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geodesic.go
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geodesic.go
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// Package offers two main functionalities: solving the "direct" and the "inverse" problems.
//
// Direct:
//
// Place a second point, given the first point, an azimuth, and a distance.
//
// # Arguments
// - lat1_deg - Latitude of 1st point [degrees] [-90.,90.]
// - lon1_deg - Longitude of 1st point [degrees] [-180., 180.]
// - azi1_deg - Azimuth at 1st point [degrees] [-180., 180.]
// - s12_m - Distance from 1st to 2nd point [meters] Value may be negative
//
// # Returns
//
// There are a variety of outputs associated with this calculation. We save computation by
// only calculating the outputs you need. You can get any and all of the following
//
// - lat2 latitude of point 2 [degrees].
// - lon2 longitude of point 2 [degrees].
// - azi2 (forward) azimuth at point 2 [degrees].
// - m12 reduced length of geodesic (meters).
// - M12 geodesic scale of point 2 relative to point 1 [dimensionless].
// - M21 geodesic scale of point 1 relative to point 2 [dimensionless].
// - S12 area under the geodesic [meters^2]
// - a12 arc length of between point 1 and point 2 [degrees].
//
// Call the appropriate function to get the output you need. The following functions are
// available for solving the Direct problem. Each describes what it returns
//
// - DirectCalcLatLon -> calculate latitude and longitude
//
// - DirectCalcLatLonAzi -> calculate latitude, longitude, and azimuth
//
// - DirectCalcLatLonAziReducedLength -> calculate latitude, longitude, azimuth, and
// reduced length of the geodesic
//
// - DirectCalcLatLonAziGeodesicScales -> calculate latitude, longitude, azimuth, and
// the geodesic scales
//
// - DirectCalcLatLonAziReducedLengthGeodesicScales -> calculate latitude, longitude,
// azimuth, reduced length, and the geodesic scales
//
// - DirectCalcAll -> calculates all of the above plus Area under the geodesic and the
// arc length between point 1 and point 2
//
// =====================================================================================
// =====================================================================================
// =====================================================================================
// Indirect:
//
// Measure the distance (and other values) between two points.
//
// # Arguments
// - lat1_deg latitude of point 1 [degrees].
// - lon1_deg longitude of point 1 [degrees].
// - lat2_deg latitude of point 2 [degrees].
// - lon2_deg longitude of point 2 [degrees].
//
// # Returns
//
// There are a variety of outputs associated with this calculation. We save computation by
// only calculating the outputs you need. You can get any and all of the following
//
// - s12 distance between point 1 and point 2 (meters).
// - azi1 azimuth at point 1 [degrees].
// - azi2 (forward) azimuth at point 2 [degrees].
// - m12 reduced length of geodesic (meters).
// - M12 geodesic scale of point 2 relative to point 1 [dimensionless].
// - M21 geodesic scale of point 1 relative to point 2 [dimensionless].
// - S12 area under the geodesic [meters^2]
// - a12 arc length of between point 1 and point 2 [degrees].
//
// Call the appropriate function to get the output you need. The following functions are
// available for solving the Direct problem. Each describes what it returns
//
// `lat1` and `lat2` should be in the range [−90°, 90°].
// The values of `azi1` and `azi2` returned are in the range
// [−180°, 180°].
//
// If either point is at a pole, the azimuth is defined by keeping the
// longitude fixed, writing `lat` = ±(90° − ε),
// and taking the limit ε → 0+.
//
// The solution to the inverse problem is found using Newton's method. If
// this fails to converge (this is very unlikely in geodetic applications
// but does occur for very eccentric ellipsoids), then the bisection method
// is used to refine the solution.
package geographiclibgo
import "math"
const WGS84_A float64 = 6378137.0
// Evaluating this as 1000000000.0 / (298257223563f_64) reduces the
// round-off error by about 10%. However, expressing the flattening as
// 1/298.257223563 is well ingrained.
