# openquake.hazardlib.geo package#

## geodetic#

Module `openquake.hazardlib.geo.geodetic` contains functions for geodetic transformations, optimized for massive calculations.

openquake.hazardlib.geo.geodetic.EARTH_ELEVATION = -8.848#

Maximum elevation on Earth in km.

openquake.hazardlib.geo.geodetic.azimuth(lons1, lats1, lons2, lats2)[source]#

Calculate the azimuth between two points or two collections of points.

Parameters are the same as for `geodetic_distance()`.

Implements an “alternative formula” from http://williams.best.vwh.net/avform.htm#Crs

Returns:

Azimuth as an angle between direction to north from first point and direction to the second point measured clockwise in decimal degrees.

openquake.hazardlib.geo.geodetic.azimuths(coos)[source]#

Compute the azimuths from an array of lines with shape (L, 2, 3)

openquake.hazardlib.geo.geodetic.distance(lons1, lats1, depths1, lons2, lats2, depths2)[source]#

Calculate a distance between two points (or collections of points) considering points’ depth.

Calls `geodetic_distance()`, finds the “vertical” distance between points by subtracting one depth from another and combine both using Pythagoras theorem.

Returns:

Distance in km, a square root of sum of squares of `geodetic` distance and vertical distance, which is just a difference between depths.

openquake.hazardlib.geo.geodetic.distance_matrix(lons, lats, diameter=12742.0)[source]#
Parameters:
• lons – array of m longitudes

• lats – array of m latitudes

Returns:

matrix of (m, m) distances

openquake.hazardlib.geo.geodetic.distance_to_arc(alon, alat, aazimuth, plons, plats)[source]#

Calculate a closest distance between a great circle arc and a point (or a collection of points).

Parameters:
• alat (float alon,) – Arc reference point longitude and latitude, in decimal degrees.

• azimuth – Arc azimuth (an angle between direction to a north and arc in clockwise direction), measured in a reference point, in decimal degrees.

• plats (float plons,) – Longitudes and latitudes of points to measure distance. Either scalar values or numpy arrays of decimal degrees.

Returns:

Distance in km, a scalar value or numpy array depending on `plons` and `plats`. A distance is negative if the target point lies on the right hand side of the arc.

Solves a spherical triangle formed by reference point, target point and a projection of target point to a reference great circle arc.

openquake.hazardlib.geo.geodetic.distance_to_semi_arc(alon, alat, aazimuth, plons, plats)[source]#

In this method we use a reference system centerd on (alon, alat) and with the y-axis corresponding to aazimuth direction to calculate the minimum distance from a semiarc with generates in (alon, alat).

Parameters are the same as for `distance_to_arc()`.

openquake.hazardlib.geo.geodetic.distances(lon, lat, lons, lats)[source]#

Calculate the geodetic distances between one point and a collection of points by using numba. Assume the parameters are in radians.

openquake.hazardlib.geo.geodetic.distances_to_arc(lon, lat, azi, lons, lats)[source]#

Calculate the distances between one arc and a collection of points by using numba. Assume the parameters are in degrees.

openquake.hazardlib.geo.geodetic.fast_azimuth(lon, lat, lons, lats)[source]#

Calculate the azimuths of a collection of points with respect to a reference point.

openquake.hazardlib.geo.geodetic.fast_distance(lon, lat, lons, lats)[source]#
openquake.hazardlib.geo.geodetic.fast_point_at(lon, lat, azimuth, distance)[source]#

Perform a forward geodetic transformation: find points lying at a given distances from a given point on a great circle arc defined by azimuth.

Parameters:
• lat (lon,) – Coordinates of the reference point, in radians

• azimuth – An azimuth of a great circle arc of interest measured in a reference point in decimal degrees.

• distance – Distance to target point in km.

Returns:

Array of shape (2, N) with longitudes and latitudes

Implements the same approach as `npoints_towards()`.

openquake.hazardlib.geo.geodetic.fast_spherical_to_cartesian(lons, lats, deps)[source]#

Return the position vectors (in Cartesian coordinates) of list of spherical coordinates.

For equations see: http://mathworld.wolfram.com/SphericalCoordinates.html.

Parameters are components of spherical coordinates in a form of scalars, lists or numpy arrays. `depths` can be `None` in which case it’s considered zero for all points.

Returns:

`np.array` of 3d vectors representing points’ coordinates in Cartesian space in km. The array has shape lons.shape + (3,). In particular, if `lons` and `lats` are scalars the result is a 3D vector and if they are vectors the result is a matrix of shape (N, 3).

See also `cartesian_to_spherical()`.

openquake.hazardlib.geo.geodetic.geodetic_distance(lons1, lats1, lons2, lats2, diameter=12742.0)[source]#

Calculate the geodetic distance between two points or two collections of points.

Parameters are coordinates in decimal degrees. They could be scalar float numbers or numpy arrays, in which case they should “broadcast together”.

Returns:

Distance in km, floating point scalar or numpy array of such.

openquake.hazardlib.geo.geodetic.intervals_between(lon1, lat1, depth1, lon2, lat2, depth2, length)[source]#

Find a list of points between two given ones that lie on the same great circle arc and are equally spaced by `length` km.

