EllipseGeometry.js

import BoundingSphere from "./BoundingSphere.js";
import Cartesian2 from "./Cartesian2.js";
import Cartesian3 from "./Cartesian3.js";
import Cartographic from "./Cartographic.js";
import Check from "./Check.js";
import ComponentDatatype from "./ComponentDatatype.js";
import defaultValue from "./defaultValue.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.js";
import EllipseGeometryLibrary from "./EllipseGeometryLibrary.js";
import Ellipsoid from "./Ellipsoid.js";
import GeographicProjection from "./GeographicProjection.js";
import Geometry from "./Geometry.js";
import GeometryAttribute from "./GeometryAttribute.js";
import GeometryAttributes from "./GeometryAttributes.js";
import GeometryInstance from "./GeometryInstance.js";
import GeometryOffsetAttribute from "./GeometryOffsetAttribute.js";
import GeometryPipeline from "./GeometryPipeline.js";
import IndexDatatype from "./IndexDatatype.js";
import CesiumMath from "./Math.js";
import Matrix3 from "./Matrix3.js";
import PrimitiveType from "./PrimitiveType.js";
import Quaternion from "./Quaternion.js";
import Rectangle from "./Rectangle.js";
import VertexFormat from "./VertexFormat.js";

const scratchCartesian1 = new Cartesian3();
const scratchCartesian2 = new Cartesian3();
const scratchCartesian3 = new Cartesian3();
const scratchCartesian4 = new Cartesian3();
const texCoordScratch = new Cartesian2();
const textureMatrixScratch = new Matrix3();
const tangentMatrixScratch = new Matrix3();
const quaternionScratch = new Quaternion();

const scratchNormal = new Cartesian3();
const scratchTangent = new Cartesian3();
const scratchBitangent = new Cartesian3();

const scratchCartographic = new Cartographic();
const projectedCenterScratch = new Cartesian3();

const scratchMinTexCoord = new Cartesian2();
const scratchMaxTexCoord = new Cartesian2();

function computeTopBottomAttributes(positions, options, extrude) {
  const vertexFormat = options.vertexFormat;
  const center = options.center;
  const semiMajorAxis = options.semiMajorAxis;
  const semiMinorAxis = options.semiMinorAxis;
  const ellipsoid = options.ellipsoid;
  const stRotation = options.stRotation;
  const size = extrude ? (positions.length / 3) * 2 : positions.length / 3;
  const shadowVolume = options.shadowVolume;

  const textureCoordinates = vertexFormat.st
    ? new Float32Array(size * 2)
    : undefined;
  const normals = vertexFormat.normal ? new Float32Array(size * 3) : undefined;
  const tangents = vertexFormat.tangent
    ? new Float32Array(size * 3)
    : undefined;
  const bitangents = vertexFormat.bitangent
    ? new Float32Array(size * 3)
    : undefined;

  const extrudeNormals = shadowVolume ? new Float32Array(size * 3) : undefined;

  let textureCoordIndex = 0;

  // Raise positions to a height above the ellipsoid and compute the
  // texture coordinates, normals, tangents, and bitangents.
  let normal = scratchNormal;
  let tangent = scratchTangent;
  let bitangent = scratchBitangent;

  const projection = new GeographicProjection(ellipsoid);
  const projectedCenter = projection.project(
    ellipsoid.cartesianToCartographic(center, scratchCartographic),
    projectedCenterScratch
  );

  const geodeticNormal = ellipsoid.scaleToGeodeticSurface(
    center,
    scratchCartesian1
  );
  ellipsoid.geodeticSurfaceNormal(geodeticNormal, geodeticNormal);

  let textureMatrix = textureMatrixScratch;
  let tangentMatrix = tangentMatrixScratch;
  if (stRotation !== 0) {
    let rotation = Quaternion.fromAxisAngle(
      geodeticNormal,
      stRotation,
      quaternionScratch
    );
    textureMatrix = Matrix3.fromQuaternion(rotation, textureMatrix);

    rotation = Quaternion.fromAxisAngle(
      geodeticNormal,
      -stRotation,
      quaternionScratch
    );
    tangentMatrix = Matrix3.fromQuaternion(rotation, tangentMatrix);
  } else {
    textureMatrix = Matrix3.clone(Matrix3.IDENTITY, textureMatrix);
    tangentMatrix = Matrix3.clone(Matrix3.IDENTITY, tangentMatrix);
  }

  const minTexCoord = Cartesian2.fromElements(
    Number.POSITIVE_INFINITY,
    Number.POSITIVE_INFINITY,
    scratchMinTexCoord
  );
  const maxTexCoord = Cartesian2.fromElements(
    Number.NEGATIVE_INFINITY,
    Number.NEGATIVE_INFINITY,
    scratchMaxTexCoord
  );

  let length = positions.length;
  const bottomOffset = extrude ? length : 0;
  const stOffset = (bottomOffset / 3) * 2;
  for (let i = 0; i < length; i += 3) {
    const i1 = i + 1;
    const i2 = i + 2;
    const position = Cartesian3.fromArray(positions, i, scratchCartesian1);

    if (vertexFormat.st) {
      const rotatedPoint = Matrix3.multiplyByVector(
        textureMatrix,
        position,
        scratchCartesian2
      );
      const projectedPoint = projection.project(
        ellipsoid.cartesianToCartographic(rotatedPoint, scratchCartographic),
        scratchCartesian3
      );
      Cartesian3.subtract(projectedPoint, projectedCenter, projectedPoint);

      texCoordScratch.x =
        (projectedPoint.x + semiMajorAxis) / (2.0 * semiMajorAxis);
      texCoordScratch.y =
        (projectedPoint.y + semiMinorAxis) / (2.0 * semiMinorAxis);

