EllipseGeometryLibrary.js

import Cartesian3 from "./Cartesian3.js";
import CesiumMath from "./Math.js";
import Matrix3 from "./Matrix3.js";
import Quaternion from "./Quaternion.js";

const EllipseGeometryLibrary = {};

const rotAxis = new Cartesian3();
const tempVec = new Cartesian3();
const unitQuat = new Quaternion();
const rotMtx = new Matrix3();

function pointOnEllipsoid(
  theta,
  rotation,
  northVec,
  eastVec,
  aSqr,
  ab,
  bSqr,
  mag,
  unitPos,
  result
) {
  const azimuth = theta + rotation;

  Cartesian3.multiplyByScalar(eastVec, Math.cos(azimuth), rotAxis);
  Cartesian3.multiplyByScalar(northVec, Math.sin(azimuth), tempVec);
  Cartesian3.add(rotAxis, tempVec, rotAxis);

  let cosThetaSquared = Math.cos(theta);
  cosThetaSquared = cosThetaSquared * cosThetaSquared;

  let sinThetaSquared = Math.sin(theta);
  sinThetaSquared = sinThetaSquared * sinThetaSquared;

  const radius =
    ab / Math.sqrt(bSqr * cosThetaSquared + aSqr * sinThetaSquared);
  const angle = radius / mag;

  // Create the quaternion to rotate the position vector to the boundary of the ellipse.
  Quaternion.fromAxisAngle(rotAxis, angle, unitQuat);
  Matrix3.fromQuaternion(unitQuat, rotMtx);

  Matrix3.multiplyByVector(rotMtx, unitPos, result);
  Cartesian3.normalize(result, result);
  Cartesian3.multiplyByScalar(result, mag, result);
  return result;
}

const scratchCartesian1 = new Cartesian3();
const scratchCartesian2 = new Cartesian3();
const scratchCartesian3 = new Cartesian3();
const scratchNormal = new Cartesian3();
/**
 * Returns the positions raised to the given heights
 * @private
 */
EllipseGeometryLibrary.raisePositionsToHeight = function (
  positions,
  options,
  extrude
) {
  const ellipsoid = options.ellipsoid;
  const height = options.height;
  const extrudedHeight = options.extrudedHeight;
  const size = extrude ? (positions.length / 3) * 2 : positions.length / 3;

  const finalPositions = new Float64Array(size * 3);

  const length = positions.length;
  const bottomOffset = extrude ? length : 0;
  for (let i = 0; i < length; i += 3) {
    const i1 = i + 1;
    const i2 = i + 2;

    const position = Cartesian3.fromArray(positions, i, scratchCartesian1);
    ellipsoid.scaleToGeodeticSurface(position, position);

    const extrudedPosition = Cartesian3.clone(position, scratchCartesian2);
    const normal = ellipsoid.geodeticSurfaceNormal(position, scratchNormal);
    const scaledNormal = Cartesian3.multiplyByScalar(
      normal,
      height,
      scratchCartesian3
    );
    Cartesian3.add(position, scaledNormal, position);

    if (extrude) {
      Cartesian3.multiplyByScalar(normal, extrudedHeight, scaledNormal);
      Cartesian3.add(extrudedPosition, scaledNormal, extrudedPosition);

      finalPositions[i + bottomOffset] = extrudedPosition.x;
      finalPositions[i1 + bottomOffset] = extrudedPosition.y;
      finalPositions[i2 + bottomOffset] = extrudedPosition.z;
    }

    finalPositions[i] = position.x;
    finalPositions[i1] = position.y;
    finalPositions[i2] = position.z;
  }

  return finalPositions;
};

const unitPosScratch = new Cartesian3();
const eastVecScratch = new Cartesian3();
const northVecScratch = new Cartesian3();
/**
 * Returns an array of positions that make up the ellipse.
 * @private
 */
EllipseGeometryLibrary.computeEllipsePositions = function (
  options,
  addFillPositions,
  addEdgePositions
) {
  const semiMinorAxis = options.semiMinorAxis;
  const semiMajorAxis = options.semiMajorAxis;
  const rotation = options.rotation;
  const center = options.center;

