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geomath.go
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geomath.go
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package geographiclibgo
import "math"
const _DIGITS uint64 = 53
const _TWO float64 = 2.0
const RAD2DEG float64 = 180.0 / math.Pi
const DEG2RAD float64 = math.Pi / 180.0
func get_epsilon() float64 {
return math.Pow(_TWO, 1.0-float64(_DIGITS))
}
func get_min_val() float64 {
return math.SmallestNonzeroFloat64
}
// sq: square a number
func sq(x float64) float64 {
return math.Pow(x, 2.0)
}
func cbrt(x float64) float64 {
y := math.Pow(math.Abs(x), 1.0/3.0)
// return y if x > 0 else (-y if x < 0 else x)
switch {
case x > 0:
return y
case x < 0:
return -y
default:
return x
}
}
// norm: normalize a two-vector
func norm(x, y float64) (float64, float64) {
r := math.Sqrt(x*x + y*y)
return (x / r), (y / r)
}
// sum: error free transformation of a sum
func sum(u, v float64) (float64, float64) {
s := u + v
up := s - v
vpp := s - up
up -= u
vpp -= v
t := -(up + vpp)
return s, t
}
// polyval: evaluate a polynomial
func polyval(n int64, p []float64, x float64) float64 {
if n < 0 {
return 0.0
} else {
y := p[0]
for _, val := range p[1 : n+1] {
y = y*x + val
}
return y
}
}
// ang_round: round an angle so that small values underflow to 0
func ang_round(x float64) float64 {
// The makes the smallest gap in x = 1/16 - nextafter(1/16, 0) = 1/2^57
// for reals = 0.7 pm on the earth if x is an angle in degrees. (This
// is about 1000 times more resolution than we get with angles around 90
// degrees.) We use this to avoid having to deal with near singular
// cases when x is non-zero but tiny (e.g., 1.0e-200).
z := 1.0 / 16.0
y := math.Abs(x)
// The compiler mustn't "simplify" z - (z - y) to y
if y < z {
y = z - (z - y)
}
if x == 0.0 {
return 0.0
} else {
if x < 0.0 {
return -y
} else {
return y
}
}
}
// ang_normalize: reduce angle to (-180,180]
func ang_normalize(x float64) float64 {
// y = Math.remainder(x, 360)
// return 180 if y == -180 else y
y := math.Remainder(x, 360.0)
if y == -180.0 {
return 180.0
} else {
return y
}
}
// lat_fix: replace angles outside [-90,90] with NaN
func lat_fix(x float64) float64 {
if math.Abs(x) > 90.0 {
return math.NaN()
} else {
return x
}
}
// ang_diff: compute y - x and reduce to [-180,180] accurately
func ang_diff(x, y float64) (float64, float64) {
d, t := sum(ang_normalize(-x), ang_normalize(y))
d = ang_normalize(d)
if d == 180.0 && t > 0.0 {
return sum(-180.0, t)
} else {
return sum(d, t)
}
}
// sincosd: compute sine and cosine of x in degrees
func sincosd(x float64) (float64, float64) {
// r = math.fmod(x, 360) if Math.isfinite(x) else Math.nan
r := math.NaN()
if !math.IsInf(x, 0) {
r = math.Mod(x, 360.0)
}
// q = 0 if Math.isnan(r) else int(round(r / 90))
q := math.Round(r / 90.0)
if math.IsNaN(r) {
q = 0
}
// r -= 90 * q; r = math.radians(r)
r -= 90.0 * q
r *= DEG2RAD
// s = math.sin(r); c = math.cos(r)
s := math.Sin(r)
c := math.Cos(r)
// q = q % 4
q = math.Mod(q, 4.0)
// if q == 1:
// s, c = c, -s
// elif q == 2:
// s, c = -s, -c
// elif q == 3:
// s, c = -c, s
if q < 0 {
q += 4
}
switch {
case q == 1:
s, c = c, -s
case q == 2:
s, c = -s, -c
case q == 3:
s, c = -c, s
}
// # Remove the minus sign on -0.0 except for sin(-0.0).
// # On Windows 32-bit with python 2.7, math.fmod(-0.0, 360) = +0.0
// # (x, c) here fixes this bug. See also Math::sincosd in the C++ library.
// # AngNormalize has a similar fix.
