Coverage for pygeodesy/vector3d.py : 98%

Hot-keys on this page
r m x p toggle line displays
j k next/prev highlighted chunk
0 (zero) top of page
1 (one) first highlighted chunk
# -*- coding: utf-8 -*-
Function L{intersection3d3}, L{intersections2}, L{parse3d}, L{sumOf}, L{trilaterate2d2} and L{trilaterate3d2}. '''
_0_0, _1_0 _xError, _xkwds, _xkwds_popitem # from pygeodesy.fsums import fsum, fsum1_ # from .fmath # from pygeodesy.formy import _radical2 # in _intersects2 below _h_, _height_, _intersection_, _name_, _near_, \ _negative_, _no_, _too_, _z_ NearestOn6Tuple, Vector3Tuple # Vector4Tuple # from pygeodesy.streprs import Fmt # from .iters # from pygeodesy.vector2d import .... # in .... below
'''Extended 3-D vector.
In a geodesy context, these may be used to represent: - earth-centered, earth-fixed cartesian (ECEF) - n-vector representing a normal to a point on earth's surface - great circle normal to vector - motion vector on earth's surface - etc. '''
'''Get the "bearing" of this vector.
@kwarg useZ: If C{True}, use the Z component, otherwise consider the Y as +Z axis.
@return: Bearing (compass C{degrees}), the counter-clockwise angle off the +Z axis. ''' x, y = hypot(x, y), self.z
'''Return the radius and center of the I{inscribed} aka I{In- circle} of a (3-D) triangle formed by this and two other points.
@arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2} if C{B{useZ} is True} otherwise L{pygeodesy.trilaterate2d2}.
@return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The C{center} and contact points C{cA}, C{cB} and C{cC}, each an instance of this (sub-)class, are co-planar with this and the two given points.
@raise ImportError: Package C{numpy} not found, not installed or older than version 1.10.
@raise IntersectionError: Near-coincident or -colinear points or a trilateration or C{numpy} issue.
@raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
@see: Function L{pygeodesy.circin6}, U{Incircle <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle<https://MathWorld.Wolfram.com/ContactTriangle.html>}. ''' except (AssertionError, TypeError, ValueError) as x: raise _xError(x, point=self, point2=point2, point3=point3)
'''Return the radius and center of the smallest circle I{through} or I{containing} this and two other (3-D) points.
@arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @kwarg circum: If C{True} return the C{circumradius} and C{circumcenter}, always, ignoring the I{Meeus}' Type I case (C{bool}). @kwarg eps: Tolerance passed to function L{pygeodesy.trilaterate3d2}.
@return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an instance of this (sub-)class, is co-planar with this and the two given points.
@raise ImportError: Package C{numpy} not found, not installed or older than version 1.10.
@raise IntersectionError: Near-concentric, -coincident or -colinear points or a trilateration or C{numpy} issue.
@raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
@see: Function L{pygeodesy.circum3} and methods L{circum4_} and L{meeus2}. ''' eps=eps, useZ=True, clas=self.classof) except (AssertionError, TypeError, ValueError) as x: raise _xError(x, point=self, point2=point2, point3=point3, circum=circum)
'''Best-fit a sphere through this and two or more other (3-D) points.
@arg points: Other points (each a C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}).
@return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center} an instance if this (sub-)class.
@raise ImportError: Package C{numpy} not found, not installed or older than version 1.10.
@raise NumPyError: Some C{numpy} issue.
@raise PointsError: Too few B{C{points}}.
@raise TypeError: One of the B{C{points}} invalid.
@see: Function L{pygeodesy.circum4_} and methods L{circum3} and L{meeus2}. '''
'''Check whether this and two other (3-D) points are colinear.
@arg point1: One point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg point2: An other point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @kwarg eps: Tolerance (C{scalar}), same units as C{x}, C{y}, and C{z}.
@return: C{True} if this point is colinear with B{C{point1}} and B{C{point2}}, C{False} otherwise.
