/// <summary>
/// The general inverse geodesic calculation.
/// </summary>
/// <param name="lat1">The latitude of point 1 (degrees).</param>
/// <param name="lon1">The longitude of point 1 (degrees).</param>
/// <param name="lat2">The latitude of point 2 (degrees).</param>
/// <param name="lon2">The longitude of point 2 (degrees).</param>
/// <param name="outmask">The mask specifying the values to calculate.</param>
/// <param name="ps12">The distance between point 1 and point 2 (meters).</param>
/// <param name="pazi1">The azimuth at point 1 (degrees).</param>
/// <param name="pazi2">The (forward) azimuth at point 2 (degrees).</param>
/// <param name="pm12">The reduced length of geodesic (meters).</param>
/// <param name="pM12">The geodesic scale of point 2 relative to point 1 (dimensionless).</param>
/// <param name="pM21">The geodesic scale of point 1 relative to point 2 (dimensionless).</param>
/// <param name="pS12">The area under the geodesic (square meters).</param>
/// <remarks>
/// g must have been initialized with a call to geod_init(). lat1
/// and lat2 should be in the range [-90deg, 90deg]; lon1 and
/// lon2 should be in the range [-540deg, 540deg).
/// </remarks>
/// <returns>a12 arc length of between point 1 and point 2 (degrees).</returns>
public double geod_geninverse(double lat1, double lon1, double lat2, double lon2, GEOD outmask,
out double ps12, out double pazi1, out double pazi2, out double pm12, out double pM12, out double pM21, out double pS12)
{
double s12=0, azi1=0, azi2=0, m12=0, M12=0, M21=0, S12=0;
double lon12;
int latsign, lonsign, swapp;
double phi, sbet1, cbet1, sbet2, cbet2, s12x=0, m12x=0;
double dn1, dn2, lam12, slam12, clam12;
double a12=0, sig12, calp1=0, salp1=0, calp2=0, salp2=0;
// index zero elements of these arrays are unused
double[] C1a=new double[nC1+1], C2a=new double[nC2+1], C3a=new double[nC3];
bool meridian;
double omg12=0;
outmask&=GEOD.OUT_ALL;
// Compute longitude difference (AngDiff does this carefully). Result is
// in [-180, 180] but -180 is only for west-going geodesics. 180 is for
// east-going and meridional geodesics.
lon12=AngDiff(AngNormalize(lon1), AngNormalize(lon2));
// If very close to being on the same half-meridian, then make it so.
lon12=AngRound(lon12);
// Make longitude difference positive.
lonsign=lon12>=0?1:-1;
lon12*=lonsign;
// If really close to the equator, treat as on equator.
lat1=AngRound(lat1);
lat2=AngRound(lat2);
// Swap points so that point with higher (abs) latitude is point 1
swapp=Math.Abs(lat1)>=Math.Abs(lat2)?1:-1;
if(swapp<0)
{
lonsign*=-1;
swapx(ref lat1, ref lat2);
}
// Make lat1 <= 0
latsign=lat1<0?1:-1;
lat1*=latsign;
lat2*=latsign;
// Now we have
//
// 0 <= lon12 <= 180
// -90 <= lat1 <= 0
// lat1 <= lat2 <= -lat1
//
// longsign, swapp, latsign register the transformation to bring the
// coordinates to this canonical form. In all cases, 1 means no change was
// made. We make these transformations so that there are few cases to
// check, e.g., on verifying quadrants in atan2. In addition, this
// enforces some symmetries in the results returned.
phi=lat1*degree;
// Ensure cbet1 = +epsilon at poles
sbet1=f1*Math.Sin(phi);
cbet1=lat1==-90?tiny:Math.Cos(phi);
norm2(ref sbet1, ref cbet1);
phi=lat2*degree;
// Ensure cbet2 = +epsilon at poles
sbet2=f1*Math.Sin(phi);
cbet2=Math.Abs(lat2)==90?tiny:Math.Cos(phi);
norm2(ref sbet2, ref cbet2);
// If cbet1 < -sbet1, then cbet2 - cbet1 is a sensitive measure of the
// |bet1| - |bet2|. Alternatively (cbet1 >= -sbet1), abs(sbet2) + sbet1 is
// a better measure. This logic is used in assigning calp2 in Lambda12.
// Sometimes these quantities vanish and in that case we force bet2 = +/-
// bet1 exactly. An example where is is necessary is the inverse problem
// 48.522876735459 0 -48.52287673545898293 179.599720456223079643
// which failed with Visual Studio 10 (Release and Debug)
if(cbet1<-sbet1)
{
if(cbet2==cbet1)
sbet2=sbet2<0?sbet1:-sbet1;
}
else
{
if(Math.Abs(sbet2)==-sbet1)
cbet2=cbet1;
}
dn1=Math.Sqrt(1+ep2*sq(sbet1));
dn2=Math.Sqrt(1+ep2*sq(sbet2));
lam12=lon12*degree;
slam12=lon12==180?0:Math.Sin(lam12);
clam12=Math.Cos(lam12); // lon12 == 90 isn't interesting
meridian=lat1==-90||slam12==0;
if(meridian)
{
// Endpoints are on a single full meridian, so the geodesic might lie on
// a meridian.
double ssig1, csig1, ssig2, csig2;
calp1=clam12; salp1=slam12; // Head to the target longitude
calp2=1; salp2=0; // At the target we're heading north
// tan(bet)=tan(sig)*cos(alp)
ssig1=sbet1; csig1=calp1*cbet1;
ssig2=sbet2; csig2=calp2*cbet2;
// sig12=sig2-sig1
sig12=Math.Atan2(maxx(csig1*ssig2-ssig1*csig2, 0.0), csig1*csig2+ssig1*ssig2);
{
double dummy;
Lengths(n, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
cbet1, cbet2, out s12x, out m12x, out dummy,
(outmask&GEOD.GEODESICSCALE)!=0, out M12, out M21, C1a, C2a);
}
// Add the check for sig12 since zero length geodesics might yield m12 <0.
// Test case was
//
// echo 20.001 0 20.001 0 | GeodSolve -i
//
// In fact, we will have sig12 > pi/2 for meridional geodesic which is
// not a shortest path.
if(sig12<1||m12x>=0)
{
m12x*=b;
s12x*=b;
a12=sig12/degree;
}
else meridian=false; // m12 < 0, i.e., prolate and too close to anti-podal
}
if(!meridian&&
sbet1==0&& // and sbet2==0
// Mimic the way Lambda12 works with calp1=0
(f<=0||lam12<=pi-f*pi))
{
// Geodesic runs along equator
calp1=calp2=0; salp1=salp2=1;
s12x=a*lam12;
sig12=omg12=lam12/f1;
m12x=b*Math.Sin(sig12);
if((outmask&GEOD.GEODESICSCALE)!=0) M12=M21=Math.Cos(sig12);
a12=lon12/f1;
}
else if(!meridian)
{
// Now point1 and point2 belong within a hemisphere bounded by a
// meridian and geodesic is neither meridional or equatorial.