      minTexCoord.x = Math.min(texCoordScratch.x, minTexCoord.x);
      minTexCoord.y = Math.min(texCoordScratch.y, minTexCoord.y);
      maxTexCoord.x = Math.max(texCoordScratch.x, maxTexCoord.x);
      maxTexCoord.y = Math.max(texCoordScratch.y, maxTexCoord.y);

      if (extrude) {
        textureCoordinates[textureCoordIndex + stOffset] = texCoordScratch.x;
        textureCoordinates[textureCoordIndex + 1 + stOffset] =
          texCoordScratch.y;
      }

      textureCoordinates[textureCoordIndex++] = texCoordScratch.x;
      textureCoordinates[textureCoordIndex++] = texCoordScratch.y;
    }

    if (
      vertexFormat.normal ||
      vertexFormat.tangent ||
      vertexFormat.bitangent ||
      shadowVolume
    ) {
      normal = ellipsoid.geodeticSurfaceNormal(position, normal);

      if (shadowVolume) {
        extrudeNormals[i + bottomOffset] = -normal.x;
        extrudeNormals[i1 + bottomOffset] = -normal.y;
        extrudeNormals[i2 + bottomOffset] = -normal.z;
      }

      if (
        vertexFormat.normal ||
        vertexFormat.tangent ||
        vertexFormat.bitangent
      ) {
        if (vertexFormat.tangent || vertexFormat.bitangent) {
          tangent = Cartesian3.normalize(
            Cartesian3.cross(Cartesian3.UNIT_Z, normal, tangent),
            tangent
          );
          Matrix3.multiplyByVector(tangentMatrix, tangent, tangent);
        }
        if (vertexFormat.normal) {
          normals[i] = normal.x;
          normals[i1] = normal.y;
          normals[i2] = normal.z;
          if (extrude) {
            normals[i + bottomOffset] = -normal.x;
            normals[i1 + bottomOffset] = -normal.y;
            normals[i2 + bottomOffset] = -normal.z;
          }
        }

        if (vertexFormat.tangent) {
          tangents[i] = tangent.x;
          tangents[i1] = tangent.y;
          tangents[i2] = tangent.z;
          if (extrude) {
            tangents[i + bottomOffset] = -tangent.x;
            tangents[i1 + bottomOffset] = -tangent.y;
            tangents[i2 + bottomOffset] = -tangent.z;
          }
        }

        if (vertexFormat.bitangent) {
          bitangent = Cartesian3.normalize(
            Cartesian3.cross(normal, tangent, bitangent),
            bitangent
          );
          bitangents[i] = bitangent.x;
          bitangents[i1] = bitangent.y;
          bitangents[i2] = bitangent.z;
          if (extrude) {
            bitangents[i + bottomOffset] = bitangent.x;
            bitangents[i1 + bottomOffset] = bitangent.y;
            bitangents[i2 + bottomOffset] = bitangent.z;
          }
        }
      }
    }
  }

  if (vertexFormat.st) {
    length = textureCoordinates.length;
    for (let k = 0; k < length; k += 2) {
      textureCoordinates[k] =
        (textureCoordinates[k] - minTexCoord.x) /
        (maxTexCoord.x - minTexCoord.x);
      textureCoordinates[k + 1] =
        (textureCoordinates[k + 1] - minTexCoord.y) /
        (maxTexCoord.y - minTexCoord.y);
    }
  }

  const attributes = new GeometryAttributes();

  if (vertexFormat.position) {
    const finalPositions = EllipseGeometryLibrary.raisePositionsToHeight(
      positions,
      options,
      extrude
    );
    attributes.position = new GeometryAttribute({
      componentDatatype: ComponentDatatype.DOUBLE,
      componentsPerAttribute: 3,
      values: finalPositions,
    });
  }

  if (vertexFormat.st) {
    attributes.st = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 2,
      values: textureCoordinates,
    });
  }

  if (vertexFormat.normal) {
    attributes.normal = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 3,
      values: normals,
    });
  }

  if (vertexFormat.tangent) {
    attributes.tangent = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 3,
      values: tangents,
    });
  }

  if (vertexFormat.bitangent) {
    attributes.bitangent = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 3,
      values: bitangents,
    });
  }

  if (shadowVolume) {
    attributes.extrudeDirection = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 3,
      values: extrudeNormals,
    });
  }

  if (extrude && defined(options.offsetAttribute)) {
    let offsetAttribute = new Uint8Array(size);
    if (options.offsetAttribute === GeometryOffsetAttribute.TOP) {
      offsetAttribute = offsetAttribute.fill(1, 0, size / 2);
    } else {
      const offsetValue =
        options.offsetAttribute === GeometryOffsetAttribute.NONE ? 0 : 1;
      offsetAttribute = offsetAttribute.fill(offsetValue);
    }

    attributes.applyOffset = new GeometryAttribute({
      componentDatatype: ComponentDatatype.UNSIGNED_BYTE,
      componentsPerAttribute: 1,
      values: offsetAttribute,
    });
  }

  return attributes;
}

function topIndices(numPts) {
  // numTriangles in half = 3 + 8 + 12 + ... = -1 + 4 + (4 + 4) + (4 + 4 + 4) + ... = -1 + 4 * (1 + 2 + 3 + ...)
  //              = -1 + 4 * ((n * ( n + 1)) / 2)
  // total triangles = 2 * numTrangles in half
  // indices = total triangles * 3;
  // Substitute numPts for n above

  const indices = new Array(12 * (numPts * (numPts + 1)) - 6);
  let indicesIndex = 0;
  let prevIndex;
  let numInterior;
  let positionIndex;
  let i;
  let j;
  // Indices triangles to the 'right' of the north vector