Parameters:
• depth1 (float lon1, lat1,) – Coordinates of a point to start placing intervals from. The first point in the resulting list has these coordinates.

• depth2 (float lon2, lat2,) – Coordinates of the other end of the great circle arc segment to put intervals on. The last resulting point might be closer to the first reference point than the second one or further, since the number of segments is taken as rounded division of length between two reference points and `length`.

• length – Required distance between two subsequent resulting points, in km.

Returns:

Tuple of three 1d numpy arrays: longitudes, latitudes and depths of resulting points respectively.

Rounds the distance between two reference points with respect to `length` and calls `npoints_towards()`.

openquake.hazardlib.geo.geodetic.min_distance_to_segment(seglons, seglats, lons, lats)[source]#

This function computes the shortest distance to a segment in a 2D reference system.

Parameters:
• seglons – A list or an array of floats specifying the longitude values of the two vertexes delimiting the segment.

• seglats – A list or an array of floats specifying the latitude values of the two vertexes delimiting the segment.

• lons – A list or a 1D array of floats specifying the longitude values of the points for which the calculation of the shortest distance is requested.

• lats – A list or a 1D array of floats specifying the latitude values of the points for which the calculation of the shortest distance is requested.

Returns:

An array of the same shape as lons which contains for each point defined by (lons, lats) the shortest distance to the segment. Distances are negative for those points that stay on the ‘left side’ of the segment direction and whose projection lies within the segment edges. For all other points, distance is positive.

openquake.hazardlib.geo.geodetic.min_geodetic_distance(a, b)[source]#

Compute the minimum distance between first mesh and each point of the second mesh when both are defined on the earth surface.

Parameters:
• a – a pair of (lons, lats) or an array of cartesian coordinates

• b – a pair of (lons, lats) or an array of cartesian coordinates

openquake.hazardlib.geo.geodetic.npoints_between(lon1, lat1, depth1, lon2, lat2, depth2, npoints)[source]#

Find a list of specified number of points between two given ones that are equally spaced along the great circle arc connecting given points.

Parameters:
• depth1 (float lon1, lat1,) – Coordinates of a point to start from. The first point in a resulting list has these coordinates.

• depth2 (float lon2, lat2,) – Coordinates of a point to finish at. The last point in a resulting list has these coordinates.

• npoints – Integer number of points to return. First and last points count, so if there have to be two intervals, `npoints` should be 3.

Returns:

Tuple of three 1d numpy arrays: longitudes, latitudes and depths of resulting points respectively.

Finds distance between two reference points and calls `npoints_towards()`.

openquake.hazardlib.geo.geodetic.npoints_towards(lon, lat, depth, azimuth, hdist, vdist, npoints)[source]#

Find a list of specified number of points starting from a given one along a great circle arc with a given azimuth measured in a given point.

Parameters:
• depth (float lon, lat,) – Coordinates of a point to start from. The first point in a resulting list has these coordinates.

• azimuth – A direction representing a great circle arc together with a reference point.

• hdist – Horizontal (geodetic) distance from reference point to the last point of the resulting list, in km.

• vdist – Vertical (depth) distance between reference and the last point, in km.

• npoints – Integer number of points to return. First and last points count, so if there have to be two intervals, `npoints` should be 3.

Returns:

Tuple of three 1d numpy arrays: longitudes, latitudes and depths of resulting points respectively.

Implements “completely general but more complicated algorithm” from http://williams.best.vwh.net/avform.htm#LL

openquake.hazardlib.geo.geodetic.point_at(lon, lat, azimuth, distance)[source]#

Perform a forward geodetic transformation: find a point lying at a given distance from a given one on a great circle arc defined by azimuth.

Parameters:
• lat (float lon,) – Coordinates of a reference point, in decimal degrees.

• azimuth – An azimuth of a great circle arc of interest measured in a reference point in decimal degrees.

• distance – Distance to target point in km.

Returns:

Tuple of two float numbers: longitude and latitude of a target point in decimal degrees respectively.

Implements the same approach as `npoints_towards()`.

openquake.hazardlib.geo.geodetic.spherical_to_cartesian(lons, lats, depths=None)[source]#

Return the position vectors (in Cartesian coordinates) of list of spherical coordinates.

For equations see: http://mathworld.wolfram.com/SphericalCoordinates.html.

Parameters are components of spherical coordinates in a form of scalars, lists or numpy arrays. `depths` can be `None` in which case it’s considered zero for all points.

Returns:

`np.array` of 3d vectors representing points’ coordinates in Cartesian space in km. The array has shape lons.shape + (3,). In particular, if `lons` and `lats` are scalars the result is a 3D vector and if they are vectors the result is a matrix of shape (N, 3).

See also `cartesian_to_spherical()`.

## line#

Module `openquake.hazardlib.geo.line` defines `Line`.

class openquake.hazardlib.geo.line.Line(points)[source]#

Bases: `object`

This class represents a geographical line, which is basically a sequence of geographical points.

A line is defined by at least two points.