const WGS84_F float64 = 1.0 / ((298257223563.0) / 1000000000.0)
const _GEODESIC_ORDER int64 = 6
const nC3x_ int64 = 15
const nC4x_ int64 = 21
func coeff_A3() [18]float64 {
return [18]float64{
-3.0, 128.0, -2.0, -3.0, 64.0, -1.0, -3.0, -1.0, 16.0, 3.0, -1.0, -2.0, 8.0, 1.0, -1.0, 2.0,
1.0, 1.0,
}
}
func coeff_C3() [45]float64 {
return [45]float64{
3.0, 128.0, 2.0, 5.0, 128.0, -1.0, 3.0, 3.0, 64.0, -1.0, 0.0, 1.0, 8.0, -1.0, 1.0, 4.0, 5.0,
256.0, 1.0, 3.0, 128.0, -3.0, -2.0, 3.0, 64.0, 1.0, -3.0, 2.0, 32.0, 7.0, 512.0, -10.0, 9.0,
384.0, 5.0, -9.0, 5.0, 192.0, 7.0, 512.0, -14.0, 7.0, 512.0, 21.0, 2560.0,
}
}
func coeff_C4() [77]float64 {
return [77]float64{
97.0, 15015.0, 1088.0, 156.0, 45045.0, -224.0, -4784.0, 1573.0, 45045.0, -10656.0, 14144.0,
-4576.0, -858.0, 45045.0, 64.0, 624.0, -4576.0, 6864.0, -3003.0, 15015.0, 100.0, 208.0, 572.0,
3432.0, -12012.0, 30030.0, 45045.0, 1.0, 9009.0, -2944.0, 468.0, 135135.0, 5792.0, 1040.0,
-1287.0, 135135.0, 5952.0, -11648.0, 9152.0, -2574.0, 135135.0, -64.0, -624.0, 4576.0, -6864.0,
3003.0, 135135.0, 8.0, 10725.0, 1856.0, -936.0, 225225.0, -8448.0, 4992.0, -1144.0, 225225.0,
-1440.0, 4160.0, -4576.0, 1716.0, 225225.0, -136.0, 63063.0, 1024.0, -208.0, 105105.0, 3584.0,
-3328.0, 1144.0, 315315.0, -128.0, 135135.0, -2560.0, 832.0, 405405.0, 128.0, 99099.0,
}
}
type Geodesic struct {
a float64
f float64
f1 float64
e2 float64
ep2 float64
n float64
b float64
c2 float64
etol2 float64
GEODESIC_ORDER int64
nC3x_ int64
nC4x_ int64
maxit1_ uint64
maxit2_ uint64
_A3x [_GEODESIC_ORDER]float64
_C3x [nC3x_]float64
_C4x [nC4x_]float64
tiny_ float64
tol0_ float64
tol1_ float64
tol2_ float64
tolb_ float64
xthresh_ float64
}
func NewGeodesic(a, f float64) Geodesic {
var maxit1_ uint64 = 20
maxit2_ := maxit1_ + _DIGITS + 10
tiny_ := math.Sqrt(get_min_val())
tol0_ := get_epsilon()
tol1_ := 200.0 * tol0_
tol2_ := math.Sqrt(tol0_)
tolb_ := tol0_ * tol2_
xthresh_ := 1000.0 * tol2_
_f1 := 1.0 - f
_e2 := f * (2.0 - f)
_ep2 := _e2 / sq(_f1)
_n := f / (2.0 - f)
_b := a * _f1
var is_f_neg float64
if f < 0.0 {
is_f_neg = -1.0
} else {
is_f_neg = 1.0
}
to_mul := eatanhe(1.0, is_f_neg*math.Sqrt(math.Abs(_e2))) / _e2
if _e2 == 0.0 {
to_mul = 1.0
}
_c2 := (sq(a) + sq(_b)*to_mul) / 2.0
_etol2 := 0.1 * tol2_ / math.Sqrt(math.Max(math.Abs(f), 0.001)*math.Min((1.0-f/2.0), 1.0)/2.0)
_A3x := [_GEODESIC_ORDER]float64{}
_C3x := [nC3x_]float64{}
_C4x := [nC4x_]float64{}
// Call a3coeff
var o int64 = 0
k := 0
coefa3 := coeff_A3()
for j := _GEODESIC_ORDER - 1; j >= 0; j-- {
m := int64(math.Min(float64(j), float64(_GEODESIC_ORDER-j-1)))