  prevIndex = 0;
  positionIndex = 1;
  for (i = 0; i < 3; i++) {
    indices[indicesIndex++] = positionIndex++;
    indices[indicesIndex++] = prevIndex;
    indices[indicesIndex++] = positionIndex;
  }

  for (i = 2; i < numPts + 1; ++i) {
    positionIndex = i * (i + 1) - 1;
    prevIndex = (i - 1) * i - 1;

    indices[indicesIndex++] = positionIndex++;
    indices[indicesIndex++] = prevIndex;
    indices[indicesIndex++] = positionIndex;

    numInterior = 2 * i;
    for (j = 0; j < numInterior - 1; ++j) {
      indices[indicesIndex++] = positionIndex;
      indices[indicesIndex++] = prevIndex++;
      indices[indicesIndex++] = prevIndex;

      indices[indicesIndex++] = positionIndex++;
      indices[indicesIndex++] = prevIndex;
      indices[indicesIndex++] = positionIndex;
    }

    indices[indicesIndex++] = positionIndex++;
    indices[indicesIndex++] = prevIndex;
    indices[indicesIndex++] = positionIndex;
  }

  // Indices for center column of triangles
  numInterior = numPts * 2;
  ++positionIndex;
  ++prevIndex;
  for (i = 0; i < numInterior - 1; ++i) {
    indices[indicesIndex++] = positionIndex;
    indices[indicesIndex++] = prevIndex++;
    indices[indicesIndex++] = prevIndex;

    indices[indicesIndex++] = positionIndex++;
    indices[indicesIndex++] = prevIndex;
    indices[indicesIndex++] = positionIndex;
  }

  indices[indicesIndex++] = positionIndex;
  indices[indicesIndex++] = prevIndex++;
  indices[indicesIndex++] = prevIndex;

  indices[indicesIndex++] = positionIndex++;
  indices[indicesIndex++] = prevIndex++;
  indices[indicesIndex++] = prevIndex;

  // Reverse the process creating indices to the 'left' of the north vector
  ++prevIndex;
  for (i = numPts - 1; i > 1; --i) {
    indices[indicesIndex++] = prevIndex++;
    indices[indicesIndex++] = prevIndex;
    indices[indicesIndex++] = positionIndex;

    numInterior = 2 * i;
    for (j = 0; j < numInterior - 1; ++j) {
      indices[indicesIndex++] = positionIndex;
      indices[indicesIndex++] = prevIndex++;
      indices[indicesIndex++] = prevIndex;

      indices[indicesIndex++] = positionIndex++;
      indices[indicesIndex++] = prevIndex;
      indices[indicesIndex++] = positionIndex;
    }

    indices[indicesIndex++] = prevIndex++;
    indices[indicesIndex++] = prevIndex++;
    indices[indicesIndex++] = positionIndex++;
  }

  for (i = 0; i < 3; i++) {
    indices[indicesIndex++] = prevIndex++;
    indices[indicesIndex++] = prevIndex;
    indices[indicesIndex++] = positionIndex;
  }
  return indices;
}

let boundingSphereCenter = new Cartesian3();

function computeEllipse(options) {
  const center = options.center;
  boundingSphereCenter = Cartesian3.multiplyByScalar(
    options.ellipsoid.geodeticSurfaceNormal(center, boundingSphereCenter),
    options.height,
    boundingSphereCenter
  );
  boundingSphereCenter = Cartesian3.add(
    center,
    boundingSphereCenter,
    boundingSphereCenter
  );
  const boundingSphere = new BoundingSphere(
    boundingSphereCenter,
    options.semiMajorAxis
  );
  const cep = EllipseGeometryLibrary.computeEllipsePositions(
    options,
    true,
    false
  );
  const positions = cep.positions;
  const numPts = cep.numPts;
  const attributes = computeTopBottomAttributes(positions, options, false);
  let indices = topIndices(numPts);
  indices = IndexDatatype.createTypedArray(positions.length / 3, indices);
  return {
    boundingSphere: boundingSphere,
    attributes: attributes,
    indices: indices,
  };
}

function computeWallAttributes(positions, options) {
  const vertexFormat = options.vertexFormat;
  const center = options.center;
  const semiMajorAxis = options.semiMajorAxis;
  const semiMinorAxis = options.semiMinorAxis;
  const ellipsoid = options.ellipsoid;
  const height = options.height;
  const extrudedHeight = options.extrudedHeight;
  const stRotation = options.stRotation;
  const size = (positions.length / 3) * 2;

  const finalPositions = new Float64Array(size * 3);
  const textureCoordinates = vertexFormat.st
    ? new Float32Array(size * 2)
    : undefined;
  const normals = vertexFormat.normal ? new Float32Array(size * 3) : undefined;
  const tangents = vertexFormat.tangent
    ? new Float32Array(size * 3)
    : undefined;
  const bitangents = vertexFormat.bitangent
    ? new Float32Array(size * 3)
    : undefined;

  const shadowVolume = options.shadowVolume;
  const extrudeNormals = shadowVolume ? new Float32Array(size * 3) : undefined;

  let textureCoordIndex = 0;

