* * The elliptical equations used here are series approximations, and their accuracy * decreases as points move farther from the central meridian of the projection. * The forward equations here are accurate to a less than a mm ±10 degrees from * the central meridian, a few mm ±15 degrees from the * central meridian and a few cm ±20 degrees from the central meridian. * The spherical equations are not approximations and should always give the * correct values. *
* * There are a number of versions of the transverse mercator projection * including the Universal (UTM) and Modified (MTM) Transverses Mercator * projections. In these cases the earth is divided into zones. For the UTM * the zones are 6 degrees wide, numbered from 1 to 60 proceeding east from * 180 degrees longitude, and between lats 84 degrees North and 80 * degrees South. The central meridian is taken as the center of the zone * and the latitude of origin is the equator. A scale factor of 0.9996 and * false easting of 500000m is used for all zones and a false northing of 10000000m * is used for zones in the southern hemisphere. *
* * NOTE: formulas used below are not those of Snyder, but rather those * from the {@code proj4} package of the USGS survey, which * have been reproduced verbatim. USGS work is acknowledged here. *
* References: *
e'² = (a²-b²)/b² = es/(1-es)
* where a is the semi-major axis length and b is the semi-minor axis
* length.
*/
private final double esp;
/**
* Meridian distance at the {@code latitudeOfOrigin}.
* Used for calculations for the ellipsoid.
*/
private final double ml0;
/**
* Contants used for the forward and inverse transform for the eliptical
* case of the Transverse Mercator.
*/
private static final double FC1= 1.00000000000000000000000, // 1/1
FC2= 0.50000000000000000000000, // 1/2
FC3= 0.16666666666666666666666, // 1/6
FC4= 0.08333333333333333333333, // 1/12
FC5= 0.05000000000000000000000, // 1/20
FC6= 0.03333333333333333333333, // 1/30
FC7= 0.02380952380952380952380, // 1/42
FC8= 0.01785714285714285714285; // 1/56
/**
* Constructs a new map projection from the supplied parameters.
*
* @param parameters The parameter values in standard units.
* @throws ParameterNotFoundException if a mandatory parameter is missing.
*/
protected TransverseMercator(final ParameterValueGroup parameters)
throws ParameterNotFoundException
{
// Fetch parameters
super(parameters);
// Compute constants
esp = excentricitySquared / (1.0 - excentricitySquared);
ml0 = mlfn(latitudeOfOrigin, sin(latitudeOfOrigin), cos(latitudeOfOrigin));
}
/**
* {@inheritDoc}
*/
public ParameterDescriptorGroup getParameterDescriptors() {
return Provider.PARAMETERS;
}
/**
* Transforms the specified (λ,φ) coordinates
* (units in radians) and stores the result in {@code ptDst} (linear distance
* on a unit sphere).
*/
protected Point2D transformNormalized(double x, double y, Point2D ptDst)
throws ProjectionException
{
double sinphi = sin(y);
double cosphi = cos(y);
double t = (abs(cosphi) > EPSILON) ? sinphi/cosphi : 0;
t *= t;
double al = cosphi*x;
double als = al*al;
al /= sqrt(1.0 - excentricitySquared * sinphi*sinphi);
double n = esp * cosphi*cosphi;
/* NOTE: meridinal distance at latitudeOfOrigin is always 0 */
y = (mlfn(y, sinphi, cosphi) - ml0 +
sinphi * al * x *
FC2 * ( 1.0 +
FC4 * als * (5.0 - t + n*(9.0 + 4.0*n) +
FC6 * als * (61.0 + t * (t - 58.0) + n*(270.0 - 330.0*t) +
FC8 * als * (1385.0 + t * ( t*(543.0 - t) - 3111.0))))));
x = al*(FC1 + FC3 * als*(1.0 - t + n +
FC5 * als * (5.0 + t*(t - 18.0) + n*(14.0 - 58.0*t) +
FC7 * als * (61.0+ t*(t*(179.0 - t) - 479.0 )))));
if (ptDst != null) {
ptDst.setLocation(x,y);
return ptDst;
}
return new Point2D.Double(x,y);
}
/**
* Transforms the specified (x,y) coordinates
* and stores the result in {@code ptDst}.