_A3x[k] = polyval(m, coefa3[o:], _n) / coefa3[o+m+1]
k += 1
o += m + 2
}
// c3coeff
o = 0
k = 0
coefc3 := coeff_C3()
for l := 1; l < int(_GEODESIC_ORDER); l++ {
for j := int(_GEODESIC_ORDER) - 1; j >= l; j-- {
m := int64(math.Min(float64(j), float64(int(_GEODESIC_ORDER)-j-1)))
_C3x[k] = polyval(m, coefc3[o:], _n) / coefc3[o+m+1]
k += 1
o += m + 2
}
}
// c4coeff
o = 0
k = 0
coefc4 := coeff_C4()
for l := 0; l < int(_GEODESIC_ORDER); l++ {
for j := int(_GEODESIC_ORDER) - 1; j >= l; j-- {
m := int64(int(_GEODESIC_ORDER) - j - 1)
_C4x[k] = polyval(m, coefc4[o:], _n) / coefc4[(o+m+1)]
k += 1
o += m + 2
}
}
return Geodesic{
a,
f,
_f1,
_e2,
_ep2,
_n,
_b,
_c2,
_etol2,
_GEODESIC_ORDER,
nC3x_,
nC4x_,
maxit1_,
maxit2_,
_A3x,
_C3x,
_C4x,
tiny_,
tol0_,
tol1_,
tol2_,
tolb_,
xthresh_,
}
}
func Wgs84() Geodesic {
return NewGeodesic(WGS84_A, WGS84_F)
}
func (g *Geodesic) EqualtorialRadius() float64 {
return g.a
}
func (g *Geodesic) Flattening() float64 {
return g.f
}
func (g *Geodesic) _A3f(eps float64) float64 {
return polyval(int64(_GEODESIC_ORDER-1), g._A3x[:], eps)
}
func (g *Geodesic) _C3f(eps float64, c []float64) {
mult := 1.0
o := 0
for l := 1; l < int(_GEODESIC_ORDER); l++ {
m := int(_GEODESIC_ORDER) - l - 1
mult *= eps
c[l] = mult * polyval(int64(m), g._C3x[o:], eps)
o += m + 1
}
}
func (g *Geodesic) _C4f(eps float64, c []float64) {
mult := 1.0
o := 0
for l := 0; l < int(_GEODESIC_ORDER); l++ {
m := int(_GEODESIC_ORDER) - l - 1
c[l] = mult * polyval(int64(m), g._C4x[o:], eps)
o += m + 1
mult *= eps
}
}
func (g *Geodesic) _Lengths(
eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2 float64,
outmask uint64,
c1a []float64,
c2a []float64,
) (float64, float64, float64, float64, float64) {
outmask &= OUT_MASK
s12b := math.NaN()
m12b := math.NaN()
m0 := math.NaN()
M12 := math.NaN()
M21 := math.NaN()
A1 := 0.0
A2 := 0.0
m0x := 0.0
J12 := 0.0
if outmask&(DISTANCE|REDUCEDLENGTH|GEODESICSCALE) != 0 {
A1 = a1m1f(eps, _GEODESIC_ORDER)
c1f(eps, c1a, int(_GEODESIC_ORDER))
if outmask&(REDUCEDLENGTH|GEODESICSCALE) != 0 {
A2 = a2m1f(eps, _GEODESIC_ORDER)
c2f(eps, c2a, int(_GEODESIC_ORDER))
m0x = A1 - A2
A2 = 1.0 + A2
}
A1 = 1.0 + A1
}
if outmask&DISTANCE != 0 {
B1 := sin_cos_series(true, ssig2, csig2, c1a) - sin_cos_series(true, ssig1, csig1, c1a)
s12b = A1 * (sig12 + B1)
if outmask&(REDUCEDLENGTH|GEODESICSCALE) != 0 {
B2 := sin_cos_series(true, ssig2, csig2, c2a) - sin_cos_series(true, ssig1, csig1, c2a)
J12 = m0x*sig12 + (A1*B1 - A2*B2)
}
} else if outmask&(REDUCEDLENGTH|GEODESICSCALE) != 0 {
for l := 1; l <= int(_GEODESIC_ORDER); l++ {
c2a[l] = A1*c1a[l] - A2*c2a[l]
}