  // Raise positions to a height above the ellipsoid and compute the
  // texture coordinates, normals, tangents, and bitangents.
  let normal = scratchNormal;
  let tangent = scratchTangent;
  let bitangent = scratchBitangent;

  const projection = new GeographicProjection(ellipsoid);
  const projectedCenter = projection.project(
    ellipsoid.cartesianToCartographic(center, scratchCartographic),
    projectedCenterScratch
  );

  const geodeticNormal = ellipsoid.scaleToGeodeticSurface(
    center,
    scratchCartesian1
  );
  ellipsoid.geodeticSurfaceNormal(geodeticNormal, geodeticNormal);
  const rotation = Quaternion.fromAxisAngle(
    geodeticNormal,
    stRotation,
    quaternionScratch
  );
  const textureMatrix = Matrix3.fromQuaternion(rotation, textureMatrixScratch);

  const minTexCoord = Cartesian2.fromElements(
    Number.POSITIVE_INFINITY,
    Number.POSITIVE_INFINITY,
    scratchMinTexCoord
  );
  const maxTexCoord = Cartesian2.fromElements(
    Number.NEGATIVE_INFINITY,
    Number.NEGATIVE_INFINITY,
    scratchMaxTexCoord
  );

  let length = positions.length;
  const stOffset = (length / 3) * 2;
  for (let i = 0; i < length; i += 3) {
    const i1 = i + 1;
    const i2 = i + 2;
    let position = Cartesian3.fromArray(positions, i, scratchCartesian1);
    let extrudedPosition;

    if (vertexFormat.st) {
      const rotatedPoint = Matrix3.multiplyByVector(
        textureMatrix,
        position,
        scratchCartesian2
      );
      const projectedPoint = projection.project(
        ellipsoid.cartesianToCartographic(rotatedPoint, scratchCartographic),
        scratchCartesian3
      );
      Cartesian3.subtract(projectedPoint, projectedCenter, projectedPoint);

      texCoordScratch.x =
        (projectedPoint.x + semiMajorAxis) / (2.0 * semiMajorAxis);
      texCoordScratch.y =
        (projectedPoint.y + semiMinorAxis) / (2.0 * semiMinorAxis);

      minTexCoord.x = Math.min(texCoordScratch.x, minTexCoord.x);
      minTexCoord.y = Math.min(texCoordScratch.y, minTexCoord.y);
      maxTexCoord.x = Math.max(texCoordScratch.x, maxTexCoord.x);
      maxTexCoord.y = Math.max(texCoordScratch.y, maxTexCoord.y);

      textureCoordinates[textureCoordIndex + stOffset] = texCoordScratch.x;
      textureCoordinates[textureCoordIndex + 1 + stOffset] = texCoordScratch.y;

      textureCoordinates[textureCoordIndex++] = texCoordScratch.x;
      textureCoordinates[textureCoordIndex++] = texCoordScratch.y;
    }

    position = ellipsoid.scaleToGeodeticSurface(position, position);
    extrudedPosition = Cartesian3.clone(position, scratchCartesian2);
    normal = ellipsoid.geodeticSurfaceNormal(position, normal);

    if (shadowVolume) {
      extrudeNormals[i + length] = -normal.x;
      extrudeNormals[i1 + length] = -normal.y;
      extrudeNormals[i2 + length] = -normal.z;
    }

    let scaledNormal = Cartesian3.multiplyByScalar(
      normal,
      height,
      scratchCartesian4
    );
    position = Cartesian3.add(position, scaledNormal, position);
    scaledNormal = Cartesian3.multiplyByScalar(
      normal,
      extrudedHeight,
      scaledNormal
    );
    extrudedPosition = Cartesian3.add(
      extrudedPosition,
      scaledNormal,
      extrudedPosition
    );

    if (vertexFormat.position) {
      finalPositions[i + length] = extrudedPosition.x;
      finalPositions[i1 + length] = extrudedPosition.y;
      finalPositions[i2 + length] = extrudedPosition.z;

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

    if (vertexFormat.normal || vertexFormat.tangent || vertexFormat.bitangent) {
      bitangent = Cartesian3.clone(normal, bitangent);
      const next = Cartesian3.fromArray(
        positions,
        (i + 3) % length,
        scratchCartesian4
      );
      Cartesian3.subtract(next, position, next);
      const bottom = Cartesian3.subtract(
        extrudedPosition,
        position,
        scratchCartesian3
      );

      normal = Cartesian3.normalize(
        Cartesian3.cross(bottom, next, normal),
        normal
      );

      if (vertexFormat.normal) {
        normals[i] = normal.x;
        normals[i1] = normal.y;
        normals[i2] = normal.z;

        normals[i + length] = normal.x;
        normals[i1 + length] = normal.y;
        normals[i2 + length] = normal.z;
      }

      if (vertexFormat.tangent) {
        tangent = Cartesian3.normalize(
          Cartesian3.cross(bitangent, normal, tangent),
          tangent
        );
        tangents[i] = tangent.x;
        tangents[i1] = tangent.y;
        tangents[i2] = tangent.z;

        tangents[i + length] = tangent.x;
        tangents[i + 1 + length] = tangent.y;
        tangents[i + 2 + length] = tangent.z;
      }

      if (vertexFormat.bitangent) {
        bitangents[i] = bitangent.x;
        bitangents[i1] = bitangent.y;
        bitangents[i2] = bitangent.z;

        bitangents[i + length] = bitangent.x;
        bitangents[i1 + length] = bitangent.y;
        bitangents[i2 + length] = bitangent.z;
      }
    }
  }

  if (vertexFormat.st) {
    length = textureCoordinates.length;
    for (let k = 0; k < length; k += 2) {
      textureCoordinates[k] =
        (textureCoordinates[k] - minTexCoord.x) /
        (maxTexCoord.x - minTexCoord.x);
      textureCoordinates[k + 1] =
        (textureCoordinates[k + 1] - minTexCoord.y) /
        (maxTexCoord.y - minTexCoord.y);
    }
  }

  const attributes = new GeometryAttributes();

  if (vertexFormat.position) {
    attributes.position = new GeometryAttribute({
      componentDatatype: ComponentDatatype.DOUBLE,
      componentsPerAttribute: 3,
      values: finalPositions,
    });
  }

  if (vertexFormat.st) {
    attributes.st = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 2,
      values: textureCoordinates,
    });
  }