@raise TypeError: Invalid B{C{point1}} or B{C{point2}}.
@see: Method L{nearestOn}. '''
'''Return the radius and I{Meeus}' Type of the smallest circle I{through} or I{containing} this and two other (3-D) points.
@arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @kwarg circum: If C{True} return the C{circumradius} and C{circumcenter} always, ignoring the I{Meeus}' Type I case (C{bool}).
@return: L{Meeus2Tuple}C{(radius, Type)}.
@raise IntersectionError: Coincident or colinear points, iff C{B{circum}=True}.
@raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
@see: Function L{pygeodesy.meeus2} and methods L{circum3} and L{circum4_}. ''' clas=self.classof) except (TypeError, ValueError) as x: raise _xError(x, point=self, point2=point2, point3=point3, circum=circum)
'''Locate the point between two points closest to this point.
@arg point1: Start point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg point2: End point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @kwarg within: If C{True} return the closest point between the given points, otherwise the closest point on the extended line through both points (C{bool}).
@return: Closest point, either B{C{point1}} or B{C{point2}} or an instance of this (sub-)class.
@raise TypeError: Invalid B{C{point1}} or B{C{point2}}.
@see: Method L{sphericalTrigonometry.LatLon.nearestOn3} and U{3-D Point-Line Distance<https://MathWorld.Wolfram.com/ Point-LineDistance3-Dimensional.html>}. '''
'''Locate the point on a path or polygon closest to this point.
The closest point is either on and within the extent of a polygon edge or the nearest of that edge's end points.
@arg points: The path or polygon points (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}[]). @kwarg closed: Optionally, close the path or polygon (C{bool}). @kwarg useZ: If C{True}, use the Z components, otherwise force C{z=INT0} (C{bool}).
@return: A L{NearestOn6Tuple}C{(closest, distance, fi, j, start, end)} with the C{closest}, the C{start} and the C{end} point each an instance of this point's (sub-)class.
@raise PointsError: Insufficient number of B{C{points}}
@raise TypeError: Non-cartesian B{C{points}}.
@note: Distances measured with method L{Vector3d.equirectangular}.
@see: Function L{nearestOn6}. ''' return nearestOn6(self, points, closed=closed, useZ=useZ) # Vector=self.classof
'''Parse an C{"x, y, z"} string to a L{Vector3d} instance.
@arg str3d: X, y and z string (C{str}), see function L{parse3d}. @kwarg sep: Optional separator (C{str}). @kwarg name: Optional instance name (C{str}), overriding this name.
@return: The instance (L{Vector3d}).
@raise VectorError: Invalid B{C{str3d}}. '''
'''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent} circles of a (3-D) triangle.
@arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
@return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.
@raise TriangleError: Near-coincident or -colinear points.
@raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
@see: Function L{pygeodesy.radii11}, U{Incircle <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}. ''' except (TypeError, ValueError) as x: raise _xError(x, point=self, point2=point2, point3=point3)
'''Return the radius and center of the C{inner} I{Soddy} circle of a (3-D) triangle.
@arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2} if C{B{useZ} is True} otherwise L{pygeodesy.trilaterate2d2}.
@return: L{Soddy4Tuple}C{(radius, center, deltas, outer)}. The C{center}, an instance of B{C{point1}}'s (sub-)class, is co-planar with the three given points.
@raise ImportError: Package C{numpy} not found, not installed or older than version 1.10.
@raise IntersectionError: Near-coincident or -colinear points or a trilateration or C{numpy} issue.
@raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
@see: Function L{pygeodesy.soddy4}. '''
'''Trilaterate this and two other circles, each given as a (2-D) center and a radius.