J12 = m0x*sig12 + (sin_cos_series(true, ssig2, csig2, c2a) - sin_cos_series(true, ssig1, csig1, c2a))
}
if outmask&REDUCEDLENGTH != 0 {
m0 = m0x
// J12 is wrong
m12b = dn2*(csig1*ssig2) - dn1*(ssig1*csig2) - csig1*csig2*J12
}
if outmask&GEODESICSCALE != 0 {
csig12 := csig1*csig2 + ssig1*ssig2
t := g.ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2)
M12 = csig12 + (t*ssig2-csig2*J12)*ssig1/dn1
M21 = csig12 - (t*ssig1-csig1*J12)*ssig2/dn2
}
return s12b, m12b, m0, M12, M21
}
func (g *Geodesic) _InverseStart(
sbet1, cbet1, dn1, sbet2, cbet2, dn2, lam12, slam12, clam12 float64,
c1a []float64,
c2a []float64,
) (float64, float64, float64, float64, float64, float64) {
sig12 := -1.0
salp2 := math.NaN()
calp2 := math.NaN()
dnm := math.NaN()
var somg12 float64
var comg12 float64
sbet12 := sbet2*cbet1 - cbet2*sbet1
cbet12 := cbet2*cbet1 + sbet2*sbet1
sbet12a := sbet2 * cbet1
sbet12a += cbet2 * sbet1
shortline := cbet12 >= 0.0 && sbet12 < 0.5 && cbet2*lam12 < 0.5
if shortline {
sbetm2 := sq(sbet1 + sbet2)
sbetm2 /= sbetm2 + sq(cbet1+cbet2)
dnm = math.Sqrt(1.0 + g.ep2*sbetm2)
omg12 := lam12 / (g.f1 * dnm)
somg12 = math.Sin(omg12)
comg12 = math.Cos(omg12)
} else {
somg12 = slam12
comg12 = clam12
}
salp1 := cbet2 * somg12
calp1 := sbet12a - cbet2*sbet1*sq(somg12)/(1.0-comg12)
if comg12 >= 0.0 {
calp1 = sbet12 + cbet2*sbet1*sq(somg12)/(1.0+comg12)
}
ssig12 := math.Hypot(salp1, calp1)
csig12 := sbet1*sbet2 + cbet1*cbet2*comg12
if shortline && (ssig12 < g.etol2) {
salp2 = cbet1 * somg12
var to_mul float64
if comg12 >= 0.0 {
to_mul = sq(somg12) / (1.0 + comg12)
} else {
to_mul = 1.0 - comg12
}
calp2 = sbet12 - cbet1*sbet2*to_mul
salp2, calp2 = norm(salp2, calp2)
sig12 = math.Atan2(ssig12, csig12)
} else if math.Abs(g.n) > 0.1 || csig12 >= 0.0 || ssig12 >= 6.0*math.Abs(g.n)*math.Pi*sq(cbet1) {
} else {
var x float64
var y float64
var betscale float64
var lamscale float64
lam12x := math.Atan2(-slam12, -clam12)
if g.f >= 0.0 {
k2 := sq(sbet1) * g.ep2
eps := k2 / (2.0*(1.0+math.Sqrt(1.0+k2)) + k2)
lamscale = g.f * cbet1 * g._A3f(eps) * math.Pi
betscale = lamscale * cbet1
x = lam12x / lamscale
y = sbet12a / betscale
} else {
cbet12a := cbet2*cbet1 - sbet2*sbet1
bet12a := math.Atan2(sbet12, cbet12a)
_, m12b, m0, _, _ := g._Lengths(
g.n,
math.Pi+bet12a,
sbet1,
-cbet1,
dn1,
sbet2,
cbet2,
dn2,
cbet1,
cbet2,
REDUCEDLENGTH,
c1a,
c2a,
)
x = -1.0 + m12b/(cbet1*cbet2*m0*math.Pi)
var betscale float64
if x < -0.01 {
betscale = sbet12a / x
} else {
betscale = -g.f * sq(cbet1) * math.Pi
}
lamscale = betscale / cbet1
y = lam12x / lamscale
}
if y > -g.tol1_ && x > -1.0-g.xthresh_ {