// Figure a starting point for Newton's method
double dnm=0;
sig12=InverseStart(sbet1, cbet1, dn1, sbet2, cbet2, dn2, lam12, out salp1, out calp1, out salp2, out calp2, out dnm, C1a, C2a);
if(sig12>=0)
{
// Short lines (InverseStart sets salp2, calp2, dnm)
s12x=sig12*b*dnm;
m12x=sq(dnm)*b*Math.Sin(sig12/dnm);
if((outmask&GEOD.GEODESICSCALE)!=0) M12=M21=Math.Cos(sig12/dnm);
a12=sig12/degree;
omg12=lam12/(f1*dnm);
}
else
{
// Newton's method. This is a straightforward solution of f(alp1) =
// lambda12(alp1) - lam12 = 0 with one wrinkle. f(alp) has exactly one
// root in the interval (0, pi) and its derivative is positive at the
// root. Thus f(alp) is positive for alp > alp1 and negative for alp <
// alp1. During the course of the iteration, a range (alp1a, alp1b) is
// maintained which brackets the root and with each evaluation of
// f(alp) the range is shrunk, if possible. Newton's method is
// restarted whenever the derivative of f is negative (because the new
// value of alp1 is then further from the solution) or if the new
// estimate of alp1 lies outside (0,pi); in this case, the new starting
// guess is taken to be (alp1a + alp1b) / 2.
double ssig1=0, csig1=0, ssig2=0, csig2=0, eps=0;
uint numit=0;
// Bracketing range
double salp1a=tiny, calp1a=1, salp1b=tiny, calp1b=-1;
bool tripn, tripb;
for(tripn=false, tripb=false; numit<maxit2; ++numit)
{
// the WGS84 test set: mean = 1.47, sd = 1.25, max = 16
// WGS84 and random input: mean = 2.85, sd = 0.60
double dv=0;
double v=Lambda12(sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1,
out salp2, out calp2, out sig12, out ssig1, out csig1, out ssig2, out csig2,
out eps, out omg12, numit<maxit1, out dv, C1a, C2a, C3a)-lam12;
// 2 * tol0 is approximately 1 ulp for a number in [0, pi].
// Reversed test to allow escape with NaNs
if(tripb||!(Math.Abs(v)>=(tripn?8:2)*tol0)) break;
// Update bracketing values
if(v>0&&(numit>maxit1||calp1/salp1>calp1b/salp1b))
{ salp1b=salp1; calp1b=calp1; }
else if(v<0&&(numit>maxit1||calp1/salp1<calp1a/salp1a))
{ salp1a=salp1; calp1a=calp1; }
if(numit<maxit1&&dv>0)
{
double dalp1=-v/dv;
double sdalp1=Math.Sin(dalp1), cdalp1=Math.Cos(dalp1), nsalp1=salp1*cdalp1+calp1*sdalp1;
if(nsalp1>0&&Math.Abs(dalp1)<pi)
{
calp1=calp1*cdalp1-salp1*sdalp1;
salp1=nsalp1;
norm2(ref salp1, ref calp1);
// In some regimes we don't get quadratic convergence because
// slope -> 0. So use convergence conditions based on epsilon
// instead of sqrt(epsilon).
tripn=Math.Abs(v)<=16*tol0;
continue;
}
}
// Either dv was not postive or updated value was outside legal
// range. Use the midpoint of the bracket as the next estimate.
// This mechanism is not needed for the WGS84 ellipsoid, but it does
// catch problems with more eccentric ellipsoids. Its efficacy is
// such for the WGS84 test set with the starting guess set to alp1 =
// 90deg:
// the WGS84 test set: mean = 5.21, sd = 3.93, max = 24
// WGS84 and random input: mean = 4.74, sd = 0.99
salp1=(salp1a+salp1b)/2;
calp1=(calp1a+calp1b)/2;
norm2(ref salp1, ref calp1);
tripn=false;
tripb=(Math.Abs(salp1a-salp1)+(calp1a-calp1)<tolb||Math.Abs(salp1-salp1b)+(calp1-calp1b)<tolb);
}
{
double dummy;
Lengths(eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
cbet1, cbet2, out s12x, out m12x, out dummy,
(outmask&GEOD.GEODESICSCALE)!=0, out M12, out M21, C1a, C2a);
}
m12x*=b;
s12x*=b;
a12=sig12/degree;
omg12=lam12-omg12;
}
}
if((outmask&GEOD.DISTANCE)!=0) s12=0+s12x; // Convert -0 to 0
if((outmask&GEOD.REDUCEDLENGTH)!=0) m12=0+m12x; // Convert -0 to 0
if((outmask&GEOD.AREA)!=0)
{
// From Lambda12: sin(alp1) * cos(bet1) = sin(alp0)
double salp0=salp1*cbet1;
double calp0=hypotx(calp1, salp1*sbet1); // calp0 > 0
double alp12;
if(calp0!=0&&salp0!=0)
{
// From Lambda12: tan(bet) = tan(sig) * cos(alp)
double ssig1=sbet1;
double csig1=calp1*cbet1;
double ssig2=sbet2;
double csig2=calp2*cbet2;
double k2=sq(calp0)*ep2;
double eps=k2/(2*(1+Math.Sqrt(1+k2))+k2);
// Multiplier = a^2 * e^2 * cos(alpha0) * sin(alpha0).
double A4=sq(a)*calp0*salp0*e2;
double[] C4a=new double[nC4];
norm2(ref ssig1, ref csig1);
norm2(ref ssig2, ref csig2);
C4f(eps, C4a);
double B41=SinCosSeries(false, ssig1, csig1, C4a, nC4);
double B42=SinCosSeries(false, ssig2, csig2, C4a, nC4);
S12=A4*(B42-B41);
}
else S12=0; // Avoid problems with indeterminate sig1, sig2 on equator
if(!meridian&&
omg12<0.75*pi&& // Long difference too big
sbet2-sbet1<1.75)
{ // Lat difference too big
// Use tan(Gamma/2)=tan(omg12/2)*(tan(bet1/2)+tan(bet2/2))/(1+tan(bet1/2)*tan(bet2/2))
// with tan(x/2)=sin(x)/(1+cos(x))
double somg12=Math.Sin(omg12);
double domg12=1+Math.Cos(omg12);
double dbet1=1+cbet1, dbet2=1+cbet2;
alp12=2*Math.Atan2(somg12*(sbet1*dbet2+sbet2*dbet1), domg12*(sbet1*sbet2+dbet1*dbet2));
}
else
{
// alp12 = alp2 - alp1, used in atan2 so no need to normalize
double salp12=salp2*calp1-calp2*salp1;
double calp12=calp2*calp1+salp2*salp1;
// The right thing appears to happen if alp1=+/-180 and alp2=0, viz
// salp12=-0 and alp12=-180. However this depends on the sign
// being attached to 0 correctly. The following ensures the correct
// behavior.
if(salp12==0&&calp12<0)
{
salp12=tiny*calp1;
calp12=-1;
}
alp12=Math.Atan2(salp12, calp12);
}
S12+=c2*alp12;
S12*=swapp*lonsign*latsign;
// Convert -0 to 0
S12+=0;
}
// Convert calp, salp to azimuth accounting for lonsign, swapp, latsign.
if(swapp<0)
{
swapx(ref salp1, ref salp2);
swapx(ref calp1, ref calp2);
if((outmask&GEOD.GEODESICSCALE)!=0)
swapx(ref M12, ref M21);
}
salp1*=swapp*lonsign; calp1*=swapp*latsign;
salp2*=swapp*lonsign; calp2*=swapp*latsign;
if((outmask&GEOD.AZIMUTH)!=0)
{
// minus signs give range [-180, 180). 0- converts -0 to +0.
azi1=0-Math.Atan2(-salp1, calp1)/degree;
azi2=0-Math.Atan2(-salp2, calp2)/degree;
}
ps12=s12;
pazi1=azi1;
pazi2=azi2;
pm12=m12;
pM12=M12;
pM21=M21;
pS12=S12;
// Returned value in [0, 180]
return a12;
}
void geod_lineinit_int(geod_geodesic g, double lat1, double lon1, double azi1, double salp1, double calp1, GEOD caps)
{
a = g.a;
f = g.f;
b = g.b;
c2 = g.c2;
f1 = g.f1;
// If caps is 0 assume the standard direct calculation
this.caps = (caps != 0 ? caps : GEOD.DISTANCE_IN | GEOD.LONGITUDE) |
GEOD.LATITUDE | GEOD.AZIMUTH | GEOD.LONG_UNROLL; // always allow latitude and azimuth and unrolling of longitude
this.lat1 = LatFix(lat1);
this.lon1 = lon1;
this.azi1 = azi1;
this.salp1 = salp1;
this.calp1 = calp1;
double cbet1, sbet1;
sincosdx(AngRound(lat1), out sbet1, out cbet1); sbet1 *= f1;
// Ensure cbet1 = +epsilon at poles
norm2(ref sbet1, ref cbet1); cbet1 = maxx(tiny, cbet1);
dn1 = Math.Sqrt(1 + g.ep2 * sq(sbet1));
// Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0),
salp0 = salp1 * cbet1; // alp0 in [0, pi/2 - |bet1|]
// Alt: calp0 = hypot(sbet1, calp1 * cbet1). The following
// is slightly better (consider the case salp1 = 0).
calp0 = hypotx(calp1, salp1 * sbet1);
// Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1).