  if (vertexFormat.normal) {
    attributes.normal = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 3,
      values: normals,
    });
  }

  if (vertexFormat.tangent) {
    attributes.tangent = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 3,
      values: tangents,
    });
  }

  if (vertexFormat.bitangent) {
    attributes.bitangent = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 3,
      values: bitangents,
    });
  }

  if (shadowVolume) {
    attributes.extrudeDirection = new GeometryAttribute({
      componentDatatype: ComponentDatatype.FLOAT,
      componentsPerAttribute: 3,
      values: extrudeNormals,
    });
  }

  if (defined(options.offsetAttribute)) {
    let offsetAttribute = new Uint8Array(size);
    if (options.offsetAttribute === GeometryOffsetAttribute.TOP) {
      offsetAttribute = offsetAttribute.fill(1, 0, size / 2);
    } else {
      const offsetValue =
        options.offsetAttribute === GeometryOffsetAttribute.NONE ? 0 : 1;
      offsetAttribute = offsetAttribute.fill(offsetValue);
    }
    attributes.applyOffset = new GeometryAttribute({
      componentDatatype: ComponentDatatype.UNSIGNED_BYTE,
      componentsPerAttribute: 1,
      values: offsetAttribute,
    });
  }

  return attributes;
}

function computeWallIndices(positions) {
  const length = positions.length / 3;
  const indices = IndexDatatype.createTypedArray(length, length * 6);
  let index = 0;
  for (let i = 0; i < length; i++) {
    const UL = i;
    const LL = i + length;
    const UR = (UL + 1) % length;
    const LR = UR + length;
    indices[index++] = UL;
    indices[index++] = LL;
    indices[index++] = UR;
    indices[index++] = UR;
    indices[index++] = LL;
    indices[index++] = LR;
  }

  return indices;
}

const topBoundingSphere = new BoundingSphere();
const bottomBoundingSphere = new BoundingSphere();

function computeExtrudedEllipse(options) {
  const center = options.center;
  const ellipsoid = options.ellipsoid;
  const semiMajorAxis = options.semiMajorAxis;
  let scaledNormal = Cartesian3.multiplyByScalar(
    ellipsoid.geodeticSurfaceNormal(center, scratchCartesian1),
    options.height,
    scratchCartesian1
  );
  topBoundingSphere.center = Cartesian3.add(
    center,
    scaledNormal,
    topBoundingSphere.center
  );
  topBoundingSphere.radius = semiMajorAxis;

  scaledNormal = Cartesian3.multiplyByScalar(
    ellipsoid.geodeticSurfaceNormal(center, scaledNormal),
    options.extrudedHeight,
    scaledNormal
  );
  bottomBoundingSphere.center = Cartesian3.add(
    center,
    scaledNormal,
    bottomBoundingSphere.center
  );
  bottomBoundingSphere.radius = semiMajorAxis;

  const cep = EllipseGeometryLibrary.computeEllipsePositions(
    options,
    true,
    true
  );
  const positions = cep.positions;
  const numPts = cep.numPts;
  const outerPositions = cep.outerPositions;
  const boundingSphere = BoundingSphere.union(
    topBoundingSphere,
    bottomBoundingSphere
  );
  const topBottomAttributes = computeTopBottomAttributes(
    positions,
    options,
    true
  );
  let indices = topIndices(numPts);
  const length = indices.length;
  indices.length = length * 2;
  const posLength = positions.length / 3;
  for (let i = 0; i < length; i += 3) {
    indices[i + length] = indices[i + 2] + posLength;
    indices[i + 1 + length] = indices[i + 1] + posLength;
    indices[i + 2 + length] = indices[i] + posLength;
  }

  const topBottomIndices = IndexDatatype.createTypedArray(
    (posLength * 2) / 3,
    indices
  );

  const topBottomGeo = new Geometry({
    attributes: topBottomAttributes,
    indices: topBottomIndices,
    primitiveType: PrimitiveType.TRIANGLES,
  });

  const wallAttributes = computeWallAttributes(outerPositions, options);
  indices = computeWallIndices(outerPositions);
  const wallIndices = IndexDatatype.createTypedArray(
    (outerPositions.length * 2) / 3,
    indices
  );

  const wallGeo = new Geometry({
    attributes: wallAttributes,
    indices: wallIndices,
    primitiveType: PrimitiveType.TRIANGLES,
  });

  const geo = GeometryPipeline.combineInstances([
    new GeometryInstance({
      geometry: topBottomGeo,
    }),
    new GeometryInstance({
      geometry: wallGeo,
    }),
  ]);

  return {
    boundingSphere: boundingSphere,
    attributes: geo[0].attributes,
    indices: geo[0].indices,
  };
}

function computeRectangle(
  center,
  semiMajorAxis,
  semiMinorAxis,
  rotation,
  granularity,
  ellipsoid,
  result
) {
  const cep = EllipseGeometryLibrary.computeEllipsePositions(
    {
      center: center,
      semiMajorAxis: semiMajorAxis,
      semiMinorAxis: semiMinorAxis,
      rotation: rotation,
      granularity: granularity,
    },
    false,
    true
  );
  const positionsFlat = cep.outerPositions;
  const positionsCount = positionsFlat.length / 3;
  const positions = new Array(positionsCount);
  for (let i = 0; i < positionsCount; ++i) {
    positions[i] = Cartesian3.fromArray(positionsFlat, i * 3);
  }
  const rectangle = Rectangle.fromCartesianArray(positions, ellipsoid, result);
  // Rectangle width goes beyond 180 degrees when the ellipse crosses a pole.
  // When this happens, make the rectangle into a "circle" around the pole
  if (rectangle.width > CesiumMath.PI) {
    rectangle.north =
      rectangle.north > 0.0
        ? CesiumMath.PI_OVER_TWO - CesiumMath.EPSILON7
        : rectangle.north;
    rectangle.south =
      rectangle.south < 0.0
        ? CesiumMath.EPSILON7 - CesiumMath.PI_OVER_TWO
        : rectangle.south;
    rectangle.east = CesiumMath.PI;
    rectangle.west = -CesiumMath.PI;
  }
  return rectangle;
}

