class Geocentric in Tinman.Terrain.Georef

The Geocentric class represents a geocentric coordinate system and provides methods for converting between geographic and cartesian coordinates.

sealed class

Geocentric

Remarks

The plain geocentric coordinate axes define a right-handed cartesian coordinate system:

• X : axis through the intersection of the equator with longitude 0°.
• Y : axis through the intersection of the equator with longitude 90°.
• Z : axis corresponding with the planet rotation axis (positive northwards).

After creating an Geocentric object, additional information must be given before non-ellipsoid height values can be used (see Vertical and Vertical). A custom matrix (see Transform) can be specified to transform the plain geocentric coordinate space.

Public / Constants

WGS84

A Geocentric object for WGS84.

public static readonly field	WGS84
type	Geocentric

Public / Attributes

SemiMajorAxis

The semi-major axis: b

public property	SemiMajorAxis { get }
type	float64
value		The value of a

SemiMinorAxis

The semi-minor axis: b

public property	SemiMinorAxis { get }
type	float64
value		The value of b

Unit

The length unit of the geocentric coordinates.

public property	Unit { get }
type	UnitOfMeasure
value	[not-null]	The length unit.

Public / Constructors

For

Creates a new instance of Geocentric.

public static method	For (GeodeticDatum datum)
type	Geocentric
params	datum	[not-null]	The geodetic datum to use.
returns		[not-null]	The Geocentric object.

Remarks:

The Meridian of datum will be used as longitude 0°.

---

Creates a new instance of Geocentric.

public static method	For (Ellipsoid ellipsoid, PrimeMeridian meridian = null)
type	Geocentric
params	ellipsoid	[not-null]	The ellipsoid.
	meridian		The prime meridian to use as longitude 0°. Defaults to null.
returns		[not-null]	The Geocentric object.

---

Creates a new instance of Geocentric.

public static method	For (float64 semiMajor, float64 semiMinor = 0, float64 meridian = 0, UnitOfMeasure unit = null)
type	Geocentric
params	semiMajor	[>0]	The semi-major axis, in cartesian units (see unit).
	semiMinor	[>=0]	The semi-minor axis, in cartesian units (see unit). If 0, the value of semiMajor will be used. Defaults to 0.
	meridian		The prime meridian to use as longitude 0°, in radians. Defaults to 0.
	unit		The cartesian unit. If null, Metre will be used. Defaults to null.
returns		[not-null]	The Geocentric object.

Public / Methods

ToGeocentric

Converts the given geographic coordinates to cartesian coordinates.

[Pure]
public method	ToGeocentric (LatLonHeight latLonHeight)
type	Vec3D
params	latLonHeight		The geographic coordinates.
returns			The geocentric coordinates.

---

Converts the given geographic coordinates to cartesian coordinates.

[Pure]
public method	ToGeocentric (Vec3D lonLatHeight, VerticalType vertical = VerticalType.Ellipsoid)
type	Vec3D
params	lonLatHeight		The geographic coordinates: X: longitude, in radians. Y: latitude, in radians. Z: height, in geocentric units (see Unit).
	vertical		The vertical coordinate type. Defaults to Ellipsoid.
returns			The geocentric coordinates.

---

Converts the given geographic coordinates to cartesian coordinates.

[Pure]
public method	ToGeocentric (Vec2D lonLat, float64 height = 0, VerticalType vertical = VerticalType.Ellipsoid)
type	Vec3D
params	lonLat		The geographic coordinates: X: longitude, in radians. Y: latitude, in radians.
	height		The height, in geocentric units (see Unit). Defaults to 0.
	vertical		The vertical coordinate type. Defaults to Ellipsoid.
returns			The geocentric coordinates.

---

Converts the given geographic coordinates to cartesian coordinates.

[Pure]
public method	ToGeocentric (LatLon latLon, float64 height = 0, VerticalType vertical = VerticalType.Ellipsoid)
type	Vec3D
params	latLon		The geographic coordinates.
	height		The height, in geocentric units (see Unit). Defaults to 0.
	vertical		The vertical coordinate type. Defaults to Ellipsoid.
returns			The geocentric coordinates.

---

Converts the given geographic coordinates to cartesian coordinates.

