resqpy.olio.vector_utilities

Utilities for working with 3D vectors in cartesian space.

note: some of these functions are redundant as they are provided by built-in numpy operations.

a vector is a one dimensional numpy array with 3 elements: x, y, z. some functions accept a tuple or list of 3 elements as an alternative to a numpy array.

Functions

add	Returns vector sum a+b.
amplify	Returns vector with direction of v, amplified by scaling.
area_of_triangle	Returns the area of the triangle defined by three vertices.
area_of_triangles	Returns numpy array of areas of triangles, optionally when projected onto xy plane.
azimuth	Returns the compass bearing in degrees of the direction of v (x = East, y = North), ignoring z.
azimuths	Returns the compass bearings in degrees of the direction of each vector in va (x = East, y = North), ignoring z.
clockwise	Returns a +ve value if 2D points a,b,c are in clockwise order, 0.0 if in line, -ve for ccw.
clockwise_sorted_indices	Returns a clockwise sorted numpy list of indices b into the points p.
clockwise_triangles	Returns a numpy array of +ve values where triangle points are in clockwise order, 0.0 if in line, -ve for ccw.
cross_product	Returns the cross product (vector product) of the two vectors.
degrees_difference	Returns the angle between two vectors, in degrees.
degrees_from_radians	Converts angle from radians to degrees.
determinant	Returns the determinant of the 3 x 3 matrix comprised of the 3 vectors.
determinant_3x3	Returns the determinant of the 3 x 3 matrix.
dot_product	Returns the dot product (scalar product) of the two vectors.
dot_products	Returns the dot products of pairs of vectors; last axis covers element of a vector.
elemental_multiply	Returns vector with products of corresponding elements of a and b.
in_circumcircle	Returns True if point d lies within the circumcircle pf ccw points a, b, c, projected onto xy plane.
in_triangle	Returns True if point d lies wholly within the triangle pf ccw points a, b, c, projected onto xy plane.
in_triangle_edged	Returns True if d lies within or on the boudnary of triangle of ccw points a,b,c projected onto xy plane.
inclination	Returns the inclination in degrees of v (angle relative to +ve z axis).
inclinations	Returns the inclination in degrees of each vector in a (angle relative to +ve z axis).
is_close	Returns True if the two points are extremely close to one another (ie.
is_obtuse_2d	Returns True if the angle at point p subtended by points p1 and p2, in xy plane, is greater than 90 degrees; else False.
isclose	Returns True if the two points are extremely close to one another (ie.
manhattan_distance	Returns the Manhattan distance between two points.
manhatten_distance	Returns the Manhattan distance between two points.
mesh_points_in_triangle	Calculates which implicit mesh points are within a triangle in 2D for normalised triangle.
meshgrid	Returns coordinate matrices from coordinate vectors x and y.
naive_2d_length	Returns the length of the vector projected onto xy plane, assuming consistent units.
naive_2d_lengths	Returns the lengths of the vectors projected onto xy plane, assuming consistent units.
naive_length	Returns the length of the vector assuming consistent units.
naive_lengths	Returns the lengths of the vectors assuming consistent units.
nan_inclinations	Returns the inclination in degrees of each vector in a (angle relative to +ve z axis), allowing NaNs.
nan_unit_vectors	Returns vectors with same direction as those in v but with unit length, allowing NaNs.
nearest_point_projected	Returns the index into points array closest to point p; projection is 'xy', 'xz' or 'yz'.
no_rotation_matrix	Returns a rotation matrix which will not move points (identity matrix).
perspective_vector	Returns a version of vector with a perspective applied.
point_distance_sqr_to_points_projected	Returns an array of projected distances squared between p and points; projection is 'xy', 'xz' or 'yz'.
point_distance_to_line_2d	Ignoring any z values, returns the xy distance of point p from line passing through l1 and l2.
point_distance_to_line_segment_2d	Ignoring any z values, returns the xy distance of point p from line segment between l1 and l2.
point_in_polygon	Calculates if a point in within a polygon in 2D.
point_in_triangle	Calculates if a point in within a triangle in 2D.