// s, c = (x, c) if x == 0 else (0.0+s, 0.0+c)
// return s, c
if x == 0.0 {
s = x
} else {
s, c = 0.0+s, 0.0+c
}
return s, c
}
// atan2_deg: compute the arc tangent of y/x in degrees
func atan2_deg(y_deg, x_deg float64) float64 {
// First convert to radians.
y_rad := y_deg * DEG2RAD
x_rad := x_deg * DEG2RAD
// Then use the atan2 function.
return math.Atan2(y_rad, x_rad) * RAD2DEG
}
func eatanhe(x float64, es float64) float64 {
if es > 0.0 {
return es * math.Atanh(es*x)
} else {
return -es * math.Atan(es*x)
}
}
// sin_cos_series: functions that used to be inside Geodesic
func sin_cos_series(sinp bool, sinx float64, cosx float64, c []float64) float64 {
k := len(c)
to_sub := 0
if sinp {
to_sub = 1
}
n := k - to_sub
var ar float64 = 2.0 * (cosx - sinx) * (cosx + sinx)
y1 := 0.0
y0 := 0.0
if n&1 != 0 {
k -= 1
y0 = c[k]
}
n /= 2
for n > 0 {
n -= 1
k -= 1
y1 = ar*y0 - y1 + c[k]
k -= 1
y0 = ar*y1 - y0 + c[k]
}
if sinp {
return 2.0 * sinx * cosx * y0
} else {
return cosx * (y0 - y1)
}
}
// astroid: solve astroid equation
func astroid(x, y float64) float64 {
p := sq(x)
q := sq(y)
r := (p + q - 1.0) / 6.0
if !(q == 0.0 && r <= 0.0) {
s := p * q / 4.0
r2 := sq(r)
r3 := r * r2
disc := s * (s + 2.0*r3)
u := r
if disc >= 0.0 {
t3 := s + r3
if t3 < 0.0 {
t3 += -math.Sqrt(disc)
} else {
t3 += math.Sqrt(disc)
}
t := cbrt(t3) // we could use built-in math.Cbrt
to_add := 0.0
if t != 0.0 {
to_add = r2 / t
}
u += t + to_add
} else {
ang := math.Atan2(math.Sqrt(-disc), -(s + r3))
u += 2.0 * r * math.Cos(ang/3.0)
}
v := math.Sqrt((sq(u) + q))
uv := u + v
if u < 0.0 {
uv = q / (v + u)
}
w := (uv - q) / (2.0 * v)
return uv / (math.Sqrt(uv+sq(w)) + w)
} else {
return 0.0
}
}
func a1m1f(eps float64, geodesic_order int64) float64 {
COEFF := [5]float64{1.0, 4.0, 64.0, 0.0, 256.0}
m := geodesic_order / 2
t := polyval(m, COEFF[:], sq(eps)) / COEFF[(m+1)]
return (t + eps) / (1.0 - eps)
}
func c1f(eps float64, c []float64, geodesic_order int) {
COEFF := [18]float64{
-1.0, 6.0, -16.0, 32.0, -9.0, 64.0, -128.0, 2048.0, 9.0, -16.0, 768.0, 3.0, -5.0, 512.0,
-7.0, 1280.0, -7.0, 2048.0,
}
eps2 := sq(eps)
d := eps
var o int64 = 0
for l := 1; l <= geodesic_order; l++ {
m := int64((geodesic_order - l) / 2)
c[l] = d * polyval(m, COEFF[o:], eps2) / COEFF[(o+m+1)]
o += m + 2
d *= eps
}
}
func c1pf(eps float64, c []float64, geodesic_order int) {
COEFF := [18]float64{
205.0, -432.0, 768.0, 1536.0, 4005.0, -4736.0, 3840.0, 12288.0, -225.0, 116.0, 384.0,
-7173.0, 2695.0, 7680.0, 3467.0, 7680.0, 38081.0, 61440.0,
}
eps2 := sq(eps)
d := eps
var o int64 = 0
for l := 1; l <= geodesic_order; l++ {
m := int64((geodesic_order - l) / 2)
c[l] = d * polyval(m, COEFF[o:], eps2) / COEFF[(o+m+1)]
o += m + 2
d *= eps
}
}
func a2m1f(eps float64, geodesic_order int64) float64 {
COEFF := []float64{-11.0, -28.0, -192.0, 0.0, 256.0}
var m int64 = geodesic_order / 2
t := polyval(m, COEFF, sq(eps)) / COEFF[(m+1)]
return (t - eps) / (1.0 + eps)
}
func c2f(eps float64, c []float64, geodesic_order int) {
COEFF := [18]float64{
1.0, 2.0, 16.0, 32.0, 35.0, 64.0, 384.0, 2048.0, 15.0, 80.0, 768.0, 7.0, 35.0, 512.0, 63.0,
1280.0, 77.0, 2048.0,
}
eps2 := sq(eps)
d := eps
var o int64 = 0
for l := 1; l <= geodesic_order; l++ {
m := int64((geodesic_order - l) / 2)
c[l] = d * polyval(m, COEFF[o:], eps2) / COEFF[(o+m+1)]
o += m + 2
d *= eps
}
}