*/
protected Point2D inverseTransformNormalized(double x, double y, Point2D ptDst)
throws ProjectionException
{
double phi = inv_mlfn(ml0 + y);
if (abs(phi) >= PI/2) {
y = y<0.0 ? -(PI/2) : (PI/2);
x = 0.0;
} else {
double sinphi = sin(phi);
double cosphi = cos(phi);
double t = (abs(cosphi) > EPSILON) ? sinphi/cosphi : 0.0;
double n = esp * cosphi*cosphi;
double con = 1.0 - excentricitySquared * sinphi*sinphi;
double d = x * sqrt(con);
con *= t;
t *= t;
double ds = d*d;
y = phi - (con*ds / (1.0 - excentricitySquared)) *
FC2 * (1.0 - ds *
FC4 * (5.0 + t*(3.0 - 9.0*n) + n*(1.0 - 4*n) - ds *
FC6 * (61.0 + t*(90.0 - 252.0*n + 45.0*t) + 46.0*n - ds *
FC8 * (1385.0 + t*(3633.0 + t*(4095.0 + 1574.0*t))))));
x = d*(FC1 - ds * FC3 * (1.0 + 2.0*t + n -
ds*FC5*(5.0 + t*(28.0 + 24* t + 8.0*n) + 6.0*n -
ds*FC7*(61.0 + t*(662.0 + t*(1320.0 + 720.0*t))))))/cosphi;
}
if (ptDst != null) {
ptDst.setLocation(x,y);
return ptDst;
}
return new Point2D.Double(x,y);
}
/**
* {@inheritDoc}
*/
@Override
protected double getToleranceForAssertions(final double longitude, final double latitude) {
if (abs(longitude - centralMeridian) > 0.26) { // 15 degrees
// When far from the valid area, use a larger tolerance.
return 2.5;
} else if (abs(longitude - centralMeridian) > 0.22) { // 12.5 degrees
return 1.0;
} else if (abs(longitude - centralMeridian) > 0.17) { // 10 degrees
return 0.5;
}
// a normal tolerance
return 1E-6;
}
/**
* Provides the transform equations for the spherical case of the
* TransverseMercator projection.
*
* @version $Id$
* @author André Gosselin
* @author Martin Desruisseaux (PMO, IRD)
* @author Rueben Schulz
*/
private static final class Spherical extends TransverseMercator {
/**
* Constructs a new map projection from the suplied parameters.
*
* @param parameters The parameter values in standard units.
* @throws ParameterNotFoundException if a mandatory parameter is missing.
*/
protected Spherical(final ParameterValueGroup parameters)
throws ParameterNotFoundException
{
super(parameters);
ensureSpherical();
}
/**
* {@inheritDoc}
*/
@Override
protected Point2D transformNormalized(double x, double y, Point2D ptDst)
throws ProjectionException
{
// Compute using ellipsoidal formulas, for comparaison later.
final double normalizedLongitude = x;
assert (ptDst = super.transformNormalized(x, y, ptDst)) != null;
double cosphi = cos(y);
double b = cosphi * sin(x);
if (abs(abs(b) - 1.0) <= EPSILON) {
throw new ProjectionException(ErrorKeys.VALUE_TEND_TOWARD_INFINITY);
}
//Using Snyder's equation for calculating y, instead of the one used in Proj4
//poential problems when y and x = 90 degrees, but behaves ok in tests
y = atan2(tan(y), cos(x)) - latitudeOfOrigin; /* Snyder 8-3 */
x = 0.5 * log((1.0+b) / (1.0-b)); /* Snyder 8-1 */
assert checkTransform(x, y, ptDst, getToleranceForSphereAssertions(normalizedLongitude));
if (ptDst != null) {
ptDst.setLocation(x,y);
return ptDst;
}
return new Point2D.Double(x,y);
}
/**
* {@inheritDoc}
*/
@Override
protected Point2D inverseTransformNormalized(double x, double y, Point2D ptDst)
throws ProjectionException
{
// Compute using ellipsoidal formulas, for comparaison later.
assert (ptDst = super.inverseTransformNormalized(x, y, ptDst)) != null;
double sinhX = sinh(x);
double cosD = cos(latitudeOfOrigin + y);
double phi = asin(sqrt((1.0 - cosD*cosD) / (1.0 + sinhX*sinhX)));
// correct for the fact that we made everything positive using sqrt(x*x)
y = ((y + latitudeOfOrigin)<0.0) ? -phi : phi;
x = (abs(sinhX) <= EPSILON && abs(cosD) <= EPSILON) ? 0.0 : atan2(sinhX,cosD);
assert checkInverseTransform(x, y, ptDst, getToleranceForSphereAssertions(x));
if (ptDst != null) {
ptDst.setLocation(x,y);
return ptDst;
}
return new Point2D.Double(x,y);
}
/**
* Maximal error tolerated for assertions in the spherical case. When assertions
* are enabled, every projection using spherical formulas is followed by a projection
* using the ellipsical formulas, and the results are compared. If a distance greater
* than the tolerance level is found, then an {@link AssertionError} will be thrown.
