fr.cnes.sirius.patrius.projections
Class Mercator

java.lang.Object
  fr.cnes.sirius.patrius.projections.AbstractProjection
      fr.cnes.sirius.patrius.projections.Mercator

All Implemented Interfaces:

IProjection, Serializable

Direct Known Subclasses:

GeneralizedFlamsteedSamson

public class Mercator
extends AbstractProjection

The Mercator projection is a cylindrical map projection which became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known loxodromes, as straight segments. While the linear scale is constant in all directions around any point, thus preserving the angles and the shapes of small objects (which makes the projection conformal), the Mercator projection distorts the size and shape of large objects, as the scale increases from the Equator to the poles, where it becomes infinite.

The mercator projection is defined by a point, called pivot. The longitude of this point is the center of X axis of projected point. The latitude of this point is used to compute the scaleFactor. The origin of Y axis is always the equator parallel. Default pivot is (lat=0,lon=0).

Is an azimuth is given to the Mercator projection, the (X,Y) frame will be rotated, as Y axis is folliwing the given cap. Default azimuth is 0.

The inverse computation can be done using series, or by an iterative way The series are two times faster, but the precision is 5e-5 meters instead of 1e-8 meters.

Since:

3.2

Version:

$Id: Mercator.java 17585 2017-05-10 13:27:59Z bignon $

Author:

Galpin Thomas

See Also:

Serialized Form

Concurrency :

not thread-safe

Field Summary

static double

MAX_LATITUDE Maximum latitude from which a Mercator transformation can be defined.

Constructor Summary

Mercator(double centralMeridian, ProjectionEllipsoid ref)
Constructor with default values : The latitude of pivot is 0 azimuth is null (no rotation) centered is false.

Mercator(GeodeticPoint pivotIn, ProjectionEllipsoid shape, double azimuthIn, boolean centeredIn, boolean seriesIn)
Complete constructor.

Method Summary

GeodeticPoint	applyInverseTo(double x, double y) Inverse projection.
GeodeticPoint	applyInverseTo(double x, double y, double alt) This is the Two standard parallel Mercator Projection model.
Vector2D	applyTo(double lat, double lon) Returns Easting value and Northing value in meters from latitude and longitude coordinates.
Vector2D	applyTo(GeodeticPoint geodeticPoint) Returns Easting value and Northing value in meters from geodetic coordinates.
boolean	canMap(GeodeticPoint coordinates) Returns a boolean depending if the geodetic point can be map with the selected projection method.
double	getAzimuth() Get the azimuth of the projection (CLOCKWISE).
double	getDistortionFactor(double lat) Returns the scale factor at a specific latitude.
EnumLineProperty	getLineProperty() Getter for line property .
double	getMaximumEastingValue() Getter for the maximum value for X projected.
double	getMaximumLatitude() Getter for the maximum latitude that the projection can map.
double	getMaximumNorthingValue() Get the maximum northing value in meters.
double	getScaleFactor(double lat) Returns the scale factor at a specific latitude.
boolean	isConformal() Inform the user if the direct transformation is a conformal 's one (If yes, it preserves angles).
boolean	isEquivalent() Inform the user if the direct transformation is an equivalent 's one (If yes, it preserves surfaces).

Methods inherited from class fr.cnes.sirius.patrius.projections.AbstractProjection

applyInverseTo, applyInverseTo, applyTo, applyToAndDiscretize, discretize, discretizeAndApplyTo, discretizeCircleAndApplyTo, discretizeRhumbAndApplyTo, getPivotPoint, getReference

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

MAX_LATITUDE

public static final double MAX_LATITUDE

Maximum latitude from which a Mercator transformation can be defined.

See Also:

Constant Field Values

Constructor Detail

Mercator

public Mercator(GeodeticPoint pivotIn,
                ProjectionEllipsoid shape,
                double azimuthIn,
                boolean centeredIn,
                boolean seriesIn)

Complete constructor. This is the One standard parallel Mercator Projection with a scale factor at the natural origin. The latitude is here defined as being the Equator. The central meridian is defined as the map center longitude in radians. The scale factor is defined at the natural origin (Equator).