if g.f >= 0.0 {
salp1 = math.Min(-x, 1.0)
calp1 = -math.Sqrt(1.0 - sq(salp1))
} else {
var to_compare float64
if x > -g.tol1_ {
to_compare = 0.0
} else {
to_compare = -1.0
}
calp1 = math.Max(x, to_compare)
salp1 = math.Sqrt(1.0 - sq(calp1))
}
} else {
k := astroid(x, y)
var to_mul float64
if g.f >= 0.0 {
to_mul = -x * k / (1.0 + k)
} else {
to_mul = -y * (1.0 + k) / k
}
omg12a := lamscale * to_mul
somg12 = math.Sin(omg12a)
comg12 = -math.Cos(omg12a)
salp1 = cbet2 * somg12
calp1 = sbet12a - cbet2*sbet1*sq(somg12)/(1.0-comg12)
}
}
if !(salp1 <= 0.0) {
salp1, calp1 = norm(salp1, calp1)
} else {
salp1 = 1.0
calp1 = 0.0
}
return sig12, salp1, calp1, salp2, calp2, dnm
}
func (g *Geodesic) _Lambda12(
sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1, slam120, clam120 float64,
diffp bool,
c1a []float64,
c2a []float64,
c3a []float64,
) (float64, float64, float64, float64, float64, float64, float64, float64, float64, float64, float64) {
if sbet1 == 0.0 && calp1 == 0.0 {
calp1 = -g.tiny_
}
salp0 := salp1 * cbet1
calp0 := math.Hypot(calp1, salp1*sbet1)
ssig1 := sbet1
somg1 := salp0 * sbet1
csig1 := calp1 * cbet1
comg1 := calp1 * cbet1
ssig1, csig1 = norm(ssig1, csig1)
var salp2 float64
if cbet2 != cbet1 {
salp2 = salp0 / cbet2
} else {
salp2 = salp1
}
var to_add float64
if cbet1 < -sbet1 {
to_add = (cbet2 - cbet1) * (cbet1 + cbet2)
} else {
to_add = (sbet1 - sbet2) * (sbet1 + sbet2)
}
calp2 := math.Abs(calp1)
if cbet2 != cbet1 || math.Abs(sbet2) != -sbet1 {
calp2 = math.Sqrt(sq(calp1*cbet1)+to_add) / cbet2
}
ssig2 := sbet2
somg2 := salp0 * sbet2
csig2 := calp2 * cbet2
comg2 := calp2 * cbet2
ssig2, csig2 = norm(ssig2, csig2)
sig12 := math.Atan2(math.Max(csig1*ssig2-ssig1*csig2, 0.0), csig1*csig2+ssig1*ssig2)
somg12 := math.Max((comg1*somg2 - somg1*comg2), 0.0)
comg12 := comg1*comg2 + somg1*somg2
eta := math.Atan2(somg12*clam120-comg12*slam120, comg12*clam120+somg12*slam120)
k2 := sq(calp0) * g.ep2
eps := k2 / (2.0*(1.0+math.Sqrt(1.0+k2)) + k2)
g._C3f(eps, c3a)
B312 := sin_cos_series(true, ssig2, csig2, c3a) - sin_cos_series(true, ssig1, csig1, c3a)
domg12 := -g.f * g._A3f(eps) * salp0 * (sig12 + B312)
lam12 := eta + domg12
var dlam12 float64
if diffp {
if calp2 == 0.0 {
dlam12 = -2.0 * g.f1 * dn1 / sbet1
} else {
_, res, _, _, _ := g._Lengths(
eps,
sig12,
ssig1,
csig1,
dn1,
ssig2,
csig2,
dn2,
cbet1,
cbet2,
REDUCEDLENGTH,
c1a,
c2a,
)
dlam12 = res
dlam12 *= g.f1 / (calp2 * cbet2)
}
} else {
dlam12 = math.NaN()
}
return lam12, salp2, calp2, sig12, ssig1, csig1, ssig2, csig2, eps, domg12, dlam12
}
func (g *Geodesic) _gen_inverse_azi(
lat1, lon1, lat2, lon2 float64,
