Source code for libpysal.cg.voronoi

"""
Voronoi tesslation of 2-d point sets.

Adapted from https://gist.github.com/pv/8036995

"""

import numpy as np
from scipy.spatial import Voronoi

__author__ = "Serge Rey <sjsrey@gmail.com>"

__all__ = ["voronoi_frames"]


def voronoi(points, radius=None):
    """Determine finite Voronoi diagram for a 2-d point set.
    See also ``voronoi_regions()``.

    Parameters
    ----------
    points : array-like
        An nx2 array of points.
    radius : float (optional)
        The distance to 'points at infinity'.

    Returns
    -------
    vor : tuple
        A two-element tuple consisting of a list and an array. Each element of
        the list contains the sequence of the indices of Voronoi vertices
        composing a Voronoi polygon (region), whereas the array contains
        the Voronoi vertex coordinates.
    
    Examples
    --------
    
    >>> points = [(10.2, 5.1), (4.7, 2.2), (5.3, 5.7), (2.7, 5.3)]
    >>> regions, coordinates = voronoi(points)
    >>> regions
    [[1, 3, 2], [4, 5, 1, 0], [0, 1, 7, 6], [9, 0, 8]]
    >>> coordinates
    array([[  4.21783296,   4.08408578],
           [  7.51956025,   3.51807539],
           [  9.4642193 ,  19.3994576 ],
           [ 14.98210684, -10.63503022],
           [ -9.22691341,  -4.58994414],
           [ 14.98210684, -10.63503022],
           [  1.78491801,  19.89803294],
           [  9.4642193 ,  19.3994576 ],
           [  1.78491801,  19.89803294],
           [ -9.22691341,  -4.58994414]])
    
    """

    vor = voronoi_regions(Voronoi(points), radius=radius)

    return vor


def voronoi_regions(vor, radius=None):
    """Finite voronoi regions for a 2-d point set. See also ``voronoi()``.

    Parameters
    ----------
    vor : scipy.spatial.Voronoi
        A planar Voronoi diagram.
    radius : float (optional)
        Distance to 'points at infinity'.
    
    Returns
    -------
    regions_vertices : tuple
        A two-element tuple consisting of a list of finite voronoi regions
        and an array Voronoi vertex coordinates.
    
    """

    new_regions = []
    new_vertices = vor.vertices.tolist()

    center = vor.points.mean(axis=0)
    if radius is None:
        radius = vor.points.ptp().max() * 2

    all_ridges = {}
    for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):
        all_ridges.setdefault(p1, []).append((p2, v1, v2))
        all_ridges.setdefault(p2, []).append((p1, v1, v2))

    for p1, region in enumerate(vor.point_region):
        vertices = vor.regions[region]

        if all(v >= 0 for v in vertices):
            new_regions.append(vertices)
            continue

        ridges = all_ridges[p1]
        new_region = [v for v in vertices if v >= 0]

        for p2, v1, v2 in ridges:
            if v2 < 0:
                v1, v2 = v2, v1
            if v1 >= 0:
                continue

            t = vor.points[p2] - vor.points[p1]
            t /= np.linalg.norm(t)
            n = np.array([-t[1], t[0]])

            midpoint = vor.points[[p1, p2]].mean(axis=0)
            direction = np.sign(np.dot(midpoint - center, n)) * n
            far_point = vor.vertices[v2] + direction * radius

            new_region.append(len(new_vertices))
            new_vertices.append(far_point.tolist())

        vs = np.asarray([new_vertices[v] for v in new_region])
        c = vs.mean(axis=0)
        angles = np.arctan2(vs[:, 1] - c[1], vs[:, 0] - c[0])
        new_region = np.array(new_region)[np.argsort(angles)]

        new_regions.append(new_region.tolist())

    regions_vertices = new_regions, np.asarray(new_vertices)

    return regions_vertices


def as_dataframes(regions, vertices, points):
    """Helper function to store finite Voronoi regions and
    originator points as geopandas (or pandas) data frames.

    Parameters
    ----------
    regions : list
        Each element of the list contains sequence of the indexes of
        voronoi vertices composing a vornoi polygon (region).
    vertices : array
        The coordinates of the vornoi vertices.
    points : array-like
        The originator points.

    Returns
    -------
    region_df : geopandas.GeoDataFrame
        Finite Voronoi polygons as geometries.
    points_df : geopandas.GeoDataFrame
        Originator points as geometries.
    
