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PyGeodesy
Package pygeodesy :: Module vector3d :: Class Vector3d
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Class Vector3d

       object --+            
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     named._Named --+        
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     named._NamedBase --+    
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vector3dBase.Vector3dBase --+
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                           Vector3d
Known Subclasses:

Extended 3-D vector.

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

Instance Methods
 
bearing(self, useZ=True)
Get this vector's "bearing", the angle off the +Z axis, clockwise.
 
circin6(self, point2, point3, eps=8.881784197001252e-16)
Return the radius and center of the inscribed aka In- circle of a (3-D) triangle formed by this and two other points.
 
circum3(self, point2, point3, circum=True, eps=8.881784197001252e-16)
Return the radius and center of the smallest circle through or containing this and two other (3-D) points.
 
circum4_(self, *points)
Best-fit a sphere through this and two or more other (3-D) points.
 
iscolinearWith(self, point1, point2, eps=2.220446049250313e-16)
Check whether this and two other (3-D) points are colinear.
 
meeus2(self, point2, point3, circum=False)
Return the radius and Meeus' Type of the smallest circle through or containing this and two other (3-D) points.
 
nearestOn(self, point1, point2, within=True)
Locate the point between two points closest to this point.
 
nearestOn6(self, points, closed=False, useZ=True)
Locate the point on a path or polygon closest to this point.
 
parse(self, str3d, sep=',', **name)
Parse an "x, y, z" string to a Vector3d instance.
 
radii11(self, point2, point3)
Return the radii of the Circum-, In-, Soddy and Tangent circles of a (3-D) triangle.
 
soddy4(self, point2, point3, eps=8.881784197001252e-16)
Return the radius and center of the inner Soddy circle of a (3-D) triangle.
 
trilaterate2d2(self, radius, center2, radius2, center3, radius3, eps=8.881784197001252e-16, z=0)
Trilaterate this and two other circles, each given as a (2-D) center and a radius.
 
trilaterate3d2(self, radius, center2, radius2, center3, radius3, eps=8.881784197001252e-16)
Trilaterate this and two other spheres, each given as a (3-D) center and a radius.

Inherited from vector3dBase.Vector3dBase: __abs__, __add__, __bool__, __ceil__, __cmp__, __div__, __divmod__, __eq__, __float__, __floor__, __floordiv__, __format__, __ge__, __gt__, __hash__, __iadd__, __idiv__, __ifloordiv__, __imatmul__, __imod__, __imul__, __init__, __int__, __ipow__, __isub__, __itruediv__, __le__, __long__, __lt__, __matmul__, __mod__, __mul__, __ne__, __neg__, __nonzero__, __pos__, __pow__, __radd__, __rdiv__, __rdivmod__, __rfloordiv__, __rmatmul__, __rmod__, __rmul__, __round__, __rpow__, __rsub__, __rtruediv__, __sub__, __truediv__, __trunc__, angleTo, apply, bools, cmp, cross, dividedBy, dot, equals, equirectangular, fabs, floats, intermediateTo, ints, isconjugateTo, isequalTo, minus, minus_, negate, others, plus, plus_, rotate, rotateAround, sum, times, times_, to3xyz, toStr, unit

Inherited from named._NamedBase: __repr__, __str__, toRepr

Inherited from named._Named: attrs, classof, copy, dup, methodname, rename, renamed, toStr2

Inherited from object: __delattr__, __getattribute__, __new__, __reduce__, __reduce_ex__, __setattr__, __sizeof__, __subclasshook__

Properties

Inherited from vector3dBase.Vector3dBase: crosserrors, euclid, homogeneous, length, length2, x, x2y2z2, xyz, xyz3, y, z

Inherited from named._Named: classname, classnaming, iteration, name, named, named2, named3, named4, sizeof

Inherited from object: __class__

Method Details

bearing (self, useZ=True)

 

Get this vector's "bearing", the angle off the +Z axis, clockwise.

