Ellipsoid

new Cesium.Ellipsoid(x, y, z)

A quadratic surface defined in Cartesian coordinates by the equation (x / a)^2 + (y / b)^2 + (z / c)^2 = 1. Primarily used by Cesium to represent the shape of planetary bodies. Rather than constructing this object directly, one of the provided constants is normally used.
Name Type Default Description
x number 0 optional The radius in the x direction.
y number 0 optional The radius in the y direction.
z number 0 optional The radius in the z direction.
Throws:
  • DeveloperError : All radii components must be greater than or equal to zero.
See:

Members

static constant Cesium.Ellipsoid.MOON : Ellipsoid

An Ellipsoid instance initialized to a sphere with the lunar radius.

static Cesium.Ellipsoid.packedLength : number

The number of elements used to pack the object into an array.

static constant Cesium.Ellipsoid.UNIT_SPHERE : Ellipsoid

An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0).

static constant Cesium.Ellipsoid.WGS84 : Ellipsoid

An Ellipsoid instance initialized to the WGS84 standard.

readonly maximumRadius : number

Gets the maximum radius of the ellipsoid.

readonly minimumRadius : number

Gets the minimum radius of the ellipsoid.
Gets one over the radii of the ellipsoid.
Gets one over the squared radii of the ellipsoid.
Gets the radii of the ellipsoid.
Gets the squared radii of the ellipsoid.
Gets the radii of the ellipsoid raise to the fourth power.

Methods

static Cesium.Ellipsoid.clone(ellipsoid, result)Ellipsoid

Duplicates an Ellipsoid instance.
Name Type Description
ellipsoid Ellipsoid The ellipsoid to duplicate.
result Ellipsoid optional The object onto which to store the result, or undefined if a new instance should be created.
Returns:
The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined)

static Cesium.Ellipsoid.fromCartesian3(cartesian, result)Ellipsoid

Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions.
Name Type Default Description
cartesian Cartesian3 Cartesian3.ZERO optional The ellipsoid's radius in the x, y, and z directions.
result Ellipsoid optional The object onto which to store the result, or undefined if a new instance should be created.
Returns:
A new Ellipsoid instance.
Throws:
  • DeveloperError : All radii components must be greater than or equal to zero.
See:

static Cesium.Ellipsoid.pack(value, array, startingIndex)Array.<number>

Stores the provided instance into the provided array.
Name Type Default Description
value Ellipsoid The value to pack.
array Array.<number> The array to pack into.
startingIndex number 0 optional The index into the array at which to start packing the elements.
Returns:
The array that was packed into

static Cesium.Ellipsoid.unpack(array, startingIndex, result)Ellipsoid

Retrieves an instance from a packed array.
Name Type Default Description
array Array.<number> The packed array.
startingIndex number 0 optional The starting index of the element to be unpacked.
result Ellipsoid optional The object into which to store the result.
Returns:
The modified result parameter or a new Ellipsoid instance if one was not provided.

cartesianArrayToCartographicArray(cartesians, result)Array.<Cartographic>

Converts the provided array of cartesians to an array of cartographics.
Name Type Description
cartesians Array.<Cartesian3> An array of Cartesian positions.
result Array.<Cartographic> optional The object onto which to store the result.
Returns:
The modified result parameter or a new Array instance if none was provided.
Example:
//Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid.
const positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73),
                 new Cesium.Cartesian3(17832.13, 83234.53, 952313.73),
                 new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)]
const cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions);

cartesianToCartographic(cartesian, result)Cartographic

Converts the provided cartesian to cartographic representation. The cartesian is undefined at the center of the ellipsoid.
Name Type Description
cartesian Cartesian3 The Cartesian position to convert to cartographic representation.
result Cartographic optional The object onto which to store the result.
Returns:
The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
Example:
//Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid.
const position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73);
const cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position);

cartographicArrayToCartesianArray(cartographics, result)Array.<Cartesian3>

Converts the provided array of cartographics to an array of Cartesians.
Name Type Description
cartographics Array.<Cartographic> An array of cartographic positions.
result Array.<Cartesian3> optional The object onto which to store the result.
Returns:
The modified result parameter or a new Array instance if none was provided.
Example:
//Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid.
const positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0),
                 new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100),
                 new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)];
const cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions);

cartographicToCartesian(cartographic, result)Cartesian3

Converts the provided cartographic to Cartesian representation.
Name Type Description
cartographic Cartographic The cartographic position.
result Cartesian3 optional The object onto which to store the result.
Returns:
The modified result parameter or a new Cartesian3 instance if none was provided.
Example:
//Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid.
const position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000);
const cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position);
Duplicates an Ellipsoid instance.
Name Type Description
result Ellipsoid optional The object onto which to store the result, or undefined if a new instance should be created.
Returns:
The cloned Ellipsoid.
Compares this Ellipsoid against the provided Ellipsoid componentwise and returns true if they are equal, false otherwise.
Name Type Description
right Ellipsoid optional The other Ellipsoid.
Returns:
true if they are equal, false otherwise.

