# 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.``EARTH_RADIUS` = 6371.0

`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.``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_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: alon, alat (float) – 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. plons, plats (float) – Longitudes and latitudes of points to measure distance. Either scalar values or numpy arrays of decimal degrees. 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.``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: lon1, lat1, depth1 (float) – Coordinates of a point to start placing intervals from. The first point in the resulting list has these coordinates. lon2, lat2, depth2 (float) – 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. 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. 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`(mlons, mlats, slons, slats, diameter=12742.0)[source]

Small wrapper around `pure_distances()`, suitable for calculating the minimum distance between first mesh and each point of the second mesh when both are defined on the earth surface.

`openquake.hazardlib.geo.geodetic.``min_idx_dst`(mlons, mlats, mdepths, slons, slats, sdepths=0, diameter=12742.0)[source]

Calculate the minimum distance between a collection of points and a point.

This function allows to calculate a closest distance to a collection of points for each point in another collection. Both collection can be of any shape, although it doesn’t make sense to use scalars for the first one.

Implements the same formula as in `geodetic_distance()` for distance along great circle arc and the same approach as in `distance()` for combining it with depth distance.

Parameters: mlats, mdepths (mlons,) – Numpy arrays of the same shape representing a first collection of points, the one distance to which is of interest – longitudes, latitudes (both in decimal degrees) and depths (in km). slats, sdepths (slons,) – Scalars, python lists or tuples or numpy arrays of the same shape, representing a second collection: a list of points to find a minimum distance from for. Indices and distances in km of the closest points. The result value is a scalar if `slons`, `slats` and `sdepths` are scalars and numpy array of the same shape of those three otherwise.
`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: lon1, lat1, depth1 (float) – Coordinates of a point to start from. The first point in a resulting list has these coordinates. lon2, lat2, depth2 (float) – 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. 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: lon, lat, depth (float) – 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. 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: lon, lat (float) – 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. 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.``pure_distances`(mlons, mlats, slons, slats)[source]
Parameters: mlons – array of m longitudes (for the rupture) mlats – array of m latitudes (for the rupture) slons – array of s longitudes (for the sites) slats – array of s latitudes (for the sites) array of (m, s) distances to be multiplied by the Earth diameter

