EPSG:3059 (LKS-92) koordināšu pārrēķins uz platuma un garuma grādiem; transform coordinates code

LKS-92.py

import math


def lks_2_latlon(x, y):
    # Ellipsoid model constants (actual values here are for WGS84) */
    UTMScaleFactor = 0.9996
    sm_a = 6378137.0
    sm_b = 6356752.314
    x -= 500000.0
    # Pirmā atšķirība no WGS84 - Kilometriņš šurpu, kilometriņš turpu.
    # Ja šis nedod korektu rezultātu, atkomentē sekojošo rindiņu.
    # y -= -6000000.0
    x /= UTMScaleFactor
    y /= UTMScaleFactor
    # Otrā atšķirība no WGS84 - Centrālais meridiāns ir citur.
    lambda0 = math.radians(24)
    # Precalculate n (Eq. 10.18) */
    n = (sm_a - sm_b) / (sm_a + sm_b)
    # Precalculate alpha_ (Eq. 10.22) */
    # (Same as alpha in Eq. 10.17) */
    alpha_ = ((sm_a + sm_b) / 2.0) * (1 + (pow(n, 2.0) / 4) + (pow(n, 4.0) / 64))
    # Precalculate y_ (Eq. 10.23) */
    y_ = y / alpha_
    # Precalculate beta_ (Eq. 10.22) */
    beta_ = (3.0 * n / 2.0) + (-27.0 * pow(n, 3.0) / 32.0) + (269.0 * pow(n, 5.0) / 512.0)
    # Precalculate gamma_ (Eq. 10.22) */
    gamma_ = (21.0 * pow(n, 2.0) / 16.0) + (-55.0 * pow(n, 4.0) / 32.0)
    # Precalculate delta_ (Eq. 10.22) */
    delta_ = (151.0 * pow(n, 3.0) / 96.0) + (-417.0 * pow(n, 5.0) / 128.0)
    # Precalculate epsilon_ (Eq. 10.22) */
    epsilon_ = (1097.0 * pow(n, 4.0) / 512.0)
    # Now calculate the sum of the series (Eq. 10.21) */
    phif = y_ + (beta_ * math.sin(2.0 * y_)) + (gamma_ * math.sin(4.0 * y_)) + (delta_ * math.sin(6.0 * y_)) + (epsilon_ * math.sin(8.0 * y_))
    #  Precalculate ep2 */
    ep2 = (pow(sm_a, 2.0) - pow(sm_b, 2.0)) / pow(sm_b, 2.0)
    # Precalculate cos (phif) */
    cf = math.cos(phif)
    # Precalculate nuf2 */
    nuf2 = ep2 * pow(cf, 2.0)
    # Precalculate Nf and initialize Nfpow */
    Nf = pow(sm_a, 2.0) / (sm_b * math.sqrt(1 + nuf2))
    Nfpow = Nf
    # Precalculate tf */
    tf = math.tan(phif)
    tf2 = tf * tf
    tf4 = tf2 * tf2
    # Precalculate fractional coefficients for x**n in the equations
    #   below to simplify the expressions for latitude and longitude. */
    x1frac = 1.0 / (Nfpow * cf)
    Nfpow *= Nf  # /* now equals Nf**2) */
    x2frac = tf / (2.0 * Nfpow)
    Nfpow *= Nf  # /* now equals Nf**3) */
    x3frac = 1.0 / (6.0 * Nfpow * cf)
    Nfpow *= Nf  # /* now equals Nf**4) */
    x4frac = tf / (24.0 * Nfpow)
    Nfpow *= Nf  # /* now equals Nf**5) */
    x5frac = 1.0 / (120.0 * Nfpow * cf)
    Nfpow *= Nf  # /* now equals Nf**6) */
    x6frac = tf / (720.0 * Nfpow)
    Nfpow *= Nf  # /* now equals Nf**7) */
    x7frac = 1.0 / (5040.0 * Nfpow * cf)
    Nfpow *= Nf  # /* now equals Nf**8) */
    x8frac = tf / (40320.0 * Nfpow)
    # Precalculate polynomial coefficients for x**n.
    #   -- x**1 does not have a polynomial coefficient. */
    x2poly = -1.0 - nuf2
    x3poly = -1.0 - 2 * tf2 - nuf2
    x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2 - 3.0 * (nuf2 * nuf2) - 9.0 * tf2 * (nuf2 * nuf2)
    x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2
    x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 + 162.0 * tf2 * nuf2
    x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2)
    x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2)
    # /* Calculate latitude */
    lat = phif + x2frac * x2poly * (x * x) + x4frac * x4poly * pow(x, 4.0) + x6frac * x6poly * pow(x, 6.0) + x8frac * x8poly * pow(x, 8.0)
    # /* Calculate longitude */
    lon = lambda0 + x1frac * x + x3frac * x3poly * pow(x, 3.0) + x5frac * x5poly * pow(x, 5.0) + x7frac * x7poly * pow(x, 7.0)
    return math.degrees(lat), math.degrees(lon)