points_direction_vector	Returns an average direction vector based on first and last non-NaN points or slices in given axis.
points_in_polygon	Calculates which points are within a polygon in 2D.
points_in_polygons	Calculates which points are within which polygons in 2D.
points_in_triangle	Calculates which points are within a triangle in 2D.
points_in_triangles	Returns 2D numpy bool array indicating which of points da are within which triangles.
points_in_triangles_aligned	Calculates which points are within which triangles in 2D for a regular mesh of aligned points.
points_in_triangles_aligned_optimised	Calculates which points are within which triangles in 2D for a regular mesh of aligned points.
points_in_triangles_aligned_optimised_old	Calculates which points are within which triangles in 2D for a regular mesh of aligned points.
points_in_triangles_aligned_optimised_serial	Calculates which points are within which triangles in 2D for a regular mesh of aligned points.
points_in_triangles_aligned_unified	Calculates which points are within which triangles in 2D for a regular mesh of aligned points.
points_in_triangles_njit	Calculates which points are within which triangles in 2D.
project_points_onto_plane	Modifies array of xyz points in situ to project onto a plane defined by a point and normal vector.
radians_difference	Returns the angle between two vectors, in radians.
radians_from_degrees	Converts angle from degrees to radians.
reverse_rotation_3d_matrix	Returns a rotation matrix which will rotate points about the y, z, then x axis by angles in degrees.
rotate_array	Returns a copy of array a with each vector rotated by the rotation matrix.
rotate_array_njit	Returns a copy of array a with each vector rotated by the rotation matrix.
rotate_vector	Returns the rotated vector.
rotate_xyz_array_around_z_axis	Returns a copy of array a suitable for presenting a cross-section using the resulting x,z values.
rotation_3d_matrix	Returns a rotation matrix which will rotate points about the x, z, then y axis by angles in degrees.
rotation_3d_matrix_njit	Returns a rotation matrix which will rotate points about the x, z, then y axis by angles in degrees.
rotation_matrix_3d_axial	Returns a rotation matrix which will rotate points about axis (0: x, 1: y, or 2: z) by angle in degrees.
rotation_matrix_3d_vector	Returns a rotation matrix which will rotate vector v to the vertical (z) axis.
rotation_matrix_3d_vector_njit	Returns a rotation matrix which will rotate points by inclination and azimuth of vector.
subtract	Returns vector difference a-b.
tilt_3d_matrix	Returns a 3D rotation matrix for applying a dip in a certain azimuth.
tilt_points	Modifies array of xyz points in situ to apply dip in direction of azimuth, about pivot point.
triangle_box	Finds the minimum and maximum x and y values of a single traingle.
triangle_normal_vector	For a triangle in 3D space, defined by 3 vertex points, returns a unit vector normal to the plane of the triangle.
triangle_normal_vector_numba	For a triangle in 3D space, defined by 3 vertex points, returns a unit vector normal to the plane of the triangle.
unit_corrected_length	Returns the length of the vector v after applying the unit_conversion factors.
unit_vector	Returns vector with same direction as v but with unit length.
unit_vector_from_azimuth	Returns horizontal unit vector in compass bearing given by azimuth (x = East, y = North).
unit_vector_from_azimuth_and_inclination	Returns unit vector with compass bearing of azimuth and inclination off +z axis.
unit_vector_njit	Returns vector with same direction as v but with unit length.
unit_vectors	Returns vectors with same direction as those in v but with unit length.
v_3d	Returns a 3D vector for a 2D or 3D vector.
vertical_intercept	Finds the y value of a straight line between two points at a given x.
vertical_intercept_nan	Finds the y value of a straight line between two points at a given x.
vertical_intercept_nan_yz	Finds the y & z values of a straight line between two points at a given x.
xy_sorted	Returns copy of points p sorted according to x or y (whichever has greater range).
xy_sorted_njit	Returns copy of points p sorted according to x or y (whichever has greater range).
zero_vector	Returns a zero vector [0.0, 0.0, 0.0].