Arguments:
  • useZ - If True, use the Z component, otherwise ignore the Z component and consider the +Y as the +Z axis.
Returns:
Bearing (compass degrees).

circin6 (self, point2, point3, eps=8.881784197001252e-16)

 

Return the radius and center of the inscribed aka In- circle of a (3-D) triangle formed by this and two other points.

Arguments:
Returns:
Circin6Tuple(radius, center, deltas, cA, cB, cC). The center and contact points cA, cB and cC, each an instance of this (sub-)class, are co-planar with this and the two given points.
Raises:
  • ImportError - Package numpy not found, not installed or older than version 1.10.
  • IntersectionError - Near-coincident or -colinear points or a trilateration or numpy issue.
  • TypeError - Invalid point2 or point3.

See Also: Function pygeodesy.circin6, Incircle and Contact Triangle.

circum3 (self, point2, point3, circum=True, eps=8.881784197001252e-16)

 

Return the radius and center of the smallest circle through or containing this and two other (3-D) points.

Arguments:
  • point2 - Second point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • point3 - Third point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • circum - If True, return the circumradius and circumcenter, always, ignoring the Meeus' Type I case (bool).
  • eps - Tolerance passed to function pygeodesy.trilaterate3d2.
Returns:
A Circum3Tuple(radius, center, deltas). The center, an instance of this (sub-)class, is co-planar with this and the two given points.
Raises:
  • ImportError - Package numpy not found, not installed or older than version 1.10.
  • IntersectionError - Near-concentric, -coincident or -colinear points or a trilateration or numpy issue.
  • TypeError - Invalid point2 or point3.

See Also: Function pygeodesy.circum3 and methods circum4_ and meeus2.

circum4_ (self, *points)

 

Best-fit a sphere through this and two or more other (3-D) points.

Arguments:
  • points - Other points (each a Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
Returns:
Circum4Tuple(radius, center, rank, residuals) with center an instance if this (sub-)class.
Raises:
  • ImportError - Package numpy not found, not installed or older than version 1.10.
  • NumPyError - Some numpy issue.
  • PointsError - Too few points.
  • TypeError - One of the points invalid.

See Also: Function pygeodesy.circum4_ and methods circum3 and meeus2.

iscolinearWith (self, point1, point2, eps=2.220446049250313e-16)

 

Check whether this and two other (3-D) points are colinear.

Arguments:
  • point1 - One point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • point2 - An other point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • eps - Tolerance (scalar), same units as x, y, and z.
Returns:
True if this point is colinear with point1 and point2, False otherwise.
Raises:
  • TypeError - Invalid point1 or point2.

See Also: Method nearestOn.

meeus2 (self, point2, point3, circum=False)

 

Return the radius and Meeus' Type of the smallest circle through or containing this and two other (3-D) points.

Arguments:
  • point2 - Second point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • point3 - Third point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • circum - If True, return the circumradius and circumcenter always, overriding Meeus' Type II case (bool).
Returns:
Meeus2Tuple(radius, Type), with Type the circumcenter iff circum=True.
Raises:
  • IntersectionError - Coincident or colinear points, iff circum=True.
  • TypeError - Invalid point2 or point3.

See Also: Function pygeodesy.meeus2 and methods circum3 and circum4_.

nearestOn (self, point1, point2, within=True)

 

Locate the point between two points closest to this point.

Arguments:
  • point1 - Start point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • point2 - End point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • within - If True, return the closest point between the given points, otherwise the closest point on the extended line through both points (bool).
Returns:
Closest point, either point1 or point2 or an instance of this (sub-)class.
Raises:
  • TypeError - Invalid point1 or point2.

See Also: Method sphericalTrigonometry.LatLon.nearestOn3 and 3-D Point-Line Distance.

nearestOn6 (self, points, closed=False, useZ=True)

 

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.

Arguments:
  • points - The path or polygon points (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple[]).
  • closed - Optionally, close the path or polygon (bool).
  • useZ - If True, use the Z components, otherwise force z=INT0 (bool).
Returns:
A NearestOn6Tuple(closest, distance, fi, j, start, end) with the closest, the start and the end point each an instance of this point's (sub-)class.
Raises:
  • PointsError - Insufficient number of points
  • TypeError - Non-cartesian points.

