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/// Geographical to cartesian (and v.v.) conversion
use crate::authoring::*;
// ----- F O R W A R D --------------------------------------------------------------
fn cart_fwd(op: &Op, _ctx: &dyn Context, operands: &mut dyn CoordinateSet) -> usize {
let n = operands.len();
let mut successes = 0;
let ellps = op.params.ellps(0);
for i in 0..n {
let mut coord = operands.get_coord(i);
coord = ellps.cartesian(&coord);
if !coord.0.iter().any(|c| c.is_nan()) {
successes += 1;
}
operands.set_coord(i, &coord);
}
successes
}
// ----- I N V E R S E --------------------------------------------------------------
fn cart_inv(op: &Op, _ctx: &dyn Context, operands: &mut dyn CoordinateSet) -> usize {
let ellps = op.params.ellps(0);
// eccentricity squared, Fukushima's E, Claessens' c3 = 1-c2`
let es = ellps.eccentricity_squared();
let b = ellps.semiminor_axis();
let a = ellps.semimajor_axis();
let ra = 1. / ellps.semimajor_axis();
// b/a: Fukushima's ec, Claessens' c4
let ar = b * ra;
// 1.5 times the fourth power of the eccentricity
let ce4 = 1.5 * es * es;
// if we're closer than this to the Z axis, we force latitude to one of the poles
let cutoff = ellps.semimajor_axis() * 1e-16;
let n = operands.len();
let mut successes = 0;
#[allow(non_snake_case)]
for i in 0..n {
let mut coord = operands.get_coord(i);
let X = coord[0];
let Y = coord[1];
let Z = coord[2];
let t = coord[3];
// The longitude is straightforward
let lam = Y.atan2(X);
// The perpendicular distance from the point coordinate to the Z-axis (HM eq. 5-28)
let p = X.hypot(Y);
// If we're close to the Z-axis, the full algorithm breaks down. But if
// we're close to the Z-axis, we also assert that the latitude is close
// to one of the poles. So we force the latitude to the relevant pole and
// compute the height as |Z| - b
if p < cutoff {
let phi = std::f64::consts::FRAC_PI_2.copysign(Z);
let h = Z.abs() - b;
coord = Coor4D::raw(lam, phi, h, t);
operands.set_coord(i, &coord);
continue;
}
let P = ra * p;
let S0 = ra * Z;
let C0 = ar * P;
// There's a lot of common subexpressions in the following which,
// in Fukushima's and Claessens' Fortranesque implementations,
// were explicitly eliminated (by introducing s02 = S0*S0, etc.).
// For clarity, we keep the full expressions here, and leave the
// elimination task to the compiler's optimizer step.
let A = S0.hypot(C0);
let F = P * A * A * A - es * C0 * C0 * C0;
let B = ce4 * S0 * S0 * C0 * C0 * P * (A - ar);
let S1 = (ar * S0 * A * A * A + es * S0 * S0 * S0) * F - B * S0;
let C1 = F * F - B * C0;
let CC = ar * C1;
let phi = S1.atan2(CC);
let h = (p * CC.abs() + Z.abs() * S1.abs() - a * CC.hypot(ar * S1)) / CC.hypot(S1);
// Bowring's height formula works better close to the ellipsoid, but requires a (sin, cos)-pair
coord = Coor4D::raw(lam, phi, h, t);
operands.set_coord(i, &coord);
if ![lam, phi, h, t].iter().any(|c| c.is_nan()) {
successes += 1;
}
}
successes
}
// ----- C O N S T R U C T O R ------------------------------------------------------
#[rustfmt::skip]
pub const GAMUT: [OpParameter; 2] = [
OpParameter::Flag { key: "inv" },
OpParameter::Text { key: "ellps", default: Some("GRS80") },
];
pub fn new(parameters: &RawParameters, _ctx: &dyn Context) -> Result<Op, Error> {
Op::basic(
parameters,
InnerOp(cart_fwd),
Some(InnerOp(cart_inv)),
&GAMUT,
)
}
// ----- T E S T S ------------------------------------------------------------------
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn roundtrip() -> Result<(), Error> {
let mut ctx = Minimal::default();
let op = ctx.op("cart")?;
let geo = [
Coor4D::geo(85., 0., 100000., 0.),
Coor4D::geo(55., 10., -100000., 0.),
Coor4D::geo(25., 20., 0., 0.),
Coor4D::geo(0., -20., 0., 0.),
Coor4D::geo(-25., 20., 10., 0.),
Coor4D::geo(-25., -20., 10., 0.),
Coor4D::geo(25., -20., 10., 0.),
];
let cart = [
Coor4D::raw(566_462.633_537_476_8, 0.0, 6_432_020.333_690_127, 0.0),
Coor4D::raw(
3_554_403.475_871_930_4,
626_737.233_120_170_7,
5_119_468.318_659_256,
0.,
),
Coor4D::raw(
5_435_195.382_145_216,
1_978_249.336_521_975_5,
2_679_074.462_877_277_8,
0.,
),
Coor4D::raw(5_993_488.273_261_571, -2_181_451.330_890_750_5, 0., 0.),
Coor4D::raw(
5_435_203.898_652_612,
1_978_252.436_277_167_4,
-2_679_078.689_059_895,
0.,
),
Coor4D::raw(
5_435_203.898_652_612,
-1_978_252.436_277_167_4,
-2_679_078.689_059_895,
0.,
),
Coor4D::raw(
5_435_203.898_652_612,
-1_978_252.436_277_167_4,
2_679_078.689_059_895,
0.,
),
];
let e = Ellipsoid::default();
// Forward
let mut operands = geo;
ctx.apply(op, Fwd, &mut operands)?;
for i in 0..4 {
assert!(operands[i].hypot3(&cart[i]) < 20e-9);
}
// Inverse
ctx.apply(op, Inv, &mut operands)?;
for i in 0..5 {
assert!(e.distance(&operands[i], &geo[i]) < 1e-8);
}
Ok(())
}
}