Package pygeodesy :: Module vector2d
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Module vector2d

2- or 3-D vectorial functions circin6, circum3, circum4_, iscolinearWith, meeus2, nearestOn, radii11 and soddy4.


Version: 22.04.21

Classes
  Circin6Tuple
6-Tuple (radius, center, deltas, cA, cB, cC) with the radius, the trilaterated center and contact points of the inscribed aka In- circle of a triangle.
  Circum3Tuple
3-Tuple (radius, center, deltas) with the circumradius and trilaterated circumcenter of the circumcircle through 3 points (aka {Meeus}' Type II circle) or the radius and center of the smallest Meeus' Type I circle.
  Circum4Tuple
4-Tuple (radius, center, rank, residuals) with radius and center of a sphere least-squares fitted through given points and the rank and residuals -if any- from numpy.linalg.lstsq.
  Meeus2Tuple
2-Tuple (radius, Type) with radius and Meeus' Type of the smallest circle containing 3 points.
  Radii11Tuple
11-Tuple (rA, rB, rC, cR, rIn, riS, roS, a, b, c, s) with the Tangent circle radii rA, rB and rC, the circumradius cR, the Incircle radius rIn aka inradius, the inner and outer Soddy circle radii riS and roS and the sides a, b and c and semi-perimeter s of a triangle, all in meter conventionally.
  Soddy4Tuple
4-Tuple (radius, center, deltas, outer) with radius and trilaterated center of the inner Soddy circle and the radius of the outer Soddy circle.
Functions
 
circin6(point1, point2, point3, eps=8.881784197e-16, useZ=True)
Return the radius and center of the inscribed aka In- circle of a (2- or 3-D) triangle.
 
circum3(point1, point2, point3, circum=True, eps=8.881784197e-16, useZ=True)
Return the radius and center of the smallest circle through or containing three (2- or 3-D) points.
 
circum4_(*points, **Vector_and_kwds)
Best-fit a sphere through three or more (3-D) points.
 
meeus2(point1, point2, point3, circum=False, useZ=True)
Return the radius and Meeus' Type of the smallest circle through or containing three (2- or 3-D) points.
 
radii11(point1, point2, point3, useZ=True)
Return the radii of the In-, Soddy and Tangent circles of a (2- or 3-D) triangle.
 
soddy4(point1, point2, point3, eps=8.881784197e-16, useZ=True)
Return the radius and center of the inner Soddy circle of a (2- or 3-D) triangle.
Variables
  __all__ = _ALL_LAZY.vector2d
Function Details

circin6 (point1, point2, point3, eps=8.881784197e-16, useZ=True)

 

Return the radius and center of the inscribed aka In- circle of a (2- or 3-D) triangle.

Arguments:
  • point1 - First point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point2 - Second point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point3 - Third point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • eps - Tolerance for function pygeodesy.trilaterate3d2 if useZ is True otherwise pygeodesy.trilaterate2d2.
  • useZ - If True, use the Z components, otherwise force z=INT0 (bool).
Returns:
Circin6Tuple(radius, center, deltas, cA, cB, cC). The center and contact points cA, cB and cC, each an instance of point1's (sub-)class, are co-planar with the three given points.
Raises:
  • ImportError - Package numpy not found, not installed or older than version 1.10 and useZ is True.
  • IntersectionError - Near-coincident or -colinear points or a trilateration or numpy issue.
  • TypeError - Invalid point1, point2 or point3.

See Also: Functions radii11 and circum3, Incircle and Contact Triangle.

circum3 (point1, point2, point3, circum=True, eps=8.881784197e-16, useZ=True)

 

Return the radius and center of the smallest circle through or containing three (2- or 3-D) points.

Arguments:
  • point1 - First point (Cartesian, Vector3d, Vector3Tuple or Vector4Tuple).
  • 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 for function pygeodesy.trilaterate3d2 if useZ is True otherwise pygeodesy.trilaterate2d2.
  • useZ - If True, use the Z components, otherwise force z=INT0 (bool).
Returns:
A Circum3Tuple(radius, center, deltas). 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 and useZ is True.
  • IntersectionError - Near-coincident or -colinear points or a trilateration or numpy issue.
  • TypeError - Invalid point1, point2 or point3.

circum4_ (*points, **Vector_and_kwds)

 

Best-fit a sphere through three or more (3-D) points.

Arguments:
  • points - The points (each a Cartesian, Vector3d, Vector3Tuple, or Vector4Tuple).
  • Vector_and_kwds - Optional class Vector=None to return the center and optional, additional Vector keyword arguments, otherwise the first points' (sub-)class.
Returns:
Circum4Tuple(radius, center, rank, residuals) with center an instance of points[0]' (sub-)class or Vector if specified.
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 is invalid.

meeus2 (point1, point2, point3, circum=False, useZ=True)

 

Return the radius and Meeus' Type of the smallest circle through or containing three (2- or 3-D) points.

Arguments:
  • point1 - First point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point2 - Second point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point3 - Third point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • circum - If True return the non-zero circumradius always, ignoring the Meeus' Type I case (bool).
  • useZ - If True, use the Z components, otherwise force z=INT0 (bool).
Returns:
Meeus2Tuple(radius, Type).
Raises:
  • IntersectionError - Near-coincident or -colinear points, iff circum=True.
  • TypeError - Invalid point1, point2 or point3.

radii11 (point1, point2, point3, useZ=True)

 

Return the radii of the In-, Soddy and Tangent circles of a (2- or 3-D) triangle.

Arguments:
  • point1 - First point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point2 - Second point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point3 - Third point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • useZ - If True, use the Z components, otherwise force z=INT0 (bool).
Returns:
Radii11Tuple(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s).
Raises:
  • TriangleError - Near-coincident or -colinear points.
  • TypeError - Invalid point1, point2 or point3.

soddy4 (point1, point2, point3, eps=8.881784197e-16, useZ=True)

 

Return the radius and center of the inner Soddy circle of a (2- or 3-D) triangle.

Arguments:
  • point1 - First point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point2 - Second point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • point3 - Third point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
  • eps - Tolerance for function pygeodesy.trilaterate3d2 if useZ is True otherwise pygeodesy.trilaterate2d2.
  • useZ - If True, use the Z components, otherwise force z=INT0 (bool).
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 and useZ is True.
  • IntersectionError - Near-coincident or -colinear points or a trilateration or numpy issue.
  • TypeError - Invalid point1, point2 or point3.

See Also: Functions radii11 and circum3.