lambert 1.0.0

lamber-rust is a crate helping to convert Lambert coordinates to WGS84
Documentation 
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use point::Point;
use zone;
use zone::Zone;
use std::f32;

/// Convert latitude to latitude iso
#[allow(dead_code)]
fn latitude_iso_from_latitude(lat: f32, e: f32) -> f32 {
    return f32::log(f32::tan(f32::consts::FRAC_PI_4+lat/2.0)*f32::powf((1.0-e*f32::sin(lat))/(1.0+e*f32::sin(lat)),e/2.0), f32::consts::E);
}

fn latitude_from_latitude_iso(lat_iso: f32, e: f32, eps: f32) -> f32 {

    let mut phi_0 = 2.0*f32::atan(f32::exp(lat_iso)) - f32::consts::FRAC_PI_2;
    let mut phi_i = 2.0*f32::atan(f32::powf((1.0+e*f32::sin(phi_0))/(1.0-e*f32::sin(phi_0)),e/2.0)*f32::exp(lat_iso)) - f32::consts::FRAC_PI_2;

    loop {

       let delta = f32::abs(phi_i - phi_0);

        if delta < eps {
            break;
        }

        phi_0 = phi_i;
        phi_i = 2.0*f32::atan(f32::powf((1.0+e*f32::sin(phi_0))/(1.0-e*f32::sin(phi_0)),e/2.0)*f32::exp(lat_iso)) - f32::consts::FRAC_PI_2;
    }

    return phi_i
}

pub fn lambert_to_geographic(org: Point, zone: Zone, lon_merid: f32, e: f32, eps: f32) -> Point {

    let n = zone::n(zone);
    let c = zone::c(zone);
    let x_s = zone::xs(zone);
    let y_s = zone::ys(zone);

    let x = org.x;
    let y = org.y;

    let r = f32::sqrt((x-x_s)*(x-x_s)+(y-y_s)*(y-y_s));

    let gamma = f32::atan((x-x_s)/(y_s-y));

    let lon = lon_merid + gamma/n;

    let lat_iso = -1.0/n*f32::log(f32::abs(r/c), f32::consts::E);

    let lat = latitude_from_latitude_iso(lat_iso, e, eps);

    return Point { x: lon, y: lat, z: org.z};
}

pub fn lambert_normal(lat: f32, a: f32, e: f32) -> f32 {
    return a/f32::sqrt(1.0-e*e*f32::sin(lat)*f32::sin(lat));
}

pub fn geographic_to_cartesian(lon: f32, lat: f32, he: f32, a: f32, e: f32) -> Point {

    let n = lambert_normal(lat, a, e);

    let mut pt = Point::new(0.0, 0.0, 0.0);
    pt.x = (n+he)*f32::cos(lat)*f32::cos(lon);

 	pt.y = (n+he)*f32::cos(lat)*f32::sin(lon);

 	pt.z = (n*(1.0-e*e)+he)*f32::sin(lat);
    return pt
}

pub fn cartesian_to_geographic(point: Point, meridien: f32, a: f32, e: f32, eps: f32) -> Point{

    let (x, y, z) = (point.x, point.y, point.z);
    let lon = meridien + f32::atan(y/x);

 	let module = f32::sqrt(x*x + y*y);

 	let mut phi_0 = f32::atan(z/(module*(1.0-(a*e*e)/f32::sqrt(x*x+y*y+z*z))));
 	let mut phi_i = f32::atan(z/module/(1.0-a*e*e*f32::cos(phi_0)/(module * f32::sqrt(1.0-e*e*f32::sin(phi_0)*f32::sin(phi_0)))));
 	let mut delta;

    loop {
        delta = f32::abs(phi_i - phi_0);
        if delta < eps {
            break;
        }
        phi_0 = phi_i;
        phi_i = f32::atan(z/module/(1.0-a*e*e*f32::cos(phi_0)/(module * f32::sqrt(1.0-e*e*f32::sin(phi_0)*f32::sin(phi_0)))));
    }

    let he = module/f32::cos(phi_i) - a/f32::sqrt(1.0-e*e*f32::sin(phi_i)*f32::sin(phi_i));
 	return Point { x:lon, y:phi_i, z: he};
}

