# Coverage for pygeodesy/vector3d.py : 91%

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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__ = '20.01.12' 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.