/**
 * A description of an ellipse on an ellipsoid. Ellipse geometry can be rendered with both {@link Primitive} and {@link GroundPrimitive}.
 *
 * @alias EllipseGeometry
 * @constructor
 *
 * @param {Object} options Object with the following properties:
 * @param {Cartesian3} options.center The ellipse's center point in the fixed frame.
 * @param {Number} options.semiMajorAxis The length of the ellipse's semi-major axis in meters.
 * @param {Number} options.semiMinorAxis The length of the ellipse's semi-minor axis in meters.
 * @param {Ellipsoid} [options.ellipsoid=Ellipsoid.WGS84] The ellipsoid the ellipse will be on.
 * @param {Number} [options.height=0.0] The distance in meters between the ellipse and the ellipsoid surface.
 * @param {Number} [options.extrudedHeight] The distance in meters between the ellipse's extruded face and the ellipsoid surface.
 * @param {Number} [options.rotation=0.0] The angle of rotation counter-clockwise from north.
 * @param {Number} [options.stRotation=0.0] The rotation of the texture coordinates counter-clockwise from north.
 * @param {Number} [options.granularity=CesiumMath.RADIANS_PER_DEGREE] The angular distance between points on the ellipse in radians.
 * @param {VertexFormat} [options.vertexFormat=VertexFormat.DEFAULT] The vertex attributes to be computed.
 *
 * @exception {DeveloperError} semiMajorAxis and semiMinorAxis must be greater than zero.
 * @exception {DeveloperError} semiMajorAxis must be greater than or equal to the semiMinorAxis.
 * @exception {DeveloperError} granularity must be greater than zero.
 *
 *
 * @example
 * // Create an ellipse.
 * const ellipse = new Cesium.EllipseGeometry({
 *   center : Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883),
 *   semiMajorAxis : 500000.0,
 *   semiMinorAxis : 300000.0,
 *   rotation : Cesium.Math.toRadians(60.0)
 * });
 * const geometry = Cesium.EllipseGeometry.createGeometry(ellipse);
 *
 * @see EllipseGeometry.createGeometry
 */
function EllipseGeometry(options) {
  options = defaultValue(options, defaultValue.EMPTY_OBJECT);

  const center = options.center;
  const ellipsoid = defaultValue(options.ellipsoid, Ellipsoid.WGS84);
  const semiMajorAxis = options.semiMajorAxis;
  const semiMinorAxis = options.semiMinorAxis;
  const granularity = defaultValue(
    options.granularity,
    CesiumMath.RADIANS_PER_DEGREE
  );
  const vertexFormat = defaultValue(options.vertexFormat, VertexFormat.DEFAULT);

  //>>includeStart('debug', pragmas.debug);
  Check.defined("options.center", center);
  Check.typeOf.number("options.semiMajorAxis", semiMajorAxis);
  Check.typeOf.number("options.semiMinorAxis", semiMinorAxis);
  if (semiMajorAxis < semiMinorAxis) {
    throw new DeveloperError(
      "semiMajorAxis must be greater than or equal to the semiMinorAxis."
    );
  }
  if (granularity <= 0.0) {
    throw new DeveloperError("granularity must be greater than zero.");
  }
  //>>includeEnd('debug');

  const height = defaultValue(options.height, 0.0);
  const extrudedHeight = defaultValue(options.extrudedHeight, height);

  this._center = Cartesian3.clone(center);
  this._semiMajorAxis = semiMajorAxis;
  this._semiMinorAxis = semiMinorAxis;
  this._ellipsoid = Ellipsoid.clone(ellipsoid);
  this._rotation = defaultValue(options.rotation, 0.0);
  this._stRotation = defaultValue(options.stRotation, 0.0);
  this._height = Math.max(extrudedHeight, height);
  this._granularity = granularity;
  this._vertexFormat = VertexFormat.clone(vertexFormat);
  this._extrudedHeight = Math.min(extrudedHeight, height);
  this._shadowVolume = defaultValue(options.shadowVolume, false);
  this._workerName = "createEllipseGeometry";
  this._offsetAttribute = options.offsetAttribute;

  this._rectangle = undefined;
  this._textureCoordinateRotationPoints = undefined;
}

/**
 * The number of elements used to pack the object into an array.
 * @type {Number}
 */
EllipseGeometry.packedLength =
  Cartesian3.packedLength +
  Ellipsoid.packedLength +
  VertexFormat.packedLength +
  9;

/**
 * Stores the provided instance into the provided array.
 *
 * @param {EllipseGeometry} value The value to pack.
 * @param {Number[]} array The array to pack into.
 * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
 *
 * @returns {Number[]} The array that was packed into
 */
EllipseGeometry.pack = function (value, array, startingIndex) {
  //>>includeStart('debug', pragmas.debug);
  Check.defined("value", value);
  Check.defined("array", array);
  //>>includeEnd('debug');

  startingIndex = defaultValue(startingIndex, 0);

  Cartesian3.pack(value._center, array, startingIndex);
  startingIndex += Cartesian3.packedLength;

  Ellipsoid.pack(value._ellipsoid, array, startingIndex);
  startingIndex += Ellipsoid.packedLength;

