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 


    Parameters
    ----------
    points      : array-like
                  nx2 array of points

    radius      : float (optional) 
                  distance to 'points at infinity'

    Returns
    -------

    regions    : list
                  each element of the list contains sequence of the indexes of Voronoi vertices composing a Voronoi polygon (region)

    coordinates : array
                  coordinates of the Voronoi vertices


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

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


    Parameters
    ----------

    vor:  Voronoi (scipy.spatial)

    radius: float (optional)
            Distance to 'points at infinity'
    """
    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())

    return new_regions, np.asarray(new_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
                  coordinates of the vornoi vertices

    points      : array-like
                  originator points


    Returns
    -------

    region_df   : GeoDataFrame
                  Finite Voronoi polygons as geometries

    points_df   : 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 originator points radius : float distance to "points at infinity" used in building voronoi cells clip : str, or 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 percent of map width to use to buffer the extent of the map, if clipping (default: .01, or 1 percent) Returns ------- _ : tuple (region_df, points_df) region_df : GeoDataFrame (if geopandas available, otherwise Pandas DataFrame) Finite Voronoi polygons as geometries points_df : GeoDataFrame (if geopandas available, otherwise Pandas DataFrame) Originator points as geometries Notes ----- If Geopandas is not available the return types will be Pandas DataFrames each with a geometry column populated with PySAL shapes. If Geopandas is available, return types are GeoDataFrames 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) return regions,vertices
def clip_voronoi_frames_to_extent(regions, vertices, clip='extent'): """ Arguments --------- regions : geopandas geodataframe dataframe containing voronoi cells to clip vertices: geopandas geodataframe dataframe containing vertices used to build voronoi cells clip : str, or 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 shapely.geometry.Polygon Returns ------- a 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