@arg radius: Radius of this circle (same C{units} as this C{x} and C{y}. @arg center2: Center of the 2nd circle (C{Cartesian}, L{Vector3d}, C{Vector2Tuple}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius2: Radius of this circle (same C{units} as this C{x} and C{y}. @arg center3: Center of the 3rd circle (C{Cartesian}, L{Vector3d}, C{Vector2Tuple}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius3: Radius of the 3rd circle (same C{units} as this C{x} and C{y}. @kwarg eps: Check the trilaterated point I{delta} on all 3 circles (C{scalar}) or C{None}. @kwarg z: Optional Z component of the trilaterated point (C{scalar}).
@return: Trilaterated point, an instance of this (sub-)class with C{z=B{z}}.
@raise IntersectionError: No intersection, near-concentric or -colinear centers, trilateration failed some other way or the trilaterated point is off one circle by more than B{C{eps}}.
@raise TypeError: Invalid B{C{center2}} or B{C{center3}}.
@raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{radius3}}.
@see: Function L{pygeodesy.trilaterate2d2}. '''
_xyr3(radius2, center2=center2) + _xyr3(radius3, center3=center3)), eps=eps, Vector=self.classof, z=z) except (AssertionError, TypeError, ValueError) as x: raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2, center3=center3, radius3=radius3)
'''Trilaterate this and two other spheres, each given as a (3-D) center and a radius.
@arg radius: Radius of this sphere (same C{units} as this C{x}, C{y} and C{z}). @arg center2: Center of the 2nd sphere (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius2: Radius of this sphere (same C{units} as this C{x}, C{y} and C{z}). @arg center3: Center of the 3rd sphere (C{Cartesian}, , L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius3: Radius of the 3rd sphere (same C{units} as this C{x}, C{y} and C{z}). @kwarg eps: Tolerance (C{scalar}), same units as C{x}, C{y}, and C{z}.
@return: 2-Tuple with two trilaterated points, each an instance of this (sub-)class. Both points are the same instance if all three spheres intersect or abut in a single point.
@raise ImportError: Package C{numpy} not found, not installed or older than version 1.10.
@raise IntersectionError: Near-concentric, -colinear, too distant or non-intersecting spheres or C{numpy} issue.
@raise NumPyError: Some C{numpy} issue.
@raise TypeError: Invalid B{C{center2}} or B{C{center3}}.
@raise UnitError: Invalid B{C{radius}}, B{C{radius2}} or B{C{radius3}}.
@note: Package U{numpy<https://PyPI.org/project/numpy>} is required, version 1.10 or later.
@see: Norrdine, A. U{I{An Algebraic Solution to the Multilateration Problem}<https://www.ResearchGate.net/publication/ 275027725_An_Algebraic_Solution_to_the_Multilateration_Problem>} and U{I{implementation}<https://www.ResearchGate.net/publication/ 288825016_Trilateration_Matlab_Code>}. ''' center2, radius2, center3, radius3, eps=eps, clas=self.classof) except (AssertionError, TypeError, ValueError) as x: raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2, center3=center3, radius3=radius3)
# (INTERNAL) Intersect two lines, see L{intersection3d3} below, # separated to allow callers to embellish any exceptions
# Get the C{s1'} and C{e1'}, corners of a right-angle # triangle with the hypotenuse thru C{s1} at bearing # C{b1} and the right angle at C{s2} raise IntersectionError(useZ=d, bearing=b1) else: # orthogonal
else: else:
if d > EPS0 and ab.length > e: # PYCHOK no cover d = d / ab.length # /= chokes PyChecker if d > e: # argonic, skew lines distance raise IntersectionError(skew_d=d, txt=_no_(_intersection_))
# co-planar, non-skew lines if b.length2 < e: # PYCHOK no cover if c.length < e: return s1, 0, 0 elif e2.minus(e1).length < e: return e1, 0, 0 # like _nearestOn2(s1, s2, e2, within=False, eps=e) raise IntersectionError(length2=ab2, txt=_no_(_intersection_))
**Vector_and_kwds): '''Compute the intersection point of two lines, each defined by two points or by a point and a bearing.
