/**
* Transform a geographic point (in radians), producing a projected result (in the units of the
* target coordinate system).
*
* @param x the geographic x ordinate (in radians)
* @param y the geographic y ordinate (in radians)
* @param dst the projected coordinate (in coordinate system units)
* @return the target coordinate
*/
private ProjCoordinate projectRadians(double x, double y, ProjCoordinate dst) {
project(x, y, dst);
if (unit == Units.DEGREES) {
// convert radians to DD
dst.x *= RTD;
dst.y *= RTD;
} else {
// assume result is in metres
dst.x = totalScale * dst.x + totalFalseEasting;
dst.y = totalScale * dst.y + totalFalseNorthing;
}
return dst;
}
public ProjCoordinate project(double lplam, double lpphi, ProjCoordinate xy) {
if (spherical) {
xy.x = Math.asin(Math.cos(lpphi) * Math.sin(lplam));
xy.y = Math.atan2(Math.tan(lpphi), Math.cos(lplam)) - projectionLatitude;
} else {
xy.y = ProjectionMath.mlfn(lpphi, n = Math.sin(lpphi), c = Math.cos(lpphi), en);
n = 1. / Math.sqrt(1. - es * n * n);
tn = Math.tan(lpphi);
t = tn * tn;
a1 = lplam * c;
c *= es * c / (1 - es);
a2 = a1 * a1;
xy.x = n * a1 * (1. - a2 * t * (C1 - (8. - t + 8. * c) * a2 * C2));
xy.y -= m0 - n * tn * a2 * (.5 + (5. - t + 6. * c) * a2 * C3);
}
return xy;
}
/**
* Inverse-transforms a point (in the units defined by the coordinate system), producing a
* geographic result (in radians)
*
* @param src the input projected coordinate (in coordinate system units)
* @param dst the inverse-projected geographic coordinate (in radians)
* @return the target coordinate
*/
public ProjCoordinate inverseProjectRadians(ProjCoordinate src, ProjCoordinate dst) {
double x;
double y;
if (unit == Units.DEGREES) {
// convert DD to radians
x = src.x * DTR;
y = src.y * DTR;
} else {
x = (src.x - totalFalseEasting) / totalScale;
y = (src.y - totalFalseNorthing) / totalScale;
}
projectInverse(x, y, dst);
if (dst.x < -Math.PI) dst.x = -Math.PI;
else if (dst.x > Math.PI) dst.x = Math.PI;
if (projectionLongitude != 0)
dst.x = ProjectionMath.normalizeLongitude(dst.x + projectionLongitude);
return dst;
}
public ProjCoordinate projectInverse(double xyx, double xyy, ProjCoordinate out) {
if (spherical) {
out.y = Math.asin(Math.sin(dd = xyy + projectionLatitude) * Math.cos(xyx));
out.x = Math.atan2(Math.tan(xyx), Math.cos(dd));
} else {
double ph1;
ph1 = ProjectionMath.inv_mlfn(m0 + xyy, es, en);
tn = Math.tan(ph1);
t = tn * tn;
n = Math.sin(ph1);
r = 1. / (1. - es * n * n);
n = Math.sqrt(r);
r *= (1. - es) * n;
dd = xyx / n;
d2 = dd * dd;
out.y = ph1 - (n * tn / r) * d2 * (.5 - (1. + 3. * t) * d2 * C3);
out.x = dd * (1. + t * d2 * (-C4 + (1. + 3. * t) * d2 * C5)) / Math.cos(ph1);
}
return out;
}
public ProjCoordinate project(ProjCoordinate in, ProjCoordinate out) {
double lon = ProjectionMath.normalizeLongitude(in.x - projectionLongitude);
double lat = in.y;
double rho, theta, hold1, hold2, hold3;
hold2 =
Math.pow(
((1.0 - eccentricity * Math.sin(lat)) / (1.0 + eccentricity * Math.sin(lat))),
0.5 * eccentricity);