* Subclasses may override this method if they need to relax the tolerance level.
*
* The default implementation allows a larger tolerance when comparing spherical to
* elliptical calculations when we are far from the central meridian (elliptical
* calculations are not valid here).
*
* @param longitude The longitude standardized (in radians) with
* {@linkplain #centralMeridian} already removed from it.
* @return The tolerance level for assertions, in meters.
*/
protected double getToleranceForSphereAssertions(final double longitude) {
if (abs(abs(longitude)- PI/2) < EPSILON_LATITUDE) { // 90 degrees
// elliptical equations are at their worst here
return 1E+18;
}
if (abs(longitude) > 0.26) { // 15 degrees
// When far from the valid area, use a very larger tolerance.
return 1E+6;
}
// a normal tolerance
return 1E-6;
}
}
/**
* Convenience method computing the zone code from the central meridian.
* Information about zones convention must be specified in argument. Two
* widely set of arguments are of Universal Transverse Mercator (UTM) and
* Modified Transverse Mercator (MTM) projections:
*
*
* UTM projection (zones numbered from 1 to 60):
*
* {@code getZone(-177, 6);}
*
* MTM projection (zones numbered from 1 to 120):
*
* {@code getZone(-52.5, -3);}
* The usual Transverse Mercator formulas are:
*
*
* The Transverse Mercator South Orientated Projection formulas are:
*
*
* Where the px and py terms are the same in both cases.
* Transforms created by this provider actually computes
* (easting,northing) = (-westing,-southing).
* This is equivalent to a {@link TransverseMercator} projection with
* {@link #falseEasting falseEasting} and {@link #falseNorthing falseNorthing} sign reverted.
* This operation is implemented as a concatenation of a North-orientated transverse mercator
* projection with an affine transform for (false easting,false northing)
* correction.
*
* @since 2.2
* @version $Id$
* @author Martin Desruisseaux (PMO, IRD)
*
* @see org.geotools.referencing.operation.DefaultMathTransformFactory
*/
public static class Provider_SouthOrientated extends Provider {
/**
* Constructs a new provider.
*/
public Provider_SouthOrientated() {
super(createDescriptorGroup(new NamedIdentifier[] {
new NamedIdentifier(Citations.EPSG, "Transverse Mercator (South Orientated)"),
new NamedIdentifier(Citations.EPSG, "9808")
}));
}
/**
* Creates a transform from the specified group of parameter values.
*
* @param parameters The group of parameter values.
* @return The created math transform.
* @throws ParameterNotFoundException if a required parameter was not found.
*/
@Override
public MathTransform createMathTransform(final ParameterValueGroup parameters)
throws ParameterNotFoundException
{
final MapProjection projection = (MapProjection) super.createMathTransform(parameters);
if (projection.falseEasting==0 && projection.falseNorthing==0) {
return projection;
}
final AffineTransform step = AffineTransform.getTranslateInstance(
-2*projection.falseEasting, -2*projection.falseNorthing);
return ConcatenatedTransform.create(ProjectiveTransform.create(step), projection);
}
}
}
*
* @param centralLongitudeZone1 Longitude in the middle of zone 1, in decimal degrees
* relative to Greenwich. Positive longitudes are toward east, and negative
* longitudes toward west.
* @param zoneWidth Number of degrees of longitudes in one zone. A positive value
* means that zones are numbered from west to east (i.e. in the direction of
* positive longitudes). A negative value means that zones are numbered from
* east to west.
* @return The zone number. First zone is numbered 1.
*/
private int getZone(final double centralLongitudeZone1, final double zoneWidth) {
final double zoneCount = abs(360 / zoneWidth);
double t;
t = centralLongitudeZone1 - 0.5*zoneWidth; // Longitude at the beginning of the first zone.
t = toDegrees(centralMeridian) - t; // Degrees of longitude between the central longitude and longitude 1.
t = floor(t/zoneWidth + EPSILON); // Number of zones between the central longitude and longitude 1.
t -= zoneCount*floor(t/zoneCount); // If negative, bring back to the interval 0 to (zoneCount-1).
return ((int) t)+1;
}
/**
* Convenience method returning the meridian in the middle of current zone. This meridian is
* typically the central meridian. This method may be invoked to make sure that the central
* meridian is correctly set.
*
* @param centralLongitudeZone1 Longitude in the middle of zone 1, in decimal degrees
* relative to Greenwich. Positive longitudes are toward east, and negative
* longitudes toward west.