@arg start1: Start point of the first line (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg end1: End point of the first line (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}) or the bearing at B{C{start1}} (compass C{degrees}). @arg start2: Start point of the second line (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg end2: End point of the second line (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}) or the bearing at B{C{start2}} (Ccompass C{degrees}). @kwarg eps: Tolerance for skew line distance and length (C{EPS}). @kwarg useZ: If C{True}, use the Z components, otherwise force C{z=INT0} (C{bool}). @kwarg Vector_and_kwds: Optional class C{B{Vector}=None} to return the intersection points and optional, additional B{C{Vector}} keyword arguments, otherwise B{C{start1}}'s (sub-)class.
@return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point} an instance of B{C{Vector}} or B{C{start1}}'s (sub-)class.
@note: The C{outside} values is C{0} for lines specified by point and bearing.
@raise IntersectionError: Invalid, skew, non-co-planar or otherwise non-intersecting lines.
@see: U{Line-line intersection<https://MathWorld.Wolfram.com/Line-LineIntersection.html>} and U{line-line distance<https://MathWorld.Wolfram.com/Line-LineDistance.html>}, U{skew lines<https://MathWorld.Wolfram.com/SkewLines.html>} and U{point-line distance<https://MathWorld.Wolfram.com/Point-LineDistance3-Dimensional.html>}. ''' except (TypeError, ValueError) as x: raise _xError(x, start1=start1, end1=end1, start2=start2, end2=end2) name=intersection3d3.__name__))
'''Compute the intersection of two spheres or circles, each defined by a (3-D) center point and a radius.
@arg center1: Center of the first sphere or circle (C{Cartesian}, 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 (C{Cartesian}, 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_and_kwds: Optional class C{B{Vector}=None} to return the intersection points and optional, additional B{C{Vector}} keyword arguments, otherwise B{C{center1}}'s (sub-)class.
@return: If B{C{sphere}} is C{True}, a 2-tuple of the C{center} and C{radius} of the intersection of the I{spheres}. The C{radius} is C{0.0} for abutting spheres (and the C{center} is aka I{radical center}).
If B{C{sphere}} is C{False}, a 2-tuple with the two intersection points of the I{circles}. For abutting circles, both points are the same instance, aka I{radical center}.
@raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles.
@raise TypeError: Invalid B{C{center1}} or B{C{center2}}.
@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>} Intersection. ''' center2, Radius_(radius2=radius2), sphere=sphere, clas=center1.classof, **Vector_and_kwds) except (TypeError, ValueError) as x: raise _xError(x, center1=center1, radius1=radius1, center2=center2, radius2=radius2)
**clas_Vector_and_kwds): # .ellipsoidalBaseDI._intersections2 # (INTERNAL) Intersect two spheres or circles, see L{intersections2} # above, separated to allow callers to embellish any exceptions
fdot(xy1, u.y, u.x, c1.y), _0_0)
raise IntersectionError(_near_(_concentric_))
# compute intersections with c1 at (0, 0) and c2 at (d, 0), like # <https://MathWorld.Wolfram.com/Circle-CircleIntersection.html> elif y < 0: # PYCHOK no cover raise IntersectionError(_negative_) else: # abutting y = _0_0 elif o < 0: # PYCHOK no cover t = d if too_d is None else too_d raise IntersectionError(_too_(Fmt.distant(t))) else: # abutting
c2 if x > EPS1 else c1.plus(u.times(x)))
else: # abutting circles
'''Check whether a point is colinear with two other (2- or 3-D) points.
@arg point: The point (L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg point1: First point (L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg point2: Second point (L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @kwarg eps: Tolerance (C{scalar}), same units as C{x}, C{y} and C{z}. @kwarg useZ: If C{True}, use the Z components, otherwise force C{z=INT0} (C{bool}).
@return: C{True} if B{C{point}} is colinear B{C{point1}} and B{C{point2}}, C{False} otherwise.
@raise TypeError: Invalid B{C{point}}, B{C{point1}} or B{C{point2}}.