// sig = 0 is nearest northward crossing of equator.
// With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line).
// With bet1 = pi/2, alp1 = -pi, sig1 = pi/2
// With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2
// Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1).
// With alp0 in (0, pi/2], quadrants for sig and omg coincide.
// No atan2(0,0) ambiguity at poles since cbet1 = +epsilon.
// With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi.
ssig1 = sbet1; somg1 = salp0 * sbet1;
csig1 = comg1 = sbet1 != 0 || calp1 != 0 ? cbet1 * calp1 : 1;
norm2(ref ssig1, ref csig1); // sig1 in (-pi, pi]
// norm2(somg1, comg1); -- don't need to normalize!
k2 = sq(calp0) * g.ep2;
double eps = k2 / (2 * (1 + Math.Sqrt(1 + k2)) + k2);
if ((this.caps & GEOD.CAP_C1) != 0)
{
double s, c;
A1m1 = geod_geodesic.A1m1f(eps);
geod_geodesic.C1f(eps, C1a);
B11 = SinCosSeries(true, ssig1, csig1, C1a, nC1);
s = Math.Sin(B11); c = Math.Cos(B11);
// tau1=sig1+B11
stau1 = ssig1 * c + csig1 * s;
ctau1 = csig1 * c - ssig1 * s;
// Not necessary because C1pa reverts C1a
// B11=-SinCosSeries(TRUE, stau1, ctau1, C1pa, nC1p);
}
if ((this.caps & GEOD.CAP_C1p) != 0)
geod_geodesic.C1pf(eps, C1pa);
if ((this.caps & GEOD.CAP_C2) != 0)
{
A2m1 = geod_geodesic.A2m1f(eps);
geod_geodesic.C2f(eps, C2a);
B21 = SinCosSeries(true, ssig1, csig1, C2a, nC2);
}
if ((this.caps & GEOD.CAP_C3) != 0)
{
g.C3f(eps, C3a);
A3c = -f * salp0 * g.A3f(eps);
B31 = SinCosSeries(true, ssig1, csig1, C3a, nC3 - 1);
}
if ((this.caps & GEOD.CAP_C4) != 0)
{
g.C4f(eps, C4a);
// Multiplier=a^2*e^2*cos(alpha0)*sin(alpha0)
A4 = sq(a) * calp0 * salp0 * g.e2;
B41 = SinCosSeries(false, ssig1, csig1, C4a, nC4);
}
a13 = s13 = double.NaN;
}
/// <summary>
/// The general direct geodesic problem.
/// </summary>
/// <param name="lat1">The atitude of point 1 (degrees).</param>
/// <param name="lon1">The longitude of point 1 (degrees).</param>
/// <param name="azi1">The azimuth at point 1 (degrees).</param>
/// <param name="flags">Bitor'ed combination of <see cref="GEOD"/> flags; GEOD.ARCMODE
/// determines the meaning of s12_a12 and GEOD.LONG_UNROLL "unrolls" lon2.</param>
/// <param name="s12_a12">If flags&GEOD.ARCMODE is 0, this is the
/// distance between point 1 and point 2 (meters); otherwise it is the
/// arc length between point 1 and point 2 (degrees); it can be negative.</param>
/// <param name="outmask">The mask specifying the values to calculate.</param>
/// <param name="plat2">The latitude of point 2 (degrees).</param>
/// <param name="plon2">The longitude of point 2 (degrees).</param>
/// <param name="pazi2">The (forward) azimuth at point 2 (degrees).</param>
/// <param name="ps12">The distance between point 1 and point 2 (meters).</param>
/// <param name="pm12">The reduced length of geodesic (meters).</param>
/// <param name="pM12">The geodesic scale of point 2 relative to point 1 (dimensionless).</param>
/// <param name="pM21">The geodesic scale of point 1 relative to point 2 (dimensionless).</param>
/// <param name="pS12">The area under the geodesic (square meters).</param>
/// <remarks>
/// g must have been initialized with a call to geod_init(). lat1
/// should be in the range [-90deg, 90deg]; lon1 and azi1
/// should be in the range [-540deg, 540deg). The function
/// value a12 equals s12_a12 if flags & GEOD.ARCMODE.
///
/// With <paramref name="flags"/> & GEOD.LONG_UNROLL bit set, the longitude is "unrolled" so
/// that the quantity lon2-lon1 indicates how many times and in
/// what sense the geodesic encircles the ellipsoid. Because lon2 might be
/// outside the normal allowed range for longitudes, [-540deg, 540deg), be sure to normalize
/// it, e.g., with fmod(lon2, 360.0) before using it in subsequent calculations.
///</remarks>
/// <returns>a12 arc length of between point 1 and point 2 (degrees).</returns>
public double geod_gendirect(double lat1, double lon1, double azi1, GEOD flags, double s12_a12, GEOD outmask,
out double plat2, out double plon2, out double pazi2, out double ps12, out double pm12, out double pM12, out double pM21, out double pS12)
{
geod_geodesicline l=new geod_geodesicline(this, lat1, lon1, azi1, outmask|((flags&GEOD.ARCMODE)!=0?GEOD.NONE:GEOD.DISTANCE_IN)); // Automatically supply GEOD_DISTANCE_IN if necessary
return l.geod_genposition(flags, s12_a12, outmask, out plat2, out plon2, out pazi2, out ps12, out pm12, out pM12, out pM21, out pS12);
}
/// <summary>
/// Specify position of point 3 in terms of either distance or arc length.
/// </summary>
/// <param name="flags">Must be either <see cref="GEOD.NOFLAGS"/> or <see cref="GEOD.ARCMODE"/> to determining the meaning of the <paramref name="s13_a13"/>.</param>
/// <param name="s13_a13">if <paramref name="flags"/> = <see cref="GEOD.NOFLAGS"/>, this is the distance from point 1 to point 3 (meters);
/// if <paramref name="flags"/> = <see cref="GEOD.ARCMODE"/>, it is the arc length from point 1 to point 3 (degrees); it can be negative.</param>
/// <remarks>
/// If <paramref name="flags"/> = <see cref="GEOD.NOFLAGS"/>, this calls <see cref="geod_setdistance"/>.
/// If <paramref name="flags"/> = <see cref="GEOD.ARCMODE"/>, the s13 is only set if the <see cref="geod_geodesicline"/>
/// object has been constructed with caps |= <see cref="GEOD.DISTANCE"/>.
/// </remarks>
public void geod_gensetdistance(GEOD flags, double s13_a13)
{
if ((flags & GEOD.ARCMODE) == GEOD.ARCMODE) geod_setarc(s13_a13);
else geod_setdistance(s13_a13);
}
/// <summary>
/// Initialize a geod_geodesicline object in terms of the inverse geodesic problem.
