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如何在Shapely中对多边形进行三角剖分？

pythontriangulationshapely
6
如何在Shapely中三角化多边形？Shapely实际上提供了triangulate()函数，但这只会将多边形的顶点作为点集进行三角剖分。对于凸多边形，解决方案是相同的，但对于非凸多边形，则会得到额外的三角形。我尝试删除所有在多边形外部的三角形，但有时候三角形可能会穿过多边形边界（见下面的图像）。我想我也可以删除它们，然后从多边形中减去剩余的三角形，并递归地对该差异的组件进行三角剖分。但是否有更简单的方法呢？
多边形三角剖分不是顶点三角剖分的子集的示例（多边形边界更宽，呈灰色，三角形边界更暗，更细）： 多边形三角剖分不是顶点三角剖分的子集的示例（多边形边界更宽，呈灰色，三角形边界更暗，更细） 生成此几何图形的代码：
from shapely.geometry import Polygon
from shapely.ops import triangulate

polygon = Polygon( [ (0,0), (0,3), (5,3), (2,4), (6,4), (6,0) ])
delauney=triangulate(polygon)
2
你所需要的是“约束三角剖分”，据我所知，shapely并不支持这个功能，但是有一个纯Python的sect库可以解决这个问题，即使是带洞的多边形也可以。 - Azat Ibrakov
1个回答
2

我已经在Delaunay triangulation algorithm in shapely producing erratic result中更新了我的答案。

import numpy as np
from shapely.geometry import Polygon
from shapely.ops import triangulate
import shapely.wkt
import geopandas as gpd
from geovoronoi import voronoi_regions_from_coords

def to_triangles(polygon):

    poly_points = []

    gdf_poly_exterior = gpd.GeoDataFrame({'geometry': [polygon.buffer(-0.0000001).exterior]}).explode().reset_index()
    for geom in gdf_poly_exterior.geometry:
        poly_points += np.array(geom.coords).tolist()

    try:
        polygon.interiors[0]
    except:
        poly_points = poly_points
    else:
        gdf_poly_interior = gpd.GeoDataFrame({'geometry': [polygon.interiors]}).explode().reset_index()
        for geom in gdf_poly_interior.geometry:
          poly_points += np.array(geom.coords).tolist()

    poly_points = np.array([item for sublist in poly_points for item in sublist]).reshape(-1,2)

    poly_shapes, pts = voronoi_regions_from_coords(poly_points, polygon)
    gdf_poly_voronoi = gpd.GeoDataFrame({'geometry': poly_shapes}).explode().reset_index()
    gdf_poly_voronoi.plot()

    tri_geom = []
    for geom in gdf_poly_voronoi.geometry:
        inside_triangles = [tri for tri in triangulate(geom) if tri.centroid.within(polygon)]
        tri_geom += inside_triangles

    gdf_poly_triangles = gpd.GeoDataFrame({'geometry': tri_geom})

    gdf_poly_exterior.plot()
    if 'gdf_poly_interior' in locals():
        gdf_poly_interior.plot()
    gdf_poly_triangles.plot()