    """

    try:
        import geopandas as gpd
    except ImportError:
        gpd = None

    try:
        from shapely.geometry import Polygon, Point
    except ImportError:
        from .shapes import Polygon, Point

    if gpd is not None:
        region_df = gpd.GeoDataFrame()
        region_df["geometry"] = [Polygon(vertices[region]) for region in regions]

        point_df = gpd.GeoDataFrame()
        point_df["geometry"] = gpd.GeoSeries(Point(pnt) for pnt in points)
    else:
        import pandas as pd

        region_df = pd.DataFrame()
        region_df["geometry"] = [
            Polygon(vertices[region].tolist()) for region in regions
        ]
        point_df = pd.DataFrame()
        point_df["geometry"] = [Point(pnt) for pnt in points]

    return region_df, point_df


[docs]def voronoi_frames(points, radius=None, clip="extent"): """Composite helper to return Voronoi regions and generator points as individual dataframes. Parameters ---------- points : array-like The originator points. radius : float The distance to "points at infinity" used in building voronoi cells. clip : str, shapely.geometry.Polygon An overloaded option about how to clip the voronoi cells. The options are: - 'none'/None: No clip is applied. Voronoi cells may be arbitrarily larger that the source map. Note that this may lead to cells that are many orders of magnitude larger in extent than the original map. Not recommended. - 'bbox'/'extent'/'bounding box': Clip the voronoi cells to the bounding box of the input points. - 'chull'/'convex hull': Clip the voronoi cells to the convex hull of the input points. - 'ashape'/'ahull': Clip the voronoi cells to the tightest hull that contains all points (e.g. the smallest alphashape, using ``libpysal.cg.alpha_shape_auto``). - Polygon: Clip to an arbitrary Polygon. tolerance : float The percent of map width to use to buffer the extent of the map, if clipping (default: .01, or 1 percent). Returns ------- reg_vtx : tuple Two ``geopandas.GeoDataFrame`` (or ``pandas.DataFrame`` if ``geopandas`` is unavailable) objects--``(region_df, points_df)``--of finite Voronoi polygons and the originator points as geometries. Notes ----- If ``geopandas`` is not available the return types will be ``pandas.DataFrame`` objects, each with a geometry column populated with PySAL shapes. If ``geopandas`` is available, return types are ``pandas.GeoDataFrame`` objects with a geometry column populated with shapely geometry types. Examples -------- >>> points = [(10.2, 5.1), (4.7, 2.2), (5.3, 5.7), (2.7, 5.3)] >>> regions_df, points_df = voronoi_frames(points) >>> regions_df.shape (4, 1) >>> regions_df.shape == points_df.shape True """ regions, vertices = voronoi(points, radius=radius) regions, vertices = as_dataframes(regions, vertices, points) if clip: regions = clip_voronoi_frames_to_extent(regions, vertices, clip=clip) reg_vtx = regions, vertices return reg_vtx
def clip_voronoi_frames_to_extent(regions, vertices, clip="extent"): """Generate a geopandas.GeoDataFrame of Voronoi cells clipped to a specified extent. Parameters ---------- regions : geopandas.GeoDataFrame A (geo)dataframe containing voronoi cells to clip. vertices : geopandas.GeoDataFrame A (geo)dataframe containing vertices used to build voronoi cells. clip : str, shapely.geometry.Polygon An overloaded option about how to clip the voronoi cells. The options are: - 'none'/None: No clip is applied. Voronoi cells may be arbitrarily larger that the source map. Note that this may lead to cells that are many orders of magnitude larger in extent than the original map. Not recommended. - 'bbox'/'extent'/'bounding box': Clip the voronoi cells to the bounding box of the input points. - 'chull'/'convex hull': Clip the voronoi cells to the convex hull of the input points. - 'ashape'/'ahull': Clip the voronoi cells to the tightest hull that contains all points (e.g. the smallest alphashape, using ``libpysal.cg.alpha_shape_auto``). - Polygon: Clip to an arbitrary Polygon. Returns ------- clipped_regions : geopandas.GeoDataFrame A ``geopandas.GeoDataFrame`` of clipped voronoi regions. """ try: from shapely.geometry import Polygon except ImportError: raise ImportError("shapely is required to clip voronoi regions") try: import geopandas except ImportError: raise ImportError("geopandas is required to clip voronoi regions") if isinstance(clip, Polygon): clipper = geopandas.GeoDataFrame(geometry=[clip]) elif clip is None: return regions elif clip.lower() == "none": return regions elif clip.lower() in ("bounds", "bounding box", "bbox", "extent"): min_x, min_y, max_x, max_y = vertices.total_bounds bounding_poly = Polygon( [ (min_x, min_y), (min_x, max_y), (max_x, max_y), (max_x, min_y), (min_x, min_y), ] ) clipper = geopandas.GeoDataFrame(geometry=[bounding_poly]) elif clip.lower() in ("chull", "convex hull", "convex_hull"): clipper = geopandas.GeoDataFrame( geometry=[vertices.geometry.unary_union.convex_hull] ) elif clip.lower() in ( "ahull", "alpha hull", "alpha_hull", "ashape", "alpha shape", "alpha_shape", ): from .alpha_shapes import alpha_shape_auto from ..weights.distance import get_points_array coordinates = get_points_array(vertices.geometry) clipper = geopandas.GeoDataFrame(geometry=[alpha_shape_auto(coordinates)]) else: raise ValueError( 'clip type "{}" not understood. Try one ' ' of the supported options: [None, "extent", ' '"chull", "ahull"]'.format(clip) ) clipped_regions = geopandas.overlay(regions, clipper, how="intersection") return clipped_regions