hold3 = Math.tan(ProjectionMath.QUARTERPI - 0.5 * lat);
hold1 = (hold3 == 0.0) ? 0.0 : Math.pow(hold3 / hold2, n);
rho = radius * f * hold1;
theta = n * lon;
out.x = rho * Math.sin(theta);
out.y = rho0 - rho * Math.cos(theta);
return out;
}
public ProjCoordinate inverseProject(ProjCoordinate in, ProjCoordinate out) {
double theta, temp, rho, t, tphi, phi = 0, delta;
theta = Math.atan(in.x / (rho0 - in.y));
out.x = (theta / n) + projectionLongitude;
temp = in.x * in.x + (rho0 - in.y) * (rho0 - in.y);
rho = Math.sqrt(temp);
if (n < 0) rho = -rho;
t = Math.pow((rho / (radius * f)), 1. / n);
tphi = ProjectionMath.HALFPI - 2.0 * Math.atan(t);
delta = 1.0;
for (int i = 0; i < 100 && delta > 1.0e-8; i++) {
temp = (1.0 - eccentricity * Math.sin(tphi)) / (1.0 + eccentricity * Math.sin(tphi));
phi = ProjectionMath.HALFPI - 2.0 * Math.atan(t * Math.pow(temp, 0.5 * eccentricity));
delta = Math.abs(Math.abs(tphi) - Math.abs(phi));
tphi = phi;
}
out.y = phi;
return out;
}
/**
* Computes the inverse projection of a given point (i.e. from projection space to geographics).
* This should be overridden for all projections.
*
* @param x the projected x ordinate (in coordinate system units)
* @param y the projected y ordinate (in coordinate system units)
* @param dst the inverse-projected geographic coordinate (in radians)
* @return the target coordinate
*/
protected ProjCoordinate projectInverse(double x, double y, ProjCoordinate dst) {
dst.x = x;
dst.y = y;
return dst;
}
/**
* Inverse-projects a point (in the units defined by the coordinate system), producing a
* geographic result (in degrees)
*
* @param src the input projected coordinate (in coordinate system units)
* @param dst the inverse-projected geographic coordinate (in degrees)
* @return the target coordinate
*/
public ProjCoordinate inverseProject(ProjCoordinate src, ProjCoordinate dst) {
inverseProjectRadians(src, dst);
dst.x *= RTD;
dst.y *= RTD;
return dst;
}
public ProjCoordinate projectInverse(double x, double y, ProjCoordinate lp) {
if (spherical) {
double c, rh, sinc, cosc;
sinc = Math.sin(c = 2. * Math.atan((rh = ProjectionMath.distance(x, y)) / akm1));
cosc = Math.cos(c);
lp.x = 0.;
switch (mode) {
case EQUATOR:
if (Math.abs(rh) <= EPS10) lp.y = 0.;
else lp.y = Math.asin(y * sinc / rh);
if (cosc != 0. || x != 0.) lp.x = Math.atan2(x * sinc, cosc * rh);
break;
case OBLIQUE:
if (Math.abs(rh) <= EPS10) lp.y = projectionLatitude;
else lp.y = Math.asin(cosc * sinphi0 + y * sinc * cosphi0 / rh);
if ((c = cosc - sinphi0 * Math.sin(lp.y)) != 0. || x != 0.)
lp.x = Math.atan2(x * sinc * cosphi0, c * rh);
break;
case NORTH_POLE:
y = -y;
case SOUTH_POLE:
if (Math.abs(rh) <= EPS10) lp.y = projectionLatitude;
else lp.y = Math.asin(mode == SOUTH_POLE ? -cosc : cosc);
lp.x = (x == 0. && y == 0.) ? 0. : Math.atan2(x, y);
break;
}
} else {
double cosphi, sinphi, tp, phi_l, rho, halfe, halfpi;
rho = ProjectionMath.distance(x, y);
switch (mode) {
case OBLIQUE:
case EQUATOR:
default: // To prevent the compiler complaining about uninitialized vars.
