Trigonometry

angle_between_points(p1, p2, dip_convention=DipDownward.NEGATIVE)

Compute angle between two points.

Parameters:

Name	Type	Description	Default
p1	ndarray	Point in 2 or 3 dimension.	required
p2	ndarray	Point in 2 or 3 dimension.	required
dip_convention	DipDownward	Convention of downward dip angle sign.	NEGATIVE

Returns:

Type	Description
Tuple[float, float]	Angles in a given Metric convention.

angle_between_vectors(v1, v2)

Compute the angle between two vectors using the dot product.

Parameters:

Name	Type	Description	Default
v1	ndarray	first cartesian vector.	required
v2	ndarray	second cartesian vector.	required

Returns:

Type	Description
float	Angle between two vectors in radians.

normalize(a, center)

(Adapted from Apach Commons normalizeAngle, MathUtils sources) Normalize an angle in a 2pi; wide interval around a center value.

This method has three main uses:

• normalize an angle between 0 and 2pi: a = normalize(a, np.pi)
• normalize an angle between -pi and +pi: a = normalize(a, 0.0)
• compute the angle between two defining angular positions: angle = normalize(end, start) - start

Parameters:

Name	Type	Description	Default
a	float	angle to be normalized (in radians).	required
center	float	center value in radians.	required

Returns:

Type	Description
float	normalized angle in radians.

Example

import geolime as geo
import numpy as np
geo.normalize(np.pi / 2, 2 * np.pi)

Output

7.853981633974483

Info

Due to numerical accuracy and since pi cannot be represented exactly, the result interval is closed, it cannot be half-closed as would be more satisfactory in a purely mathematical view.

rot_x(gamma, deg=True, clockwise=False)

Rotation against the X axis.

Parameters:

Name	Type	Description	Default
gamma	float	Rotation angle.	required
deg	bool	True if theta is in degrees.	True
clockwise	bool	if True clockwise, if False counter-clockwise rotation.	False

Returns:

Type	Description
ndarray	Rotation matrix.

rot_y(beta, deg=True, clockwise=False)

Rotation against the Y axis.

Parameters:

Name	Type	Description	Default
beta	float	Rotation angle.	required
deg	bool	True if theta is in degrees.	True
clockwise	bool	if True clockwise, if False counter-clockwise rotation.	False

Returns:

Type	Description
ndarray	Rotation matrix.

rot_z(alpha, deg=True, clockwise=False)

Rotation against the Z axis.

Parameters:

Name	Type	Description	Default
alpha	float	Rotation angle.	required
deg	bool	True if theta is in degrees.	True
clockwise	bool	if True clockwise, if False counter-clockwise rotation.	False

Returns:

Type	Description
ndarray	Rotation matrix.

rot_zxz(angles, deg=True, clockwise=[False, False, False])

Example of a convention.

Parameters:

Name	Type	Description	Default
angles	Vector	Description of parameter angles.	required
deg	bool	Description of parameter deg.	True
clockwise	List[bool]	Clockwise if set to True, counter-clockwise otherwise.	[False, False, False]

Returns:

Type	Description
ndarray	A rotation matrix.

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Last update: 2022-01-06