Parameters:

points (list of `Point` instances) – The sequence of points defining this line.

average_azimuth()[source]#

Calculate and return weighted average azimuth of all line’s segments in decimal degrees. Uses formula from http://en.wikipedia.org/wiki/Mean_of_circular_quantities >>> from openquake.hazardlib.geo.point import Point as P >>> ‘%.1f’ % Line([P(0, 0), P(1e-5, 1e-5)]).average_azimuth() ‘45.0’ >>> ‘%.1f’ % Line([P(0, 0), P(0, 1e-5), P(1e-5, 1e-5)] … ).average_azimuth() ‘45.0’ >>> line = Line([P(0, 0), P(-2e-5, 0), P(-2e-5, 1.154e-5)]) >>> ‘%.1f’ % line.average_azimuth() ‘300.0’

flip()[source]#

Returns a new line with the points flipped. Here is an example, taking advantage of the string representation of Lines in terms of geohashes of 5 letters (~2 km of precision):

```>>> line = Line([Point(1, 2), Point(1, 3)])
>>> print(line)
s02eq_s089n
>>> print(line.flip())
s089n_s02eq
>>> line.get_azimuths()
[0.0]
>>> line.flip().get_azimuths()
[180.0]
>>> line = Line([Point(1, 0), Point(2, 0)])
>>> line.get_azimuths()
[90.0]
>>> line.flip().get_azimuths()
[270.0]
```
classmethod from_coo(coo)[source]#

Build a Line object for an array of coordinates, assuming they have e been cleaned already, i.e. there are no adjacent duplicate points

classmethod from_vectors(lons, lats, deps=None)[source]#

Creates a line from three numpy.ndarray instances containing longitude, latitude and depths values

get_azimuths()[source]#

Return the azimuths of all the segments composing the polyline

get_length() float[source]#

Calculate the length of the line as a sum of lengths of all its segments.

Returns:

Total length in km.

get_lengths() ndarray[source]#

Calculate a numpy.ndarray instance with the length of the segments composing the polyline.

Returns:

Segments length in km.

get_tuw(mesh)[source]#

Computes the U and T coordinates of the GC2 method for a mesh of points.

Parameters:

mesh – An instance of `openquake.hazardlib.geo.mesh.Mesh`

get_ui_ti(mesh, uhat, that)[source]#

Compute the t and u coordinates. ti and ui have shape (num_segments x num_sites).

horizontal()[source]#

Check if this line is horizontal (i.e. all depths of points are equal).

Returns bool:

True if this line is horizontal, false otherwise.

init(coo)[source]#
keep_corners(delta)[source]#

Removes the points where the change in direction is lower than a tolerance value and returns a new line.

Parameters:

delta – An angle in decimal degrees

on_surface()[source]#

Check if this line is defined on the surface (i.e. all points are on the surfance, depth=0.0).

Returns bool:

True if this line is on the surface, false otherwise.

property points#
resample(sect_len: float, orig_extremes=False)[source]#

Resample this line into sections. The first point in the resampled line corresponds to the first point in the original line. Starting from the first point in the original line, a line segment is defined as the line connecting the last point in the resampled line and the next point in the original line.

Parameters:
• sect_len (float) – The length of the section, in km.

• original_extremes (bool) – A boolean controlling the way in which the last point is added. When true the first and last point match the original extremes. When false the last point is at a sect_len distance from the previous one, before or after the last point.

Returns:

A new line resampled into sections based on the given length.

resample_to_num_points(num_points)[source]#

Resample the line to a specified number of points.

Parameters:

num_points – Integer number of points the resulting line should have.

Returns:

A new line with that many points as requested.

property sut_hat#

Return the unit vectors defining the local origin for each segment of the trace.

Parameters:
• sx – The vector with the x coordinates of the trace

• sy – The vector with the y coordinates of the trace

Returns:

Two arrays of size n x 3 (when n is the number of segments composing the trace

openquake.hazardlib.geo.line.find_t(pnt0, pnt1, ref_pnt, distance)[source]#

Find the point on the segment within pnt0 and pnt1 at distance from ref_pnt. See https://tinyurl.com/meyt4ft3

Parameters:
• pnt0 – A 1D `numpy.ndarray` instance of length 3

• pnt1 – A 1D `numpy.ndarray` instance of length 3

• ref_pnt – A 1D `numpy.ndarray` instance of length 3

• distance – A float with the distance in km from ref_pnt to the point on the segment.

Returns:

A 1D `numpy.ndarray` instance of length 3

openquake.hazardlib.geo.line.get_ti_weights(ui, ti, segments_len)[source]#
Returns:

(weights, idx_on_trace)

openquake.hazardlib.geo.line.get_tuw(lam0, phi0, coo, slen, uhat, that, lons, lats)[source]#
Returns:

array of float32 of shape (N, 3)

openquake.hazardlib.geo.line.get_ui_ti(lam0, phi0, coo, lons, lats, uhat, that)[source]#

Compute the t and u coordinates. ti and ui have shape (num_segments x num_sites).

openquake.hazardlib.geo.line.get_versor(arr)[source]#

Returns the versor (i.e. a unit vector) of a vector

openquake.hazardlib.geo.line.line_get_tu(ui, ti, sl, weights)[source]#

Compute the T and U quantitities.

