geodesy 0.15.0

A platform for experiments with geodetic transformations and data flow
Documentation 
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//! Transverse Mercator, following [Bowring (1989)](crate::bibliography::Bibliography::Bow89)
use crate::authoring::*;

// ----- F O R W A R D -----------------------------------------------------------------

// Forward transverse mercator, following Bowring (1989)
fn fwd(op: &Op, _ctx: &dyn Context, operands: &mut dyn CoordinateSet) -> usize {
    let ellps = op.params.ellps(0);
    let eps = ellps.second_eccentricity_squared();
    let lat_0 = op.params.lat(0).to_radians();
    let lon_0 = op.params.lon(0).to_radians();
    let x_0 = op.params.x(0);
    let y_0 = op.params.y(0);
    let k_0 = op.params.k(0);

    let mut successes = 0_usize;
    let n = operands.len();
    for i in 0..n {
        let mut coord = operands.get_coord(i);

        let lat = coord[1] + lat_0;
        let (s, c) = lat.sin_cos();
        let cc = c * c;
        let ss = s * s;

        let dlon = coord[0] - lon_0;
        let oo = dlon * dlon;

        #[allow(non_snake_case)]
        let N = ellps.prime_vertical_radius_of_curvature(lat);
        let z = eps * dlon.powi(3) * c.powi(5) / 6.;
        let sd2 = (dlon / 2.).sin();

        let theta_2 = (2. * s * c * sd2 * sd2).atan2(ss + cc * dlon.cos());

        // Easting
        let sd = dlon.sin();
        coord[0] = x_0 + k_0 * N * ((c * sd).atanh() + z * (1. + oo * (36. * cc - 29.) / 10.));

        // Northing
        let m = ellps.meridian_latitude_to_distance(lat);
        let znos4 = z * N * dlon * s / 4.;
        let ecc = 4. * eps * cc;
        coord[1] = y_0 + k_0 * (m + N * theta_2 + znos4 * (9. + ecc + oo * (20. * cc - 11.)));
        operands.set_coord(i, &coord);
        successes += 1;
    }

    successes
}

// ----- I N V E R S E -----------------------------------------------------------------

// Inverse transverse mercator, following Bowring (1989)
fn inv(op: &Op, _ctx: &dyn Context, operands: &mut dyn CoordinateSet) -> usize {
    let ellps = op.params.ellps(0);
    let eps = ellps.second_eccentricity_squared();
    let lat_0 = op.params.lat(0).to_radians();
    let lon_0 = op.params.lon(0).to_radians();
    let x_0 = op.params.x(0);
    let y_0 = op.params.y(0);
    let k_0 = op.params.k(0);

    let mut successes = 0_usize;
    let n = operands.len();
    for i in 0..n {
        let mut coord = operands.get_coord(i);
        // Footpoint latitude, i.e. the latitude of a point on the central meridian
        // having the same northing as the point of interest
        let lat = ellps.meridian_distance_to_latitude((coord[1] - y_0) / k_0);
        let (s, c) = lat.sin_cos();
        let t = s / c;
        let cc = c * c;
        #[allow(non_snake_case)]
        let N = ellps.prime_vertical_radius_of_curvature(lat);
        let x = (coord[0] - x_0) / (k_0 * N);
        let xx = x * x;
        let theta_4 = x.sinh().atan2(c);
        let theta_5 = (t * theta_4.cos()).atan();

        // Latitude
        let xet = xx * xx * eps * t / 24.;
        coord[1] = lat_0 + (1. + cc * eps) * (theta_5 - xet * (9. - 10. * cc)) - eps * cc * lat;

        // Longitude
        let approx = lon_0 + theta_4;
        let coef = eps / 60. * xx * x * c;
        coord[0] = approx - coef * (10. - 4. * xx / cc + xx * cc);
        operands.set_coord(i, &coord);

        successes += 1;
    }

    successes
}

// ----- C O N S T R U C T O R ---------------------------------------------------------

#[rustfmt::skip]
pub const GAMUT: [OpParameter; 7] = [
    OpParameter::Flag { key: "inv" },
    OpParameter::Text { key: "ellps", default: Some("GRS80") },

    OpParameter::Real { key: "lat_0", default: Some(0_f64) },
    OpParameter::Real { key: "lon_0", default: Some(0_f64) },
    OpParameter::Real { key: "x_0",   default: Some(0_f64) },
    OpParameter::Real { key: "y_0",   default: Some(0_f64) },

    OpParameter::Real { key: "k_0",   default: Some(1_f64) },
];

pub fn new(parameters: &RawParameters, _ctx: &dyn Context) -> Result<Op, Error> {
    Op::basic(parameters, InnerOp(fwd), Some(InnerOp(inv)), &GAMUT)
}

#[rustfmt::skip]
pub const UTM_GAMUT: [OpParameter; 4] = [
    OpParameter::Flag { key: "inv" },
    OpParameter::Flag { key: "south" },
    OpParameter::Text { key: "ellps", default: Some("GRS80") },
    OpParameter::Natural { key: "zone", default: None },
];

pub fn utm(parameters: &RawParameters, _ctx: &dyn Context) -> Result<Op, Error> {
    let def = &parameters.instantiated_as;
    let mut params = ParsedParameters::new(parameters, &UTM_GAMUT)?;

    // The UTM zone should be an integer between 1 and 60
    let zone = params.natural("zone")?;
    if !(1..61).contains(&zone) {
        return Err(Error::General(
            "UTM: 'zone' must be an integer in the interval 1..60",
        ));
    }