/// </summary>
/// <param name="g">The <see cref="geod_geodesic"/> object specifying the ellipsoid.</param>
/// <param name="lat1">Latitude of point 1 (degrees).</param>
/// <param name="lon1">Longitude of point 1 (degrees).</param>
/// <param name="lat2">Latitude of point 2 (degrees).</param>
/// <param name="lon2">Longitude of point 2 (degrees).</param>
/// <param name="caps">Bitor'ed combination of <see cref="geod_mask"/> values. See remarks for more informations.</param>
/// <remarks>
/// <paramref name="caps"/> bitor'ed combination of geod_mask() values specifying
/// the capabilities the geod_geodesicline object should possess, i.e., which
/// quantities can be returned in calls to geod_position() and
/// geod_genposition().
///
/// This function sets point 3 of the geod_geodesicline to correspond to point
/// 2 of the direct geodesic problem. See geod_lineinit() for more
/// information.
/// </remarks>
public void geod_inverseline(geod_geodesic g, double lat1, double lon1, double lat2, double lon2, GEOD caps)
{
double salp1, calp1, dummy;
double a12 = g.geod_geninverse_int(lat1, lon1, lat2, lon2, out dummy, out salp1, out calp1, out dummy, out dummy, out dummy, out dummy, out dummy, out dummy);
double azi1 = atan2dx(salp1, calp1);
caps = caps != 0 ? caps : GEOD.DISTANCE_IN | GEOD.LONGITUDE;
// Ensure that a12 can be converted to a distance
if ((caps & (GEOD.OUT_ALL & GEOD.DISTANCE_IN)) != 0) caps |= GEOD.DISTANCE;
geod_lineinit_int(g, lat1, lon1, azi1, salp1, calp1, caps);
geod_setarc(a12);
}
/// <summary>
/// geod_gendirectline : Initialize a geod_geodesicline object in terms of the direct geodesic
/// problem specified in terms of either distance or arc length.
/// </summary>
/// <param name="g">The <see cref="geod_geodesic"/> object specifying the ellipsoid.</param>
/// <param name="lat1">Latitude of point 1 (degrees).</param>
/// <param name="lon1">Longitude of point 1 (degrees).</param>
/// <param name="azi1">Azimuth at point 1 (degrees).</param>
/// <param name="flags">Must be either <see cref="GEOD.NOFLAGS"/> or <see cref="GEOD.ARCMODE"/> to determining the meaning of the <paramref name="s12_a12"/>.</param>
/// <param name="s12_a12">if <paramref name="flags"/> = <see cref="GEOD.NOFLAGS"/>, this is the distance from point 1 to point 2 (meters);
/// if <paramref name="flags"/> = <see cref="GEOD.ARCMODE"/>, it is the arc length from point 1 to point 2 (degrees); it can be negative.</param>
/// <param name="caps">Bitor'ed combination of <see cref="geod_mask"/> values. See remarks for more informations.</param>
/// <remarks>
/// <paramref name="caps"/> bitor'ed combination of geod_mask() values specifying
/// the capabilities the geod_geodesicline object should possess, i.e., which
/// quantities can be returned in calls to geod_position() and
/// geod_genposition().
///
/// This function sets point 3 of the geod_geodesicline to correspond to point
/// 2 of the direct geodesic problem. See geod_lineinit() for more
/// information.
/// </remarks>
public geod_geodesicline(geod_geodesic g, double lat1, double lon1, double azi1, GEOD flags, double s12_a12, GEOD caps) : this(g, lat1, lon1, azi1, caps)
{
geod_gensetdistance(flags, s12_a12);
}
/// <summary>
/// The general position function.
/// </summary>
/// <param name="flags">Bitor'ed combination of <see cref="GEOD"/> flags; GEOD.ARCMODE
/// determines the meaning of s12_a12 and GEOD.LONG_UNROLL "unrolls" lon2; if flags&GEOD.ARCMODE is 0,
/// then l must have been initialized with caps|=GEOD.DISTANCE_IN.</param>
/// <param name="s12_a12">If flags&GEOD_ARCMODE is 0, this is the
/// distance from point 1 to point 2 (meters); otherwise it is the
/// arc length from point 1 to point 2 (degrees); it can be negative.</param>
/// <param name="plat2">The latitude of point 2 (degrees).</param>
/// <param name="plon2">The longitude of point 2 (degrees); requires
/// that l was initialized with caps|=GEOD.LONGITUDE.</param>
/// <param name="pazi2">The (forward) azimuth at point 2 (degrees).</param>
/// <param name="ps12">The distance from point 1 to point 2 (meters); requires that
/// l was initialized with caps|=GEOD.DISTANCE.</param>
/// <param name="pm12">The reduced length of geodesic (meters);
/// requires that l was initialized with caps|=GEOD.REDUCEDLENGTH.</param>
/// <param name="pM12">The geodesic scale of point 2 relative to point 1 (dimensionless);
/// requires that l was initialized with caps|=GEOD.GEODESICSCALE.</param>
/// <param name="pM21">The geodesic scale of point 1 relative to point 2 (dimensionless);
/// requires that l was initialized with caps|=GEOD.GEODESICSCALE.</param>
/// <param name="pS12">The area under the geodesic (square meters); requires that l
/// was initialized with caps|=GEOD.AREA.</param>
/// <remarks>
/// l must have been initialized with a call to geod_lineinit() with caps|=GEOD.DISTANCE_IN.
/// The value azi2 returned is in the range [-180deg, 180deg).
///
/// Requesting a value which l is not capable of computing
/// is not an error; the corresponding argument will not be altered.
///
/// With <paramref name="flags"/> & GEOD.LONG_UNROLL bit set, the longitude is "unrolled" so
/// that the quantity lon2-lon1 indicates how many times and in
/// what sense the geodesic encircles the ellipsoid.
///</remarks>
/// <returns>a12 arc length from point 1 to point 2 (degrees).</returns>
public double geod_genposition(GEOD flags, double s12_a12,
out double plat2, out double plon2, out double pazi2, out double ps12, out double pm12, out double pM12, out double pM21, out double pS12)
{
double lat2 = 0, lon2 = 0, azi2 = 0, s12 = 0, m12 = 0, M12 = 0, M21 = 0, S12 = 0;
// Avoid warning about uninitialized B12.
double sig12, ssig12, csig12, B12 = 0, AB1 = 0;
double omg12, lam12, lon12;
double ssig2, csig2, sbet2, cbet2, somg2, comg2, salp2, calp2, dn2;
GEOD outmask = GEOD.LATITUDE | GEOD.LONGITUDE | GEOD.AZIMUTH | GEOD.DISTANCE | GEOD.REDUCEDLENGTH | GEOD.GEODESICSCALE | GEOD.AREA;
outmask &= caps & GEOD.OUT_ALL;
if (!(((flags & GEOD.ARCMODE) != 0 || (caps & (GEOD.DISTANCE_IN & GEOD.OUT_ALL)) != 0)))
{
plat2 = plon2 = pazi2 = ps12 = pm12 = pM12 = pM21 = pS12 = 0;
// Uninitialized or impossible distance calculation requested
return NaN;
}
if ((flags & GEOD.ARCMODE) != 0)
{
// Interpret s12_a12 as spherical arc length
sig12 = s12_a12 * degree;
sincosdx(s12_a12, out ssig12, out csig12);
}
else
{
// Interpret s12_a12 as distance
double tau12 = s12_a12 / (b * (1 + A1m1));
double s = Math.Sin(tau12);
double c = Math.Cos(tau12);
// tau2=tau1+tau12
B12 = -SinCosSeries(true, stau1 * c + ctau1 * s, ctau1 * c - stau1 * s, C1pa, nC1p);
sig12 = tau12 - (B12 - B11);
ssig12 = Math.Sin(sig12); csig12 = Math.Cos(sig12);
if (Math.Abs(f) > 0.01)
{
// Reverted distance series is inaccurate for |f|>1/100, so correct
// sig12 with 1 Newton iteration. The following table shows the
// approximate maximum error for a=WGS_a() and various f relative to
// GeodesicExact.