Parameters:
• ui – A `numpy.ndarray` instance of cardinality (num segments x num sites)

• ti – A `numpy.ndarray` instance of cardinality (num segments x num sites)

• sl – A `numpy.ndarray` instance with the segments’ length

• weights – A `numpy.ndarray` instance of cardinality (num segments x num sites)

## mesh#

Module `openquake.hazardlib.geo.mesh` defines classes `Mesh` and its subclass `RectangularMesh`.

class openquake.hazardlib.geo.mesh.Mesh(lons, lats, depths=None, round=None)[source]#

Bases: `object`

Mesh object represent a collection of points and provides the most efficient way of keeping those collections in memory.

Parameters:
• lons – A numpy array of longitudes. Can be 1D or 2D.

• lats – Numpy array of latitudes. The array must be of the same shape as `lons`.

• depths – Either `None`, which means that all points the mesh consists of are lying on the earth surface (have zero depth) or numpy array of the same shape as previous two.

Mesh object can also be created from a collection of points, see `from_points_list()`.

DIST_TOLERANCE = 0.005#

Tolerance level to be used in various spatial operations when approximation is required – set to 5 meters.

property depths#
classmethod from_coords(coords, sort=True)[source]#

Create a mesh object from a list of 3D coordinates (by sorting them)

Params coords:

list of coordinates

Parameters:

sort – flag (default True)

Returns:

a `Mesh` instance

classmethod from_points_list(points, round=None)[source]#

Create a mesh object from a collection of points.

Parameters:

point – List of `Point` objects.

Returns:

An instance of `Mesh` with one-dimensional arrays of coordinates from `points`.

get_closest_points(mesh)[source]#

Find closest point of this mesh for each point in the other mesh

Returns:

`Mesh` object of the same shape as mesh with closest points from this one at respective indices.

get_convex_hull()[source]#

Get a convex polygon object that contains projections of all the points of the mesh.

Returns:

Instance of `openquake.hazardlib.geo.polygon.Polygon` that is a convex hull around all the points in this mesh. If the original mesh had only one point, the resulting polygon has a square shape with a side length of 10 meters. If there were only two points, resulting polygon is a stripe 10 meters wide.

get_distance_matrix()[source]#

Compute and return distances between each pairs of points in the mesh.

This method requires that the coordinate arrays are one-dimensional. NB: the depth of the points is ignored

Warning

Because of its quadratic space and time complexity this method is safe to use for meshes of up to several thousand points. For mesh of 10k points it needs ~800 Mb for just the resulting matrix and four times that much for intermediate storage.

Returns:

Two-dimensional numpy array, square matrix of distances. The matrix has zeros on main diagonal and positive distances in kilometers on all other cells. That is, value in cell (3, 5) is the distance between mesh’s points 3 and 5 in km, and it is equal to value in cell (5, 3).

get_joyner_boore_distance(mesh, unstructured=False)[source]#

Compute and return Joyner-Boore distance to each point of `mesh`. Point’s depth is ignored.

See `openquake.hazardlib.geo.surface.base.BaseSurface.get_joyner_boore_distance()` for definition of this distance.

Returns:

numpy array of distances in km of the same shape as `mesh`. Distance value is considered to be zero if a point lies inside the polygon enveloping the projection of the mesh or on one of its edges.

get_min_distance(mesh)[source]#

Compute and return the minimum distance from the mesh to each point in another mesh.

Returns:

numpy array of distances in km of shape (self.size, mesh.size)

Method doesn’t make any assumptions on arrangement of the points in either mesh and instead calculates the distance from each point of this mesh to each point of the target mesh and returns the lowest found for each.

property lats#
property lons#
property shape#

Return the shape of this mesh.

Returns tuple:

The shape of this mesh as (rows, columns)

property xyz#
Returns:

an array of shape (N, 3) with the cartesian coordinates

class openquake.hazardlib.geo.mesh.RectangularMesh(lons, lats, depths=None, round=None)[source]#

Bases: `Mesh`

A specification of `Mesh` that requires coordinate numpy-arrays to be two-dimensional.

Rectangular mesh is meant to represent not just an unordered collection of points but rather a sort of table of points, where index of the point in a mesh is related to it’s position with respect to neighbouring points.

classmethod from_points_list(points, round=None)[source]#

Create a rectangular mesh object from a list of lists of points. Lists in a list are supposed to have the same length.

Parameters:

point – List of lists of `Point` objects.

get_cell_dimensions()[source]#

Calculate centroid, width, length and area of each mesh cell.

Returns:

Tuple of four elements, each being 2d numpy array. Each array has both dimensions less by one the dimensions of the mesh, since they represent cells, not vertices. Arrays contain the following cell information:

1. centroids, 3d vectors in a Cartesian space,

2. length (size along row of points) in km,

3. width (size along column of points) in km,

4. area in square km.

get_mean_inclination_and_azimuth()[source]#

Calculate weighted average inclination and azimuth of the mesh surface.