  // Computing the arc-length of the ellipse is too expensive to be practical. Estimating it using the
  // arc length of the sphere is too inaccurate and creates sharp edges when either the semi-major or
  // semi-minor axis is much bigger than the other. Instead, scale the angle delta to make
  // the distance along the ellipse boundary more closely match the granularity.
  const granularity = options.granularity * 8.0;

  const aSqr = semiMinorAxis * semiMinorAxis;
  const bSqr = semiMajorAxis * semiMajorAxis;
  const ab = semiMajorAxis * semiMinorAxis;

  const mag = Cartesian3.magnitude(center);

  const unitPos = Cartesian3.normalize(center, unitPosScratch);
  let eastVec = Cartesian3.cross(Cartesian3.UNIT_Z, center, eastVecScratch);
  eastVec = Cartesian3.normalize(eastVec, eastVec);
  const northVec = Cartesian3.cross(unitPos, eastVec, northVecScratch);

  // The number of points in the first quadrant
  let numPts = 1 + Math.ceil(CesiumMath.PI_OVER_TWO / granularity);

  const deltaTheta = CesiumMath.PI_OVER_TWO / (numPts - 1);
  let theta = CesiumMath.PI_OVER_TWO - numPts * deltaTheta;
  if (theta < 0.0) {
    numPts -= Math.ceil(Math.abs(theta) / deltaTheta);
  }

  // If the number of points were three, the ellipse
  // would be tessellated like below:
  //
  //         *---*
  //       / | \ | \
  //     *---*---*---*
  //   / | \ | \ | \ | \
  //  / .*---*---*---*. \
  // * ` | \ | \ | \ | `*
  //  \`.*---*---*---*.`/
  //   \ | \ | \ | \ | /
  //     *---*---*---*
  //       \ | \ | /
  //         *---*
  // The first and last column have one position and fan to connect to the adjacent column.
  // Each other vertical column contains an even number of positions.
  const size = 2 * (numPts * (numPts + 2));
  const positions = addFillPositions ? new Array(size * 3) : undefined;
  let positionIndex = 0;
  let position = scratchCartesian1;
  let reflectedPosition = scratchCartesian2;

  const outerPositionsLength = numPts * 4 * 3;
  let outerRightIndex = outerPositionsLength - 1;
  let outerLeftIndex = 0;
  const outerPositions = addEdgePositions
    ? new Array(outerPositionsLength)
    : undefined;

  let i;
  let j;
  let numInterior;
  let t;
  let interiorPosition;

  // Compute points in the 'eastern' half of the ellipse
  theta = CesiumMath.PI_OVER_TWO;
  position = pointOnEllipsoid(
    theta,
    rotation,
    northVec,
    eastVec,
    aSqr,
    ab,
    bSqr,
    mag,
    unitPos,
    position
  );
  if (addFillPositions) {
    positions[positionIndex++] = position.x;
    positions[positionIndex++] = position.y;
    positions[positionIndex++] = position.z;
  }
  if (addEdgePositions) {
    outerPositions[outerRightIndex--] = position.z;
    outerPositions[outerRightIndex--] = position.y;
    outerPositions[outerRightIndex--] = position.x;
  }
  theta = CesiumMath.PI_OVER_TWO - deltaTheta;
  for (i = 1; i < numPts + 1; ++i) {
    position = pointOnEllipsoid(
      theta,
      rotation,
      northVec,
      eastVec,
      aSqr,
      ab,
      bSqr,
      mag,
      unitPos,
      position
    );
    reflectedPosition = pointOnEllipsoid(
      Math.PI - theta,
      rotation,
      northVec,
      eastVec,
      aSqr,
      ab,
      bSqr,
      mag,
      unitPos,
      reflectedPosition
    );

