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# -*- coding: utf-8 -*- 

 

u'''Generic 3-D vector base class L{Vector3d} and function L{sumOf}. 

 

Pure Python implementation of vector-based functions by I{(C) Chris 

Veness 2011-2015} published under the same MIT Licence**, see 

U{Vector-based geodesy 

<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.fmath import EPS, fdot, fStr, fsum, hypot, hypot_, \ 

isscalar, len2, map1, _IsNotError 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import LatLon2Tuple, _NamedBase, PhiLam2Tuple, \ 

Vector3Tuple, _xattrs 

from pygeodesy.utily import degrees90, degrees180, property_RO 

 

from math import atan2, cos, sin 

 

# all public constants, classes and functions 

__all__ = _ALL_LAZY.vector3d + ('Vector3d', 'sumOf') 

__version__ = '19.10.21' 

 

try: 

_cmp = cmp 

except NameError: # Python 3+ 

def _cmp(a, b): 

return +1 if a > b else ( 

-1 if a < b else 0) 

 

 

def _xyzn4(xyz, y, z, Error=TypeError): # imported by .ecef.py 

'''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple. 

''' 

try: 

t = xyz.x, xyz.y, xyz.z 

except AttributeError: 

t = xyz, y, z 

try: 

x, y, z = map1(float, *t) 

except (TypeError, ValueError) as x: 

raise Error('%s invalid: %r, %s' % ('xyz, y or z', t, x)) 

 

return x, y, z, getattr(xyz, 'name', '') 

 

 

def _xyzhdn6(xyz, y, z, height, datum, ll, Error=TypeError): # .cartesianBase.py, .nvectorBase.py 

'''(INTERNAL) Get an C{(x, y, z, h, d, name)} 6-tuple. 

''' 

x, y, z, n = _xyzn4(xyz, y, z, Error=Error) 

 

h = height or getattr(xyz, 'height', None) \ 

or getattr(xyz, 'h', None) \ 

or getattr(ll, 'height', None) 

 

d = datum or getattr(xyz, 'datum', None) \ 

or getattr(ll, 'datum', None) 

 

return x, y, z, h, d, n 

 

 

class CrossError(ValueError): 

'''Error raised for zero or near-zero vectorial cross products, 

occurring for coincident or colinear points, paths or bearings. 

''' 

pass 

 

 

def crosserrors(raiser=None): 

'''Get/set raising of vectorial cross product errors. 

 

@keyword raiser: Use C{True} to throw or C{False} to ignore 

L{CrossError} exceptions. Use C{None} to 

leave the setting unchanged. 

 

@return: Previous setting (C{bool}). 

''' 

t = Vector3d._crosserrors 

if raiser in (True, False): 

Vector3d._crosserrors = raiser 

return t 

 

 

class VectorError(ValueError): 

'''L{Vector3d} or C{*Nvector} issue. 

''' 

pass 

 

 

class Vector3d(_NamedBase): 

'''Generic 3-D vector manipulation. 

 

In a geodesy context, these may be used to represent: 

- n-vector representing a normal to point on earth's surface 

- earth-centered, earth-fixed vector (= n-vector for spherical model) 

- great circle normal to vector 

- motion vector on earth's surface 

- etc. 

''' 

_crosserrors = True # set by function crosserrors above 

 

_fromll = None #: (INTERNAL) original ll. 

_length = None #: (INTERNAL) cached length. 

_united = None #: (INTERNAL) cached norm, unit. 

 

_x = 0 #: (INTERNAL) X component. 

_y = 0 #: (INTERNAL) Y component. 

_z = 0 #: (INTERNAL) Z component. 

 

def __init__(self, x, y, z, ll=None, name=''): 

'''New 3-D vector. 

 

The vector may be normalised, or use x/y/z values for 

height relative to the surface of the sphere or ellipsoid, 

distance from earth centre, etc. 

 

@param x: X component of vector (C{scalar}). 

@param y: Y component of vector (C{scalar}). 

@param z: Z component of vector (C{scalar}). 

