Mercator (parent patrimoine de base SIRIUS 4.1 API)

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:

$Id$

Author:

Galpin Thomas

See Also:

Serialized Form

Concurrency :

not thread-safe

Field Summary

Fields
Modifier and Type Field and Description

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

Fields
Modifier and Type	Field and Description
`static double`	`MAX_LATITUDE` Maximum latitude from which a Mercator transformation can be defined.

Constructor Summary

Constructors
Constructor and Description
`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

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`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 PatriusException
```
    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:
    
    PatriusException - thrown if projection could not be computed
  - applyTo
```
public Vector2D applyTo(double lat,
                        double lon)
                 throws PatriusException
```
    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:
    
    PatriusException - thrown if projection could not be computed
  - applyInverseTo
```
public GeodeticPoint applyInverseTo(double x,
                                    double y,
                                    double alt)
                             throws PatriusException
```
    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:
    
    PatriusException - thrown if inverse projection could not be computed
  - applyInverseTo
```
public GeodeticPoint applyInverseTo(double x,
                                    double y)
                             throws PatriusException
```
    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:
    
    PatriusException - 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

Class Mercator

Field Summary

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Field Detail

MAX_LATITUDE

Constructor Detail

Mercator

Mercator

Method Detail

canMap

applyTo

applyTo

applyInverseTo

applyInverseTo

isConformal

isEquivalent

getLineProperty

getMaximumLatitude

getMaximumEastingValue

getAzimuth

getMaximumNorthingValue

getScaleFactor

getDistortionFactor