// erri = the error in the inverse solution (nm)
// errd = the error in the direct solution (series only) (nm)
// errda = the error in the direct solution (series + 1 Newton) (nm)
//
// f erri errd errda
// -1/5 12e6 1.2e9 69e6
// -1/10 123e3 12e6 765e3
// -1/20 1110 108e3 7155
// -1/50 18.63 200.9 27.12
// -1/100 18.63 23.78 23.37
// -1/150 18.63 21.05 20.26
// 1/150 22.35 24.73 25.83
// 1/100 22.35 25.03 25.31
// 1/50 29.80 231.9 30.44
// 1/20 5376 146e3 10e3
// 1/10 829e3 22e6 1.5e6
// 1/5 157e6 3.8e9 280e6
ssig2 = ssig1 * csig12 + csig1 * ssig12;
csig2 = csig1 * csig12 - ssig1 * ssig12;
B12 = SinCosSeries(true, ssig2, csig2, C1a, nC1);
double serr = (1 + A1m1) * (sig12 + (B12 - B11)) - s12_a12 / b;
sig12 = sig12 - serr / Math.Sqrt(1 + k2 * sq(ssig2));
ssig12 = Math.Sin(sig12); csig12 = Math.Cos(sig12);
// Update B12 below
}
}
// sig2=sig1+sig12
ssig2 = ssig1 * csig12 + csig1 * ssig12;
csig2 = csig1 * csig12 - ssig1 * ssig12;
dn2 = Math.Sqrt(1 + k2 * sq(ssig2));
if ((outmask & (GEOD.DISTANCE | GEOD.REDUCEDLENGTH | GEOD.GEODESICSCALE)) != 0)
{
if ((flags & GEOD.ARCMODE) != 0 || Math.Abs(f) > 0.01)
B12 = SinCosSeries(true, ssig2, csig2, C1a, nC1);
AB1 = (1 + A1m1) * (B12 - B11);
}
// sin(bet2)=cos(alp0)*sin(sig2)
sbet2 = calp0 * ssig2;
// Alt: cbet2=hypot(csig2, salp0*ssig2);
cbet2 = hypotx(salp0, calp0 * csig2);
if (cbet2 == 0) cbet2 = csig2 = tiny; // I.e., salp0=0, csig2=0. Break the degeneracy in this case
// tan(alp0) = cos(sig2)*tan(alp2)
salp2 = salp0; calp2 = calp0 * csig2; // No need to normalize
if ((outmask & GEOD.DISTANCE) != 0) s12 = (flags & GEOD.ARCMODE) != 0 ? b * ((1 + A1m1) * sig12 + AB1) : s12_a12;
if ((outmask & GEOD.LONGITUDE) != 0)
{
double E = copysignx(1, salp0); // east or west going?
// tan(omg2)=sin(alp0)*tan(sig2)
somg2 = salp0 * ssig2; comg2 = csig2; // No need to normalize
// omg12=omg2-omg1
omg12 = (flags & GEOD.LONG_UNROLL) != 0 ?
E * (sig12
- (Math.Atan2(ssig2, csig2) - Math.Atan2(ssig1, csig1))
+ (Math.Atan2(E * somg2, comg2) - Math.Atan2(E * somg1, comg1))) :
Math.Atan2(somg2 * comg1 - comg2 * somg1, comg2 * comg1 + somg2 * somg1);
lam12 = omg12 + A3c * (sig12 + (SinCosSeries(true, ssig2, csig2, C3a, nC3 - 1) - B31));
lon12 = lam12 / degree;
lon2 = (flags & GEOD.LONG_UNROLL) != 0 ? lon1 + lon12 : AngNormalize(AngNormalize(lon1) + AngNormalize(lon12));
}
if ((outmask & GEOD.LATITUDE) != 0) lat2 = atan2dx(sbet2, f1 * cbet2);
if ((outmask & GEOD.AZIMUTH) != 0) azi2 = atan2dx(salp2, calp2);
if ((outmask & (GEOD.REDUCEDLENGTH | GEOD.GEODESICSCALE)) != 0)
{
double B22 = SinCosSeries(true, ssig2, csig2, C2a, nC2);
double AB2 = (1 + A2m1) * (B22 - B21);
double J12 = (A1m1 - A2m1) * sig12 + (AB1 - AB2);
if ((outmask & GEOD.REDUCEDLENGTH) != 0)
// Add parens around (csig1 * ssig2) and (ssig1 * csig2) to ensure
// accurate cancellation in the case of coincident points.
m12 = b * ((dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2)) - csig1 * csig2 * J12);
if ((outmask & GEOD.GEODESICSCALE) != 0)
{
double t = k2 * (ssig2 - ssig1) * (ssig2 + ssig1) / (dn1 + dn2);
M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1;
M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2;
}
}
if ((outmask & GEOD.AREA) != 0)
{
double B42 = SinCosSeries(false, ssig2, csig2, C4a, nC4);
double salp12, calp12;
if (calp0 == 0 || salp0 == 0)
{
// alp12=alp2-alp1, used in atan2 so no need to normalize
salp12 = salp2 * calp1 - calp2 * salp1;
calp12 = calp2 * calp1 + salp2 * salp1;
}
else
{
// tan(alp)=tan(alp0)*sec(sig)
// tan(alp2-alp1)=(tan(alp2)-tan(alp1))/(tan(alp2)*tan(alp1)+1)
// =calp0*salp0*(csig1-csig2)/(salp0^2+calp0^2*csig1*csig2)
// If csig12>0, write
// csig1-csig2=ssig12*(csig1*ssig12/(1+csig12)+ssig1)
// else
// csig1-csig2=csig1*(1-csig12)+ssig12*ssig1
// No need to normalize
salp12 = calp0 * salp0 * (csig12 <= 0 ? csig1 * (1 - csig12) + ssig12 * ssig1 : ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1));
calp12 = sq(salp0) + sq(calp0) * csig1 * csig2;
}
S12 = c2 * Math.Atan2(salp12, calp12) + A4 * (B42 - B41);
}
plat2 = lat2;
plon2 = lon2;
pazi2 = azi2;
ps12 = s12;
pm12 = m12;
pM12 = M12;
pM21 = M21;
pS12 = S12;
return (flags & GEOD.ARCMODE) != 0 ? s12_a12 : sig12 / degree;
}
/// <summary>
/// geod_directline : Initialize a geod_geodesicline object in terms of the direct geodesic problem.
/// </summary>
/// <param name="g">The <see cref="geod_geodesic"/> object specifying the ellipsoid.</param>
/// <param name="lat1">Latitude of point 1 (degrees).</param>
/// <param name="lon1">Longitude of point 1 (degrees).</param>
/// <param name="azi1">Azimuth at point 1 (degrees).</param>
/// <param name="s12">Distance from point 1 to point 2 (meters); it can be negative.</param>
/// <param name="caps">Bitor'ed combination of <see cref="geod_mask"/> values. See remarks for more informations.</param>
/// <remarks>
/// <paramref name="caps"/> bitor'ed combination of geod_mask() values specifying
/// the capabilities the geod_geodesicline object should possess, i.e., which
/// quantities can be returned in calls to geod_position() and
/// geod_genposition().
///
/// This function sets point 3 of the geod_geodesicline to correspond to point
/// 2 of the direct geodesic problem. See geod_lineinit() for more
/// information.