@keyword ll: Optional, original latlon (C{LatLon}). 

@keyword name: Optional name (C{str}). 

''' 

self._x = x 

self._y = y 

self._z = z 

if ll: 

self._fromll = ll 

if name: 

self.name = name 

 

def __add__(self, other): 

'''Add this to an other vector (L{Vector3d}). 

 

@return: Vectorial sum (L{Vector3d}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

return self.plus(other) 

# __iadd__ = __add__ 

__radd__ = __add__ 

 

def __abs__(self): 

'''Return the norm of this vector. 

 

@return: Norm, unit length (C{float}); 

''' 

return self.length 

 

def __cmp__(self, other): # Python 2- 

'''Compare this and an other vector 

 

@param other: The other vector (L{Vector3d}). 

 

@return: -1, 0 or +1 (C{int}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return _cmp(self.length, other.length) 

 

def __div__(self, scalar): 

'''Divide this vector by a scalar. 

 

@param scalar: The divisor (C{scalar}). 

 

@return: Quotient (L{Vector3d}). 

 

@raise TypeError: Non-scalar B{C{scalar}}. 

''' 

return self.dividedBy(scalar) 

# __itruediv__ = __div__ 

__truediv__ = __div__ 

 

def __eq__(self, other): 

'''Is this vector equal to an other vector? 

 

@param other: The other vector (L{Vector3d}). 

 

@return: C{True} if equal, C{False} otherwise. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return self.isequalTo(other) 

 

def __ge__(self, other): 

'''Is this vector longer than or equal to an other vector? 

 

@param other: The other vector (L{Vector3d}). 

 

@return: C{True} if so, C{False} otherwise. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return self.length >= other.length 

 

def __gt__(self, other): 

'''Is this vector longer than an other vector? 

 

@param other: The other vector (L{Vector3d}). 

 

@return: C{True} if so, C{False} otherwise. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return self.length > other.length 

 

def __le__(self, other): # Python 3+ 

'''Is this vector shorter than or equal to an other vector? 

 

@param other: The other vector (L{Vector3d}). 

 

@return: C{True} if so, C{False} otherwise. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return self.length <= other.length 

 

def __lt__(self, other): # Python 3+ 

'''Is this vector shorter than an other vector? 

 

@param other: The other vector (L{Vector3d}). 

 

@return: C{True} if so, C{False} otherwise. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return self.length < other.length 

 

# Luciano Ramalho, "Fluent Python", page 397, O'Reilly 2016 

def __matmul__(self, other): # PYCHOK Python 3.5+ ... c = a @ b 

'''Compute the cross product of this and an other vector. 

 

@param other: The other vector (L{Vector3d}). 

 

@return: Cross product (L{Vector3d}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

return self.cross(other) 

# __imatmul__ = __matmul__ 

 

def __mul__(self, scalar): 

'''Multiply this vector by a scalar 

 

@param scalar: Factor (C{scalar}). 

 

@return: Product (L{Vector3d}). 

''' 

return self.times(scalar) 

# __imul__ = __mul__ 

# __rmul__ = __mul__ 

 

def __ne__(self, other): 

'''Is this vector not equal to an other vector? 

 

@param other: The other vector (L{Vector3d}). 

 

@return: C{True} if so, C{False} otherwise. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return not self.isequalTo(other) 

 

def __neg__(self): 

'''Negate this vector. 

 

@return: Negative (L{Vector3d}) 

''' 

return self.negate() 

 

def __pos__(self): 

'''Copy this vector. 

 

@return: Positive (L{Vector3d}) 

''' 

return self.copy() 

 

# Luciano Ramalho, "Fluent Python", page 397, O'Reilly 2016 

def __rmatmul__(self, other): # PYCHOK Python 3.5+ ... c = a @ b 

'''Compute the cross product of an other and this vector. 

 

@param other: The other vector (L{Vector3d}). 

 

@return: Cross product (L{Vector3d}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return other.cross(self) 

 

def __rsub__(self, other): 

'''Subtract this vector from an other vector. 

 

@param other: The other vector (L{Vector3d}). 