polygon_1 = Polygon([(0, 0), (0, 3), (5, 3), (2, 4), (6, 4), (6, 0)])
polygon_2 = Polygon([(3.0, 0.0), (2.0, 0.0), (2.0, 0.75), (2.5, 0.75), (2.5, 0.6), (2.25, 0.6), (2.25, 0.2), (3.0, 0.2), (3.0, 0.0)])
poly_3_wkt = 'POLYGON ((-74.05644319847762 4.664371152795165, -74.05701264773319 4.663503533579181, -74.05770573357918 4.662810447733186, -74.05896428283818 4.662056102337443, -74.05990224838993 4.661771573597983, -74.06224145161008 4.661772473597984, -74.06317941716183 4.662057002337444, -74.06443796642083 4.662811347733187, -74.06572065226682 4.664052233579182, -74.06921901369725 4.668360960588712, -74.07141674761461 4.670691972117472, -74.07635895116509 4.673818151938486, -74.07894493390593 4.675834266094067, -74.08192435226682 4.679424333579181, -74.08891615226682 4.688383433579182, -74.08958587724112 4.689463067989243, -74.09086467349047 4.690719228823506, -74.09790275116509 4.694460551938487, -74.10034036642082 4.696114147733187, -74.10386724657296 4.698958762835078, -74.10814346936803 4.700870863662334, -74.10930545161006 4.700957773597984, -74.11043741716183 4.701320402337444, -74.11139045116509 4.701828051938487, -74.11214813390593 4.702449866094067, -74.11445885226682 4.704984433579183, -74.11521319766256 4.706242982838176, -74.11590442640203 4.70845234838992, -74.11611382363337 4.710865185701647, -74.11554750632175 4.71273208368413, -74.11467343390593 4.713910633905932, -74.11305131716183 4.714994497662556, -74.11211335161008 4.715279026402015, -74.11073328554708 4.715355222566556, -74.11041129766257 4.716545717161825, -74.1094660522668 4.718057466420818, -74.10756213390592 4.720161033905933, -74.10568445116508 4.721873348061513, -74.10420772338625 4.722584201678661, -74.10275629999998 4.7227995, -74.10130487661371 4.722584201678661, -74.09995094883489 4.721945648061514, -74.09403374773316 4.716245366420819, -74.09338219367824 4.71525808368413, -74.09288787359796 4.71387655161008, -74.09288787359796 4.711925648389919, -74.0936469519385 4.710096948834901, -74.09548963357916 4.708043347733187, -74.09763068874044 4.70677727898599, -74.09460666784895 4.704312469919607, -74.09203589291714 4.702595752799392, -74.08765371631586 4.700417706321742, -74.08459603357916 4.698508252266813, -74.08273894773316 4.696641066420818, -74.08206922275886 4.695561432010757, -74.08118604773318 4.694727366420818, -74.0717936025263 4.682825210334004, -74.06562484883489 4.678834648061513, -74.06390001213198 4.677314420684328, -74.0535710885149 4.739037649974117, -74.05520778283815 4.737937702337444, -74.05712119999998 4.7375571, -74.06045152338628 4.738003698321339, -74.06217206642083 4.738923347733187, -74.06340970632175 4.74043141631587, -74.06393542640203 4.74187004838992, -74.06400742363337 4.743335585701648, -74.063537026402 4.74698295161008, -74.06279044806149 4.748785351165098, -74.06139073691359 4.75018144712255, -74.0609743487264 4.751890490745711, -74.06128649999999 4.753612599999999, -74.06107120167866 4.755064023386272, -74.06039964806149 4.756487551165098, -74.0594142664208 4.757574752266813, -74.05806621716184 4.758372197662556, -74.05615280000001 4.7587528, -74.05377854838993 4.758482026402016, -74.0507277649826 4.757844764394359, -74.05055722640202 4.75945045161008, -74.04983964400328 4.762451751932777, -74.04873032640204 4.76925805161008, -74.04829449766255 4.770818617161826, -74.04766074258318 4.772140089033794, -74.04726809766255 4.773711517161825, -74.04651375226682 4.774970066420818, -74.04542655116509 4.775955448061513, -74.04410012338627 4.776582801678661, -74.04215861429836 4.776774023633361, -74.04029171631588 4.776207706321742, -74.03878364773318 4.774970066420818, -74.03800540233745 4.773666917161825, -74.03729177636662 4.771281485701648, -74.03727967636664 