, ellipsoid) {
  const firstCartesian = Cartesian3_default.normalize(
    ellipsoid.cartographicToCartesian(start, scratchCart2),
    scratchCart1
  );
  const lastCartesian = Cartesian3_default.normalize(
    ellipsoid.cartographicToCartesian(end, scratchCart2),
    scratchCart2
  );
  Check_default.typeOf.number.greaterThanOrEquals(
    "value",
    Math.abs(
      Math.abs(Cartesian3_default.angleBetween(firstCartesian, lastCartesian)) - Math.PI
    ),
    0.0125
  );
  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_default.clone(
    start,
    ellipsoidRhumbLine._start
  );
  ellipsoidRhumbLine._start.height = 0;
  ellipsoidRhumbLine._end = Cartographic_default.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) {
    return Cartographic_default.clone(start, result);
  }
  const ellipticitySquared = ellipticity * ellipticity;
  let longitude;
  let latitude;
  let deltaLongitude;
  if (Math.abs(Math_default.PI_OVER_TWO - Math.abs(heading)) > Math_default.EPSILON8) {
    const M1 = calculateM(ellipticity, major, start.latitude);
    const deltaM = distance * Math.cos(heading);
    const M2 = M1 + deltaM;
    latitude = calculateInverseM(M2, ellipticity, major);
    if (Math.abs(heading) < Math_default.EPSILON10) {
      longitude = Math_default.negativePiToPi(start.longitude);
    } else {
      const sigma1 = calculateSigma(ellipticity, start.latitude);
      const sigma2 = calculateSigma(ellipticity, latitude);
      deltaLongitude = Math.tan(heading) * (sigma2 - sigma1);
      longitude = Math_default.negativePiToPi(start.longitude + deltaLongitude);
    }
  } else {
    latitude = start.latitude;
    let localRad;
    if (ellipticity === 0) {
      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) {
      longitude = Math_default.negativePiToPi(start.longitude + deltaLongitude);
    } else {
      longitude = Math_default.negativePiToPi(start.longitude - deltaLongitude);
    }
  }
  if (defined_default(result)) {
    result.longitude = longitude;
    result.latitude = latitude;
    result.height = 0;
    return result;
  }
  return new Cartographic_default(longitude, latitude, 0);
}
function EllipsoidRhumbLine(start, end, ellipsoid) {
  const e = ellipsoid ?? Ellipsoid_default.default;
  this._ellipsoid = e;
  this._start = new Cartographic_default();
  this._end = new Cartographic_default();
  this._heading = void 0;
  this._distance = void 0;
  this._ellipticity = void 0;
  this._ellipticitySquared = void 0;
  if (defined_default(start) && defined_default(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() {
      Check_default.defined("distance", this._distance);
      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() {
      Check_default.defined("distance", this._distance);
      return this._heading;
    }
  }
});
EllipsoidRhumbLine.fromStartHeadingDistance = function(start, heading, distance, ellipsoid, result) {
  Check_default.defined("start", start);
  Check_default.defined("heading", heading);
  Check_default.defined("distance", distance);
  Check_default.typeOf.number.greaterThan("distance", distance, 0);
  const e = ellipsoid ?? Ellipsoid_default.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 = Math_default.negativePiToPi(heading);
  const end = interpolateUsingSurfaceDistance(
    start,
    heading,
    distance,
    e.maximumRadius,
    ellipticity
  );
  if (!defined_default(result) || defined_default(ellipsoid) && !ellipsoid.equals(result.ellipsoid)) {
    return new EllipsoidRhumbLine(start, end, e);
  }
  result.setEndPoints(start, end);
  return result;
};
EllipsoidRhumbLine.prototype.setEndPoints = function(start, end) {
  Check_default.defined("start", start);
  Check_default.defined("end", end);
  computeProperties(this, start, end, this._ellipsoid);
};
EllipsoidRhumbLine.prototype.interpolateUsingFraction = function(fraction, result) {
  return this.interpolateUsingSurfaceDistance(
    fraction * this._distance,
    result
  );
};
EllipsoidRhumbLine.prototype.interpolateUsingSurfaceDistance = function(distance, result) {
  Check_default.typeOf.number("distance", distance);
  if (!defined_default(this._distance) || this._distance === 0) {
    throw new DeveloperError_default(
      "EllipsoidRhumbLine must have distinct start and end set."