    // The scaling factor is 0.9996 by definition of UTM
    params.real.insert("k_0", 0.9996);

    // The center meridian is determined by the zone
    params.real.insert("lon_0", -183. + 6. * zone as f64);

    // The base parallel is by definition the equator
    params.real.insert("lat_0", 0.);

    // The false easting is 500000 m by definition of UTM
    params.real.insert("x_0", 500_000.);

    // The false northing is 0 m by definition of UTM
    params.real.insert("y_0", 0.);
    // or 10_000_000 m if using the southern aspect
    if params.boolean("south") {
        params.real.insert("y_0", 10_000_000.0);
    }

    let descriptor = OpDescriptor::new(def, InnerOp(fwd), Some(InnerOp(inv)));

    Ok(Op {
        descriptor,
        params,
        steps: None,
    })
}

// ----- T E S T S ---------------------------------------------------------------------

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn btmerc() -> Result<(), Error> {
        let mut ctx = Minimal::default();
        let definition = "btmerc k_0=0.9996 lon_0=9 x_0=500000";
        let op = ctx.op(definition)?;

        // Validation values from PROJ:
        // echo 12 55 0 0 | cct -d18 +proj=utm +zone=32 | clip
        #[rustfmt::skip]
        let geo = [
            Coor4D::geo( 55.,  12., 0., 0.),
            Coor4D::geo(-55.,  12., 0., 0.),
            Coor4D::geo( 55., -6., 0., 0.),
            Coor4D::geo(-55., -6., 0., 0.)
        ];

        #[rustfmt::skip]
        let projected = [
            Coor4D::raw( 691_875.632_139_661, 6_098_907.825_005_012, 0., 0.),
            Coor4D::raw( 691_875.632_139_661,-6_098_907.825_005_012, 0., 0.),
            Coor4D::raw(-455_673.814_189_040, 6_198_246.671_090_279, 0., 0.),
            Coor4D::raw(-455_673.814_189_040,-6_198_246.671_090_279, 0., 0.)
        ];

        let mut operands = geo;
        ctx.apply(op, Fwd, &mut operands)?;
        for i in 0..operands.len() {
            assert!(operands[i].hypot2(&projected[i]) < 5e-3);
        }

        ctx.apply(op, Inv, &mut operands)?;
        for i in 0..operands.len() {
            assert!(operands[i].hypot2(&geo[i]) < 10e-8);
        }
        Ok(())
    }

    #[test]
    fn butm() -> Result<(), Error> {
        let mut ctx = Minimal::default();
        let definition = "butm zone=32";
        let op = ctx.op(definition)?;

        // Validation values from PROJ:
        // echo 12 55 0 0 | cct -d18 +proj=utm +zone=32 | clip
        #[rustfmt::skip]
        let geo = [
            Coor4D::geo( 55.,  12., 0., 0.),
            Coor4D::geo(-55.,  12., 0., 0.),
            Coor4D::geo( 55., -6., 0., 0.),
            Coor4D::geo(-55., -6., 0., 0.)
        ];

        #[rustfmt::skip]
        let projected = [
            Coor4D::raw( 691_875.632_139_661, 6_098_907.825_005_012, 0., 0.),
            Coor4D::raw( 691_875.632_139_661,-6_098_907.825_005_012, 0., 0.),
            Coor4D::raw(-455_673.814_189_040, 6_198_246.671_090_279, 0., 0.),
            Coor4D::raw(-455_673.814_189_040,-6_198_246.671_090_279, 0., 0.)
        ];

        let mut operands = geo;
        ctx.apply(op, Fwd, &mut operands)?;
        for i in 0..operands.len() {
            assert!(operands[i].hypot2(&projected[i]) < 5e-3);
        }

        ctx.apply(op, Inv, &mut operands)?;
        for i in 0..operands.len() {
            assert!(operands[i].hypot2(&geo[i]) < 10e-8);
        }
        Ok(())
    }

    #[test]
    fn butm_south() -> Result<(), Error> {
        let mut ctx = Minimal::default();
        let op = ctx.op("butm zone=32 south")?;

        #[rustfmt::skip]
        let geo = [
            Coor4D::geo( 55.,  12., 0., 0.),
            Coor4D::geo(-55.,  12., 0., 0.),
            Coor4D::geo( 55., -6., 0., 0.),
            Coor4D::geo(-55., -6., 0., 0.)
        ];

        #[rustfmt::skip]
        let projected = [
            Coor4D::raw( 691_875.632_139_661, 1e7+6_098_907.825_005_012, 0., 0.),
            Coor4D::raw( 691_875.632_139_661, 1e7-6_098_907.825_005_012, 0., 0.),
            Coor4D::raw(-455_673.814_189_040, 1e7+6_198_246.671_090_279, 0., 0.),
            Coor4D::raw(-455_673.814_189_040, 1e7-6_198_246.671_090_279, 0., 0.)
        ];

        let mut operands = geo;
        ctx.apply(op, Fwd, &mut operands)?;
        for i in 0..operands.len() {
            assert!(operands[i].hypot2(&projected[i]) < 5e-3);
        }

        ctx.apply(op, Inv, &mut operands)?;
        for i in 0..operands.len() {
            assert!(operands[i].hypot2(&geo[i]) < 10e-8);
        }

        Ok(())
    }
}