fr.cnes.sirius.patrius.projections

Class GeneralizedFlamsteedSamson

java.lang.Object

fr.cnes.sirius.patrius.projections.AbstractProjection

fr.cnes.sirius.patrius.projections.Mercator

fr.cnes.sirius.patrius.projections.GeneralizedFlamsteedSamson

All Implemented Interfaces:

IProjection, Serializable

public class GeneralizedFlamsteedSamson
extends Mercator

Despite the common name, the "Sanson-Flamsteed" projection was not first studied by either Nicholas Sanson (ca. 1650) or John Flamsteed (1729, published posthumously), but possibly by Mercator — at least it was included for maps of South America in later editions (1606) of Mercator's atlas, and has been referred to as the Mercator equal-area projection, or Mercator-Sanson. Since in the normal aspect all meridians are sinusoids, it is also called sinusoidal, and can be easily deduced. The sinusoidal projection is equal-area and preserves distances along the horizontals, i.e. all parallels in an equatorial map are standard lines — but only the central meridian. Although the equatorial band is reproduced with little distortion, the polar caps suffer from poor legibility due to shearing.

Since:

3.2

Version:

$Id$

Author:

Galpin Thomas

See Also:

http://www.progonos.com/furuti/MapProj/Normal/ProjPCyl/projPCyl.html#SansonFlamsteed, Serialized Form

Concurrency :

not thread-safe

Field Summary

Fields inherited from class fr.cnes.sirius.patrius.projections.Mercator

MAX_LATITUDE

Constructor Summary

Constructors

Constructor and Description
GeneralizedFlamsteedSamson(EllipsoidPoint pivotPoint, double cap) Constructor : Mercator constructor is used with : a pivot point including reference ellipsoid a cap parameter centered set to true parameter series set to false indicating that inverse transformation is done with iterations : slower but more accurate

Method Summary

Modifier and Type	Method and Description
EllipsoidPoint	applyInverseTo(double x, double y) Inverse projection. Returns geodetic coordinates.
EllipsoidPoint	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(EllipsoidPoint point) Returns Easting value and Northing value in meters from the point coordinates.
EnumLineProperty	getLineProperty() Getter for the line property.
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.Mercator

canMap, getAzimuth, getDistortionFactor, getMaximumEastingValue, getMaximumLatitude, getMaximumNorthingValue, getScaleFactor

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

Constructor Detail

GeneralizedFlamsteedSamson

public GeneralizedFlamsteedSamson(EllipsoidPoint pivotPoint,
                                  double cap)

Constructor : Mercator constructor is used with :

• a pivot point including reference ellipsoid
• a cap
• parameter centered set to true
• parameter series set to false indicating that inverse transformation is done with iterations : slower but more accurate

Parameters:

pivotPoint - pivot point. It also contains reference ellipsoid

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

Method Detail

applyTo

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

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

Specified by:

applyTo in interface IProjection

Overrides:

applyTo in class Mercator

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 - if projection could not be computed

applyTo

public Vector2D applyTo(EllipsoidPoint point)
                 throws PatriusException

Returns Easting value and Northing value in meters from the point coordinates.

Specified by:

applyTo in interface IProjection

Overrides:

applyTo in class Mercator

Parameters:

point - the point to transform

Returns:

Vector2D containing Easting value and Northing value in meters

Throws:

PatriusException - if projection could not be computed

applyInverseTo

public EllipsoidPoint 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.

Specified by:

applyInverseTo in interface IProjection

Overrides:

applyInverseTo in class Mercator

Parameters:

x - abscissa coordinate

y - ordinate coordinate

alt - altitude coordinate

Returns:

coordinate

Throws:

PatriusException - if inverse projection could not be computed

applyInverseTo

public EllipsoidPoint 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.

Specified by:

applyInverseTo in interface IProjection

Overrides:

applyInverseTo in class Mercator

Parameters:

x - abscissa coordinate

y - ordinate coordinate

Returns:

geodetic coordinates

Throws:

PatriusException - 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).

Specified by:

isConformal in interface IProjection

Overrides:

isConformal in class Mercator

Returns:

a boolean

isEquivalent

public boolean isEquivalent()

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

Specified by:

isEquivalent in interface IProjection

Overrides:

isEquivalent in class Mercator

Returns:

a boolean

getLineProperty

public EnumLineProperty getLineProperty()

Getter for the line property.

Specified by:

getLineProperty in interface IProjection

Overrides:

getLineProperty in class Mercator

Returns:

line property