  VertexFormat.pack(value._vertexFormat, array, startingIndex);
  startingIndex += VertexFormat.packedLength;

  array[startingIndex++] = value._semiMajorAxis;
  array[startingIndex++] = value._semiMinorAxis;
  array[startingIndex++] = value._rotation;
  array[startingIndex++] = value._stRotation;
  array[startingIndex++] = value._height;
  array[startingIndex++] = value._granularity;
  array[startingIndex++] = value._extrudedHeight;
  array[startingIndex++] = value._shadowVolume ? 1.0 : 0.0;
  array[startingIndex] = defaultValue(value._offsetAttribute, -1);

  return array;
};

const scratchCenter = new Cartesian3();
const scratchEllipsoid = new Ellipsoid();
const scratchVertexFormat = new VertexFormat();
const scratchOptions = {
  center: scratchCenter,
  ellipsoid: scratchEllipsoid,
  vertexFormat: scratchVertexFormat,
  semiMajorAxis: undefined,
  semiMinorAxis: undefined,
  rotation: undefined,
  stRotation: undefined,
  height: undefined,
  granularity: undefined,
  extrudedHeight: undefined,
  shadowVolume: undefined,
  offsetAttribute: undefined,
};

/**
 * Retrieves an instance from a packed array.
 *
 * @param {Number[]} array The packed array.
 * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
 * @param {EllipseGeometry} [result] The object into which to store the result.
 * @returns {EllipseGeometry} The modified result parameter or a new EllipseGeometry instance if one was not provided.
 */
EllipseGeometry.unpack = function (array, startingIndex, result) {
  //>>includeStart('debug', pragmas.debug);
  Check.defined("array", array);
  //>>includeEnd('debug');

  startingIndex = defaultValue(startingIndex, 0);

  const center = Cartesian3.unpack(array, startingIndex, scratchCenter);
  startingIndex += Cartesian3.packedLength;

  const ellipsoid = Ellipsoid.unpack(array, startingIndex, scratchEllipsoid);
  startingIndex += Ellipsoid.packedLength;

  const vertexFormat = VertexFormat.unpack(
    array,
    startingIndex,
    scratchVertexFormat
  );
  startingIndex += VertexFormat.packedLength;

  const semiMajorAxis = array[startingIndex++];
  const semiMinorAxis = array[startingIndex++];
  const rotation = array[startingIndex++];
  const stRotation = array[startingIndex++];
  const height = array[startingIndex++];
  const granularity = array[startingIndex++];
  const extrudedHeight = array[startingIndex++];
  const shadowVolume = array[startingIndex++] === 1.0;
  const offsetAttribute = array[startingIndex];

  if (!defined(result)) {
    scratchOptions.height = height;
    scratchOptions.extrudedHeight = extrudedHeight;
    scratchOptions.granularity = granularity;
    scratchOptions.stRotation = stRotation;
    scratchOptions.rotation = rotation;
    scratchOptions.semiMajorAxis = semiMajorAxis;
    scratchOptions.semiMinorAxis = semiMinorAxis;
    scratchOptions.shadowVolume = shadowVolume;
    scratchOptions.offsetAttribute =
      offsetAttribute === -1 ? undefined : offsetAttribute;

    return new EllipseGeometry(scratchOptions);
  }

  result._center = Cartesian3.clone(center, result._center);
  result._ellipsoid = Ellipsoid.clone(ellipsoid, result._ellipsoid);
  result._vertexFormat = VertexFormat.clone(vertexFormat, result._vertexFormat);
  result._semiMajorAxis = semiMajorAxis;
  result._semiMinorAxis = semiMinorAxis;
  result._rotation = rotation;
  result._stRotation = stRotation;
  result._height = height;
  result._granularity = granularity;
  result._extrudedHeight = extrudedHeight;
  result._shadowVolume = shadowVolume;
  result._offsetAttribute =
    offsetAttribute === -1 ? undefined : offsetAttribute;

  return result;
};

/**
 * Computes the bounding rectangle based on the provided options
 *
 * @param {Object} options Object with the following properties:
 * @param {Cartesian3} options.center The ellipse's center point in the fixed frame.
 * @param {Number} options.semiMajorAxis The length of the ellipse's semi-major axis in meters.
 * @param {Number} options.semiMinorAxis The length of the ellipse's semi-minor axis in meters.
 * @param {Ellipsoid} [options.ellipsoid=Ellipsoid.WGS84] The ellipsoid the ellipse will be on.
 * @param {Number} [options.rotation=0.0] The angle of rotation counter-clockwise from north.
 * @param {Number} [options.granularity=CesiumMath.RADIANS_PER_DEGREE] The angular distance between points on the ellipse in radians.
 * @param {Rectangle} [result] An object in which to store the result
 *
 * @returns {Rectangle} The result rectangle
 */
EllipseGeometry.computeRectangle = function (options, result) {
  options = defaultValue(options, defaultValue.EMPTY_OBJECT);

  const center = options.center;
  const ellipsoid = defaultValue(options.ellipsoid, Ellipsoid.WGS84);
  const semiMajorAxis = options.semiMajorAxis;
  const semiMinorAxis = options.semiMinorAxis;
  const granularity = defaultValue(
    options.granularity,
    CesiumMath.RADIANS_PER_DEGREE
  );
  const rotation = defaultValue(options.rotation, 0.0);

  //>>includeStart('debug', pragmas.debug);
  Check.defined("options.center", center);
  Check.typeOf.number("options.semiMajorAxis", semiMajorAxis);
  Check.typeOf.number("options.semiMinorAxis", semiMinorAxis);
  if (semiMajorAxis < semiMinorAxis) {
    throw new DeveloperError(
      "semiMajorAxis must be greater than or equal to the semiMinorAxis."
    );
  }
  if (granularity <= 0.0) {
    throw new DeveloperError("granularity must be greater than zero.");
  }
  //>>includeEnd('debug');

  return computeRectangle(
    center,
    semiMajorAxis,
    semiMinorAxis,
    rotation,
    granularity,
    ellipsoid,
    result
  );
};