    );
  }
  return interpolateUsingSurfaceDistance(
    this._start,
    this._heading,
    distance,
    this._ellipsoid.maximumRadius,
    this._ellipticity,
    result
  );
};
EllipsoidRhumbLine.prototype.findIntersectionWithLongitude = function(intersectionLongitude, result) {
  Check_default.typeOf.number("intersectionLongitude", intersectionLongitude);
  if (!defined_default(this._distance) || this._distance === 0) {
    throw new DeveloperError_default(
      "EllipsoidRhumbLine must have distinct start and end set."
    );
  }
  const ellipticity = this._ellipticity;
  const heading = this._heading;
  const absHeading = Math.abs(heading);
  const start = this._start;
  intersectionLongitude = Math_default.negativePiToPi(intersectionLongitude);
  if (Math_default.equalsEpsilon(
    Math.abs(intersectionLongitude),
    Math.PI,
    Math_default.EPSILON14
  )) {
    intersectionLongitude = Math_default.sign(start.longitude) * Math.PI;
  }
  if (!defined_default(result)) {
    result = new Cartographic_default();
  }
  if (Math.abs(Math_default.PI_OVER_TWO - absHeading) <= Math_default.EPSILON8) {
    result.longitude = intersectionLongitude;
    result.latitude = start.latitude;
    result.height = 0;
    return result;
  } else if (Math_default.equalsEpsilon(
    Math.abs(Math_default.PI_OVER_TWO - absHeading),
    Math_default.PI_OVER_TWO,
    Math_default.EPSILON8
  )) {
    if (Math_default.equalsEpsilon(
      intersectionLongitude,
      start.longitude,
      Math_default.EPSILON12
    )) {
      return void 0;
    }
    result.longitude = intersectionLongitude;
    result.latitude = Math_default.PI_OVER_TWO * Math_default.sign(Math_default.PI_OVER_TWO - heading);
    result.height = 0;
    return result;
  }
  const phi1 = start.latitude;
  const eSinPhi1 = ellipticity * Math.sin(phi1);
  const leftComponent = Math.tan(0.5 * (Math_default.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)
    ) - Math_default.PI_OVER_TWO;
  } while (!Math_default.equalsEpsilon(newPhi, phi, Math_default.EPSILON12));
  result.longitude = intersectionLongitude;
  result.latitude = newPhi;
  result.height = 0;
  return result;
};
EllipsoidRhumbLine.prototype.findIntersectionWithLatitude = function(intersectionLatitude, result) {
  Check_default.typeOf.number("intersectionLatitude", intersectionLatitude);
  if (!defined_default(this._distance) || this._distance === 0) {
    throw new DeveloperError_default(
      "EllipsoidRhumbLine must have distinct start and end set."
    );
  }
  const ellipticity = this._ellipticity;
  const heading = this._heading;
  const start = this._start;
  if (Math_default.equalsEpsilon(
    Math.abs(heading),
    Math_default.PI_OVER_TWO,
    Math_default.EPSILON8
  )) {
    return;
  }
  const sigma1 = calculateSigma(ellipticity, start.latitude);
  const sigma2 = calculateSigma(ellipticity, intersectionLatitude);
  const deltaLongitude = Math.tan(heading) * (sigma2 - sigma1);
  const longitude = Math_default.negativePiToPi(start.longitude + deltaLongitude);
  if (defined_default(result)) {
    result.longitude = longitude;
    result.latitude = intersectionLatitude;
    result.height = 0;
    return result;
  }
  return new Cartographic_default(longitude, intersectionLatitude, 0);
};
var EllipsoidRhumbLine_default = EllipsoidRhumbLine;

export {
  EllipsoidRhumbLine_default
};
