resqpy.olio.vector_utilitiesΒΆ

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.

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_polygons_parallel

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_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 back points about 3 axes by angles in degrees.

rotate_array

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 3 axes 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 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_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.

zero_vector

Returns a zero vector [0.0, 0.0, 0.0].