/// </remarks>
public geod_geodesicline(geod_geodesic g, double lat1, double lon1, double azi1, double s12, GEOD caps) : this(g, lat1, lon1, azi1, GEOD.NOFLAGS, s12, caps)
{ }
/// <summary>
/// geod_lineinit : Initialize a geod_geodesicline object.
/// </summary>
/// <param name="g">The <see cref="geod_geodesic"/> object specifying the ellipsoid.</param>
/// <param name="lat1">Latitude of point 1 (degrees).</param>
/// <param name="lon1">Longitude of point 1 (degrees).</param>
/// <param name="azi1">Azimuth at point 1 (degrees).</param>
/// <param name="caps">Bitor'ed combination of <see cref="geod_mask"/> values. See remarks for more informations.</param>
/// <remarks>
/// <paramref name="caps"/> bitor'ed combination of geod_mask() values specifying
/// the capabilities the geod_geodesicline object should possess, i.e., which
/// quantities can be returned in calls to geod_position() and
/// geod_genposition().
///
/// <paramref name="lat1"/> should be in the range [-90deg, 90deg].
///
/// The geod_mask values are:
/// - caps|=GEOD_LATITUDE for the latitude lat2; this is added automatically,
/// - caps|=GEOD_LONGITUDE for the latitude lon2,
/// - caps|=GEOD_AZIMUTH for the latitude azi2; this is added automatically,
/// - caps|=GEOD_DISTANCE for the distance s12,
/// - caps|=GEOD_REDUCEDLENGTH for the reduced length m12,
/// - caps|=GEOD_GEODESICSCALE for the geodesic scales M12 and M21,
/// - caps|=GEOD_AREA for the area S12,
/// - caps|=GEOD_DISTANCE_IN permits the length of the
/// geodesic to be given in terms of s12; without this capability the
/// length can only be specified in terms of arc length.
///
/// A value of caps=0 is treated as GEOD.LATITUDE|GEOD.LONGITUDE|GEOD.AZIMUTH|GEOD.DISTANCE_IN
/// (to support the solution of the "standard" direct problem).
///
/// When initialized by this function, point 3 is undefined (s13 = a13 = NaN).
/// </remarks>
public geod_geodesicline(geod_geodesic g, double lat1, double lon1, double azi1, GEOD caps)
{
azi1 = AngNormalize(azi1);
double salp1, calp1;
// Guard against underflow in salp0
sincosdx(AngRound(azi1), out salp1, out calp1);
geod_lineinit_int(g, lat1, lon1, azi1, salp1, calp1, caps);
}
/// <summary>
/// Initialize a geod_geodesicline object.
/// </summary>
/// <param name="g">The <see cref="geod_geodesic"/> object specifying the ellipsoid.</param>
/// <param name="lat1">Latitude of point 1 (degrees).</param>
/// <param name="lon1">Longitude of point 1 (degrees).</param>
/// <param name="azi1">Azimuth at point 1 (degrees).</param>
/// <param name="caps">Bitor'ed combination of <see cref="geod_mask"/> values. See remarks for more informations.</param>
/// <remarks>
/// <paramref name="caps"/> bitor'ed combination of geod_mask() values specifying
/// the capabilities the geod_geodesicline object should possess, i.e., which
/// quantities can be returned in calls to geod_position() and
/// geod_genposition().
///
/// <paramref name="lat1"/> should be in the range [-90deg, 90deg].
/// <paramref name="lon1"/> and <paramref name="azi1"/> should be in the range [-540deg, 540deg).
///
/// The geod_mask values are:
/// - caps|=GEOD_LATITUDE for the latitude lat2; this is added automatically,
/// - caps|=GEOD_LONGITUDE for the latitude lon2,
/// - caps|=GEOD_AZIMUTH for the latitude azi2; this is added automatically,
/// - caps|=GEOD_DISTANCE for the distance s12,
/// - caps|=GEOD_REDUCEDLENGTH for the reduced length m12,
/// - caps|=GEOD_GEODESICSCALE for the geodesic scales M12 and M21,
/// - caps|=GEOD_AREA for the area S12,
/// - caps|=GEOD_DISTANCE_IN permits the length of the
/// geodesic to be given in terms of s12; without this capability the
/// length can only be specified in terms of arc length.
///
/// A value of caps=0 is treated as GEOD.LATITUDE|GEOD.LONGITUDE|GEOD.AZIMUTH|GEOD.DISTANCE_IN
/// (to support the solution of the "standard" direct problem).
/// </remarks>
public geod_geodesicline(geod_geodesic g, double lat1, double lon1, double azi1, GEOD caps)
{
a = g.a;
f = g.f;
b = g.b;
c2 = g.c2;
f1 = g.f1;
// If caps is 0 assume the standard direct calculation
this.caps = (caps != 0?caps:GEOD.DISTANCE_IN | GEOD.LONGITUDE) |
GEOD.LATITUDE | GEOD.AZIMUTH | GEOD.LONG_UNROLL; // always allow latitude and azimuth and unrolling of longitude
this.lat1 = lat1;
this.lon1 = lon1;
// Guard against underflow in salp0
this.azi1 = AngRound(AngNormalize(azi1));
// alp1 is in [0, pi]
double alp1 = this.azi1 * degree;
// Enforce sin(pi)==0 and cos(pi/2)==0. Better to face the ensuing
// problems directly than to skirt them.
salp1 = this.azi1 == -180?0:Math.Sin(alp1);
calp1 = Math.Abs(this.azi1) == 90?0:Math.Cos(alp1);
double phi = lat1 * degree;
// Ensure cbet1=+epsilon at poles
double sbet1 = f1 * Math.Sin(phi);
double cbet1 = Math.Abs(lat1) == 90?tiny:Math.Cos(phi);
norm2(ref sbet1, ref cbet1);
dn1 = Math.Sqrt(1 + g.ep2 * sq(sbet1));
// Evaluate alp0 from sin(alp1)*cos(bet1)=sin(alp0),
salp0 = salp1 * cbet1; // alp0 in [0, pi/2-|bet1|]
// Alt: calp0=hypot(sbet1, calp1*cbet1). The following
// is slightly better (consider the case salp1=0).
calp0 = hypotx(calp1, salp1 * sbet1);
// Evaluate sig with tan(bet1)=tan(sig1)*cos(alp1).
// sig = 0 is nearest northward crossing of equator.
// With bet1=0, alp1=pi/2, we have sig1=0 (equatorial line).
// With bet1=pi/2, alp1=-pi, sig1=pi/2
// With bet1=-pi/2, alp1=0, sig1=-pi/2
// Evaluate omg1 with tan(omg1)=sin(alp0)*tan(sig1).
// With alp0 in (0, pi/2], quadrants for sig and omg coincide.
// No atan2(0, 0) ambiguity at poles since cbet1=+epsilon.
