Trigonometry

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

Compute angle between two points.

Parameters:

Name	Type	Description	Default
p1	np.ndarray	Point in 2 or 3 dimension.	required
p2	np.ndarray	Point in 2 or 3 dimension.	required
dip_convention	DipDownward	Convention of downward dip angle sign.	DipDownward.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	np.ndarray	first cartesian vector.	required
v2	np.ndarray	second cartesian vector.	required

Returns:

Type	Description
float	Angle between two vectors in radians.

arithmetic(angle)

Convert an angle from geographic to arithmetic.

Parameters:

Name	Type	Description	Default
angle	float	angle to be converted in radians.	required

Returns:

Type	Description
float	arithmetic angle in radians

Example

import geolime as geo
import numpy as np
geo.arithmetic(np.pi / 2)

Output

0.0

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.

plane_to_dir(azimuth, dip, pitch, deg=True, dip_convention=DipDownward.NEGATIVE)

Convert plane angles to line angles. For experimental variography, we check the pairs of distances along a direction and not a plane. When considering direction, we only have to compute the angle between a unit direction vector with the pairs direction (refer to the angle_between_vectors function)

Parameters:

Name	Type	Description	Default
azimuth	float	azimuth of plane.	required
dip	float	dip of plane.	required
pitch	float	pitch of plane.	required
deg	bool	angle type.	True
dip_convention	DipDownward	Convention of downward dip angle sign.	DipDownward.NEGATIVE

Returns:

Type	Description
Tuple[float, float]	Returns trend and plunge angles in radians.

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

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.	True

Returns:

Type	Description
np.ndarray	Rotation matrix.

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

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.	True

Returns:

Type	Description
np.ndarray	Rotation matrix.

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

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.	True

Returns:

Type	Description
np.ndarray	Rotation matrix.

rot_zyx(angles, deg=True, clockwise=True)

Example of a convention.

Parameters:

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

Returns:

Type	Description
np.ndarray	A rotation matrix.

rotational_angles(angles, dip_convention=DipDownward.NEGATIVE)

Compute the angles in radians necessary for matrix rotation operation from geographic azimuth, dip and pitch angles defined in degrees

Parameters:

Name	Type	Description	Default
angles	Angles	[azimuth, dip, pitch] or azimuth, all in degrees.	required
dip_convention	DipDownward	Convention of downward dip angle sign.	DipDownward.NEGATIVE

Returns:

Type	Description
Angles	Returns angles in radians ready to be piped into rotation transforms.