org.geotoolkit.referencing.operation.projection
Class Mercator

Object
  FormattableObject
      AbstractMathTransform
          AbstractMathTransform2D
              UnitaryProjection
                  Mercator

All Implemented Interfaces:

Serializable, Formattable, Parameterized, LenientComparable, MathTransform, MathTransform2D

@Immutable
public class Mercator
extends UnitaryProjection

Mercator Cylindrical Projection (EPSG codes 9804, 9805). See the Mercator projection on MathWorld for an overview. See any of the following providers for a list of programmatic parameters:

• Mercator1SP
• Mercator2SP
• PseudoMercator
• MillerCylindrical

Description
The parallels and the meridians are straight lines and cross at right angles; this projection thus produces rectangular charts. The scale is true along the equator (by default) or along two parallels equidistant of the equator (if a scale factor other than 1 is used).

This projection is used to represent areas close to the equator. It is also often used for maritime navigation because all the straight lines on the chart are loxodrome lines, i.e. a ship following this line would keep a constant azimuth on its compass.

This implementation handles both the 1 and 2 standard parallel cases. For Mercator_1SP (EPSG code 9804), the line of contact is the equator. For Mercator_2SP (EPSG code 9805) lines of contact are symmetrical about the equator.

Behavior at poles
The projection of 90°N gives positive infinity. The projection of 90°S gives negative infinity. Projection of a latitude outside the [-90-ε ... 90+ε]° range produces NaN.

References

• John P. Snyder (Map Projections - A Working Manual,
  U.S. Geological Survey Professional Paper 1395, 1987)
• "Coordinate Conversions and Transformations including Formulas",
  EPSG Guidence Note Number 7, Version 19.

Since:

1.0

Version:

3.18

Author:

André Gosselin (MPO), Martin Desruisseaux (MPO, IRD, Geomatys), Rueben Schulz (UBC), Simon Reynard (Geomatys), Rémi Maréchal (Geomatys)

See Also:

TransverseMercator, ObliqueMercator, Serialized Form

Module:

referencing/geotk-referencing (download)

View source code for this class

Nested Class Summary

Nested classes/interfaces inherited from class UnitaryProjection

UnitaryProjection.Parameters

Field Summary

Fields inherited from class UnitaryProjection

excentricity, excentricitySquared

Fields inherited from class FormattableObject

EPSG, GEOTIFF, INTERNAL, OGC, SINGLE_LINE

Constructor Summary

protected

Mercator(UnitaryProjection.Parameters parameters) Constructs a new map projection from the supplied parameters.

Method Summary

static MathTransform2D	create(ParameterDescriptorGroup descriptor, ParameterValueGroup values) Creates a Mercator projection from the given parameters.
Matrix	derivative(Point2D point) Gets the derivative of this transform at a point.
ParameterDescriptorGroup	getParameterDescriptors() Returns the parameter descriptors for this unitary projection.
protected void	inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) Transforms the specified (x,y) coordinates and stores the result in dstPts (angles in radians).
protected void	transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) Transforms the specified (λ,φ) coordinates (units in radians) and stores the result in dstPts (linear distance on a unit sphere).
void	transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) Converts a list of coordinate point ordinal values.

Methods inherited from class UnitaryProjection

computeHashCode, equals, finish, getParameterValues, getUnmarshalledParameters, inverse, resetWarnings, rollLongitude, unrollLongitude

Methods inherited from class AbstractMathTransform2D

getSourceDimensions, getTargetDimensions, transform

Methods inherited from class AbstractMathTransform

createTransformedShape, derivative, ensureNonNull, equals, formatWKT, getName, hashCode, isIdentity, rollLongitude, transform, transform, transform, transform

Methods inherited from class FormattableObject

getDefaultIndentation, print, setDefaultIndentation, toString, toWKT, toWKT, toWKT

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface MathTransform2D

createTransformedShape

Methods inherited from interface MathTransform

derivative, isIdentity, toWKT, transform, transform, transform, transform

Constructor Detail

Mercator

protected Mercator(UnitaryProjection.Parameters parameters)

Constructs a new map projection from the supplied parameters.