@see: Function L{nearestOn}. '''
'''Locate the point between two points closest to a reference (2- or 3-D).
@arg point: Reference point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg point1: Start point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg point2: End point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @kwarg within: If C{True} return the closest point between both given points, otherwise the closest point on the extended line through both points (C{bool}). @kwarg useZ: If C{True}, use the Z components, otherwise force C{z=INT0} (C{bool}). @kwarg Vector: Class to return closest point (C{Cartesian}, L{Vector3d} or C{Vector3Tuple}) or C{None}. @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if C{B{Vector} is None}.
@return: Closest point, either B{C{point1}} or B{C{point2}} or an instance of the B{C{point}}'s (sub-)class or B{C{Vector}} if not C{None}.
@raise TypeError: Invalid B{C{point}}, B{C{point1}} or B{C{point2}}.
@see: U{3-D Point-Line Distance<https://MathWorld.Wolfram.com/Point-LineDistance3-Dimensional.html>}, C{Cartesian} and C{LatLon} methods C{nearestOn}, method L{sphericalTrigonometry.LatLon.nearestOn3} and function L{sphericalTrigonometry.nearestOn3}. '''
p = Vector(p.x, p.y, **_xkwds(Vector_kwds, z=p.z, name=nearestOn.__name__)) else: # ignore Vector_kwds
# (INTERNAL) Closest point and fraction, see L{nearestOn} above, # separated to allow callers to embellish any exceptions else: # see comments in .points.nearestOn5 else:
'''Locate the point on a path or polygon closest to a reference point.
The closest point is either on and within the extent of a polygon edge or the nearest of that edge's end points.
@arg point: Reference point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg points: The path or polygon points (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}[]). @kwarg closed: Optionally, close the path or polygon (C{bool}). @kwarg useZ: If C{True}, use the Z components, otherwise force C{z=INT0} (C{bool}). @kwarg Vector_and_kwds: Optional class C{B{Vector}=None} to return the closest point and optional, additional B{C{Vector}} keyword arguments, otherwise B{C{point}}'s (sub-)class.
@return: A L{NearestOn6Tuple}C{(closest, distance, fi, j, start, end)} with the C{closest}, the C{start} and the C{end} point each an instance of the B{C{Vector}} keyword argument of if {B{Vector}=None} or not specified, an instance of the B{C{point}}'s (sub-)class.
@raise PointsError: Insufficient number of B{C{points}}
@raise TypeError: Non-cartesian B{C{point}} and B{C{points}}.
@note: Distances measured with method L{Vector3d.equirectangular}.
@see: Method C{LatLon.nearestOn6} or function L{nearestOn5} for geodetic points. '''
# return a named C{Vector} or C{clas} instance
# check named vector instance, return Vector3d .Ellipsoid.height4, .formy.hartzell, .vector2d
except AttributeError: # no .x, .y or .z attr pass raise _xotherError(Vector3d(0, 0, 0), v, name=_name_i(name, i), up=2)
'''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 C{B{Vector} is None}.
@return: A B{C{Vector}} instance or if B{C{Vector}} is C{None}, a named L{Vector3Tuple}C{(x, y, z)}.
@raise VectorError: Invalid B{C{str3d}}. ''' raise _ValueError(len=n) except (TypeError, ValueError) as x: raise VectorError(str3d=str3d, txt=str(x)) Vector(*v, **Vector_kwds)), parse3d.__name__)
'''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 C{B{Vector} is None}.
@return: Vectorial sum as B{C{Vector}} or if B{C{Vector}} is C{None}, a named 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)) Vector(*v, **Vector_kwds)), sumOf.__name__)
eps=None, **Vector_and_kwds): '''Trilaterate three circles, each given as a (2-D) center and a radius.