[Pure]
public method	ToGeocentric (float64 latitude, float64 longitude, float64 height = 0)
type	Vec3D
params	latitude		The latitude, in radians.
	longitude		The longitude, in radians.
	height		The ellipsoid height, in geocentric units (see Unit). Defaults to 0.
returns			The geocentric coordinates.

---

Converts the given geographic coordinates to cartesian coordinates.

[Pure]
public method	ToGeocentric (float64 latitude, float64 longitude, float64 height, VerticalType vertical)
type	Vec3D
params	latitude		The latitude, in radians.
	longitude		The longitude, in radians.
	height		The height, in geocentric units (see Unit).
	vertical		The vertical coordinate type.
returns			The geocentric coordinates.

ToGeographic2D

Converts the given cartesian coordinates to geographic coordinates.

[Pure]
public method	ToGeographic2D (Vec3D v)
type	Vec2D
params	v		The cartesian coordinates.
returns			The geographic coordinates: X: longitude, in radians Y: latitude, in radians.

---

Converts the given cartesian coordinates to geographic coordinates.

[Pure]
public method	ToGeographic2D (float64 x, float64 y, float64 z)
type	Vec2D
params	x		The cartesian X-coordinate.
	y		The cartesian Y-coordinate.
	z		The cartesian Z-coordinate.
returns			The geographic coordinates: X: longitude, in radians Y: latitude, in radians.

ToGeographic3D

Converts the given cartesian coordinates to geographic coordinates.

[Pure]
public method	ToGeographic3D (Vec3D v)
type	Vec3D
params	v		The cartesian coordinates.
returns			The geographic coordinates: X: longitude, in radians Y: latitude, in radians Z: ellipsoid height, in cartesian units (see Unit).

---

Converts the given cartesian coordinates to geographic coordinates.

[Pure]
public method	ToGeographic3D (float64 x, float64 y, float64 z)
type	Vec3D
params	x		The cartesian X-coordinate.
	y		The cartesian Y-coordinate.
	z		The cartesian Z-coordinate.
returns			The geographic coordinates: X: longitude, in radians Y: latitude, in radians Z: ellipsoid height, in cartesian units (see Unit).

ToLatLon

Converts the given cartesian coordinates to geographic coordinates.

[Pure]
public method	ToLatLon (Vec3D v)
type	LatLon
params	v		The cartesian coordinates.
returns			The geographic coordinates: X: longitude, in radians Y: latitude, in radians Z: ellipsoid height, in cartesian units (see Unit).

---

Converts the given cartesian coordinates to geographic coordinates.

[Pure]
public method	ToLatLon (float64 x, float64 y, float64 z)
type	LatLon
params	x		The cartesian X-coordinate.
	y		The cartesian Y-coordinate.
	z		The cartesian Z-coordinate.
returns			The geographic coordinates: X: longitude, in radians Y: latitude, in radians Z: ellipsoid height, in cartesian units (see Unit).

ToLatLonHeight

Converts the given cartesian coordinates to geographic coordinates.

[Pure]
public method	ToLatLonHeight (Vec3D v, VerticalType vertical)
type	LatLonHeight
params	v		The cartesian coordinates.
	vertical		The vertical coordinate type.
returns			The geographic coordinates: X: longitude, in radians Y: latitude, in radians Z: ellipsoid height, in cartesian units (see Unit).

---

Converts the given cartesian coordinates to geographic coordinates.

[Pure]
public method	ToLatLonHeight (float64 x, float64 y, float64 z, VerticalType vertical)
type	LatLonHeight
params	x		The cartesian X-coordinate.
	y		The cartesian Y-coordinate.
	z		The cartesian Z-coordinate.
	vertical		The vertical coordinate type.
returns			The geographic coordinates: X: longitude, in radians Y: latitude, in radians Z: ellipsoid height, in cartesian units (see Unit).

ToNormal

Computes the surface normal vector for the given geographic coordinates.

[Pure]
public method	ToNormal (Vec2D lonLat)
type	Vec3D
params	lonLat		The geographic coordinates: X: longitude, in radians. Y: latitude, in radians.
returns			The unit-length surface normal vector.

---

Computes the surface normal vector for the given geographic coordinates.

[Pure]
public method	ToNormal (LatLon latLon)
type	Vec3D
params	latLon		The geographic coordinates.
returns			The unit-length surface normal vector.