// With alp0=0, omg1=0 for alp1=0, omg1=pi for alp1=pi.
ssig1 = sbet1; somg1 = salp0 * sbet1;
csig1 = comg1 = sbet1 != 0 || calp1 != 0?cbet1 * calp1:1;
norm2(ref ssig1, ref csig1); // sig1 in (-pi, pi]
// norm2(ref somg1, ref comg1); -- don't need to normalize!
k2 = sq(calp0) * g.ep2;
double eps = k2 / (2 * (1 + Math.Sqrt(1 + k2)) + k2);
if ((this.caps & GEOD.CAP_C1) != 0)
{
double s, c;
A1m1 = geod_geodesic.A1m1f(eps);
geod_geodesic.C1f(eps, C1a);
B11 = SinCosSeries(true, ssig1, csig1, C1a, nC1);
s = Math.Sin(B11); c = Math.Cos(B11);
// tau1=sig1+B11
stau1 = ssig1 * c + csig1 * s;
ctau1 = csig1 * c - ssig1 * s;
// Not necessary because C1pa reverts C1a
// B11=-SinCosSeries(TRUE, stau1, ctau1, C1pa, nC1p);
}
if ((this.caps & GEOD.CAP_C1p) != 0)
{
geod_geodesic.C1pf(eps, C1pa);
}
if ((this.caps & GEOD.CAP_C2) != 0)
{
A2m1 = geod_geodesic.A2m1f(eps);
geod_geodesic.C2f(eps, C2a);
B21 = SinCosSeries(true, ssig1, csig1, C2a, nC2);
}
if ((this.caps & GEOD.CAP_C3) != 0)
{
g.C3f(eps, C3a);
A3c = -f *salp0 *g.A3f(eps);
B31 = SinCosSeries(true, ssig1, csig1, C3a, nC3 - 1);
}
if ((this.caps & GEOD.CAP_C4) != 0)
{
g.C4f(eps, C4a);
// Multiplier=a^2*e^2*cos(alpha0)*sin(alpha0)
A4 = sq(a) * calp0 * salp0 * g.e2;
B41 = SinCosSeries(false, ssig1, csig1, C4a, nC4);
}
}
/// <summary>
/// The general position function.
/// </summary>
/// <param name="flags">Bitor'ed combination of <see cref="GEOD"/> flags; GEOD.ARCMODE
/// determines the meaning of s12_a12 and GEOD.LONG_UNROLL "unrolls" lon2; if flags&GEOD.ARCMODE is 0,
/// then l must have been initialized with caps|=GEOD.DISTANCE_IN.</param>
/// <param name="s12_a12">If flags&GEOD_ARCMODE is 0, this is the
/// distance between point 1 and point 2 (meters); otherwise it is the
/// arc length between point 1 and point 2 (degrees); it can be negative.</param>
/// <param name="outmask">The mask specifying the values to calculate.</param>
/// <param name="plat2">The latitude of point 2 (degrees).</param>
/// <param name="plon2">The longitude of point 2 (degrees); requires
/// that l was initialized with caps|=GEOD.LONGITUDE.</param>
/// <param name="pazi2">The (forward) azimuth at point 2 (degrees).</param>
/// <param name="ps12">The distance between point 1 and point 2 (meters); requires that
/// l was initialized with caps|=GEOD.DISTANCE.</param>
/// <param name="pm12">The reduced length of geodesic (meters);
/// requires that l was initialized with caps|=GEOD.REDUCEDLENGTH.</param>
/// <param name="pM12">The geodesic scale of point 2 relative to point 1 (dimensionless);
/// requires that l was initialized with caps|=GEOD.GEODESICSCALE.</param>
/// <param name="pM21">The geodesic scale of point 1 relative to point 2 (dimensionless);
/// requires that l was initialized with caps|=GEOD.GEODESICSCALE.</param>
/// <param name="pS12">The area under the geodesic (square meters); requires that l
/// was initialized with caps|=GEOD.AREA.</param>
/// <remarks>
/// l must have been initialized with a call to geod_lineinit() with caps|=GEOD.DISTANCE_IN.
/// The value azi2 returned is in the range [-180deg, 180deg).
///
/// Requesting a value which l is not capable of computing
/// is not an error; the corresponding argument will not be altered.
///
/// With <paramref name="flags"/> & GEOD.LONG_UNROLL bit set, the longitude is "unrolled" so
/// that the quantity lon2-lon1 indicates how many times and in
/// what sense the geodesic encircles the ellipsoid. Because lon2 might be
/// outside the normal allowed range for longitudes, [-540deg, 540deg), be sure to normalize
/// it, e.g., with fmod(lon2, 360.0) before using it in subsequent calculations.
///</remarks>
/// <returns>a12 arc length of between point 1 and point 2 (degrees).</returns>
public double geod_genposition(GEOD flags, double s12_a12, GEOD outmask,
out double plat2, out double plon2, out double pazi2, out double ps12, out double pm12, out double pM12, out double pM21, out double pS12)
{
double lat2 = 0, lon2 = 0, azi2 = 0, s12 = 0, m12 = 0, M12 = 0, M21 = 0, S12 = 0;
// Avoid warning about uninitialized B12.
double sig12, ssig12, csig12, B12 = 0, AB1 = 0;
double omg12, lam12, lon12;
double ssig2, csig2, sbet2, cbet2, somg2, comg2, salp2, calp2, dn2;
outmask &= caps & GEOD.OUT_ALL;
if (!(((flags & GEOD.ARCMODE) != 0 || (caps & GEOD.DISTANCE_IN & GEOD.OUT_ALL) != 0)))
{
plat2 = plon2 = pazi2 = ps12 = pm12 = pM12 = pM21 = pS12 = 0;
// Uninitialized or impossible distance calculation requested
return(NaN);
}
if ((flags & GEOD.ARCMODE) != 0)
{
// Interpret s12_a12 as spherical arc length
sig12 = s12_a12 * degree;
double s12a = Math.Abs(s12_a12);
s12a -= 180 * Math.Floor(s12a / 180);
ssig12 = s12a == 0?0:Math.Sin(sig12);
csig12 = s12a == 90?0:Math.Cos(sig12);
}
else
{
// Interpret s12_a12 as distance
double tau12 = s12_a12 / (b * (1 + A1m1));
double s = Math.Sin(tau12);
double c = Math.Cos(tau12);
// tau2=tau1+tau12
B12 = -SinCosSeries(true, stau1 * c + ctau1 * s, ctau1 * c - stau1 * s, C1pa, nC1p);
sig12 = tau12 - (B12 - B11);
ssig12 = Math.Sin(sig12); csig12 = Math.Cos(sig12);
if (Math.Abs(f) > 0.01)
{
// Reverted distance series is inaccurate for |f|>1/100, so correct
// sig12 with 1 Newton iteration. The following table shows the
// approximate maximum error for a=WGS_a() and various f relative to
// GeodesicExact.
// erri = the error in the inverse solution (nm)
// errd = the error in the direct solution (series only) (nm)
// errda = the error in the direct solution (series + 1 Newton) (nm)
//
// f erri errd errda
// -1/5 12e6 1.2e9 69e6
// -1/10 123e3 12e6 765e3
// -1/20 1110 108e3 7155
// -1/50 18.63 200.9 27.12
// -1/100 18.63 23.78 23.37
// -1/150 18.63 21.05 20.26
// 1/150 22.35 24.73 25.83
// 1/100 22.35 25.03 25.31
// 1/50 29.80 231.9 30.44
// 1/20 5376 146e3 10e3
// 1/10 829e3 22e6 1.5e6
// 1/5 157e6 3.8e9 280e6
ssig2 = ssig1 * csig12 + csig1 * ssig12;
csig2 = csig1 * csig12 - ssig1 * ssig12;
B12 = SinCosSeries(true, ssig2, csig2, C1a, nC1);
double serr = (1 + A1m1) * (sig12 + (B12 - B11)) - s12_a12 / b;
sig12 = sig12 - serr / Math.Sqrt(1 + k2 * sq(ssig2));
ssig12 = Math.Sin(sig12); csig12 = Math.Cos(sig12);
// Update B12 below
}
}
// sig2=sig1+sig12
ssig2 = ssig1 * csig12 + csig1 * ssig12;
csig2 = csig1 * csig12 - ssig1 * ssig12;
dn2 = Math.Sqrt(1 + k2 * sq(ssig2));
if ((outmask & (GEOD.DISTANCE | GEOD.REDUCEDLENGTH | GEOD.GEODESICSCALE)) != 0)
{
if ((flags & GEOD.ARCMODE) != 0 || Math.Abs(f) > 0.01)
{
B12 = SinCosSeries(true, ssig2, csig2, C1a, nC1);
}
AB1 = (1 + A1m1) * (B12 - B11);
}
// sin(bet2)=cos(alp0)*sin(sig2)
sbet2 = calp0 * ssig2;
// Alt: cbet2=hypot(csig2, salp0*ssig2);
cbet2 = hypotx(salp0, calp0 * csig2);
if (cbet2 == 0)
{
cbet2 = csig2 = tiny; // I.e., salp0=0, csig2=0. Break the degeneracy in this case
}
// tan(alp0) = cos(sig2)*tan(alp2)
salp2 = salp0; calp2 = calp0 * csig2; // No need to normalize
if ((outmask & GEOD.DISTANCE) != 0)
{
s12 = (flags & GEOD.ARCMODE) != 0?b * ((1 + A1m1) * sig12 + AB1):s12_a12;
}
if ((outmask & GEOD.LONGITUDE) != 0)
{
int E = salp0 < 0?-1:1; // east or west going?
