101 lines
2.5 KiB
Python
101 lines
2.5 KiB
Python
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import numpy as np
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class Lambert:
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def __init__(
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self,
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X0=1.7e6,
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Y0=2.2e6,
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lambda0=3,
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phi0=43,
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phi1=42.25,
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phi2=43.75,
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a=6378137,
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e=0.081819190842622,
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):
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self._X0 = X0
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self._Y0 = Y0
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self._lambda0 = np.radians(lambda0)
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self._phi0 = np.radians(phi0)
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self._phi1 = np.radians(phi1)
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self._phi2 = np.radians(phi2)
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self._a = a
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self._e = e
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self._set_n()
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self._set_rho0()
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def cartesian(self, lam, phi):
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lam = np.radians(lam)
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phi = np.radians(phi)
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theta = self._n * (lam - self._lambda0)
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rho = self._rho(phi)
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rho0 = self._rho(self._phi0)
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X = self._X0 + rho * np.sin(theta)
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Y = self._Y0 + rho0 - rho * np.cos(theta)
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return X, Y
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def _set_n(self):
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self._n = (
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np.log(np.cos(self._phi2) / np.cos(self._phi1))
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+ (
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np.log(
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(1 - (self._e * np.sin(self._phi1) ** 2))
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/ (1 - (self._e * np.sin(self._phi2) ** 2))
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)
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/ 2
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)
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) / (
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np.log(
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(
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np.tan(self._phi1 / 2 + np.pi / 4)
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* (
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(1 - self._e * np.sin(self._phi2))
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* (1 + self._e * np.sin(self._phi1))
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)
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** (self._e / 2)
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)
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/ (
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np.tan(self._phi2 / 2 + np.pi / 4)
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* (
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(1 + self._e * np.sin(self._phi2))
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* (1 - self._e * np.sin(self._phi1))
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)
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** (self._e / 2)
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)
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)
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)
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def _set_rho0(self):
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self._rho0 = (
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self._a
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* np.cos(self._phi1)
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/ (self._n * np.sqrt(1 - self._e**2 * np.sin(self._phi1) ** 2))
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* (
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np.tan(self._phi1 / 2 + np.pi / 4)
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* (
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(1 - self._e * np.sin(self._phi1))
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/ (1 + self._e * np.sin(self._phi1))
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)
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** (self._e / 2)
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)
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** self._n
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)
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def _rho(self, phi):
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return (
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self._rho0
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* (
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1
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/ np.tan(phi / 2 + np.pi / 4)
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* ((1 + self._e * np.sin(phi)) / (1 - self._e * np.sin(phi)))
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** (self._e / 2)
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)
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** self._n
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)
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