Parameters:

pivotIn - pivot point used for projection

shape - reference shape used for projection

azimuthIn - is angle from the north direction to the current direction in CLOCKWISE sense

centeredIn - if true, Y coordinates equal 0 in pivot point. The rotation if around pivot.

seriesIn - boolean indicating if the inverse projection uses a direct method with series, or an iterative method

Mercator

public Mercator(double centralMeridian,
                ProjectionEllipsoid ref)

Constructor with default values :

• The latitude of pivot is 0
• azimuth is null (no rotation)
• centered is false.

Parameters:

centralMeridian - central meridian

ref - reference shape

Method Detail

canMap

public final boolean canMap(GeodeticPoint coordinates)

Returns a boolean depending if the geodetic point can be map with the selected projection method..

Parameters:

coordinates - geodetic point to test if representable.

Returns:

True if the geodetic point can be represented on the map with the chosen projection method.

applyTo

public Vector2D applyTo(GeodeticPoint geodeticPoint)
                 throws OrekitException

Returns Easting value and Northing value in meters from geodetic coordinates.

Parameters:

geodeticPoint - the geodetic point to transform.

Returns:

Vector2D containing Easting value and Northing value in meters.

Throws:

OrekitException - thrown if projection could not be computed

applyTo

public Vector2D applyTo(double lat,
                        double lon)
                 throws OrekitException

Returns Easting value and Northing value in meters from latitude and longitude coordinates.

Parameters:

lat - latitude of the point to project.

lon - longitude of the point to project.

Returns:

Vector2D containing Easting value and Northing value in meters.

Throws:

OrekitException - thrown if projection could not be computed

applyInverseTo

public GeodeticPoint applyInverseTo(double x,
                                    double y,
                                    double alt)
                             throws OrekitException

This is the Two standard parallel Mercator Projection model. The latitude and the longitude of the given point to convert can be defined from any natural origin and the user can set the altitude.

Parameters:

x - abscissa coordinate

y - ordinate coordinate

alt - altitude coordinate

Returns:

coordinate

Throws:

OrekitException - thrown if inverse projection could not be computed

applyInverseTo

public GeodeticPoint applyInverseTo(double x,
                                    double y)
                             throws OrekitException

Inverse projection. Returns geodetic coordinates. This is the inverse transformation process to convert two dimensional map coordinates into geodetics one. The iterative method used is a Newton-Raphson iterative process. We're searching the solution of F(phi) = 0. At each iterations, we compute a new value of phi : phi' = phi - F(phi)/F'(phi) where phi is the trial value, F(phi) = y(phi) - phi, with y(phi) the direct Mercator transformation, and F'(phi) the derive function of y(phi). The stop condition is satisfied when F(phi) < epsilon (here equal at 1E-14). This method returns geodetic coordinates. The iterative process stop if the iteration's number is bigger than 100.

Parameters:

x - abscissa coordinate

y - ordinate coordinate

Returns:

geodetic coordinates.

Throws:

OrekitException - thrown if inverse projection could not be computed

isConformal

public boolean isConformal()

Inform the user if the direct transformation is a conformal 's one (If yes, it preserves angles).

Returns:

a boolean.

isEquivalent

public boolean isEquivalent()

Inform the user if the direct transformation is an equivalent 's one (If yes, it preserves surfaces).

Returns:

a boolean.

getLineProperty

public EnumLineProperty getLineProperty()

Getter for line property .

Returns:

line property.

getMaximumLatitude

public final double getMaximumLatitude()

Getter for the maximum latitude that the projection can map.

Returns:

Maximum latitude that the projection can map.

getMaximumEastingValue

public final double getMaximumEastingValue()

Getter for the maximum value for X projected.

Returns:

the Maximum value for X projected.

getAzimuth

public double getAzimuth()

Get the azimuth of the projection (CLOCKWISE).

Returns:

the azimuth (CLOCKWISE)

getMaximumNorthingValue

public final double getMaximumNorthingValue()

Get the maximum northing value in meters.

Returns:

maximum northing value in meters.

getScaleFactor

public final double getScaleFactor(double lat)

Returns the scale factor at a specific latitude. The result is the fraction Mercator distance / real distance.

Parameters:

lat - latitude

Returns:

the scale factor

getDistortionFactor

public final double getDistortionFactor(double lat)

Returns the scale factor at a specific latitude. The result is the fraction Mercator distance / real distance.

Specified by:

getDistortionFactor in class AbstractProjection

Parameters:

lat - latitude

Returns:

the distortion factor