    if (addFillPositions) {
      positions[positionIndex++] = position.x;
      positions[positionIndex++] = position.y;
      positions[positionIndex++] = position.z;

      numInterior = 2 * i + 2;
      for (j = 1; j < numInterior - 1; ++j) {
        t = j / (numInterior - 1);
        interiorPosition = Cartesian3.lerp(
          position,
          reflectedPosition,
          t,
          scratchCartesian3
        );
        positions[positionIndex++] = interiorPosition.x;
        positions[positionIndex++] = interiorPosition.y;
        positions[positionIndex++] = interiorPosition.z;
      }

      positions[positionIndex++] = reflectedPosition.x;
      positions[positionIndex++] = reflectedPosition.y;
      positions[positionIndex++] = reflectedPosition.z;
    }

    if (addEdgePositions) {
      outerPositions[outerRightIndex--] = position.z;
      outerPositions[outerRightIndex--] = position.y;
      outerPositions[outerRightIndex--] = position.x;
      outerPositions[outerLeftIndex++] = reflectedPosition.x;
      outerPositions[outerLeftIndex++] = reflectedPosition.y;
      outerPositions[outerLeftIndex++] = reflectedPosition.z;
    }

    theta = CesiumMath.PI_OVER_TWO - (i + 1) * deltaTheta;
  }

  // Compute points in the 'western' half of the ellipse
  for (i = numPts; i > 1; --i) {
    theta = CesiumMath.PI_OVER_TWO - (i - 1) * deltaTheta;

    position = pointOnEllipsoid(
      -theta,
      rotation,
      northVec,
      eastVec,
      aSqr,
      ab,
      bSqr,
      mag,
      unitPos,
      position
    );
    reflectedPosition = pointOnEllipsoid(
      theta + Math.PI,
      rotation,
      northVec,
      eastVec,
      aSqr,
      ab,
      bSqr,
      mag,
      unitPos,
      reflectedPosition
    );

    if (addFillPositions) {
      positions[positionIndex++] = position.x;
      positions[positionIndex++] = position.y;
      positions[positionIndex++] = position.z;

      numInterior = 2 * (i - 1) + 2;
      for (j = 1; j < numInterior - 1; ++j) {
        t = j / (numInterior - 1);
        interiorPosition = Cartesian3.lerp(
          position,
          reflectedPosition,
          t,
          scratchCartesian3
        );
        positions[positionIndex++] = interiorPosition.x;
        positions[positionIndex++] = interiorPosition.y;
        positions[positionIndex++] = interiorPosition.z;
      }

      positions[positionIndex++] = reflectedPosition.x;
      positions[positionIndex++] = reflectedPosition.y;
      positions[positionIndex++] = reflectedPosition.z;
    }

    if (addEdgePositions) {
      outerPositions[outerRightIndex--] = position.z;
      outerPositions[outerRightIndex--] = position.y;
      outerPositions[outerRightIndex--] = position.x;
      outerPositions[outerLeftIndex++] = reflectedPosition.x;
      outerPositions[outerLeftIndex++] = reflectedPosition.y;
      outerPositions[outerLeftIndex++] = reflectedPosition.z;
    }
  }

  theta = CesiumMath.PI_OVER_TWO;
  position = pointOnEllipsoid(
    -theta,
    rotation,
    northVec,
    eastVec,
    aSqr,
    ab,
    bSqr,
    mag,
    unitPos,
    position
  );

  const r = {};
  if (addFillPositions) {
    positions[positionIndex++] = position.x;
    positions[positionIndex++] = position.y;
    positions[positionIndex++] = position.z;
    r.positions = positions;
    r.numPts = numPts;
  }
  if (addEdgePositions) {
    outerPositions[outerRightIndex--] = position.z;
    outerPositions[outerRightIndex--] = position.y;
    outerPositions[outerRightIndex--] = position.x;
    r.outerPositions = outerPositions;
  }

  return r;
};
export default EllipseGeometryLibrary;