Note: Distances measured with method Vector3d.equirectangular.

See Also: Function nearestOn6.

parse (self, str3d, sep=',', **name)

 

Parse an "x, y, z" string to a Vector3d instance.

Arguments:
  • str3d - X, y and z string (str), see function parse3d.
  • sep - Optional separator (str).
  • name - Optional instance name=NN (str), overriding this name.
Returns:
The instance (Vector3d).
Raises:

radii11 (self, point2, point3)

 

Return the radii of the Circum-, In-, Soddy and Tangent circles of a (3-D) triangle.

Arguments:
  • point2 - Second point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point3 - Third point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
Returns:
Radii11Tuple(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s).
Raises:
  • TriangleError - Near-coincident or -colinear points.
  • TypeError - Invalid point2 or point3.

See Also: Function pygeodesy.radii11, Incircle, Soddy Circles and Tangent Circles.

soddy4 (self, point2, point3, eps=8.881784197001252e-16)

 

Return the radius and center of the inner Soddy circle of a (3-D) triangle.

Arguments:
Returns:
Soddy4Tuple(radius, center, deltas, outer). The center, an instance of point1's (sub-)class, is co-planar with the three given points.
Raises:
  • ImportError - Package numpy not found, not installed or older than version 1.10.
  • IntersectionError - Near-coincident or -colinear points or a trilateration or numpy issue.
  • TypeError - Invalid point2 or point3.

See Also: Function pygeodesy.soddy4.

trilaterate2d2 (self, radius, center2, radius2, center3, radius3, eps=8.881784197001252e-16, z=0)

 

Trilaterate this and two other circles, each given as a (2-D) center and a radius.

Arguments:
  • radius - Radius of this circle (same units as this x and y.
  • center2 - Center of the 2nd circle (Cartesian, Vector3d, Vector2Tuple, Vector3Tuple or Vector4Tuple).
  • radius2 - Radius of this circle (same units as this x and y.
  • center3 - Center of the 3rd circle (Cartesian, Vector3d, Vector2Tuple, Vector3Tuple or Vector4Tuple).
  • radius3 - Radius of the 3rd circle (same units as this x and y.
  • eps - Tolerance to check the trilaterated point delta on all 3 circles (scalar) or None for no checking.
  • z - Optional Z component of the trilaterated point (scalar).
Returns:
Trilaterated point, an instance of this (sub-)class with z=z.
Raises:
  • IntersectionError - No intersection, near-concentric or -colinear centers, trilateration failed some other way or the trilaterated point is off one circle by more than eps.
  • TypeError - Invalid center2 or center3.
  • UnitError - Invalid radius1, radius2 or radius3.

See Also: Function pygeodesy.trilaterate2d2.

trilaterate3d2 (self, radius, center2, radius2, center3, radius3, eps=8.881784197001252e-16)

 

Trilaterate this and two other spheres, each given as a (3-D) center and a radius.

Arguments:
  • radius - Radius of this sphere (same units as this x, y and z).
  • center2 - Center of the 2nd sphere (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • radius2 - Radius of this sphere (same units as this x, y and z).
  • center3 - Center of the 3rd sphere (Cartesian, , Vector3d, Vector3Tuple or Vector4Tuple).
  • radius3 - Radius of the 3rd sphere (same units as this x, y and z).
  • eps - Pertubation tolerance (scalar), same units as x, y and z or None for no pertubations.
Returns:
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.
Raises:
  • ImportError - Package numpy not found, not installed or older than version 1.10.
  • IntersectionError - Near-concentric, -colinear, too distant or non-intersecting spheres or numpy issue.
  • NumPyError - Some numpy issue.
  • TypeError - Invalid center2 or center3.
  • UnitError - Invalid radius, radius2 or radius3.

Note: Package numpy is required, version 1.10 or later.

See Also: Norrdine, A. An Algebraic Solution to the Multilateration Problem and implementation.


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