Parameters:

parameters - The parameters of the projection to be created.

Method Detail

create

public static MathTransform2D create(ParameterDescriptorGroup descriptor,
                                     ParameterValueGroup values)

Creates a Mercator projection from the given parameters. The descriptor argument is usually one of the PARAMETERS constants defined in Mercator1SP or Mercator2SP, but is not restricted to. If a different descriptor is supplied, it is user's responsibility to ensure that it is suitable to a Mercator projection.

Parameters:

descriptor - Typically one of Mercator1SP.PARAMETERS, Mercator2SP.PARAMETERS or MillerCylindrical.PARAMETERS.

values - The parameter values of the projection to create.

Returns:

The map projection.

Since:

3.00

getParameterDescriptors

public ParameterDescriptorGroup getParameterDescriptors()

Returns the parameter descriptors for this unitary projection. Note that the returned descriptor is about the unitary projection, not the full one. Consequently the current implementation returns the descriptor of Mercator1SP in all cases, because the 2SP case is implemented as 1SP with a different scale factor.

Specified by:

getParameterDescriptors in interface Parameterized

Overrides:

getParameterDescriptors in class AbstractMathTransform2D

Returns:

The parameter descriptors for this math transform, or null.

See Also:

OperationMethod.getParameters()

transform

protected void transform(double[] srcPts,
                         int srcOff,
                         double[] dstPts,
                         int dstOff)
                  throws ProjectionException

Transforms the specified (λ,φ) coordinates (units in radians) and stores the result in dstPts (linear distance on a unit sphere).

Specified by:

transform in class UnitaryProjection

Parameters:

srcPts - The array containing the source point coordinate, as (longitude, latitude) angles in radians.

srcOff - The offset of the point to be converted in the source array.

dstPts - the array into which the converted point coordinate is returned (may be the same than srcPts). Ordinates will be in a dimensionless unit, as a linear distance on a unit sphere or ellipse.

dstOff - The offset of the location of the converted point that is stored in the destination array.

Throws:

ProjectionException - if the point can't be converted.

transform

public void transform(double[] srcPts,
                      int srcOff,
                      double[] dstPts,
                      int dstOff,
                      int numPts)
               throws TransformException

Converts a list of coordinate point ordinal values.

Note: We override the super-class method only as an optimization in the special case where the target coordinates are written at the same locations than the source coordinates. In such case, we can take advantage of the fact that the λ value is not modified by the unitary Mercator projection.

Specified by:

transform in interface MathTransform

Overrides:

transform in class UnitaryProjection

Parameters:

srcPts - The array containing the source point coordinates.

srcOff - The offset to the first point to be converted in the source array.

dstPts - The array into which the converted point coordinates are returned. May be the same than srcPts.

dstOff - The offset to the location of the first converted point that is stored in the destination array.

numPts - The number of point objects to be converted.

Throws:

TransformException - if a point can't be converted.

inverseTransform

protected void inverseTransform(double[] srcPts,
                                int srcOff,
                                double[] dstPts,
                                int dstOff)
                         throws ProjectionException

Transforms the specified (x,y) coordinates and stores the result in dstPts (angles in radians).

Specified by:

inverseTransform in class UnitaryProjection

Parameters:

srcPts - The array containing the source point coordinate, as linear distance on a unit sphere or ellipse.

srcOff - The offset of the point to be converted in the source array.

dstPts - the array into which the converted point coordinate is returned (may be the same than srcPts). Ordinates will be (longitude, latitude) angles in radians.

dstOff - The offset of the location of the converted point that is stored in the destination array.

Throws:

ProjectionException - if the point can't be converted.

derivative

public Matrix derivative(Point2D point)
                  throws ProjectionException

Gets the derivative of this transform at a point.

Specified by:

derivative in interface MathTransform2D

Overrides:

derivative in class AbstractMathTransform

Parameters:

point - The coordinate point where to evaluate the derivative.

Returns:

The derivative at the specified point as a 2×2 matrix.

Throws:

ProjectionException - if the derivative can't be evaluated at the specified point.

Since:

3.18

See Also:

MathTransform2D.derivative(Point2D)