porepy.geometry.distances module

The module contains functions for distance computations.

point_pointset(p, pset, exponent=2)

Compute distance between a point and a set of points.

Parameters

• p (ndarray) –

  shape=(nd, 1)

  Point from which distances will be computed.

• pset (ndarray) –

  shape=(nd, num_points)

  Point cloud to which we compute distances.

• exponent (Union[float, int]) –

  default=2

  Exponent of the norm used.

Returns

Array of distances (shape=(num_points,)).

Return type

ndarray

points_polygon(p, poly, tol=1e-5)

Compute distance from points to a polygon. Also find closest point on the polygon.

Parameters

• p (ndarray) –

  shape=(nd, num_points)

  Points for which we will compute distances.

• poly (ndarray) –

  shape=(nd, num_vertexes)

  Vertexes of polygon. Edges are formed by subsequent points.

• tol (float) –

  default=1e-5

  Tolerance to be used.

Returns

A tuple of 3 elements.

ndarray: shape=(num_points,)

Distance from points to polygon.

ndarray: shape=(nd, num_points,)

For each point, the closest point on the polygon.

ndarray: shape=(num_points)

True if the point is found in the interior, False if on a bounding segment.

Return type

tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

points_segments(p, start, end)

Compute distances between points and line segments.

The function also returns the closest points on the segments.

Parameters

• p (ndarray) –

  shape=(nd, num_points)

  Individual points.

• start (ndarray) –

  shape=(nd, num_segments)

  Start points of segments.

• end (ndarray) –

  shape=(nd, num_segments)

  End point of segments.

Returns

A tuple of 2 elements.

ndarray: shape=(num_points, num_segments)

Distances.

ndarray: shape=(num_points, num_segments, nd)

Points on the segments closest to the individual points.

Return type

tuple[numpy.ndarray, numpy.ndarray]

pointset(p, max_diag=False)

Compute mutual distance between all points in a point set.

Parameters

• p (ndarray) –

  shape=(nd, num_points)

  A set of points.

• max_diag (bool) –

  default=False

  If True, the diagonal value corresponding to each point is set to twice the maximum of the distances for that point, rather than 0.

Returns

Array of distances between points (shape=(num_points, num_points)).

Return type

ndarray

segment_overlap_segment_set(start, end, start_set, end_set, return_indices=False, tol=1e-5)

Detects whether a given segment overlaps the segments in a set.

The function currently works only for 2D geometries: nd == 2.

Parameters

• start (ndarray) –

  shape=(nd,)

  Start point of a segment.

• end (ndarray) –

  shape=(nd,)

  End point of a segment.

• start_set (ndarray) –

  shape=(nd, num_segments)

  Start points of the set of segments.

• end_set (ndarray) –

  shape=(nd, num_segments)

  End points of the set of segments.

• return_indices (bool) –

  default=False

  Whether the function should also return indices of overlappings.

• tol (float) –

  default=1e-5

  Tolerance to be used.

Returns

If return_indices==True, we return a tuple of 2 elements.

bool:

True if the segment overlaps any of the segments in the set, False otherwise.

ndarray: shape=(num_overlapping,)

Indices of overlappings.

Otherwise, the 0th element of the tuple is returned.

Return type

Union[bool, tuple[bool, numpy.ndarray]]

segment_segment_set(start, end, start_set, end_set)

Compute distance and closest points between a segment and a set of segments.

Note

Algorithm can be found at http://geomalgorithms.com/code.html (see file “C07_Line_Line_Distance.cpp”, function dist3D_Segment_to_Segment()).

Parameters

• start (ndarray) –

  shape=(nd, 1)

  Start point of the main segment.

• end (ndarray) –

  shape=(nd, 1)

  End point of the main segment.

• start_set (ndarray) –

  shape=(nd, num_segments)

  Start points for the segment set.

• end_set (ndarray) –

  shape=(nd, num_segments)

  End points for the segment set.

Returns

A tuple of 3 elements.

ndarray: shape=(num_segments,)

The distance from the main segment to each of the segments in the set.

ndarray: shape=(nd, num_segments)

For each segment in the segment set, the point closest on the main segment.

ndarray: shape=(nd, num_segments)

For each segment in the segment set, the point closest on the secondary segment.

Return type

tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

segment_set(start, end)

Compute distance and closest points between sets of line segments.

Parameters

• start (ndarray) –

  shape=(nd, num_segments)

  Start points of segments.

• end (ndarray) –

  shape=(nd, num_segments)

  End points of segments.

Returns

A tuple of 2 elements.

ndarray: shape=(num_segments, num_segments)

Distances between segments.

ndarray: shape=(num_segments, num_segments, nd)

For segment i and j, element [i, j] gives the point on i closest to segment j.

Return type

tuple[numpy.ndarray, numpy.ndarray]

segments_polygon(start, end, poly, tol=1e-5)

Compute the distance from line segments to a polygon.

Parameters

• start (ndarray) –

  shape=(nd, num_segments)

  One endpoint of segments.

• end (ndarray) –

  shape=(nd, num_segments)

  Other endpoint of segments.

• poly (ndarray) –

  shape=(nd, n_vert)

  Vertexes of polygon.

• tol (float) –

  default=1e-5

  Tolerance to be used.

Returns

A tuple of 2 elements.

ndarray: (shape=(num_segments,), dtype=double)

Distance from segment to polygon.

ndarray: shape=(nd, num_segments)

Closest point.

Return type

tuple[numpy.ndarray, numpy.ndarray]