 

@return: Difference (L{Vector3d}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

return other.minus(self) 

 

def __sub__(self, other): 

'''Subtract an other vector from this vector. 

 

@param other: The other vector (L{Vector3d}). 

 

@return: Difference (L{Vector3d}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

return self.minus(other) 

# __isub__ = __sub__ 

 

def _update(self, updated): 

'''(INTERNAL) Clear caches. 

''' 

if updated: # reset caches 

self._length = self._united = None 

 

def _xcopy(self, *attrs): 

'''(INTERNAL) Make copy with add'l, subclass attributes. 

''' 

return _xattrs(self.classof(self.x, self.y, self.z), 

self, '_length', '_united', *attrs) # _crosserrors 

 

def angleTo(self, other, vSign=None): 

'''Compute the angle between this and an other vector. 

 

@param other: The other vector (L{Vector3d}). 

@keyword vSign: Optional vector, if supplied (and out of the 

plane of this and the other), angle is signed 

positive if this->other is clockwise looking 

along vSign or negative in opposite direction, 

otherwise angle is unsigned. 

 

@return: Angle (C{radians}). 

 

@raise TypeError: If B{C{other}} or B{C{vSign}} not a L{Vector3d}. 

''' 

x = self.cross(other) 

s = x.length 

if s < EPS: 

return 0.0 

# use vSign as reference to get sign of s 

if vSign and x.dot(vSign) < 0: 

s = -s 

return atan2(s, self.dot(other)) 

 

def copy(self): 

'''Copy this vector. 

 

@return: The copy (L{Vector3d} or subclass thereof). 

''' 

return self._xcopy() 

 

def cross(self, other, raiser=None): 

'''Compute the cross product of this and an other vector. 

 

@param other: The other vector (L{Vector3d}). 

@keyword raiser: Optional, L{CrossError} label if raised (C{str}). 

 

@return: Cross product (L{Vector3d}). 

 

@raise CrossError: Zero or near-zero cross product and both 

B{C{raiser}} and L{crosserrors} set. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

 

x = self.y * other.z - self.z * other.y 

y = self.z * other.x - self.x * other.z 

z = self.x * other.y - self.y * other.x 

 

if raiser and self.crosserrors and max(map1(abs, x, y, z)) < EPS: 

t = 'coincident' if self.isequalTo(other) else 'colinear' 

r = getattr(other, '_fromll', None) or other 

raise CrossError('%s %s: %r' % (t, raiser, r)) 

 

return self.classof(x, y, z) 

 

@property 

def crosserrors(self): 

'''Get L{CrossError} exceptions (C{bool}). 

''' 

return self._crosserrors 

 

@crosserrors.setter # PYCHOK setter! 

def crosserrors(self, raiser): 

'''Raise L{CrossError} exceptions (C{bool}). 

''' 

self._crosserrors = bool(raiser) 

 

def dividedBy(self, factor): 

'''Divide this vector by a scalar. 

 

@param factor: The divisor (C{scalar}). 

 

@return: New, scaled vector (L{Vector3d}). 

 

@raise TypeError: Non-scalar B{C{factor}}. 

 

@raise VectorError: Invalid or zero B{C{factor}}. 

''' 

if not isscalar(factor): 

raise _IsNotError('scalar', factor=factor) 

try: 

return self.times(1.0 / factor) 

except (ValueError, ZeroDivisionError): 

raise VectorError('%s invalid: %r' % ('factor', factor)) 

 

def dot(self, other): 

'''Compute the dot (scalar) product of this and an other vector. 

 

@param other: The other vector (L{Vector3d}). 

 

@return: Dot product (C{float}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

 

return fdot(self.to3xyz(), *other.to3xyz()) 

 

def equals(self, other, units=False): 

'''DEPRECATED, use method C{isequalTo}. 

''' 

return self.isequalTo(other, units=units) 

 

def isequalTo(self, other, units=False): 

'''Check if this and an other vector are equal or equivalent. 

 

@param other: The other vector (L{Vector3d}). 

@keyword units: Optionally, compare the normalized, 

unit version of both vectors. 