## 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 one point.

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
>>> str(Line([P(0, 0), P(1e-5, 1e-5)]).average_azimuth())
'45.0'
>>> str(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'
```
`get_length`()[source]

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

Returns: Total length in km.
`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.
`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.
`resample`(section_length)[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. The line segment is then split into sections of length equal to `section_length`. The resampled line is obtained by concatenating all sections.

The number of sections in a line segment is calculated as follows: `round(segment_length / section_length)`.

Note that the resulting line has a length that is an exact multiple of `section_length`, therefore its length is in general smaller or greater (depending on the rounding) than the length of the original line.

For a straight line, the difference between the resulting length and the original length is at maximum half of the `section_length`. For a curved line, the difference my be larger, because of corners getting cut.

Parameters: section_length (float) – The length of the section, in km. A new line resampled into sections based on the given length. An instance of `Line`
`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. A new line with that many points as requested.

## mesh¶

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

class `openquake.hazardlib.geo.mesh.``Mesh`(lons, lats, depths=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 longitude values of points. Array may be of arbitrary shape. lats – Numpy array of latitude values. 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.

classmethod `from_coords`(coords)[source]

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

Params coords: list of coordinates a `Mesh` instance
classmethod `from_points_list`(points)[source]

Create a mesh object from a collection of points.

Parameters: point – List of `Point` objects. 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 one in `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 all the points lie on Earth surface (have zero depth) and coordinate arrays are one-dimensional.

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_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 the same shape as `mesh`.

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.

`shape`

Return the shape of this mesh.

Returns tuple: The shape of this mesh as (rows, columns)
class `openquake.hazardlib.geo.mesh.``RectangularMesh`(lons, lats, depths=None)[source]

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)[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: centroids, 3d vectors in a Cartesian space, length (size along row of points) in km, width (size along column of points) in km, area in square km.
`get_joyner_boore_distance`(mesh)[source]

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

See `openquake.hazardlib.geo.surface.base.BaseQuadrilateralSurface.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_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: points vectors, vectors directed from each point (excluding the last column) to the next one in a same row →, vectors directed from each point (excluding the first row) to the previous one in a same column ↑, 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.``build_array`(lons_lats_depths)[source]

Convert a list of n triples into a composite numpy array with fields lon, lat, depth and shape (n,) + lons.shape.

`openquake.hazardlib.geo.mesh.``sqrt`(array)[source]
`openquake.hazardlib.geo.mesh.``surface_to_mesh`(surface)[source]
Parameters: surface – a Surface object a 3D array of dtype point3d

## nodalplane¶

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

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). ValueError – If any of parameters exceeds the definition range.
`assert_equal`(other, ignore=())
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. The azimuth, value in a range `[0, 360)`. float
`closer_than`(mesh, radius)[source]

Check for proximity of points in the `mesh`.

Parameters: mesh – `openquake.hazardlib.geo.mesh.Mesh` instance. radius – Proximity measure in km. 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. The distance. 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. 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). The list of equally spaced points. 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. 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. The point at the given distances. Instance of `Point`
`to_polygon`(radius)[source]

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

Parameters: radius – Required radius of a new polygon, in km. Instance of `Polygon` that approximates a circle around the point with specified radius.
`wkt2d`

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

`x`

Alias for .longitude

`y`

Alias for .latitude

`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. ValueError – If `points` contains less than three unique points or if polygon perimeter intersects itself.
`assert_equal`(other, ignore=())
`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. 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. 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. 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.
`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.

class `openquake.hazardlib.geo.utils.``GeographicObjects`(objects, getlon=operator.attrgetter('lon'), getlat=operator.attrgetter('lat'))[source]

Bases: `object`

Store a collection of geographic objects, i.e. objects with longitudes and latitudes. By default extracts the coordinates from the attributes .lon and .lat, but you can provide your own getters. It is possible to extract the closest object to a given location by calling the method .get_closest(lon, lat).

`get_closest`(lon, lat)[source]

Get the closest object to the given longitude and latitude and its distance.

Parameters: lon – longitude in degrees lat – latitude in degrees max_distance – distance in km (or None)
class `openquake.hazardlib.geo.utils.``OrthographicProjection`(west, east, north, south)[source]

Bases: `object`

Callable object to compute orthographic projections. See the docstring of get_orthographic_projection.

`assert_equal`(other, ignore=())
classmethod `from_lons_lats`(lons, lats)[source]
class `openquake.hazardlib.geo.utils.``SphericalBB`(west, east, north, south)

Bases: `tuple`

`east`

Alias for field number 1

`north`

Alias for field number 2

`south`

Alias for field number 3

`west`

Alias for field number 0

`openquake.hazardlib.geo.utils.``cartesian_to_spherical`(vectors)[source]

Return the spherical coordinates for coordinates in Cartesian space.

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

Parameters: vectors – Array of 3d vectors in Cartesian space. Tuple of three arrays of the same shape as `vectors` representing longitude (decimal degrees), latitude (decimal degrees) and depth (km) in specified order.
`openquake.hazardlib.geo.utils.``clean_points`(points)[source]

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

`openquake.hazardlib.geo.utils.``cross_idl`(lon1, lon2)[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.``get_longitudinal_extent`(lon1, lon2)[source]

Return the distance between two longitude values as an angular measure. Parameters represent two longitude values in degrees.

Returns: Float, the angle between `lon1` and `lon2` in degrees. Value is positive if `lon2` is on the east from `lon1` and negative otherwise. Absolute value of the result doesn’t exceed 180 for valid parameters values.
`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_orthographic_projection`(west, east, north, south)[source]

Create and return a projection object for a given bounding box.

Returns: 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).

`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. 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.``normalized`(vector)[source]

Get unit vector for a given one.

Parameters: vector – Numpy vector as coordinates in Cartesian space, or an array of such. 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. 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. Numpy array of distances in units of coordinate system. Points that lie inside the polygon have zero distance.
`openquake.hazardlib.geo.utils.``spherical_to_cartesian`(lons, lats, depths)[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: `numpy.array` of 3d vectors representing points’ coordinates in Cartesian space. The array has the same shape as parameter arrays. In particular it means that if `lons` and `lats` are scalars, the result is a single 3d vector. Vector of length `1` represents distance of 1 km.

See also `cartesian_to_spherical()`.

`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`.