Coverage for pygeodesy/vector3d.py : 93%

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# -*- coding: utf-8 -*-
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 '''
property_doc_, property_RO, _xkwds _TypeError, _ValueError _datum_, _h_, _height_, _invalid_, _Missing, \ _name_, _near_concentric_, NN, _other_, _PARENTH_, \ _scalar_, _too_distant_fmt_, _y_, _z_
'''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple. ''' except (TypeError, ValueError) as x: d = dict(zip(('xyz', _y_, _z_), t)) raise Error(txt=str(x), **d)
'''(INTERNAL) Get an C{(x, y, z, h, d, name)} 6-tuple. '''
or getattr(xyz, _h_, None) \ or getattr(ll, _height_, None)
or getattr(ll, _datum_, None)
'''L{Vector3d} or C{*Nvector} issue. '''
'''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. '''
'''New 3-D L{Vector3d}.
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}). '''
'''Add this to an other vector (L{Vector3d}).
@return: Vectorial sum (L{Vector3d}).
@raise TypeError: Incompatible B{C{other}} C{type}. ''' # __iadd__ = __add__
'''Return the norm of this vector.
@return: Norm, unit length (C{float}); ''' return self.length
'''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}. ''' +1 if self.length > other.length else 0)
'''Divide this vector by a scalar.
@arg scalar: The divisor (C{scalar}).
@return: Quotient (L{Vector3d}).
@raise TypeError: Non-scalar B{C{scalar}}. ''' # __itruediv__ = __div__
'''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}. '''
'''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}. '''
'''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}. '''
'''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}. '''
'''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}. '''
# Luciano Ramalho, "Fluent Python", page 397, O'Reilly 2016 '''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}. ''' # __imatmul__ = __matmul__
'''Multiply this vector by a scalar
@arg scalar: Factor (C{scalar}).
@return: Product (L{Vector3d}). ''' # __imul__ = __mul__ # __rmul__ = __mul__
'''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}. '''
'''Negate this vector.
@return: Negative (L{Vector3d}) ''' return self.negate()
'''Copy this vector.
@return: Positive (L{Vector3d}) ''' return self.copy()
# Luciano Ramalho, "Fluent Python", page 397, O'Reilly 2016 '''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}. '''
'''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)
'''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}. ''' # __isub__ = __sub__
'''(INTERNAL) Zap cached attributes if updated. ''' '_united', '_xyz', *attrs)
'''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.
@return: Angle (C{radians}).
@raise TypeError: If B{C{other}} or B{C{vSign}} not a L{Vector3d}. ''' # use vSign as reference to get sign of s
'''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}. '''
raise CrossError(raiser, r, txt=t)
def crosserrors(self): '''Get L{CrossError} exceptions (C{bool}). '''
def crosserrors(self, raiser): '''Raise L{CrossError} exceptions (C{bool}). ''' self._crosserrors = bool(raiser)
'''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}}. ''' raise _IsnotError(_scalar_, factor=factor) except (ValueError, ZeroDivisionError): raise VectorError(factor=factor)
'''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}. '''
def equals(self, other, units=False): # PYCHOK no cover '''DEPRECATED, use method C{isequalTo}. ''' return self.isequalTo(other, units=units)
'''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 for equality (C{scalar}).
@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 '''
else:
def length(self): '''Get the length (norm, magnitude) of this vector (C{float}). '''
'''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.y - other.y, self.z - other.z)
'''Return this vector in opposite direction.
@return: New, opposite vector (L{Vector3d}). '''
def _N_vector(self): '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) '''
'''Refined class comparison.
@arg other: The other vector (L{Vector3d}). @kwarg name: Optional, other's name (C{str}). @kwarg up: Number of call stack frames up (C{int}).
@return: The B{C{other}} if compatible.
@raise TypeError: Incompatible B{C{other}} C{type}. ''' raise
'''Parse an C{"x, y, z"} string.
@arg str3d: X, y and z values (C{str}). @kwarg sep: Optional separator (C{str}).
@return: New vector (L{Vector3d}).
@raise VectorError: Invalid B{C{str3d}}. '''
'''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.y + other.y, self.z + other.z)
'''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}. '''
# multiply p by a quaternion-derived rotation matrix 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): # PYCHOK no cover '''DEPRECATED, use method C{rotate}. ''' return self.rotate(axis, theta)
'''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}}. ''' raise _IsnotError(_scalar_, factor=factor) self.y * factor, self.z * factor)
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)
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)
def to3xyz(self): # PYCHOK no cover '''DEPRECATED, use property C{xyz}.