---

Computes the surface normal vector for the given geographic coordinates.

[Pure]
public method	ToNormal (float64 latitude, float64 longitude)
type	Vec3D
params	latitude		The latitude, in radians.
	longitude		The longitude, in radians.
returns			The unit-length surface normal vector.

ToVerticalOffset

Computes the offset from the given vertical coordinate type to ellipsoid height.

[Pure]
public method	ToVerticalOffset (Vec2D lonLat, VerticalType vertical)
type	float64
params	lonLat		The geographic coordinates: X: longitude, in radians. Y: latitude, in radians.
	vertical		The vertical coordinate type.
returns			The vertical offset.

Remarks:

The returned offset is defined as follows:

offset     = ellipsoid  - coordinate
ellipsoid  = coordinate + offset
coordinate = ellipsoid  - offset

where coordinate is the vertical coordinate of type vertical and ellipsoid is the ellipsoid height of some point in world-space.

---

Computes the offset from the given vertical coordinate type to ellipsoid height.

[Pure]
public method	ToVerticalOffset (LatLon latLon, VerticalType vertical)
type	float64
params	latLon		The geographic coordinates.
	vertical		The vertical coordinate type.
returns			The vertical offset.

Remarks:

The returned offset is defined as follows:

offset     = ellipsoid  - coordinate
ellipsoid  = coordinate + offset
coordinate = ellipsoid  - offset

where coordinate is the vertical coordinate of type vertical and ellipsoid is the ellipsoid height of some point in world-space.

---

Computes the offset from the given vertical coordinate type to ellipsoid height.

[Pure]
public method	ToVerticalOffset (float64 latitude, float64 longitude, VerticalType vertical)
type	float64
params	latitude		The latitude, in radians.
	longitude		The longitude, in radians.
	vertical		The vertical coordinate type.
returns			The vertical offset.

Remarks:

The returned offset is defined as follows:

offset     = ellipsoid  - coordinate
ellipsoid  = coordinate + offset
coordinate = ellipsoid  - offset

where coordinate is the vertical coordinate of type vertical and ellipsoid is the ellipsoid height of some point in world-space.

ToVerticalType

Translates the given geographic coordinates to the specified vertical coordinate type.

[Pure]
public method	ToVerticalType (LatLonHeight coords, VerticalType vertical)
type	LatLonHeight
params	coords		The geographic coordinates.
	vertical		The target vertical coordinate type.
returns			The resulting coordinates.

Transform

Transform the geocentric coordinate space.

[Pure]
public method	Transform (Mat4D matrix)
type	Geocentric
params	matrix		The transformation matrix.
returns		[not-null]	The resulting Geocentric object.

Remarks:

The output coordinates of ToGeocentric are transformed by matrix. The input coordinates of ToGeographic are transformed by the inverse of matrix. The output vectors of ToNormal are transformed by the inverse transpose of matrix.

Vertical

Provides additional objects for handling the vertical coordinate types HeightMesh.

[Pure]
public method	Vertical (HeightAboveGround mesh)
type	Geocentric
params	mesh		The geocentric terrain mesh or null. The terrain mesh is used to compute vertical values of type HeightMesh. If null, Height values will computed instead. The geometry (see IGeometry) of the terrain mesh is assumed to be based on the same coordinate system as this object.
returns		[not-null]	The resulting Geocentric object.

---

Provides additional objects for handling the vertical coordinate types Gravity and Height.

[Pure]
public method	Vertical (IHeightmap gravity, IHeightmap elevation, bool elevationMode)
type	Geocentric
params	gravity		The gravity-related vertical offsets or null. The heightmap elevation is interpreted as the difference from the ellipsoid surface to the equipotential surface of the gravity model. If null, all gravity-related vertical offsets are assumed to be zero.
	elevation		The elevation model or null. The heightmap elevation is interpreted according to elevationMode. If null, all elevation values are assumed to be zero.
	elevationMode		Defines how to interpret elevation values: true: Elevation values are relative to the gravity model. false: Elevation values are relative to the ellipsoid surface.
returns		[not-null]	The resulting Geocentric object.

Remarks:

The given heightmaps are assumed to be of type Cube and to have the same geodetic datum as this object is using.