Class Mercator
- All Implemented Interfaces:
Serializable
,Parameterized
,LenientComparable
,MathTransform
,MathTransform2D
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 (variant A) (EPSG code 9804), the line of contact is the equator. For Mercator (variant B) (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 … 90]° range produces NaN.- Since:
- 0.6
- See Also:
Defined in the sis-referencing
module
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Nested Class Summary
Nested classes/interfaces inherited from class NormalizedProjection
NormalizedProjection.ParameterRole
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Field Summary
Fields inherited from class NormalizedProjection
eccentricity, eccentricitySquared
Fields inherited from class AbstractMathTransform2D
DIMENSION
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Constructor Summary
ConstructorsConstructorDescriptionMercator
(OperationMethod method, Parameters parameters) Creates a Mercator projection from the given parameters. -
Method Summary
Modifier and TypeMethodDescriptionReturns the sequence of normalization →this
→ denormalization transforms as a whole.getDomain
(DomainDefinition criteria) Returns the domain of input coordinates.protected void
inverseTransform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff) Converts the specified (x,y) coordinates and stores the result indstPts
(angles in radians).transform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) Projects the specified coordinates (implementation-specific units) and stores the result indstPts
.void
transform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) Converts a list of coordinate tuples.Methods inherited from class NormalizedProjection
computeHashCode, equals, getContextualParameters, getParameterDescriptors, getParameterValues, inverse, tryConcatenate
Methods inherited from class AbstractMathTransform2D
createTransformedShape, derivative, getSourceDimensions, getTargetDimensions, transform
Methods inherited from class AbstractMathTransform
derivative, equals, formatTo, hashCode, isIdentity, transform, transform, transform, transform
Methods inherited from class FormattableObject
print, toString, toString, toWKT
Methods inherited from class Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Methods inherited from interface MathTransform
derivative, isIdentity, toWKT, transform, transform, transform, transform
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Constructor Details
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Mercator
Creates a Mercator projection from the given parameters. Themethod
argument can be the description of one of the following:- "Mercator (variant A)", also known as "Mercator (1SP)".
- "Mercator (variant B)", also known as "Mercator (2SP)".
- "Mercator (variant C)".
- "Mercator (Spherical)".
- "Mercator Auxiliary Sphere".
- "Popular Visualisation Pseudo Mercator".
- "Miller Cylindrical".
- Parameters:
method
- description of the projection parameters.parameters
- the parameter values of the projection to create.
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Method Details
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createMapProjection
Returns the sequence of normalization →this
→ denormalization transforms as a whole. The transform returned by this method expects (longitude, latitude) coordinates in degrees and returns (x,y) coordinates in metres.The non-linear part of the returned transform will be
this
transform, except if the ellipsoid is spherical. In the latter case,this
transform may be replaced by a simplified implementation.- Overrides:
createMapProjection
in classNormalizedProjection
- Parameters:
factory
- the factory to use for creating the transform.- Returns:
- the map projection from (λ,φ) to (x,y) coordinates.
- Throws:
FactoryException
- if an error occurred while creating a transform.- See Also:
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getDomain
Returns the domain of input coordinates. For a Mercator projection other than Miller variant, the limit is arbitrarily set to 84° of latitude North and South. This is consistent with the "World Mercator" domain of validity defined by EPSG:3395, which is 80°S to 84°N.The range of longitude values is set to an arbitrary range larger than −180° … +180°, because the Mercator projection is mathematically capable to handle coordinates beyond that range even if those coordinates have no real world meaning. This expansion can facilitate the projection of envelopes, geometries or rasters.
- Overrides:
getDomain
in classAbstractMathTransform
- Parameters:
criteria
- controls the definition of transform domain.- Returns:
- estimation of a domain where this transform is considered numerically applicable.
- Since:
- 1.3
- See Also:
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transform
public Matrix transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) throws ProjectionException Projects the specified coordinates (implementation-specific units) and stores the result indstPts
. In addition, opportunistically computes the projection derivative ifderivate
istrue
. The results must be multiplied by the denormalization matrix before to get linear distances.- Specified by:
transform
in classNormalizedProjection
- Parameters:
srcPts
- the array containing the source point coordinates, as (longitude, latitude) angles in radians.srcOff
- the offset of the single coordinate tuple to be converted in the source array.dstPts
- the array into which the converted coordinates is returned (may be the same thansrcPts
). Coordinates will be expressed in a dimensionless unit, as a linear distance on a unit sphere or ellipse.dstOff
- the offset of the location of the converted coordinates that is stored in the destination array.derivate
-true
for computing the derivative, orfalse
if not needed.- Returns:
- the matrix of the projection derivative at the given source position,
or
null
if thederivate
argument isfalse
. - Throws:
ProjectionException
- if the coordinates cannot be converted.- See Also:
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transform
public void transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws TransformException Converts a list of coordinate tuples. This method performs the same calculation than abovetransform(double[], int, double[], int, boolean)
method, but is overridden for efficiency.- Specified by:
transform
in interfaceMathTransform
- Overrides:
transform
in classAbstractMathTransform
- Parameters:
srcPts
- the array containing the source point coordinates.srcOff
- the offset to the first point to be transformed in the source array.dstPts
- the array into which the transformed point coordinates are returned. May be the same thansrcPts
.dstOff
- the offset to the location of the first transformed point that is stored in the destination array.numPts
- the number of point objects to be transformed.- Throws:
TransformException
- if a point cannot be converted.
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inverseTransform
protected void inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) throws ProjectionException Converts the specified (x,y) coordinates and stores the result indstPts
(angles in radians).- Specified by:
inverseTransform
in classNormalizedProjection
- Parameters:
srcPts
- the array containing the source point coordinates, 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 coordinates is returned (may be the same thansrcPts
). Coordinates 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 cannot be converted.
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