 

@return: C{True} if vectors are identical, C{False} otherwise. 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

 

@example: 

 

>>> v1 = Vector3d(52.205, 0.119) 

>>> v2 = Vector3d(52.205, 0.119) 

>>> e = v1.isequalTo(v2) # True 

''' 

self.others(other) 

 

if units: 

d = self.unit().minus(other.unit()) 

else: 

d = self.minus(other) 

return max(map(abs, d.to3xyz())) < EPS 

 

@property_RO 

def length(self): 

'''Get the length (norm, magnitude) of this vector (C{float}). 

''' 

if self._length is None: 

self._length = hypot_(self.x, self.y, self.z) 

return self._length 

 

def minus(self, other): 

'''Subtract an other vector from this vector. 

 

@param other: The other vector (L{Vector3d}). 

 

@return: New vector difference (L{Vector3d}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

 

return self.classof(self.x - other.x, 

self.y - other.y, 

self.z - other.z) 

 

def negate(self): 

'''Return this vector in opposite direction. 

 

@return: New, opposite vector (L{Vector3d}). 

''' 

return self.classof(-self.x, -self.y, -self.z) 

 

def others(self, other, name='other'): 

'''Refined class comparison. 

 

@param other: The other vector (L{Vector3d}). 

@keyword name: Optional, other's name (C{str}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

try: 

_NamedBase.others(self, other, name=name) 

except TypeError: 

if not isinstance(other, Vector3d): 

raise 

 

def parse(self, str3d, sep=','): 

'''Parse an "x, y, z" string representing a L{Vector3d}. 

 

@param str3d: X, y and z value (C{str}). 

@keyword sep: Optional separator (C{str}). 

 

@return: New vector (L{Vector3d}). 

 

@raise VectorError: Invalid B{C{str3d}}. 

''' 

try: 

v = [float(v.strip()) for v in str3d.split(sep)] 

if len(v) != 3: 

raise ValueError 

except (TypeError, ValueError): 

raise VectorError('%s invalid: %r' % ('str3d', str3d)) 

 

return self.classof(*v) 

 

def plus(self, other): 

'''Add this vector and an other vector. 

 

@param other: The other vector (L{Vector3d}). 

 

@return: Vectorial sum (L{Vector3d}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

self.others(other) 

 

return self.classof(self.x + other.x, 

self.y + other.y, 

self.z + other.z) 

 

sum = plus # alternate name 

 

def rotate(self, axis, theta): 

'''Rotate this vector around an axis by a specified angle. 

 

See U{Rotation matrix from axis and angle 

<https://WikiPedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle>} 

and U{Quaternion-derived rotation matrix 

<https://WikiPedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix>}. 

 

@param axis: The axis being rotated around (L{Vector3d}). 

@param theta: The angle of rotation (C{radians}). 

 

@return: New, rotated vector (L{Vector3d}). 

 

@JSname: I{rotateAround}. 

''' 

self.others(axis, name='axis') 

 

c = cos(theta) 

a = axis.unit() # axis being rotated around 

b = a.times(1 - c) 

s = a.times(sin(theta)) 

 

p = self.unit().to3xyz() # point being rotated 

 

# multiply p by a quaternion-derived rotation matrix 

return self.classof(fdot(p, a.x * b.x + c, a.x * b.y - s.z, a.x * b.z + s.y), 

fdot(p, a.y * b.x + s.z, a.y * b.y + c, a.y * b.z - s.x), 

fdot(p, a.z * b.x - s.y, a.z * b.y + s.x, a.z * b.z + c)) 

 

def rotateAround(self, axis, theta): 

'''DEPRECATED, use method C{rotate}. 

''' 

return self.rotate(axis, theta) 

 

def times(self, factor): 

'''Multiply this vector by a scalar. 

 

@param factor: Scale factor (C{scalar}). 

 

@return: New, scaled vector (L{Vector3d}). 

 

@raise TypeError: Non-scalar B{C{factor}}. 