outmask uint64,
) (
a12 float64,
s12 float64,
azi1 float64,
azi2 float64,
m12 float64,
M12 float64,
M21 float64,
S12 float64,
) {
azi1 = math.NaN()
azi2 = math.NaN()
outmask &= OUT_MASK
a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12 := g._gen_inverse(
lat1, lon1, lat2, lon2, outmask,
)
if outmask&AZIMUTH != 0 {
azi1 = atan2_deg(salp1, calp1)
azi2 = atan2_deg(salp2, calp2)
}
return a12, s12, azi1, azi2, m12, M12, M21, S12
}
func (g *Geodesic) _gen_inverse(lat1, lon1, lat2, lon2 float64, outmask uint64) (
a12 float64,
s12 float64,
salp1 float64,
calp1 float64,
salp2 float64,
calp2 float64,
m12 float64,
M12 float64,
M21 float64,
S12 float64,
) {
a12 = math.NaN()
s12 = math.NaN()
m12 = math.NaN()
M12 = math.NaN()
M21 = math.NaN()
S12 = math.NaN()
outmask &= OUT_MASK
lon12, lon12s := ang_diff(lon1, lon2)
var lonsign float64
if lon12 >= 0.0 {
lonsign = 1.0
} else {
lonsign = -1.0
}
lon12 = lonsign * ang_round(lon12)
lon12s = ang_round((180.0 - lon12) - lonsign*lon12s)
lam12 := lon12 * DEG2RAD
var slam12 float64
var clam12 float64
if lon12 > 90.0 {
slam12, clam12 = sincosd(lon12s)
clam12 = -clam12
} else {
slam12, clam12 = sincosd(lon12)
}
lat1 = ang_round(lat_fix(lat1))
lat2 = ang_round(lat_fix(lat2))
var swapp float64
if math.Abs(lat1) < math.Abs(lat2) {
swapp = -1.0
} else {
swapp = 1.0
}
if swapp < 0.0 {
lonsign *= -1.0
lat2, lat1 = lat1, lat2
}
var latsign float64
if lat1 < 0.0 {
latsign = 1.0
} else {
latsign = -1.0
}
lat1 *= latsign
lat2 *= latsign
sbet1, cbet1 := sincosd(lat1)
sbet1 *= g.f1
sbet1, cbet1 = norm(sbet1, cbet1)
cbet1 = math.Max(cbet1, g.tiny_)
sbet2, cbet2 := sincosd(lat2)
sbet2 *= g.f1
sbet2, cbet2 = norm(sbet2, cbet2)
cbet2 = math.Max(cbet2, g.tiny_)
if cbet1 < -sbet1 {
if cbet2 == cbet1 {
if sbet2 < 0.0 {
sbet2 = sbet1
} else {
sbet2 = -sbet1
}
}
} else if math.Abs(sbet2) == -sbet1 {
cbet2 = cbet1
}
dn1 := math.Sqrt(1.0 + g.ep2*sq(sbet1))
dn2 := math.Sqrt(1.0 + g.ep2*sq(sbet2))
const CARR_SIZE uint64 = uint64(_GEODESIC_ORDER) + 1
C1a := [CARR_SIZE]float64{}
C2a := [CARR_SIZE]float64{}
C3a := [_GEODESIC_ORDER]float64{}
meridian := lat1 == -90.0 || slam12 == 0.0
calp1 = 0.0
salp1 = 0.0
calp2 = 0.0
salp2 = 0.0
ssig1 := 0.0
csig1 := 0.0
ssig2 := 0.0
csig2 := 0.0
var sig12 float64
s12x := 0.0
m12x := 0.0
if meridian {
calp1 = clam12
salp1 = slam12
calp2 = 1.0
salp2 = 0.0
ssig1 = sbet1
csig1 = calp1 * cbet1
ssig2 = sbet2
csig2 = calp2 * cbet2
sig12 = math.Atan2(math.Max((csig1*ssig2-ssig1*csig2), 0.0), csig1*csig2+ssig1*ssig2)
res1, res2, _, res4, res5 := g._Lengths(
g.n,
sig12,
ssig1,
csig1,
dn1,
ssig2,
csig2,
dn2,
cbet1,