#[cfg(test)]
mod tests {

    macro_rules! assert_delta {
        ( $left:expr, $right:expr, $d:expr ) => {
            {
                if $left > $right {
                    if ($left - $right) > $d {
                        panic!("left: {} | right: {} | delta: {}\n", $left, $right, ($left - $right));
                    }
                } else {
                    if ($right - $left) > $d {
                        panic!("left: {} | right: {} | delta: {}\n", $left, $right, ($right - $left));
                    }
                }
            }
        };
    }

    use point::Point;
    use zone::Zone;

    use super::lambert_to_geographic;

    #[test]
    fn test_lambert_to_geographic() {
        let expected = Point::new(0.145512099,0.872664626, 0.0);
        let org = Point::new(1029705.083, 272723.849, 0.0);

        let delta = 1e-7;
        let dest = lambert_to_geographic(org, Zone::LambertI, ::consts::LON_MERID_GREENWICH, ::consts::E_CLARK_IGN, delta);
        assert_delta!(dest.x, expected.x, delta);
        assert_delta!(dest.y, expected.y, delta);
        assert_delta!(dest.z, expected.z, delta);
    }

    
    use super::lambert_normal;
    
    #[test]
    fn test_lambert_normal() {
        let n = 6393174.9755;
        let lat = 0.97738438100;
        let a = 6378388.0000;
        let e = 0.081991890;

        let calc = lambert_normal(lat,a,e);
        assert_eq!(n, calc);
    }

    use super::geographic_to_cartesian;

    #[test]
    fn test_geographic_to_cartesian() {
        let lon:[f32; 3] = [0.01745329248 ,0.00290888212 ,0.00581776423];
        let lat:[f32; 3] = [0.02036217457,0.00000000000 ,-0.03199770300];
        let he:[f32; 3] = [100.0000,10.0000 ,2000.0000];
        let a:[f32; 3] = [6378249.2000 ,6378249.2000 ,6378249.2000];
        let e:[f32; 3] = [0.08248325679 ,0.08248325679 ,0.08248325679];

        let points  = vec![
            Point::new(6376064.6955, 111294.6230, 128984.7250),
            Point::new(6378232.2149, 18553.5780, 0.0),
            Point::new(6376897.5369, 37099.7050, -202730.9070)
            ];

        let delta = 1e-1;
        for i in 0..points.len() {
            let pt  = geographic_to_cartesian(lon[i],lat[i],he[i],a[i],e[i]);

            assert_delta!(pt.x,points[i].x, delta);
            assert_delta!(pt.y,points[i].y, delta);
            assert_delta!(pt.z,points[i].z, delta);
        }
    }

    
    use super::cartesian_to_geographic;

    #[test]
    fn test_cartesian_to_geographic() {

        let a: [f32; 3] = [6378249.2000, 6378249.2000 ,6378249.2000];
        let e: [f32; 3] = [0.08248325679, 0.08248325679, 0.08248325679];
        let x: [f32; 3] = [6376064.6950, 6378232.2150, 6376897.5370];
        let y: [f32; 3] = [111294.6230, 18553.5780, 37099.7050];
        let z: [f32; 3] = [128984.7250, 0.0000, -202730.9070];
        let eps: [f32; 3] = [1e-11,1e-11,1e-11];

        let lon: [f32; 3] = [0.01745329248, 0.00290888212, 0.00581776423];
        let lat: [f32; 3] = [0.02036217457, 0.00000000000, -0.03199770301];
        let he: [f32; 3] = [99.9995, 10.0001, 2000.0001];

        let delta = 1e-8;
        for i in 0..3 {
            let sample = Point::new(x[i],y[i],z[i]);

            let val = cartesian_to_geographic(sample,::consts::LON_MERID_PARIS,a[i],e[i],eps[i]);

            assert_delta!(val.x,lon[i],delta);
            assert_delta!(val.y,lat[i],delta);
            assert_delta!(val.z,he[i],1e-3);
        }
    }

    
    use super::latitude_from_latitude_iso;

    #[test]
    fn test_latitude_from_latitude_iso() {
        let lat_iso: [f32; 3] = [1.00552653648,-0.30261690060 ,0.2000000000];
        let e: [f32; 3] = [0.08199188998,0.08199188998,0.08199188998];
        let eps: [f32; 3] = [1.0e-11,1.0e-11,1.0e-11];

        let phi: [f32; 3] = [0.87266462600, -0.29999999997 ,0.19998903369];

            for index in 0..3 {
                let result = latitude_from_latitude_iso(lat_iso[index], e[index], eps[index]);
                assert_delta!(result, phi[index], 1e-7);
            }
    }
}