Returns:

Tuple of two float numbers: inclination angle in a range [0, 90] and azimuth in range [0, 360) (in decimal degrees).

The mesh is triangulated, the inclination and azimuth for each triangle is computed and average values weighted on each triangle’s area are calculated. Azimuth is always defined in a way that inclination angle doesn’t exceed 90 degree.

get_mean_width()[source]#

Calculate and return (weighted) mean width (km) of a mesh surface.

The length of each mesh column is computed (summing up the cell widths in a same column), and the mean value (weighted by the mean cell length in each column) is returned.

get_middle_point()[source]#

Return the middle point of the mesh.

Returns:

An instance of `Point`.

The middle point is taken from the middle row and a middle column of the mesh if there are odd number of both. Otherwise the geometric mean point of two or four middle points.

triangulate()[source]#

Convert mesh points to vectors in Cartesian space.

Returns:

Tuple of four elements, each being 2d numpy array of 3d vectors (the same structure and shape as the mesh itself). Those arrays are:

1. points vectors,

2. vectors directed from each point (excluding the last column) to the next one in a same row →,

3. vectors directed from each point (excluding the first row) to the previous one in a same column ↑,

4. vectors pointing from a bottom left point of each mesh cell to top right one ↗.

So the last three arrays of vectors allow to construct triangles covering the whole mesh.

openquake.hazardlib.geo.mesh.calc_azimuth(points, along_azimuth, tl_area, br_area)[source]#
openquake.hazardlib.geo.mesh.calc_inclination(earth_surface_tangent_normal, tl_normal, tl_area, br_normal, br_area)[source]#
openquake.hazardlib.geo.mesh.debug_plot(polygons)[source]#
openquake.hazardlib.geo.mesh.sqrt(array)[source]#
openquake.hazardlib.geo.mesh.surface_to_arrays(surface)[source]#
Parameters:

surface – a (Multi)Surface object

Returns:

a list of S arrays of shape (3, N, M)

## nodalplane#

Module `openquake.hazardlib.geo.nodalplane` implements `NodalPlane`.

class openquake.hazardlib.geo.nodalplane.NP(strike, dip, rake)#

Bases: `tuple`

dip#

Alias for field number 1

rake#

Alias for field number 2

strike#

Alias for field number 0

class openquake.hazardlib.geo.nodalplane.NodalPlane(strike, dip, rake)[source]#

Bases: `object`

Nodal plane represents earthquake rupture orientation and propagation direction.

Parameters:
• strike – Angle between line created by the intersection of rupture plane and the North direction (defined between 0 and 360 degrees).

• dip – Angle between earth surface and fault plane (defined between 0 and 90 degrees).

• rake – Angle describing rupture propagation direction (defined between -180 and +180 degrees).

Raises:

ValueError – If any of parameters exceeds the definition range.

classmethod check_dip(dip)[source]#

Check if `dip` is in range `(0, 90]` and raise `ValueError` otherwise.

classmethod check_rake(rake)[source]#

Check if `rake` is in range `(-180, 180]` and raise `ValueError` otherwise.

classmethod check_strike(strike)[source]#

Check if `strike` is in range `[0, 360)` and raise `ValueError` otherwise.

## point#

Module `openquake.hazardlib.geo.point` defines `Point`.

class openquake.hazardlib.geo.point.Point(longitude, latitude, depth=0.0)[source]#

Bases: `object`

This class represents a geographical point in terms of longitude, latitude, and depth (with respect to the Earth surface).

Parameters:
• longitude (float) – Point longitude, in decimal degrees.

• latitude (float) – Point latitude, in decimal degrees.

• depth (float) – Point depth (default to 0.0), in km. Depth > 0 indicates a point below the earth surface, and depth < 0 above the earth surface.

EQUALITY_DISTANCE = 0.001#

The distance between two points for them to be considered equal, in km.

azimuth(point)[source]#

Compute the azimuth (in decimal degrees) between this point and the given point.

Parameters:

point (Instance of `Point`) – Destination point.

Returns:

The azimuth, value in a range `[0, 360)`.

Return type:

float

Check for proximity of points in the `mesh`.

Parameters:
Returns:

Numpy array of boolean values in the same shape as the mesh coordinate arrays with `True` on indexes of points that are not further than `radius` km from this point. Function `distance()` is used to calculate distances to points of the mesh. Points of the mesh that lie exactly `radius` km away from this point also have `True` in their indices.

distance(point)[source]#

Compute the distance (in km) between this point and the given point.

Distance is calculated using pythagoras theorem, where the hypotenuse is the distance and the other two sides are the horizontal distance (great circle distance) and vertical distance (depth difference between the two locations).

Parameters:

point (Instance of `Point`) – Destination point.

Returns:

The distance.

Return type:

float

distance_to_mesh(mesh, with_depths=True)[source]#

Compute distance (in km) between this point and each point of `mesh`.

Parameters:
• mesh`Mesh` of points to calculate distance to.

• with_depths – If `True` (by default), distance is calculated between actual point and the mesh, geodetic distance of projections is combined with vertical distance (difference of depths). If this is set to `False`, only geodetic distance between projections is calculated.

