porepy.geometry.geometry_property_checks module

This module contains functions for (boolean) inquiries about geometric objects, and relations between objects.

is_ccw_polygon(poly)[source]

Determine if the vertices of a polygon are sorted counterclockwise.

The method computes the winding number of the polygon, see below references.

The algorithm should work for non-convex polygons. If the polygon is self-intersecting (e.g. shaped like the number 8), the number returned will reflect whether the method is ‘mostly’ cw or ccw.

Note

The test can not be used to determine whether the vertexes of a polygon are ordered in a natural fashion, that is, not self-intersecting.

Examples

>>> is_ccw_polygon(np.array([[0, 1, 0], [0, 0, 1]]))
True
>>> is_ccw_polygon(np.array([[0, 0, 1], [0, 1, 0]]))
False

References

  1. StackOverflow question 1165647

  2. http://blog.element84.com/polygon-winding.html

See also

is_ccw_polyline()

Parameters

poly (ndarray) –

shape=(2, n)

Polygon vertices. n is number of points.

Returns

True if the polygon is ccw.

Return type

bool

is_ccw_polyline(p1, p2, p3, tol=0, default=False)[source]

Checks if a polyline of three points goes in a counterclockwise direction.

The line segment going from p1 to p2 is tested vs. a third point to determine whether the combined line segments (polyline) is part of a counterclockwise circle. The function can test both one and several points vs. the same line segment.

The test is positive if the test point lies to left of the line running from p1 to p2.

The function is intended for 2D points; higher-dimensional coordinates will be ignored.

Extensions to lines with more than three points should be straightforward, the input points should be merged into a 2d array.

Examples

>>> p1 = np.array([0, 0])
>>> p2 = np.array([1, 1])
>>> p3 = np.array([[0.5, 0.3, 0.5], [0.2, 0.7, 0.1]])
>>> is_ccw_polyline(p1, p2, p3)
[False True False]

>>> p1 = np.array([0, 0])
>>> p2 = np.array([1, 1])
>>> p3 = np.array([0.5, 0.3])
>>> is_ccw_polyline(p1, p2, p3)
False

See also

is_ccw_polygon()

Parameters

  • p1 (ndarray) –

    shape=(2,)

    First point on dividing line.

  • p2 (ndarray) –

    shape=(2,)

    Second point on dividing line.

  • p3 (ndarray) –

    (shape=(2,) or shape=(2, n))

    Point(s) to be tested. For one point, only arrays of shape=(2,) is accepted. For two or more points the array will have shape=(2, n), where the first row corresponds to x-coordinates and the second row corresponds to y-coordinates. See examples.

  • tol (float) –

    default=0

    Tolerance used in the comparison, can be used to account for rounding errors.

  • default (bool) –

    default=False

    Mode returned if the point is within the tolerance. Should be set according to what is desired behavior of the function (will vary with application).

Returns

An array of booleans, with one entry for each point in p3. True if the point is to the left of the line segment p1-p2.

Return type

ndarray

point_in_cell(poly, p, if_make_planar=True)[source]

Check whether a point is inside a cell.

Note

A similar behavior could be reached using is_inside_polygon(), however the current implementation deals with concave cells as well. Not sure which is the best, in terms of performance, for convex cells.

Parameters

  • poly (ndarray) –

    shape=(3, n)

    Vertexes of polygon. The segments are formed by connecting subsequent columns of poly.

  • p (ndarray) –

    shape=(3, 1)

    Point to be tested.

  • if_make_planar (bool) –

    default=True

    The cell needs to lie on (s, t) plane. If not already done, this flag need to be used. Projects the points to the plane of the polygon.

Returns

True if the point is inside the cell. If a point is on the boundary of the cell the result may be either True or False.

Return type

bool

point_in_polygon(poly, p, default=False)[source]

Check if a set of points are inside a polygon.

The polygon need not be convex.

References

  1. Original source code from Mark Dickenson

Parameters

  • poly (ndarray) –

    shape=(2, num_poly)

    Vertexes of polygon. The segments are formed by connecting subsequent columns of poly.

  • p (ndarray) –

    shape=(2, num_pt)

    Points to be tested.

  • default (bool) –

    default=False

    Default behavior if the point is close to the boundary of the polygon.

Returns

A boolean array containing True for each of the points that are inside polygon.

Return type

ndarray

point_in_polyhedron(polyhedron, test_points, tol=1e-10)[source]

Test whether a set of point is inside a polyhedron.

Parameters

  • polyhedron (Union[ndarray, list[numpy.ndarray]]) –

    shape=(num_sides, 3, num_polygon_vertices)

    Each outer element represents a side of the polyhedron, and each side is assumed to be a convex polygon.

  • test_points (ndarray) –

    shape=(3, np)

    Points to be tested.

  • tol (float) –

    default=1e-10

    Geometric tolerance, used in comparison of points.

Returns

For each point, element i is True if test_points[:, i] is inside the polygon, else it is False.

Return type

ndarray

points_are_collinear(pts, tol=1e-5)[source]

Check if the points lie on a line.

Parameters

  • pts (ndarray) –

    shape=(3, n)

    The points.

  • tol (float) –

    default=1e-5

    Absolute tolerance used in comparison.

Returns

True if the points lie on a line.

Return type

bool

points_are_planar(pts, normal=None, tol=1e-5)[source]

Check if the points lie on a plane.

Parameters

  • pts (ndarray) –

    shape=(3, np)

    The points.

  • normal (Optional[ndarray]) –

    default=None

    The normal of the plane, otherwise at least three points are required.

  • tol (float) –

    default=1e-5

    Geometric tolerance for test.

Returns

True if the points lie on a plane.

Return type

bool

polygon_hanging_nodes(p, edges, tol=1e-8)[source]

Find hanging nodes of a polygon.

Parameters

  • p (ndarray) –

    shape=(nd, n_pt)

    Point coordinates. Number of rows is number of dimensions, number of columns is number of points.

  • edges (ndarray) –

    shape=(2, num_edges)

    Indices, referring to columns in p, of edges in the polygon. Should be ordered so that edges[1, i] == edges[0, i+1], and edges[0, 0] == edges[1, -1].

  • tol (float) –

    default=1e-8

    Tolerance for when two segments will be considered parallel.

Returns

Index of edges with hanging nodes. For an index i, the lines defined by edges[:, i] and edges[:, i+1] (or edges[:, 0] if i == edges.shape[1] - 1) are parallel.

Return type

ndarray