LKS_UTM_SCALE_FACTOR = 0.9996


def latlon_2_lks(lat, lon):
    lat = math.radians(lat)
    lon = math.radians(lon)
    # /* Ellipsoid model constants (actual values here are for GRS80) */
    sm_a = 6378137.0
    sm_b = 6356752.314140
    xy = []
    # // lks_MapLatLonToXY (lat, lon, lks_UTMCentralMeridian (zone), xy)
    phi = lat
    lambda_ = lon
    lambda0 = math.radians(24)
    # /* Precalculate ep2 */
    ep2 = (sm_a * sm_a - sm_b * sm_b) / sm_b / sm_b
    # /* Precalculate nu2 */
    nu2 = ep2 * math.cos(phi) * math.cos(phi)
    # /* Precalculate N */
    N = sm_a * sm_a / (sm_b * math.sqrt(1 + nu2))
    # /* Precalculate t */
    t = math.tan(phi)
    t2 = t * t
    # /* Precalculate l */
    l = lambda_ - lambda0
    # /* Precalculate coefficients for l**n in the equations below
    # so a normal human being can read the expressions for easting
    # and northing
    # -- l**1 and l**2 have coefficients of 1.0 */
    l3coef = 1.0 - t2 + nu2
    l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2)
    l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2 - 58.0 * t2 * nu2
    l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2 - 330.0 * t2 * nu2
    l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2)
    l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2)
    # /* Calculate easting (x) */
    x = N * math.cos(phi) * l + (N / 6.0 * pow(math.cos(phi), 3.0) * l3coef * pow(l, 3.0)) + (
            N / 120.0 * pow(math.cos(phi), 5.0) * l5coef * pow(l, 5.0)) + (N / 5040.0 * pow(math.cos(phi), 7.0) * l7coef * pow(l, 7.0))
    # /* Calculate northing (y) */
    y = lks_arc_length_of_meridian(phi) + (t / 2.0 * N * pow(math.cos(phi), 2.0) * pow(l, 2.0)) + (
            t / 24.0 * N * pow(math.cos(phi), 4.0) * l4coef * pow(l, 4.0)) + (t / 720.0 * N * pow(math.cos(phi), 6.0) * l6coef * pow(l, 6.0)) + (
                t / 40320.0 * N * pow(math.cos(phi), 8.0) * l8coef * pow(l, 8.0))
    x = x * LKS_UTM_SCALE_FACTOR + 500000.0
    # Ja šis nedod korektu rezultātu, pamēģiniet noņemt 6000000 vai 10000000
    # Ja jums izdosies, lūdzu pierakstiet komentāros
    y = y * LKS_UTM_SCALE_FACTOR - 6000000.0
    if y < 0.0:
        y = y + 10000000.0
    return x, y


def lks_arc_length_of_meridian(phi):
    # /* Precalculate n */
    sm_a = 6378137.0
    sm_b = 6356752.314140
    n = (sm_a - sm_b) / (sm_a + sm_b)
    # /* Precalculate alpha */
    alpha = ((sm_a + sm_b) / 2.0) * (1.0 + (pow(n, 2.0) / 4.0) + (pow(n, 4.0) / 64.0))
    # /* Precalculate beta */
    beta = (-3.0 * n / 2.0) + (9.0 * pow(n, 3.0) / 16.0) + (-3.0 * pow(n, 5.0) / 32.0)
    # /* Precalculate gamma */
    gamma = (15.0 * pow(n, 2.0) / 16.0) + (-15.0 * pow(n, 4.0) / 32.0)
    # /* Precalculate delta */
    delta = (-35.0 * pow(n, 3.0) / 48.0) + (105.0 * pow(n, 5.0) / 256.0)
    # /* Precalculate epsilon */
    epsilon = (315.0 * pow(n, 4.0) / 512.0)
    # /* Now calculate the sum of the series and return */
    result = alpha * (phi + (beta * math.sin(2.0 * phi)) + (gamma * math.sin(4.0 * phi)) + (delta * math.sin(6.0 * phi)) + (epsilon * math.sin(8.0 * phi)))
    return result

This is a Python adaptation of PHP code written by @laacz: https://gist.github.com/laacz/2597627

Links to check conversion:

1. https://epsg.io/transform#s_srs=3059&t_srs=4326
2. http://neogeo.lv/ekartes/koord2/