Returns:

Numpy array of floats of the same shape as `mesh` with distance values in km in respective indices.

equally_spaced_points(point, distance)[source]#

Compute the set of points equally spaced between this point and the given point.

Parameters:
• point (Instance of `Point`) – Destination point.

• distance (float) – Distance between points (in km).

Returns:

The list of equally spaced points.

Return type:

list of `Point` instances

classmethod from_vector(vector)[source]#

Create a point object from a 3d vector in Cartesian space.

Parameters:

vector – Tuple, list or numpy array of three float numbers representing point coordinates in Cartesian 3d space.

Returns:

A `Point` object created from those coordinates.

on_surface()[source]#

Check if this point is defined on the surface (depth is 0.0).

Returns bool:

True if this point is on the surface, false otherwise.

point_at(horizontal_distance, vertical_increment, azimuth)[source]#

Compute the point with given horizontal, vertical distances and azimuth from this point.

Parameters:
• horizontal_distance (float) – Horizontal distance, in km.

• vertical_increment (float) – Vertical increment, in km. When positive, the new point has a greater depth. When negative, the new point has a smaller depth.

Returns:

The point at the given distances.

Return type:

Instance of `Point`

round(digits=5)[source]#
Returns:

a new Point with lon, lat, depth rounded to 5 digits

Create a circular polygon with specified radius centered in the point.

Parameters:

Returns:

Instance of `Polygon` that approximates a circle around the point with specified radius.

property wkt2d#

Generate WKT (Well-Known Text) to represent this point in 2 dimensions (ignoring depth).

property x#

Alias for .longitude

property y#

Alias for .latitude

property z#

Alias for .depth

## polygon#

class openquake.hazardlib.geo.polygon.Polygon(points)[source]#

Bases: `object`

Polygon objects represent an area on the Earth surface.

Parameters:

points – The list of `Point` objects defining the polygon vertices. The points are connected by great circle arcs in order of appearance. Polygon segment should not cross another polygon segment. At least three points must be defined.

Raises:

ValueError – If `points` contains less than three unique points or if polygon perimeter intersects itself.

property centroid#
Returns:

the centroid of the underlying 2D polygon

property coords#

Coordinates of the polygon as a linear ring, rounded to 5 digits

dilate(dilation)[source]#

Extend the polygon to a specified buffer distance.

Note

In extreme cases where dilation of a polygon creates holes, thus resulting in a multi-polygon, we discard the holes and simply return the ‘exterior’ of the shape.

Parameters:

dilation – Distance in km to extend polygon borders to.

Returns:

New `Polygon` object with (in general) more vertices and border that is approximately `dilation` km far (measured perpendicularly to edges and circularly to vertices) from the border of original polygon.

discretize(mesh_spacing)[source]#

Get a mesh of uniformly spaced points inside the polygon area with distance of `mesh_spacing` km between.

Returns:

An instance of `Mesh` that holds the points data. Mesh is created with no depth information (all the points are on the Earth surface).

classmethod from_wkt(wkt_string)[source]#

Create a polygon object from a WKT (Well-Known Text) string.

Parameters:

wkt_string – A standard WKT polygon string.

Returns:

New `Polygon` object.

get_bbox()[source]#

Returns a simple 2D bounding box from the extrema of lons and lats

intersects(mesh)[source]#

Check for intersection with each point of the `mesh`.

Mesh coordinate values are in decimal degrees.

Parameters:

mesh`openquake.hazardlib.geo.mesh.Mesh` instance.

Returns:

Numpy array of bool values in the same shapes in the input coordinate arrays with `True` on indexes of points that lie inside the polygon or on one of its edges and `False` for points that neither lie inside nor touch the boundary.

property wkt#

Generate WKT (Well-Known Text) to represent this polygon.

openquake.hazardlib.geo.polygon.UPSAMPLING_STEP_KM = 100#

Polygon upsampling step for long edges, in kilometers. See `get_resampled_coordinates()`.

openquake.hazardlib.geo.polygon.get_resampled_coordinates(lons, lats)[source]#

Resample polygon line segments and return the coordinates of the new vertices. This limits distortions when projecting a polygon onto a spherical surface.

Parameters define longitudes and latitudes of a point collection in the form of lists or numpy arrays.

Returns:

A tuple of two numpy arrays: longitudes and latitudes of resampled vertices.

## utils#

Module `openquake.hazardlib.geo.utils` contains functions that are common to several geographical primitives and some other low-level spatial operations.

exception openquake.hazardlib.geo.utils.BBoxError[source]#

Bases: `ValueError`

Bounding box too large

class openquake.hazardlib.geo.utils.OrthographicProjection(west, east, north, south)[source]#

Bases: `object`

Callable OrthographicProjection object that can perform both forward and reverse projection (converting from longitudes and latitudes to x and y values on 2d-space and vice versa). The call takes three arguments: first two are numpy arrays of longitudes and latitudes or abscissae and ordinates of points to project and the third one is a boolean that allows to choose what operation is requested – is it forward or reverse one. `True` value given to third positional argument (or keyword argument “reverse”) indicates that the projection of points in 2d space back to earth surface is needed. The default value for “reverse” argument is `False`, which means forward projection (degrees to kilometers).