@return: A L{Vector3Tuple}C{(x, y, z)}. ''' return self.xyz
'''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}). '''
'''Normalize this vector to unit length.
@kwarg ll: Optional, original location (C{LatLon}).
@return: Normalized vector (L{Vector3d}). ''' else:
def x(self): '''Get the X component (C{float}). '''
def xyz(self): '''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}). '''
def y(self): '''Get the Y component (C{float}). '''
def z(self): '''Get the Z component (C{float}). '''
Vector=None, **Vector_kwds): '''Compute the intersection of two spheres or circles, each defined by a center point and a radius.
@arg center1: Center of the first sphere or circle (L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius1: Radius of the first sphere or circle (same units as the B{C{center1}} coordinates). @arg center2: Center of the second sphere or circle (L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius2: Radius of the second sphere or circle (same units as the B{C{center1}} and B{C{center2}} coordinates). @kwarg sphere: If C{True} compute the center and radius of the intersection of two spheres. If C{False}, ignore the C{z}-component and compute the intersection of two circles (C{bool}). @kwarg Vector: Class to return intersections (L{Vector3d} or C{Vector3Tuple}) or C{None} for L{Vector3d}. @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if B{C{Vector=None}}.
@return: 2-Tuple of the C{center} and C{radius} of the intersection of the spheres if B{C{sphere}} is C{True}. The C{radius} is C{0.0} for abutting spheres. Otherwise, a 2-tuple of the intersection points of two circles. For abutting circles, both intersection points are the same B{C{Vector}} instance.
@raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles.
@raise UnitError: Invalid B{C{radius1}} or B{C{radius2}}.
@see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere- SphereIntersection.html>} and U{circle-circle <https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} intersections. '''
Vector=Vector, **Vector_kwds)
except (TypeError, ValueError) as x: raise IntersectionError(center1=center1, radius1=radius1, center2=center2, radius2=radius2, txt=str(x))
Vector=None, **Vector_kwds): # (INTERNAL) Intersect of two spheres or circles, see L{intersections2} # above, separated to allow callers to embellish any exceptions
else:
fdot(xy1, u.y, u.x, c1.y), 0)
raise ValueError(_near_concentric_)
# gap == d - (r1 + r2) # compute intersections with c1 at (0, 0) and c2 at (d, 0), like # <https://MathWorld.Wolfram.com/Circle-CircleIntersection.html> elif y < 0: raise ValueError(_invalid_) else: # abutting y = 0 elif o < 0: t = d if too_d is None else too_d raise ValueError(_too_distant_fmt_ % (t,)) else: # abutting x, y = r1, 0
c2 if x > EPS1 else c1.plus(u.times(x))) else: # abutting circles t = _xVector(c1, u, x, 0) t = t, t
# x coord [0..d] of the "radical line", perpendicular to # the x-axis line between both centers (0, 0) and (d, 0)
# return "radical ratio" and radical line x coord
'''Parse an C{"x, y, z"} string.
@arg str3d: X, y and z values (C{str}). @kwarg sep: Optional separator (C{str}). @kwarg Vector: Optional class (L{Vector3d}). @kwarg Vector_kwds: Optional B{C{Vector}} keyword arguments, ignored if B{C{Vector=None}}.
@return: New B{C{Vector}} or if B{C{Vector}} is C{None}, a L{Vector3Tuple}C{(x, y, z)}.
@raise VectorError: Invalid B{C{str3d}}. ''' raise ValueError except (TypeError, ValueError) as x: raise VectorError(str3d=str3d, txt=str(x))
Vector(*v, **Vector_kwds)
'''Compute the vectorial sum of several vectors.
@arg vectors: Vectors to be added (L{Vector3d}[]). @kwarg Vector: Optional class for the vectorial sum (L{Vector3d}). @kwarg Vector_kwds: Optional B{C{Vector}} keyword arguments, ignored if B{C{Vector=None}}.
@return: Vectorial sum as B{C{Vector}} or if B{C{Vector}} is C{None}, a L{Vector3Tuple}C{(x, y, z)}.
@raise VectorError: No B{C{vectors}}. ''' raise VectorError(vectors=n, txt=_Missing)
fsum(v.y for v in vectors), fsum(v.z for v in vectors))
# **) 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. |