geocentricSurfaceNormal(cartesian, result)Cartesian3

Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.
Name Type Description
cartesian Cartesian3 The Cartesian for which to to determine the geocentric normal.
result Cartesian3 optional The object onto which to store the result.
Returns:
The modified result parameter or a new Cartesian3 instance if none was provided.

geodeticSurfaceNormal(cartesian, result)Cartesian3

Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
Name Type Description
cartesian Cartesian3 The Cartesian position for which to to determine the surface normal.
result Cartesian3 optional The object onto which to store the result.
Returns:
The modified result parameter or a new Cartesian3 instance if none was provided, or undefined if a normal cannot be found.

geodeticSurfaceNormalCartographic(cartographic, result)Cartesian3

Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
Name Type Description
cartographic Cartographic The cartographic position for which to to determine the geodetic normal.
result Cartesian3 optional The object onto which to store the result.
Returns:
The modified result parameter or a new Cartesian3 instance if none was provided.

getLocalCurvature(surfacePosition, result)Cartesian2

Computes the ellipsoid curvatures at a given position on the surface.
Name Type Description
surfacePosition Cartesian3 The position on the ellipsoid surface where curvatures will be calculated.
result Cartesian2 optional The cartesian to which to copy the result, or undefined to create and return a new instance.
Returns:
The local curvature of the ellipsoid surface at the provided position, in east and north directions.
Throws:

getSurfaceNormalIntersectionWithZAxis(position, buffer, result)Cartesian3|undefined

Computes a point which is the intersection of the surface normal with the z-axis.
Name Type Default Description
position Cartesian3 the position. must be on the surface of the ellipsoid.
buffer number 0.0 optional A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid. In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center. In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis). Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2
result Cartesian3 optional The cartesian to which to copy the result, or undefined to create and return a new instance.
Returns:
the intersection point if it's inside the ellipsoid, undefined otherwise
Throws:

scaleToGeocentricSurface(cartesian, result)Cartesian3

Scales the provided Cartesian position along the geocentric surface normal so that it is on the surface of this ellipsoid.
Name Type Description
cartesian Cartesian3 The Cartesian position to scale.
result Cartesian3 optional The object onto which to store the result.
Returns:
The modified result parameter or a new Cartesian3 instance if none was provided.

scaleToGeodeticSurface(cartesian, result)Cartesian3

Scales the provided Cartesian position along the geodetic surface normal so that it is on the surface of this ellipsoid. If the position is at the center of the ellipsoid, this function returns undefined.
Name Type Description
cartesian Cartesian3 The Cartesian position to scale.
result Cartesian3 optional The object onto which to store the result.
Returns:
The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.

surfaceArea(rectangle)number

Computes an approximation of the surface area of a rectangle on the surface of an ellipsoid using Gauss-Legendre 10th order quadrature.
Name Type Description
rectangle Rectangle The rectangle used for computing the surface area.
Returns:
The approximate area of the rectangle on the surface of this ellipsoid.
Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'.
Returns:
A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.

transformPositionFromScaledSpace(position, result)Cartesian3

Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying its components by the result of Ellipsoid#radii.
Name Type Description
position Cartesian3 The position to transform.
result Cartesian3 optional The position to which to copy the result, or undefined to create and return a new instance.
Returns:
The position expressed in the unscaled space. The returned instance is the one passed as the result parameter if it is not undefined, or a new instance of it is.

transformPositionToScaledSpace(position, result)Cartesian3

Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying its components by the result of Ellipsoid#oneOverRadii.
Name Type Description
position Cartesian3 The position to transform.
result Cartesian3 optional The position to which to copy the result, or undefined to create and return a new instance.
Returns:
The position expressed in the scaled space. The returned instance is the one passed as the result parameter if it is not undefined, or a new instance of it is.
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