Raises `ValueError` in forward projection mode if any of the target points is further than 90 degree (along the great circle arc) from the projection center.

Parameters are given as floats, representing decimal degrees (first two are longitudes and last two are latitudes). They define a bounding box in a spherical coordinates of the collection of points that is about to be projected. The center point of the projection (coordinates (0, 0) in Cartesian space) is set to the middle point of that bounding box. The resulting projection is defined for spherical coordinates that are not further from the bounding box center than 90 degree on the great circle arc.

The result projection is of type Orthographic. This projection is prone to distance, area and angle distortions everywhere outside of the center point, but still can be used for checking shapes: verifying if line intersects itself (like in `line_intersects_itself()`) or if point is inside of a polygon (like in `openquake.hazardlib.geo.polygon.Polygon.discretize()`). It can be also used for measuring distance to an extent of around 700 kilometers (error doesn’t exceed 1 km up until then).

classmethod from_lons_lats(lons, lats)[source]#
class openquake.hazardlib.geo.utils.PolygonPlotter(ax)[source]#

Bases: `object`

Add polygons to a given axis object

set_lim(xs=(), ys=())[source]#
exception openquake.hazardlib.geo.utils.SiteAssociationError[source]#

Bases: `Exception`

Raised when there are no sites close enough

openquake.hazardlib.geo.utils.angular_distance(km, lat=0, lat2=None)[source]#

Return the angular distance of two points at the given latitude.

```>>> '%.3f' % angular_distance(100, lat=40)
'1.174'
>>> '%.3f' % angular_distance(100, lat=80)
'5.179'
```
openquake.hazardlib.geo.utils.angular_mean(degrees, weights=None)[source]#

Given an array of angles in degrees, returns its angular mean. If weights are passed, assume sum(weights) == 1.

```>>> angular_mean([179, -179])
180.0
>>> angular_mean([-179, 179])
180.0
>>> angular_mean([-179, 179], [.75, .25])
-179.4999619199226
```
openquake.hazardlib.geo.utils.angular_mean_weighted(degrees, weights)[source]#
openquake.hazardlib.geo.utils.assoc(objects, sitecol, assoc_dist, mode)[source]#

Associate geographic objects to a site collection.

Parameters:
• objects – something with .lons, .lats or [‘lon’] [‘lat’], or a list of lists of objects with a .location attribute (i.e. assets_by_site)

• assoc_dist – the maximum distance for association

• mode – if ‘strict’ fail if at least one site is not associated if ‘error’ fail if all sites are not associated

Returns:

(filtered site collection, filtered objects)

openquake.hazardlib.geo.utils.assoc_to_polygons(polygons, data, sitecol, mode)[source]#

Associate data from a shapefile with polygons to a site collection :param polygons: polygon shape data :param data: rest of the data belonging to the shapes :param sitecol: a (filtered) site collection :param mode: ‘strict’, ‘warn’ or ‘filter’ :returns: filtered site collection, filtered objects, discarded

openquake.hazardlib.geo.utils.bbox2poly(bbox)[source]#
Parameters:

bbox – a geographic bounding box West-East-North-South

Returns:

a list of pairs corrisponding to the bbox polygon

openquake.hazardlib.geo.utils.cartesian_to_spherical(arrayN3)[source]#

Return the spherical coordinates for coordinates in Cartesian space.

This function does an opposite to `spherical_to_cartesian()`.

Parameters:

arrayN3 – Array of cartesian coordinates of shape (N, 3)

Returns:

Array of shape (3, N) representing longitude (decimal degrees), latitude (decimal degrees) and depth (km) in specified order.

openquake.hazardlib.geo.utils.check_extent(lons, lats, msg='')[source]#
Parameters:
• lons – an array of longitudes (more than one)

• lats – an array of latitudes (more than one)

Params msg:

message to display in case of too large extent

Returns:

(dx, dy, dz) in km (rounded)

openquake.hazardlib.geo.utils.clean_points(points)[source]#

Given a list of points, return a new list with adjacent duplicate points removed.

Parameters:

points – a list of Point instances or a list of 3D arrays

openquake.hazardlib.geo.utils.cross_idl(lon1, lon2, *lons)[source]#

Return True if two longitude values define line crossing international date line.

```>>> cross_idl(-45, 45)
False
>>> cross_idl(-180, -179)
False
>>> cross_idl(180, 179)
False
>>> cross_idl(45, -45)
False
>>> cross_idl(0, 0)
False
>>> cross_idl(-170, 170)
True
>>> cross_idl(170, -170)
True
>>> cross_idl(-180, 180)
True
```
openquake.hazardlib.geo.utils.fix_lon(lon)[source]#
Returns:

a valid longitude in the range -180 <= lon < 180

```>>> fix_lon(11)
11
>>> fix_lon(181)
-179
>>> fix_lon(-182)
178
```
openquake.hazardlib.geo.utils.geohash(lons, lats, length)[source]#