/**
 * Computes the geometric representation of a ellipse on an ellipsoid, including its vertices, indices, and a bounding sphere.
 *
 * @param {EllipseGeometry} ellipseGeometry A description of the ellipse.
 * @returns {Geometry|undefined} The computed vertices and indices.
 */
EllipseGeometry.createGeometry = function (ellipseGeometry) {
  if (
    ellipseGeometry._semiMajorAxis <= 0.0 ||
    ellipseGeometry._semiMinorAxis <= 0.0
  ) {
    return;
  }

  const height = ellipseGeometry._height;
  const extrudedHeight = ellipseGeometry._extrudedHeight;
  const extrude = !CesiumMath.equalsEpsilon(
    height,
    extrudedHeight,
    0,
    CesiumMath.EPSILON2
  );

  ellipseGeometry._center = ellipseGeometry._ellipsoid.scaleToGeodeticSurface(
    ellipseGeometry._center,
    ellipseGeometry._center
  );
  const options = {
    center: ellipseGeometry._center,
    semiMajorAxis: ellipseGeometry._semiMajorAxis,
    semiMinorAxis: ellipseGeometry._semiMinorAxis,
    ellipsoid: ellipseGeometry._ellipsoid,
    rotation: ellipseGeometry._rotation,
    height: height,
    granularity: ellipseGeometry._granularity,
    vertexFormat: ellipseGeometry._vertexFormat,
    stRotation: ellipseGeometry._stRotation,
  };
  let geometry;
  if (extrude) {
    options.extrudedHeight = extrudedHeight;
    options.shadowVolume = ellipseGeometry._shadowVolume;
    options.offsetAttribute = ellipseGeometry._offsetAttribute;
    geometry = computeExtrudedEllipse(options);
  } else {
    geometry = computeEllipse(options);

    if (defined(ellipseGeometry._offsetAttribute)) {
      const length = geometry.attributes.position.values.length;
      const offsetValue =
        ellipseGeometry._offsetAttribute === GeometryOffsetAttribute.NONE
          ? 0
          : 1;
      const applyOffset = new Uint8Array(length / 3).fill(offsetValue);
      geometry.attributes.applyOffset = new GeometryAttribute({
        componentDatatype: ComponentDatatype.UNSIGNED_BYTE,
        componentsPerAttribute: 1,
        values: applyOffset,
      });
    }
  }

  return new Geometry({
    attributes: geometry.attributes,
    indices: geometry.indices,
    primitiveType: PrimitiveType.TRIANGLES,
    boundingSphere: geometry.boundingSphere,
    offsetAttribute: ellipseGeometry._offsetAttribute,
  });
};

/**
 * @private
 */
EllipseGeometry.createShadowVolume = function (
  ellipseGeometry,
  minHeightFunc,
  maxHeightFunc
) {
  const granularity = ellipseGeometry._granularity;
  const ellipsoid = ellipseGeometry._ellipsoid;

  const minHeight = minHeightFunc(granularity, ellipsoid);
  const maxHeight = maxHeightFunc(granularity, ellipsoid);

  return new EllipseGeometry({
    center: ellipseGeometry._center,
    semiMajorAxis: ellipseGeometry._semiMajorAxis,
    semiMinorAxis: ellipseGeometry._semiMinorAxis,
    ellipsoid: ellipsoid,
    rotation: ellipseGeometry._rotation,
    stRotation: ellipseGeometry._stRotation,
    granularity: granularity,
    extrudedHeight: minHeight,
    height: maxHeight,
    vertexFormat: VertexFormat.POSITION_ONLY,
    shadowVolume: true,
  });
};

function textureCoordinateRotationPoints(ellipseGeometry) {
  const stRotation = -ellipseGeometry._stRotation;
  if (stRotation === 0.0) {
    return [0, 0, 0, 1, 1, 0];
  }

  const cep = EllipseGeometryLibrary.computeEllipsePositions(
    {
      center: ellipseGeometry._center,
      semiMajorAxis: ellipseGeometry._semiMajorAxis,
      semiMinorAxis: ellipseGeometry._semiMinorAxis,
      rotation: ellipseGeometry._rotation,
      granularity: ellipseGeometry._granularity,
    },
    false,
    true
  );
  const positionsFlat = cep.outerPositions;
  const positionsCount = positionsFlat.length / 3;
  const positions = new Array(positionsCount);
  for (let i = 0; i < positionsCount; ++i) {
    positions[i] = Cartesian3.fromArray(positionsFlat, i * 3);
  }

  const ellipsoid = ellipseGeometry._ellipsoid;
  const boundingRectangle = ellipseGeometry.rectangle;
  return Geometry._textureCoordinateRotationPoints(
    positions,
    stRotation,
    ellipsoid,
    boundingRectangle
  );
}

Object.defineProperties(EllipseGeometry.prototype, {
  /**
   * @private
   */
  rectangle: {
    get: function () {
      if (!defined(this._rectangle)) {
        this._rectangle = computeRectangle(
          this._center,
          this._semiMajorAxis,
          this._semiMinorAxis,
          this._rotation,
          this._granularity,
          this._ellipsoid
        );
      }
      return this._rectangle;
    },
  },
  /**
   * For remapping texture coordinates when rendering EllipseGeometries as GroundPrimitives.
   * @private
   */
  textureCoordinateRotationPoints: {
    get: function () {
      if (!defined(this._textureCoordinateRotationPoints)) {
        this._textureCoordinateRotationPoints = textureCoordinateRotationPoints(
          this
        );
      }
      return this._textureCoordinateRotationPoints;
    },
  },
});
export default EllipseGeometry;