4.770004014298352, -74.03747549832134 4.769002476613728, -74.03843161386389 4.767199327773277, -74.04047532279198 4.75512284897233, -74.0369408023945 4.754256982815782, -74.03025007661371 4.753148101678661, -74.02876484883491 4.752415548061514, -74.02767764773319 4.751430166420819, -74.02692330233745 4.750171617161826, -74.02654087636664 4.748620285701648, -74.02683367636664 4.736912214298353, -74.02739999367826 4.73504531631587, -74.02863763357918 4.733537247733187, -74.03035817661373 4.732617598321339, -74.03229968570164 4.732426376366639, -74.03372301716183 4.732782902337444, -74.03534513390593 4.733866766094067, -74.03621920632175 4.73504531631587, -74.03676491551958 4.736773285680133, -74.04355019487681 4.738452884397855, -74.04767016881966 4.714185707761746, -74.04885077359798 4.706409648389919, -74.05027314410287 4.698677293675041, -74.05045487359796 4.696561148389919, -74.05077748485968 4.695365046361829, -74.05289107166563 4.682999393176747, -74.05422957359798 4.67404324838992, -74.05473458359565 4.671889824337649, -74.05543207359798 4.667273848389919, -74.05644319847762 4.664371152795165))'
polygon_3 = shapely.wkt.loads(poly_3_wkt)
poly_4_wkt = 'Polygon ((22.11315279161000547 -25.09231820047121886, 21.62718174901616663 -26.2204652636354929, 22.01769419395764515 -27.5308514677724574, 23.33675845242663982 -28.13831527101475416, 24.77731547154409597 -27.47010508744822488, 24.86409601486442256 -26.98413404485438605, 23.92686614700487624 -26.97545599052235232, 24.55168605891124045 -26.38534829594411946, 25.86207226304820495 -26.14236277464719649, 26.1918383276654545 -26.70643630622933529, 25.92281864337243391 -27.30522205513960188, 26.69516547892335723 -26.88867544720202218, 26.75591185924758975 -26.19443110063939528, 25.93149669770446764 -25.73449422104165407, 25.51495008976689149 -25.98615779667060366, 25.14179375348947687 -25.69978200371352273, 24.68185687389173566 -25.25720123277984541, 23.85744171234861355 -26.09029444865500125, 23.71859284303608462 -26.81925101254575949, 22.81607519250466964 -26.2204652636354929, 23.26733401777037713 -25.343981776100172, 23.17187542011801682 -24.90140100516649824, 22.77268492084450457 -24.55427883188518123, 22.11315279161000547 -25.09231820047121886),(22.46027496489132247 -25.79524060136588304, 22.01769419395764515 -26.19443110063939528, 22.2172894435943995 -26.38534829594411946, 22.45159691055928874 -26.48948494792850994, 22.55573356254368278 -26.53287521958867501, 22.49498718221945381 -26.75850463222153053, 22.92021184448906368 -26.68908019756526784, 22.33010414991082726 -26.32460191561988694, 22.5817677255397804 -26.02087001399873856, 22.93756795315312758 -25.3786939934283069, 22.81607519250466964 -25.343981776100172, 22.46027496489132247 -25.79524060136588304),(23.10245098546175413 -27.53952952210448757, 22.54705550821164906 -27.47010508744822488, 22.81607519250466964 -27.05355847951064874, 23.64049035404779175 -27.17505124015910667, 23.692558680039987 -27.59159784809668636, 23.18055347445005054 -27.85193947805767323, 23.10245098546175413 -27.53952952210448757),(24.24795415729009207 -26.20310915497142901, 24.36076886360651983 -25.94276752501044214, 24.70789103688783328 -25.95144557934247587, 24.81202768887222732 -25.95144557934247587, 24.77731547154409597 -25.78656254703384931, 25.0810473731652479 -25.91673336201434097, 25.07236931883321418 -26.10765055731906514, 24.65582271089563449 -26.15104082897923021, 24.34341275494245238 -26.38534829594411946, 24.24795415729009207 -26.20310915497142901))'
polygon_4 = shapely.wkt.loads(poly_4_wkt)

to_triangles(polygon_1)
非常好的解决方案，对我非常有用。只是评论一下，根据先前代码给出的警告，现在所有使用 explode() 函数的地方都应该传递参数 index_parts=True 以避免警告（由于代码更改以符合 pandas 的要求）。 - maynouf
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