@arg x1: Center C{x} coordinate of the 1st circle (C{scalar}). @arg y1: Center C{y} coordinate of the 1st circle (C{scalar}). @arg radius1: Radius of the 1st circle (C{scalar}). @arg x2: Center C{x} coordinate of the 2nd circle (C{scalar}). @arg y2: Center C{y} coordinate of the 2nd circle (C{scalar}). @arg radius2: Radius of the 2nd circle (C{scalar}). @arg x3: Center C{x} coordinate of the 3rd circle (C{scalar}). @arg y3: Center C{y} coordinate of the 3rd circle (C{scalar}). @arg radius3: Radius of the 3rd circle (C{scalar}). @kwarg eps: Check the trilaterated point I{delta} on all 3 circles (C{scalar}) or C{None}. @kwarg Vector_and_kwds: Optional class C{B{Vector}=None} to return the trilateration and optional, additional B{C{Vector}} keyword arguments, otherwise (L{Vector3d}).
@return: Trilaterated point as C{B{Vector}(x, y, **B{Vector_kwds})} or L{Vector2Tuple}C{(x, y)} if C{B{Vector} is None}..
@raise IntersectionError: No intersection, near-concentric or -colinear centers, trilateration failed some other way or the trilaterated point is off one circle by more than B{C{eps}}.
@raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{radius3}}.
@see: U{Issue #49<https://GitHub.com/mrJean1/PyGeodesy/issues/49>}, U{Find X location using 3 known (X,Y) location using trilateration <https://math.StackExchange.com/questions/884807>} and function L{pygeodesy.trilaterate3d2}. ''' x2, y2, radius2, x3, y3, radius3, eps=eps, **Vector_and_kwds)
eps=EPS, **Vector_and_kwds): '''Trilaterate three spheres, each given as a (3-D) center and a radius.
@arg center1: Center of the 1st sphere (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius1: Radius of the 1st sphere (same C{units} as C{x}, C{y} and C{z}). @arg center2: Center of the 2nd sphere (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius2: Radius of this sphere (same C{units} as C{x}, C{y} and C{z}). @arg center3: Center of the 3rd sphere (C{Cartesian}, L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @arg radius3: Radius of the 3rd sphere (same C{units} as C{x}, C{y} and C{z}). @kwarg eps: Tolerance (C{scalar}), same units as C{x}, C{y}, and C{z}. @kwarg Vector_and_kwds: Optional class C{B{Vector}=None} to return the trilateration and optional, additional B{C{Vector}} keyword arguments, otherwise B{C{center1}}'s (sub-)class.
@return: 2-Tuple with two trilaterated points, each a B{C{Vector}} instance. Both points are the same instance if all three spheres abut/intersect in a single point.
@raise ImportError: Package C{numpy} not found, not installed or older than version 1.10.
@raise IntersectionError: Near-concentric, -colinear, too distant or non-intersecting spheres.
@raise NumPyError: Some C{numpy} issue.
@raise TypeError: Invalid B{C{center1}}, B{C{center2}} or B{C{center3}}.
@raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{radius3}}.
@see: Norrdine, A. U{I{An Algebraic Solution to the Multilateration Problem}<https://www.ResearchGate.net/publication/ 275027725_An_Algebraic_Solution_to_the_Multilateration_Problem>}, the U{I{implementation}<https://www.ResearchGate.net/publication/ 288825016_Trilateration_Matlab_Code>} and function L{pygeodesy.trilaterate2d2}. ''' Radius_(radius1=radius1, low=eps), center2, radius2, center3, radius3, eps=eps, clas=center1.classof, **Vector_and_kwds) except (AssertionError, TypeError, ValueError) as x: raise _xError(x, center1=center1, radius1=radius1, center2=center2, radius2=radius2, center3=center3, radius3=radius3)
'''(INTERNAL) Get an C{(h, d, name)} 3-tuple. ''' or getattr(xyz, _h_, None) \ or getattr(ll, _height_, None)
or getattr(ll, _datum_, None)
# **) MIT License # # Copyright (C) 2016-2022 -- 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. |