cbet2,
outmask|DISTANCE|REDUCEDLENGTH,
C1a[:],
C2a[:],
)
s12x = res1
m12x = res2
M12 = res4
M21 = res5
if sig12 < 1.0 || m12x >= 0.0 {
if sig12 < 3.0*g.tiny_ {
sig12 = 0.0
m12x = 0.0
s12x = 0.0
}
m12x *= g.b
s12x *= g.b
a12 = sig12 * RAD2DEG
} else {
meridian = false
}
}
somg12 := 2.0
comg12 := 0.0
omg12 := 0.0
var dnm float64
eps := 0.0
if !meridian && sbet1 == 0.0 && (g.f <= 0.0 || lon12s >= g.f*180.0) {
calp1 = 0.0
calp2 = 0.0
salp1 = 1.0
salp2 = 1.0
s12x = g.a * lam12
sig12 = lam12 / g.f1
omg12 = lam12 / g.f1
m12x = g.b * math.Sin(sig12)
if outmask&GEODESICSCALE != 0 {
M12 = math.Cos(sig12)
M21 = math.Cos(sig12)
}
a12 = lon12 / g.f1
} else if !meridian {
res1, res2, res3, res4, res5, res6 := g._InverseStart(
sbet1, cbet1, dn1, sbet2, cbet2, dn2, lam12, slam12, clam12, C1a[:], C2a[:],
)
sig12 = res1
salp1 = res2
calp1 = res3
salp2 = res4
calp2 = res5
dnm = res6
if sig12 >= 0.0 {
s12x = sig12 * g.b * dnm
m12x = sq(dnm) * g.b * math.Sin(sig12/dnm)
if outmask&GEODESICSCALE != 0 {
M12 = math.Cos(sig12 / dnm)
M21 = math.Cos(sig12 / dnm)
}
a12 = sig12 * RAD2DEG
omg12 = lam12 / (g.f1 * dnm)
} else {
tripn := false
tripb := false
salp1a := g.tiny_
calp1a := 1.0
salp1b := g.tiny_
calp1b := -1.0
domg12 := 0.0
for numit := uint64(0); numit < g.maxit2_; numit++ {
res1, res2, res3, res4, res5, res6, res7, res8, res9, res10, res11 := g._Lambda12(
sbet1,
cbet1,
dn1,
sbet2,
cbet2,
dn2,
salp1,
calp1,
slam12,
clam12,
numit < g.maxit1_,
C1a[:],
C2a[:],
C3a[:],
)
v := res1
salp2 = res2
calp2 = res3
sig12 = res4
ssig1 = res5
csig1 = res6
ssig2 = res7
csig2 = res8
eps = res9
domg12 = res10
dv := res11
var to_mul float64
if tripn {
to_mul = 8.0
} else {
to_mul = 1.0
}
if tripb || !(math.Abs(v) >= to_mul*g.tol0_) {
break
}
if v > 0.0 && (numit > g.maxit1_ || calp1/salp1 > calp1b/salp1b) {
salp1b = salp1
calp1b = calp1
} else if v < 0.0 && (numit > g.maxit1_ || calp1/salp1 < calp1a/salp1a) {
salp1a = salp1
calp1a = calp1
}
if numit < g.maxit1_ && dv > 0.0 {
dalp1 := -v / dv
sdalp1 := math.Sin(dalp1)
cdalp1 := math.Cos(dalp1)
nsalp1 := salp1*cdalp1 + calp1*sdalp1
if nsalp1 > 0.0 && math.Abs(dalp1) < math.Pi {
calp1 = calp1*cdalp1 - salp1*sdalp1
salp1 = nsalp1
salp1, calp1 = norm(salp1, calp1)
tripn = math.Abs(v) <= 16.0*g.tol0_
continue
}
}
salp1 = (salp1a + salp1b) / 2.0
calp1 = (calp1a + calp1b) / 2.0
salp1, calp1 = norm(salp1, calp1)
tripn = false
tripb = math.Abs(salp1a-salp1)+(calp1a-calp1) < g.tolb_ || math.Abs(salp1-salp1b)+(calp1-calp1b) < g.tolb_
}
var to_cmp uint64
if outmask&(REDUCEDLENGTH|GEODESICSCALE) != 0 {
to_cmp = DISTANCE
} else {
to_cmp = EMPTY
}
