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# -*- coding: utf-8 -*- 

 

u'''I{Veness}' 3-D vector base class C{Vector3dBase}. 

 

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>}. 

''' 

 

from pygeodesy.basics import copysign0, map1 

from pygeodesy.errors import CrossError, VectorError 

from pygeodesy.fmath import euclid_, fdot, hypot_, hypot2_ 

from pygeodesy.formy import n_xyz2latlon, n_xyz2philam, sincos2 

from pygeodesy.interns import EPS, EPS0, NN, PI, PI2, _coincident_, \ 

_colinear_, _COMMASPACE_, _1_0 

from pygeodesy.named import _NamedBase, _xother3 

from pygeodesy.namedTuples import Vector3Tuple # Vector4Tuple 

from pygeodesy.props import deprecated_method, Property_RO, property_doc_ 

from pygeodesy.streprs import Fmt, strs 

from pygeodesy.units import Float, Scalar 

# from pygeodesy.utily import sincos2 # from .formy 

 

from math import atan2 

 

__all__ = () 

__version__ = '21.07.02' 

 

 

class Vector3dBase(_NamedBase): # XXX or _NamedTuple or Vector3Tuple? 

'''(INTERNAL) Generic 3-D vector base class. 

 

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 cartesian (= spherical n-vector) 

- great circle normal to vector 

- motion vector on earth's surface 

- etc. 

''' 

_crosserrors = True # un/set by .errors.crosserrors 

 

_fromll = None # original latlon, '_fromll' 

_x = 0 # X component 

_y = 0 # Y component 

_z = 0 # Z component 

 

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

'''New L{Vector3d} or C{Vector3dBase} instance. 

 

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. 

 

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

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

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

@kwarg ll: Optional latlon reference (C{LatLon}). 

@kwarg 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 __abs__(self): 

'''Return the norm of this vector. 

 

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

''' 

return self.length 

 

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 __cmp__(self, other): # Python 2- 

'''Compare this and an other vector 

 

@arg 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 -1 if self.length < other.length else ( 

+1 if self.length > other.length else 0) 

 

cmp = __cmp__ 

 

def __div__(self, scalar): 

'''Divide this vector by a scalar. 

 

@arg 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? 

 

@arg 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? 

 

@arg 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? 

 

@arg 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? 

 

@arg 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? 

 

@arg 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. 

 

@arg 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 

 

@arg 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? 

 

@arg 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. 

 

@arg 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. 

 

@arg 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. 

 

@arg 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 angleTo(self, other, vSign=None, wrap=False): 

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

 

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

@kwarg 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. 

@kwarg wrap: Wrap/unroll the angle to +/-PI (C{bool}). 

 

@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 

# use vSign as reference to set sign of s 

if s and vSign and x.dot(vSign) < 0: 

s = -s 

 

a = atan2(s, self.dot(other)) 

if wrap and abs(a) > PI: 

a -= copysign0(PI2, a) 

return a 

 

def cross(self, other, raiser=None): # raiser=NN 

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

 

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

@kwarg 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(raiser, r, txt=t) 

 

return self.classof(x, y, z) 

 

@property_doc_('''raise or ignore L{CrossError} exceptions (C{bool}).''') 

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. 

 

@arg 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}}. 

''' 

f = Scalar(factor=factor) 

try: 

return self.times(_1_0 / f) 

except (ValueError, ZeroDivisionError) as x: 

raise VectorError(factor=factor, txt=str(x)) 

 

def dot(self, other): 

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

 

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

 

@return: Dot product (C{float}). 

 

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

''' 

if other is self: 

d = self.length2 

else: 

self.others(other) 

d = fdot(self.xyz, *other.xyz) 

return d 

 

@deprecated_method 

def equals(self, other, units=False): # PYCHOK no cover 

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

''' 

return self.isequalTo(other, units=units) 

 

@Property_RO 

def euclid(self): 

'''Approximate the length (norm, magnitude) of this vector. 

 

@see: Function L{euclid_} and properties C{length} and C{length2}. 

''' 

return Float(euclid=euclid_(self.x, self.y, self.z)) 

 

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

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

 

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

@kwarg units: Optionally, compare the normalized, unit 

version of both vectors. 

@kwarg eps: Tolerance (C{scalar}), same units as C{x}, 

C{y}, and C{z}. 