// tan(omg2)=sin(alp0)*tan(sig2)
somg2 = salp0 * ssig2; comg2 = csig2; // No need to normalize
// omg12=omg2-omg1
omg12 = (flags & GEOD.LONG_UNROLL) != 0?
E * (sig12
- (Math.Atan2(ssig2, csig2) - Math.Atan2(ssig1, csig1))
+ (Math.Atan2(E * somg2, comg2) - Math.Atan2(E * somg1, comg1))):
Math.Atan2(somg2 * comg1 - comg2 * somg1, comg2 * comg1 + somg2 * somg1);
lam12 = omg12 + A3c * (sig12 + (SinCosSeries(true, ssig2, csig2, C3a, nC3 - 1) - B31));
lon12 = lam12 / degree;
// Use AngNormalize2 because longitude might have wrapped multiple times.
lon2 = (flags & GEOD.LONG_UNROLL) != 0?lon1 + lon12:AngNormalize(AngNormalize(lon1) + AngNormalize2(lon12));
}
if ((outmask & GEOD.LATITUDE) != 0)
{
lat2 = Math.Atan2(sbet2, f1 * cbet2) / degree;
}
if ((outmask & GEOD.AZIMUTH) != 0)
{
azi2 = 0 - Math.Atan2(-salp2, calp2) / degree; // minus signs give range [-180, 180). 0- converts -0 to +0.
}
if ((outmask & (GEOD.REDUCEDLENGTH | GEOD.GEODESICSCALE)) != 0)
{
double B22 = SinCosSeries(true, ssig2, csig2, C2a, nC2);
double AB2 = (1 + A2m1) * (B22 - B21);
double J12 = (A1m1 - A2m1) * sig12 + (AB1 - AB2);
if ((outmask & GEOD.REDUCEDLENGTH) != 0)
{
// Add parens around (csig1 * ssig2) and (ssig1 * csig2) to ensure
// accurate cancellation in the case of coincident points.
m12 = b * ((dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2)) - csig1 * csig2 * J12);
}
if ((outmask & GEOD.GEODESICSCALE) != 0)
{
double t = k2 * (ssig2 - ssig1) * (ssig2 + ssig1) / (dn1 + dn2);
M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1;
M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2;
}
}
if ((outmask & GEOD.AREA) != 0)
{
double B42 = SinCosSeries(false, ssig2, csig2, C4a, nC4);
double salp12, calp12;
if (calp0 == 0 || salp0 == 0)
{
// alp12=alp2-alp1, used in atan2 so no need to normalize
salp12 = salp2 * calp1 - calp2 * salp1;
calp12 = calp2 * calp1 + salp2 * salp1;
// The right thing appears to happen if alp1=+/-180 and alp2=0, viz
// salp12=-0 and alp12=-180. However this depends on the sign being
// attached to 0 correctly. The following ensures the correct
// behavior.
if (salp12 == 0 && calp12 < 0)
{
salp12 = tiny * calp1;
calp12 = -1;
}
}
else
{
// tan(alp)=tan(alp0)*sec(sig)
// tan(alp2-alp1)=(tan(alp2)-tan(alp1))/(tan(alp2)*tan(alp1)+1)
// =calp0*salp0*(csig1-csig2)/(salp0^2+calp0^2*csig1*csig2)
// If csig12>0, write
// csig1-csig2=ssig12*(csig1*ssig12/(1+csig12)+ssig1)
// else
// csig1-csig2=csig1*(1-csig12)+ssig12*ssig1
// No need to normalize
salp12 = calp0 * salp0 * (csig12 <= 0?csig1 * (1 - csig12) + ssig12 * ssig1:ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1));
calp12 = sq(salp0) + sq(calp0) * csig1 * csig2;
}
S12 = c2 * Math.Atan2(salp12, calp12) + A4 * (B42 - B41);
}
plat2 = lat2;
plon2 = lon2;
pazi2 = azi2;
ps12 = s12;
pm12 = m12;
pM12 = M12;
pM21 = M21;
pS12 = S12;
return((flags & GEOD.ARCMODE) != 0?s12_a12:sig12 / degree);
}
/// <summary>
/// The general direct geodesic problem.
/// </summary>
/// <param name="lat1">The atitude of point 1 (degrees).</param>
/// <param name="lon1">The longitude of point 1 (degrees).</param>
/// <param name="azi1">The azimuth at point 1 (degrees).</param>
/// <param name="flags">Bitor'ed combination of <see cref="GEOD"/> flags;
/// GEOD.ARCMODE determines the meaning of s12_a12 and
/// GEOD.LONG_UNROLL "unrolls" lon2.</param>
/// <param name="s12_a12">If flags&GEOD.ARCMODE is 0, this is the distance
/// from point 1 to point 2 (meters); otherwise it is the arc length
/// from point 1 to point 2 (degrees); it can be negative.</param>
/// <param name="plat2">The latitude of point 2 (degrees).</param>
/// <param name="plon2">The longitude of point 2 (degrees).</param>
/// <param name="pazi2">The (forward) azimuth at point 2 (degrees).</param>
/// <param name="ps12">The distance from point 1 to point 2 (meters).</param>
/// <param name="pm12">The reduced length of geodesic (meters).</param>
/// <param name="pM12">The geodesic scale of point 2 relative to point 1 (dimensionless).</param>
/// <param name="pM21">The geodesic scale of point 1 relative to point 2 (dimensionless).</param>
/// <param name="pS12">The area under the geodesic (square meters).</param>
/// <remarks>
/// g must have been initialized with a call to geod_init(). lat1
/// should be in the range [-90deg, 90deg]. The function
/// value a12 equals s12_a12 if flags & GEOD.ARCMODE.
///
/// With <paramref name="flags"/> & GEOD.LONG_UNROLL bit set, the longitude is "unrolled" so
/// that the quantity lon2-lon1 indicates how many times and in
/// what sense the geodesic encircles the ellipsoid.
///</remarks>
/// <returns>a12 arc length of from point 1 to point 2 (degrees).</returns>
public double geod_gendirect(double lat1, double lon1, double azi1, GEOD flags, double s12_a12,
out double plat2, out double plon2, out double pazi2, out double ps12, out double pm12, out double pM12, out double pM21, out double pS12)
{
GEOD outmask = GEOD.LATITUDE | GEOD.LONGITUDE | GEOD.AZIMUTH | GEOD.DISTANCE | GEOD.REDUCEDLENGTH | GEOD.GEODESICSCALE | GEOD.AREA;
geod_geodesicline l = new geod_geodesicline(this, lat1, lon1, azi1, outmask | ((flags & GEOD.ARCMODE) != 0 ? GEOD.NONE : GEOD.DISTANCE_IN)); // Automatically supply GEOD_DISTANCE_IN if necessary
return l.geod_genposition(flags, s12_a12, out plat2, out plon2, out pazi2, out ps12, out pm12, out pM12, out pM21, out pS12);
}