* @param zoneWidth Number of degrees of longitudes in one zone. A positive value
* means that zones are numbered from west to east (i.e. in the direction of
* positive longitudes). A negative value means that zones are numbered from
* east to west.
* @return The central meridian.
*/
private double getCentralMedirian(final double centralLongitudeZone1, final double zoneWidth) {
double t;
t = centralLongitudeZone1 + (getZone(centralLongitudeZone1, zoneWidth)-1)*zoneWidth;
t -= 360 * floor((t+180) / 360); // Bring back into [-180..+180] range.
return t;
}
/**
* Convenience method computing the zone code from the central meridian.
*
* @return The zone number, using the scalefactor and false easting
* to decide if this is a UTM or MTM case. Returns 0 if the
* case of the projection cannot be determined.
*/
public int getZone() {
// UTM
if (scaleFactor == 0.9996 && falseEasting == 500000.0) {
return getZone(-177, 6);
}
// MTM
if (scaleFactor == 0.9999 && falseEasting == 304800.0){
return getZone(-52.5, -3);
}
// unknown
throw new IllegalStateException(Errors.format(ErrorKeys.UNKNOW_PROJECTION_TYPE));
}
/**
* Convenience method returning the meridian in the middle of current zone. This meridian is
* typically the central meridian. This method may be invoked to make sure that the central
* meridian is correctly set.
*
* @return The central meridian, using the scalefactor and false easting
* to decide if this is a UTM or MTM case. Returns {@link Double#NaN}
* if the case of the projection cannot be determined.
*/
public double getCentralMeridian() {
// UTM
if (scaleFactor == 0.9996 && falseEasting == 500000.0) {
return getCentralMedirian(-177, 6);
}
// MTM
if (scaleFactor == 0.9999 && falseEasting == 304800.0){
return getCentralMedirian(-52.5, -3);
}
// unknown
throw new IllegalStateException(Errors.format(ErrorKeys.UNKNOW_PROJECTION_TYPE));
}
/**
* Returns a hash value for this projection.
*/
@Override
public int hashCode() {
final long code = Double.doubleToLongBits(ml0);
return ((int)code ^ (int)(code >>> 32)) + 37*super.hashCode();
}
/**
* Compares the specified object with this map projection for equality.
*/
@Override
public boolean equals(final Object object) {
if (object == this) {
// Slight optimization
return true;
}
// Relevant parameters are already compared in MapProjection
return super.equals(object);
}
//////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////
//////// ////////
//////// PROVIDERS ////////
//////// ////////
//////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////
/**
* The {@linkplain org.geotools.referencing.operation.MathTransformProvider math transform
* provider} for a {@linkplain TransverseMercator Transverse Mercator} projection (EPSG code
* 9807).
*
* @since 2.1
* @version $Id$
* @author Martin Desruisseaux (PMO, IRD)
* @author Rueben Schulz
*
* @see org.geotools.referencing.operation.DefaultMathTransformFactory
*/
public static class Provider extends AbstractProvider {
/**
* Returns a descriptor group for the specified parameters.
*/
static ParameterDescriptorGroup createDescriptorGroup(final ReferenceIdentifier[] identifiers) {
return createDescriptorGroup(identifiers, new ParameterDescriptor[] {
SEMI_MAJOR, SEMI_MINOR,
CENTRAL_MERIDIAN, LATITUDE_OF_ORIGIN,
SCALE_FACTOR, FALSE_EASTING,
FALSE_NORTHING
});
}
/**
* The parameters group.
*/
static final ParameterDescriptorGroup PARAMETERS = createDescriptorGroup(new NamedIdentifier[] {
new NamedIdentifier(Citations.OGC, "Transverse_Mercator"),
new NamedIdentifier(Citations.EPSG, "Transverse Mercator"),
new NamedIdentifier(Citations.EPSG, "Gauss-Kruger"),
new NamedIdentifier(Citations.EPSG, "9807"),
new NamedIdentifier(Citations.GEOTIFF, "CT_TransverseMercator"),
new NamedIdentifier(Citations.ESRI, "Transverse_Mercator"),
new NamedIdentifier(Citations.ESRI, "Gauss_Kruger"),
new NamedIdentifier(Citations.GEOTOOLS, Vocabulary.formatInternational(
VocabularyKeys.TRANSVERSE_MERCATOR_PROJECTION))
});
/**
* Constructs a new provider.
*/
public Provider() {
super(PARAMETERS);
}
/**
* Constructs a new provider with the specified parameters.
*/
Provider(final ParameterDescriptorGroup descriptor) {
super(descriptor);
}
/**
* Returns the operation type for this map projection.
*/
@Override
public Class
*
*
*
*