Module resections

3-Point resection using Cassini's method.

Arguments:

• pointA - First point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• pointB - Second point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• pointC - Center point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• alpha - Angle subtended by triangle side pointA to pointC (degrees, non-negative).
• beta - Angle subtended by triangle side pointB to pointC (degrees, non-negative).
• useZ - If True, use and interpolate the Z component, otherwise force z=0 (bool).

Returns:

Survey point, an instance of pointA's (sub-)class.

Raises:

• ResectionError - Near-coincident, -colinear or -concyclic points or negative or invalid alpha or beta.
• TypeError - Invalid pointA, pointB or pointM.

3-Point resection using Collins' method.

Arguments:

• pointA - First point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• pointB - Second point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• pointC - Center point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• alpha - Angle subtended by triangle side pointA to pointC (degrees, non-negative).
• beta - Angle subtended by triangle side pointB to pointC (degrees, non-negative).
• useZ - If True, use and interpolate the Z component, otherwise force z=0 (bool).

Returns:

Collins5Tuple(pointP, pointH, a, b, c) with survey pointP, auxiliary pointH, each an instance of pointA's (sub-)class and triangle sides a, b and c.

Raises:

• ResectionError - Near-coincident, -colinear or -concyclic points or negative or invalid alpha or beta.
• TypeError - Invalid pointA, pointB or pointM.

3-Point resection using Tienstra's formula.

Arguments:

• pointA - First point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• pointB - Second point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• pointC - Third point (Cartesian, Vector3d, Vector3Tuple, Vector4Tuple or Vector2Tuple if useZ=False).
• alpha - Angle subtended by triangle side pointB to pointC (degrees, non-negative).
• beta - Angle subtended by triangle side pointA to pointC (degrees, non-negative) or None if gamma is not None.
• gamma - Angle subtended by triangle side pointA to pointB (degrees, non-negative) or None if beta is not None.
• useZ - If True, use and interpolate the Z component, otherwise force z=0 (bool).

Returns:

Tienstra7Tuple(pointP, A, B, C, a, b, c) with survey pointP, an instance of pointA's (sub-)class and triangle angles A, B and C in degrees and triangle sides a, b and c.

Raises:

• ResectionError - Near-coincident, -colinear or -concyclic points or sum of alpha, beta and gamma not 360 or negative alpha, beta or gamma.
• TypeError - Invalid pointA, pointB or pointC.