''' 

if not isscalar(factor): 

raise _IsNotError('scalar', factor=factor) 

return self.classof(self.x * factor, 

self.y * factor, 

self.z * factor) 

 

def to2ab(self): 

'''Convert this vector to (geodetic) lat- and longitude in C{radians}. 

 

@return: A L{PhiLam2Tuple}C{(phi, lam)}. 

 

@example: 

 

>>> v = Vector3d(0.500, 0.500, 0.707) 

>>> a, b = v.to2ab() # 0.785323, 0.785398 

''' 

a = atan2(self.z, hypot(self.x, self.y)) 

b = atan2(self.y, self.x) 

return self._xnamed(PhiLam2Tuple(a, b)) 

 

def to2ll(self): 

'''Convert this vector to (geodetic) lat- and longitude in C{degrees}. 

 

@return: A L{LatLon2Tuple}C{(lat, lon)}. 

 

@example: 

 

>>> v = Vector3d(0.500, 0.500, 0.707) 

>>> a, b = v.to2ll() # 44.99567, 45.0 

''' 

a, b = self.to2ab() 

r = LatLon2Tuple(degrees90(a), degrees180(b)) 

return self._xnamed(r) 

 

def to3xyz(self): 

'''Return this vector as a 3-tuple. 

 

@return: A L{Vector3Tuple}C{(x, y, z)}. 

''' 

return self._xnamed(Vector3Tuple(self.x, self.y, self.z)) 

 

def toStr(self, prec=5, fmt='(%s)', sep=', '): # PYCHOK expected 

'''Return a string representation of this vector. 

 

@keyword prec: Optional number of decimal places (C{int}). 

@keyword fmt: Optional, enclosing format to use (C{str}). 

@keyword sep: Optional separator between components (C{str}). 

 

@return: Vector as "(x, y, z)" (C{str}). 

''' 

return fmt % (fStr(self.to3xyz(), prec=prec, sep=sep),) 

 

def unit(self, ll=None): 

'''Normalize this vector to unit length. 

 

@keyword ll: Optional, original latlon (C{LatLon}). 

 

@return: Normalized vector (L{Vector3d}). 

''' 

if self._united is None: 

n = self.length 

if n > EPS and abs(n - 1) > EPS: 

u = self.dividedBy(n) 

u._length = 1 

else: 

u = self.copy() 

u._fromll = ll or self._fromll 

self._united = u._united = u 

return self._united 

 

@property_RO 

def x(self): 

'''Get the X component (C{float}). 

''' 

return self._x 

 

@property_RO 

def y(self): 

'''Get the Y component (C{float}). 

''' 

return self._y 

 

@property_RO 

def z(self): 

'''Get the Z component (C{float}). 

''' 

return self._z 

 

 

def sumOf(vectors, Vector=Vector3d, **kwds): 

'''Compute the vectorial sum of several vectors. 

 

@param vectors: Vectors to be added (L{Vector3d}[]). 

@keyword Vector: Optional class for the vectorial sum (L{Vector3d}). 

@keyword kwds: Optional, additional B{C{Vector}} keyword arguments, 

ignored if C{B{Vector}=None}. 

 

@return: Vectorial sum (B{C{Vector}}). 

 

@raise VectorError: No B{C{vectors}}. 

''' 

n, vectors = len2(vectors) 

if n < 1: 

raise VectorError('no vectors: %r' & (n,)) 

 

r = Vector3Tuple(fsum(v.x for v in vectors), 

fsum(v.y for v in vectors), 

fsum(v.z for v in vectors)) 

if Vector is not None: 

r = Vector(r.x, r.y, r.z, **kwds) # PYCHOK x, y, z 

return r 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

# Permission is hereby granted, free of charge, to any person obtaining a 

# copy of this software and associated documentation files (the "Software"), 

# to deal in the Software without restriction, including without limitation 

# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

# and/or sell copies of the Software, and to permit persons to whom the 

# Software is furnished to do so, subject to the following conditions: 

# 

# The above copyright notice and this permission notice shall be included 

# in all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

# OTHER DEALINGS IN THE SOFTWARE.