lengthmask := outmask | to_cmp
res1, res2, _, res4, res5 = g._Lengths(
eps, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2, cbet1, cbet2, lengthmask,
C1a[:], C2a[:],
)
s12x = res1
m12x = res2
M12 = res4
M21 = res5
m12x *= g.b
s12x *= g.b
a12 = sig12 * RAD2DEG
if outmask&AREA != 0 {
sdomg12 := math.Sin(domg12)
cdomg12 := math.Cos(domg12)
somg12 = slam12*cdomg12 - clam12*sdomg12
comg12 = clam12*cdomg12 + slam12*sdomg12
}
}
}
if outmask&DISTANCE != 0 {
s12 = 0.0 + s12x
}
if outmask&REDUCEDLENGTH != 0 {
m12 = 0.0 + m12x
}
if outmask&AREA != 0 {
salp0 := salp1 * cbet1
calp0 := math.Hypot(calp1, salp1*sbet1)
if calp0 != 0.0 && salp0 != 0.0 {
ssig1 = sbet1
csig1 = calp1 * cbet1
ssig2 = sbet2
csig2 = calp2 * cbet2
k2 := sq(calp0) * g.ep2
eps = k2 / (2.0*(1.0+math.Sqrt(1.0+k2)) + k2)
A4 := sq(g.a) * calp0 * salp0 * g.e2
ssig1, csig1 = norm(ssig1, csig1)
ssig2, csig2 = norm(ssig2, csig2)
C4a := [_GEODESIC_ORDER]float64{}
g._C4f(eps, C4a[:])
B41 := sin_cos_series(false, ssig1, csig1, C4a[:])
B42 := sin_cos_series(false, ssig2, csig2, C4a[:])
S12 = A4 * (B42 - B41)
} else {
S12 = 0.0
}
if !meridian && somg12 > 1.0 {
somg12, comg12 = math.Sincos(omg12)
}
var alp12 float64
if !meridian && comg12 > -0.7071 && sbet2-sbet1 < 1.75 {
domg12 := 1.0 + comg12
dbet1 := 1.0 + cbet1
dbet2 := 1.0 + cbet2
alp12 = 2.0 * math.Atan2(somg12*(sbet1*dbet2+sbet2*dbet1), domg12*(sbet1*sbet2+dbet1*dbet2))
} else {
salp12 := salp2*calp1 - calp2*salp1
calp12 := calp2*calp1 + salp2*salp1
if salp12 == 0.0 && calp12 < 0.0 {
salp12 = g.tiny_ * calp1
calp12 = -1.0
}
alp12 = math.Atan2(salp12, calp12)
}
S12 += g.c2 * alp12
S12 *= swapp * lonsign * latsign
S12 += 0.0
}
if swapp < 0.0 {
salp2, salp1 = salp1, salp2
calp2, calp1 = calp1, calp2
if outmask&GEODESICSCALE != 0 {
M21, M12 = M12, M21
}
}
salp1 *= swapp * lonsign
calp1 *= swapp * latsign
salp2 *= swapp * lonsign
calp2 *= swapp * latsign
return a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12
}
// _gen_direct returns (a12, lat2, lon2, azi2, s12, m12, M12, M21, S12, outmask)
func (g *Geodesic) _gen_direct(
lat1 float64,
lon1 float64,
azi1 float64,
arcmode bool,
s12_a12 float64,
outmask uint64,
) (float64, float64, float64, float64, float64, float64, float64, float64, float64, uint64) {
if !arcmode {
outmask |= DISTANCE_IN
}
line := NewGeodesicLineWithCapability(*g, lat1, lon1, azi1, outmask)
a12, lat2, lon2, azi2, s12, m12, M12, M21, S12 := line._gen_position(arcmode, s12_a12, outmask)
return a12, lat2, lon2, azi2, s12, m12, M12, M21, S12, outmask
}
// LatLon represents latitude and longitude of a point. All units in degrees