cosphi = Math.cos(tp = 2. * Math.atan2(rho * cosphi0, akm1));
sinphi = Math.sin(tp);
phi_l = Math.asin(cosphi * sinphi0 + (y * sinphi * cosphi0 / rho));
tp = Math.tan(.5 * (ProjectionMath.HALFPI + phi_l));
x *= sinphi;
y = rho * cosphi0 * cosphi - y * sinphi0 * sinphi;
halfpi = ProjectionMath.HALFPI;
halfe = .5 * e;
break;
case NORTH_POLE:
y = -y;
case SOUTH_POLE:
phi_l = ProjectionMath.HALFPI - 2. * Math.atan(tp = -rho / akm1);
halfpi = -ProjectionMath.HALFPI;
halfe = -.5 * e;
break;
}
for (int i = 8; i-- != 0; phi_l = lp.y) {
sinphi = e * Math.sin(phi_l);
lp.y = 2. * Math.atan(tp * Math.pow((1. + sinphi) / (1. - sinphi), halfe)) - halfpi;
if (Math.abs(phi_l - lp.y) < EPS10) {
if (mode == SOUTH_POLE) lp.y = -lp.y;
lp.x = (x == 0. && y == 0.) ? 0. : Math.atan2(x, y);
return lp;
}
}
throw new ConvergenceFailureException("Iteration didn't converge");
}
return lp;
}
public ProjCoordinate project(double lam, double phi, ProjCoordinate xy) {
double coslam = Math.cos(lam);
double sinlam = Math.sin(lam);
double sinphi = Math.sin(phi);
if (spherical) {
double cosphi = Math.cos(phi);
switch (mode) {
case EQUATOR:
xy.y = 1. + cosphi * coslam;
if (xy.y <= EPS10) throw new ProjectionException();
xy.x = (xy.y = akm1 / xy.y) * cosphi * sinlam;
xy.y *= sinphi;
break;
case OBLIQUE:
xy.y = 1. + sinphi0 * sinphi + cosphi0 * cosphi * coslam;
if (xy.y <= EPS10) throw new ProjectionException();
xy.x = (xy.y = akm1 / xy.y) * cosphi * sinlam;
xy.y *= cosphi0 * sinphi - sinphi0 * cosphi * coslam;
break;
case NORTH_POLE:
coslam = -coslam;
phi = -phi;
case SOUTH_POLE:
if (Math.abs(phi - ProjectionMath.HALFPI) < TOL) throw new ProjectionException();
xy.x = sinlam * (xy.y = akm1 * Math.tan(ProjectionMath.QUARTERPI + .5 * phi));
xy.y *= coslam;
break;
}
} else {
double sinX = 0, cosX = 0, X, A;
if (mode == OBLIQUE || mode == EQUATOR) {
sinX = Math.sin(X = 2. * Math.atan(ssfn(phi, sinphi, e)) - ProjectionMath.HALFPI);
cosX = Math.cos(X);
}
switch (mode) {
case OBLIQUE:
A = akm1 / (cosphi0 * (1. + sinphi0 * sinX + cosphi0 * cosX * coslam));
xy.y = A * (cosphi0 * sinX - sinphi0 * cosX * coslam);
xy.x = A * cosX;
break;
case EQUATOR:
A = 2. * akm1 / (1. + cosX * coslam);
xy.y = A * sinX;
xy.x = A * cosX;
break;
case SOUTH_POLE:
phi = -phi;
coslam = -coslam;
sinphi = -sinphi;
case NORTH_POLE:
xy.x = akm1 * ProjectionMath.tsfn(phi, sinphi, e);
xy.y = -xy.x * coslam;
break;
}
xy.x = xy.x * sinlam;
}
return xy;
}