 

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

 

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

''' 

self.others(other) 

 

if units: 

d = self.unit().minus(other.unit()) 

else: 

d = self.minus(other) 

return max(map(abs, d.xyz)) < eps 

 

@Property_RO 

def length(self): # __dict__ value overwritten by Property_RO C{_united} 

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

 

@see: Properties L{length2} and L{euclid}. 

''' 

return Float(length=hypot_(self.x, self.y, self.z)) 

 

@Property_RO 

def length2(self): # __dict__ value overwritten by Property_RO C{_united} 

'''Get the length I{squared} of this vector (C{float}). 

 

@see: Property L{length}. 

''' 

return Float(length2=hypot2_(self.x, self.y, self.z)) 

 

def minus(self, other): 

'''Subtract an other vector from this vector. 

 

@arg 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) 

 

@Property_RO 

def _N_vector(self): 

'''(INTERNAL) Get the (C{nvectorBase._N_vector_}) 

''' 

from pygeodesy.nvectorBase import _N_vector_ 

return _N_vector_(*self.xyz, name=self.name) 

 

def others(self, *other, **name_other_up): 

'''Refined class comparison. 

 

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

@kwarg name_other_up: Overriding C{name=other} and C{up=1} 

keyword arguments. 

 

@return: The B{C{other}} if compatible. 

 

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

''' 

other, name, up = _xother3(self, other, **name_other_up) 

if not isinstance(other, Vector3dBase): 

_NamedBase.others(self, other, name=name, up=up + 1) 

return other 

 

def plus(self, other): 

'''Add this vector and an other vector. 

 

@arg 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>}. 

 

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

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

 

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

 

@JSname: I{rotateAround}. 

''' 

s, c = sincos2(theta) 

 

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

b = a.times(_1_0 - c) 

s = a.times(s) 

 

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

# multiply p by a quaternion-derived rotation matrix 

ax, ay, az = a.x, a.y, a.z 

bx, by, bz = b.x, b.y, b.z 

sx, sy, sz = s.x, s.y, s.z 

return self.classof(fdot(p, ax * bx + c, ax * by - sz, ax * bz + sy), 

fdot(p, ay * bx + sz, ay * by + c, ay * bz - sx), 

fdot(p, az * bx - sy, az * by + sx, az * bz + c)) 

 

@deprecated_method 

def rotateAround(self, axis, theta): # PYCHOK no cover 

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

return self.rotate(axis, theta) 

 

def times(self, factor): 

'''Multiply this vector by a scalar. 

 

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

 

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

 

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

''' 

f = Scalar(factor=factor) 

return self.classof(self.x * f, self.y * f, self.z * f) 

 

@deprecated_method 

def to2ab(self): # PYCHOK no cover 

'''DEPRECATED, use property C{Nvector.philam}. 

 

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

''' 

return n_xyz2philam(self.x, self.y, self.z) 

 

@deprecated_method 

def to2ll(self): # PYCHOK no cover 

'''DEPRECATED, use property C{Nvector.latlon}. 

 

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

''' 

return n_xyz2latlon(self.x, self.y, self.z) 

 

@deprecated_method 

def to3xyz(self): # PYCHOK no cover 

'''DEPRECATED, use property L{xyz}. 

''' 

return self.xyz 

 

def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected 

'''Return a string representation of this vector. 

 

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

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

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

 

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

''' 

t = sep.join(strs(self.xyz, prec=prec)) 

return (fmt % (t,)) if fmt else t 

 

def unit(self, ll=None): 

'''Normalize this vector to unit length. 

 

@kwarg ll: Optional, original location (C{LatLon}). 

 

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

''' 

u = self._united 

if ll: 

u._fromll = ll 

return u 

 

@Property_RO 

def _united(self): # __dict__ value overwritten below 

'''(INTERNAL) Get normalized vector (L{Vector3d}). 

''' 

n = self.length 

if n > EPS0 and abs(n - _1_0) > EPS0: 

u = self._xnamed(self.dividedBy(n)) 

u._overwrite(length=_1_0, length2=_1_0, _united=u) 

else: 

u = self.copy() 

u._overwrite(_united=u) 

if self._fromll: 

u._fromll = self._fromll 

return u 

 

@Property_RO 

def x(self): 

'''Get the X component (C{float}). 

''' 

return self._x 

 

@Property_RO 

def xyz(self): 

'''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}). 

''' 

return Vector3Tuple(self.x, self.y, self.z, name=self.name) 

 

@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 

 

# **) MIT License 

# 

# Copyright (C) 2016-2021 -- 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.