Encode a position given in lon, lat into a geohash of the given lenght

```>>> arr = CODE32[geohash(F64([10., 10.]), F64([45., 46.]), length=5)]
>>> [row.tobytes() for row in arr]
[b'spzpg', b'u0pje']
```
openquake.hazardlib.geo.utils.geohash3(lons, lats)[source]#
Returns:

a geohash of length 3 as a 16 bit integer

```>>> geohash3(F64([10., 10.]), F64([45., 46.]))
array([24767, 26645], dtype=uint16)
```
openquake.hazardlib.geo.utils.geohash5(coords)[source]#
Returns:

a geohash of length 5*len(points) as a string

```>>> coords = numpy.array([[10., 45.], [11., 45.]])
>>> geohash5(coords)
'spzpg_spzzf'
```
openquake.hazardlib.geo.utils.geolocate(lonlats, geom_df, exclude=())[source]#
Parameters:
• lonlats – array of shape (N, 2) of (lon, lat)

• geom_df – DataFrame of geometries keyed by a “code” field

Returns:

codes associated to the points

openquake.hazardlib.geo.utils.get_bounding_box(obj, maxdist)[source]#

Return the dilated bounding box of a geometric object.

Parameters:
• obj – an object with method .get_bounding_box, or with an attribute .polygon or a list of locations

• maxdist – maximum distance in km

openquake.hazardlib.geo.utils.get_dist(array, point)[source]#
Parameters:
• array – an array of shape (3,) or (N, 3)

• point – an array of shape (3)

Returns:

distances(s) from the reference point

openquake.hazardlib.geo.utils.get_middle_point(lon1, lat1, lon2, lat2)[source]#

Given two points return the point exactly in the middle lying on the same great circle arc.

Parameters are point coordinates in degrees.

Returns:

Tuple of longitude and latitude of the point in the middle.

openquake.hazardlib.geo.utils.get_spherical_bounding_box(lons, lats)[source]#

Given a collection of points find and return the bounding box, as a pair of longitudes and a pair of latitudes.

Parameters define longitudes and latitudes of a point collection respectively in a form of lists or numpy arrays.

Returns:

A tuple of four items. These items represent western, eastern, northern and southern borders of the bounding box respectively. Values are floats in decimal degrees.

Raises:

ValueError – If points collection has the longitudinal extent of more than 180 degrees (it is impossible to define a single hemisphere bound to poles that would contain the whole collection).

openquake.hazardlib.geo.utils.line_intersects_itself(lons, lats, closed_shape=False)[source]#

Return `True` if line of points intersects itself. Line with the last point repeating the first one considered intersecting itself.

The line is defined by lists (or numpy arrays) of points’ longitudes and latitudes (depth is not taken into account).

Parameters:

closed_shape – If `True` the line will be checked twice: first time with its original shape and second time with the points sequence being shifted by one point (the last point becomes first, the first turns second and so on). This is useful for checking that the sequence of points defines a valid `Polygon`.

openquake.hazardlib.geo.utils.min_distance(xyz, xyzs)[source]#
Parameters:
• xyz – an array of shape (3,)

• xyzs – an array of shape (N, 3)

Returns:

the minimum euclidean distance between the point and the points

openquake.hazardlib.geo.utils.normalized(vector)[source]#

Get unit vector for a given one.

Parameters:

vector – Numpy vector as coordinates in Cartesian space, or an array of such.

Returns:

Numpy array of the same shape and structure where all vectors are normalized. That is, each coordinate component is divided by its vector’s length.

openquake.hazardlib.geo.utils.plane_fit(points)[source]#

This fits an n-dimensional plane to a set of points. See http://stackoverflow.com/questions/12299540/plane-fitting-to-4-or-more-xyz-points

Parameters:

points – An instance of :class:~numpy.ndarray. The number of columns must be equal to three.

Returns:

A point on the plane and the normal to the plane.

openquake.hazardlib.geo.utils.point_to_polygon_distance(polygon, pxx, pyy)[source]#

Calculate the distance to polygon for each point of the collection on the 2d Cartesian plane.

Parameters:
• polygon – Shapely “Polygon” geometry object.

• pxx – List or numpy array of abscissae values of points to calculate the distance from.

• pyy – Same structure as `pxx`, but with ordinate values.

Returns:

Numpy array of distances in units of coordinate system. Points that lie inside the polygon have zero distance.

openquake.hazardlib.geo.utils.project_direct(lambda0, phi0, lons, lats)[source]#
openquake.hazardlib.geo.utils.project_reverse(lambda0, phi0, lons, lats)[source]#
openquake.hazardlib.geo.utils.triangle_area(e1, e2, e3)[source]#

Get the area of triangle formed by three vectors.

Parameters are three three-dimensional numpy arrays representing vectors of triangle’s edges in Cartesian space.

Returns:

Float number, the area of the triangle in squared units of coordinates, or numpy array of shape of edges with one dimension less.

Uses Heron formula, see http://mathworld.wolfram.com/HeronsFormula.html.

## Module contents#

Package `openquake.hazardlib.geo` contains implementations of different geographical primitives, such as `Point`, `Line` `Polygon` and `Mesh`, as well as different `surface` implementations and utility class `NodalPlane`.